Investigations of Crevice Corrosion Using Computational Modeling

and Microfabrication Techniques

A Thesis

Presented to

the Faculty of the School of Engineering and Applied Science

University of Virginia

In Partial Fulfillment

of the Requirements for the Degree

Master of Science (Materials Science and Engineering)

by

Jason S. Lee

September 2001

ii

Approval Sheet

This thesis is submitted in partial fulfillment of the

requirements for the degree of

Master of Science (Materials Science and Engineering)

______________________ Jason S. Lee

This thesis has been read and approved by the examining committee:

______________________ Robert G. Kelly

(Advisor)

______________________ John C. Scully

(Committee Chairman)

______________________ Michael L. Reed

Accepted for the School of Engineering and Applied Science:

______________________ Dean, School of Engineering

and Applied Science

September 2001

iii

ABSTRACT

Crevice corrosion is a type of localized corrosion that arises due to the formation

of an occluded volume by pressing some surface against a metal surface. In this work,

the crevice corrosion behavior of the nickel / 0.5 M H2SO4 system was studied using

microfabrication techniques and computational modeling.

In the interest of increasing speed, most computational models of corrosion have

idealized crevice geometries. This has been achieved by assuming that the crevice does

not have any irregularities in its dimensions. However, this approach does not allow

accurate comparison with results obtained from crevices found in practice or crevices

fabricated using standard machining techniques. Microfabrication techniques were

chosen to bridge the gap between experimental and model results due to their ability to

create crevices which are not only ideal in geometry, but also on the scale of real crevices

(0.1 – 10 µm).

In a previous work, fabrication techniques used in the semiconductor industry

were adapted to create rigorously defined crevices. These crevices were assembled from

two pieces: the former and the substrate. The former defined the gap of the crevice while

the substrate was the site of the metal electrode in question. Due to limitations of these

techniques, the results obtained could not be directly compared to those obtained from

modeling. In this study, improvements were made to these techniques that allowed direct

comparison with results obtained from modeling. Specifically, the thickness of metal on

the electrode was increased by an order of magnitude to allow for longer experiments to

be performed. Also, a technique was developed to allow a plate of Ni200 to be used as

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the substrate. This technique can be expanded to virtually any metal/electrolyte system

for study.

Modeling results indicated that crevice gaps, which exceeded 2% of the crevice

length, resulted in deviation from linear behavior of the proposed scaling law xcrit2/gap.

This deviation was shown to occur when the entire active peak of the polarization curve

did not reside on the crevice wall. Results from microfabricated crevices also showed

excellent agreement with the modeling results.

The effect of increasing surface area in the active region due to surface

penetration was shown to have little effect on the value of xcrit, even after significant

corrosion. However, the decrease in solution conductivity due to the increase in the

concentration of Ni2+ ions from corrosion at the active site was shown to have significant

affects for values greater than 1.0 M.

The competing forces of natural convection (due to density differences) and

surface tension during active corrosion were also examined. Results suggest that the role

of natural convection decreased with decreasing gap size. At gaps sizes below 93 µm, the

band of greatest attack across the width of the crevice was seen to distort, whereas at

larger gaps, the attack remained straight. It was shown that as the gap size decreased, the

surface tension of the crevice solution increased, while the gravity force pulling down on

the solution decreased causing natural convection to become less effective at keeping the

crevice solution free of Ni2+ ions. As well, the longer a crevice was allowed to actively

corrode, the more distortion in the attack band was seen which also indicated that natural

convection was unable to keep Ni2+ ions from building up in the crevice.

v

ACKNOWLEDGEMENTS

I would like to thank my advisor Rob Kelly for all his support during my years

here. He is more than just a mentor; he is a friend.

I would also like to thank Michael Reed for sharing his knowledge of microfabrication with me.

I want to thank Sheri Wang for teaching me an incredible number of microfab techniques, and only allowing me to destroy only one piece of equipment – I bet no one had ever seen a metal evaporator filled with water.

I would also like to thank everyone on the 3rd floor. From faculty such as John Scully, who always had an open door for my questions, to the students such as Jackie Williams and Rob Leggat, who made life tolerable during the long hours.

And I would especially thank my mom and dad for all their support. I would

never have gotten to where I am today without them.

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TABLE OF CONTENTS

ABSTRACT................................................................................................................................... iii ACKNOWLEDGEMENTS............................................................................................................ v TABLE OF CONTENTS............................................................................................................... vi LIST OF TABLES......................................................................................................................... ix LIST OF FIGURES ........................................................................................................................ x LIST OF SYMBOLS ................................................................................................................... xvi CHAPTER 1. INTRODUCTION .................................................................................................. 1 CHAPTER 2. BACKGROUND .................................................................................................... 4

2.1 Modeling......................................................................................................................... 4 2.1.1 Motivations for Modeling ....................................................................................... 4 2.1.2 Governing Equations .............................................................................................. 5 2.1.3 Common Simplifications ........................................................................................ 8 2.1.4 Numerical Methods for Solving............................................................................ 10

2.2 CREVICERv2............................................................................................................... 11 2.2.1 Overview............................................................................................................... 11 2.2.2 Improvements ....................................................................................................... 13

2.3 Scaling Laws................................................................................................................. 13 2.3.1 Definition .............................................................................................................. 13 2.3.2 Previous Work ...................................................................................................... 14

2.4 Microfabrication ........................................................................................................... 21 2.5 Convection and Surface Tension .................................................................................. 24

2.5.1 Definitions............................................................................................................. 24 2.5.2 Corrosion Consequences....................................................................................... 26

CHAPTER 3. THESIS OBJECTIVES ........................................................................................ 28 CHAPTER 4. EXPERIMENTAL PROCEDURES..................................................................... 30

4.1 Microfabrication ........................................................................................................... 30 4.1.1 Crevice Formers.................................................................................................... 31 4.1.2 Crevice Substrates................................................................................................. 32

4.1.2.1 Silicon Wafers.............................................................................................. 32 4.1.2.2 Ni200 Plate................................................................................................... 35

4.1.3 Experimental Setup............................................................................................... 37 4.1.3.1 Crevice Assembly ........................................................................................ 37 4.1.3.2 Potentiodynamic Scans ................................................................................ 39 4.1.3.3 Equipment .................................................................................................... 40

4.1.4 Crevice Assembly Experiments............................................................................ 41 4.2 Modeling....................................................................................................................... 42

4.2.1 Scaling Law Investigation Follow-up................................................................... 42

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4.2.1.1 Effect of Larger Gap Sizes........................................................................... 42 4.2.1.2 Investigation of Boundary Condition Characteristics.................................. 43

4.2.2 Crevice Corrosion Experiments............................................................................ 43 4.2.2.1 Comparisons to Experiments on Microfabricated Crevices ........................ 43 4.2.2.2 Effect of Crevice Area and Electrolyte Conductivity on xcrit ...................... 44

CHAPTER 5. RESULTS............................................................................................................. 45

5.1 Microfabrication ........................................................................................................... 45 5.1.1 Formers ................................................................................................................. 45 5.1.2 Substrates .............................................................................................................. 48

5.1.2.1 Silicon Wafer Based .................................................................................... 48 5.1.2.2 Ni200-Based Substrate................................................................................. 56

5.1.3 Electrochemistry of Substrates ............................................................................. 58 5.1.3.1 Silicon-Based ............................................................................................... 58 5.1.3.2 Ni200 Based................................................................................................. 59

5.1.4 Physical Chemistry of Electrolytes....................................................................... 61 5.2 Microfabricated Crevice Experiments .......................................................................... 63

5.2.1 Effect of Gap Size and Experiment Duration on xcrit............................................ 66 5.2.2 Effect of Potential on xcrit...................................................................................... 78 5.2.3 Attack Morphology............................................................................................... 80

5.3 Modeling....................................................................................................................... 87 5.3.1 Scaling Law Investigation Follow-up................................................................... 87

5.3.1.1 Effect of Larger Gap Sizes........................................................................... 88 5.3.1.2 Investigation of Boundary Condition Characteristics.................................. 92

5.3.2 Crevice Corrosion Experiments............................................................................ 95 5.3.2.1 Effect of Crevice Gap on xcrit....................................................................... 98 5.3.2.2 Effect of Potential on xcrit........................................................................... 101 5.3.2.3 Comparisons to Experiments on Microfabricated Crevices ...................... 103 5.3.2.4 Effect of Crevice Area and Electrolyte Conductivity on xcrit .................... 105

CHAPTER 6. DISCUSSION..................................................................................................... 113

6.1 Performance of Microfabricated Formers and Substrates .......................................... 113 6.2 Physical Chemistry of Electrolytes..................................................................... 117 6.3 Scaling Law Investigation Follow-Up................................................................ 119 6.3.1 Investigation of Boundary Condition Characteristics......................................... 119 6.3.2 Effect of Larger Gap Sizes.................................................................................. 120

6.4 Comparison of Model and Experimental Results ....................................................... 124 6.4.1 Potential Effects on xcrit ...................................................................................... 124 6.4.2 Gap, Area, and Electrolyte Effects on xcrit .......................................................... 125 6.4.2 Attack Morphology............................................................................................. 133

CHAPTER 7. CONCLUSIONS ................................................................................................ 143 CHAPTER 8. FUTURE WORK................................................................................................ 147 REFERENCES ........................................................................................................................... 151

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APPENDIX A: MICROFABRICATION PROCESSING SHEETS.......................................... 156 APPENDIX B: CODE ADDITIONS TO CREVICERv2 .......................................................... 168

ix

LIST OF TABLES

Table 1: Chemical composition of Ni200........................................................................ 30 Table 2: Former heights determined by SU-8 type and spin coater speed. ..................... 46 Table 3: Statistics of silicon-based substrates.................................................................. 52 Table 4: Un-patterned silicon wafers with electroplated nickel for potentiodynamic

testing........................................................................................................................ 56 Table 5: Ni200-based substrate statistics......................................................................... 57 Table 6: Potentiodynamic scans performed on nn-patterned wafers with electroplated

nickel......................................................................................................................... 59 Table 7: Potentiodynamic scans performed on Ni200 samples in 0.5 H2SO4 with variable

NiSO4 concentration, and physical chemistry measurements of each solution. ....... 62 Table 8: Results of crevice hold experiments with variable gap, experimental duration,

and hold potential...................................................................................................... 65 Table 9: Characteristics of DeJong’s boundary conditions. ............................................ 92 Table 10: Fit parameters used to mathematically describe the polarization curve in

Figure (47). ............................................................................................................... 97 Table 11: Results of crevice holds modeled by CREVICERv2. ..................................... 98 Table 12: Fit parameters for Pickering’s 50-hour profile. .............................................. 106 Table 13: Fit parameters for Pickering’s 150-hour profile. ........................................... 106 Table 14: Results of crevice experiments modeled by CREVICERv2 with area

compensation, solution conductivity, and profile as variables. .............................. 109 Table 15: Results from applying Pickering’s model to the crevice current modeled by

CREVICERv2......................................................................................................... 122

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LIST OF FIGURES

Figure 1: A schematic of a crevice formed by a former and substrate. ............................. 1 Figure 2: Schematic of an ideal crevice indicating the crevice gap, width, and length

dimensions. ............................................................................................................... 14 Figure 3: Schematic illustrations of the crevice corrosion attack on the crevice wall (left),

and E(x) distribution and resulting I(x) current densities on the crevice wall (right). Adapted from Pickering[6]. ...................................................................................... 17

Figure 4: Six different boundary conditions used by DeJong to investigate scaling

laws[12]..................................................................................................................... 19 Figure 5: xcrit

2 vs. G and xcrit vs. G plots from DeJong[12] of the six boundary conditions.................................................................................................................................... 20

Figure 6: Process for fabricating crevice formers. a) Step 2, wet oxidation. b) Step 3,

photolithography. c) Step 4, oxide etch. d) Step 5, photoresist removal. e) Step 6, silicon etching. .......................................................................................................... 22

Figure 7: Process for fabricating crevice substrates. a) Step 2, wet oxidation. b) Step 3

and Step 4, two-layer photolithography. c) Step 5, oxide etch. d) Step 6, metal evaporation. e) Step 7, metal lift-off. ........................................................................ 23

Figure 8: A schematic of how capillary forces and gravity acting on a solution volume

reach equilibrium at a certain height......................................................................... 25 Figure 9: Schematic of individual crevice substrate after dicing..................................... 33 Figure 10: The ‘mousetrap’ used during the electroplating step to make electrical contact

on the wafer............................................................................................................... 35 Figure 11: a) Polished sample of Ni200 to be used as a crevice substrate; b) Polished

sample mounted in epoxy for use in potentiodynamic experiments. The nickel ribbon was attached to the sample before the sample was covered in epoxy to allow for an electrical connection to be made. ................................................................... 36

Figure 12: A schematic of the crevice assembly. Only the crevice mouth was placed into

the solution. The solution wicked up the entire crevice length due to capillary action......................................................................................................................... 39

Figure 13: The mask used to pattern the crevice formers. The dark regions on the mask

define the crevice walls............................................................................................. 45

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Figure 14: Comparison of old and new former fabrication techniques. (a) and (b) schematics of new and old former, (c) and (d) images of new and old formers, (e) and (f) comparison of former surface roughness using a confocal laser scanning microscope. Notice that the new former has a roughness that is half of the one from the old technique. ...................................................................................................... 47

Figure 15: Image of the SU-8 on a former cut away using a focused-ion beam. ............ 48 Figure 16: Comparison of substrates fabricated from the old and new techniques. (a)

Schematic of new substrate, electroplated nickel thickness of ~17µm; (b) Schematic of old substrate, evaporated nickel thickness 0.4 µm max; (c) Image of new substrate with a 7 x 10 mm electrode and electrical contact patch; (d) Image of old substrate, electrical connection was made by adhering a platinum wire to its back. 50

Figure 17: The jagged edge of a substrate fabricated using the old technique. The new

technique improved upon this by coating the substrate with protective photoresist layers before dicing................................................................................................... 51

Figure 18: The mask design used to pattern the electrode area and contact patch onto the

substrates................................................................................................................... 51 Figure 19: Comparison of the electrochemical behavior of an old substrate with only 0.3

µm nickel thickness, a new substrate with 8.7 µm of electroplated nickel, and Ni200. Notice the behavior of the thicker nickel is more comparable to Ni200 than the thin nickel substrate.......................................................................................................... 53

Figure 20: A profilometer scan of a silicon-based substrate across the electrode width

after electroplating. Note the x-axis is 1000 times the scale that the y-axis. ........... 54 Figure 21: Image of a cross-section of a silicon-based substrate after electroplating. The

area was exposed using a focused-ion beam............................................................. 55 Figure 22: The surface of a Ni200 sample after polishing to 1200 grit. .......................... 58 Figure 23: Polarization behavior of silicon-based electroplated nickel substrates. Notice

the lack of reproducibility in peak and passive current densities for different substrates in 0.5 m H2SO4. The lack of reproducibility ultimately led to these substrates being replaced with the Ni200 substrates................................................. 59

Figure 24: Potentiodynamic scans of Ni200 substrates in 0.5 m H2SO4 with various

concentrations of NiSO4. The electrochemical behavior remains constant until the NiSO4 concentration increases above 0.028M, where an increase in peak current density and a loss of the double bump shape is lost. ................................................ 61

Figure 25: Conductivity as a function of nickel concentration........................................ 62

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Figure 26: (a) 86 µm former face-down on a Ni200 substrate; (b) a close-up view of the crevice sidewall formed by the SU-8 on the former. The edge of the SU-8 on the substrates is the pink dashed line. It is hard to see due to the surface of the substrate being highly reflective. ............................................................................................. 64

Figure 27: An example of a corroded crevice substrate with a 35 µm gap held at +0.6 V

(SCE) for 30 mins. Notice the three distinct regions of morphology, passive, active, and variable............................................................................................................... 66

Figure 28: Crevice holds of 14 µm gap with 0.6 V (SCE) hold potential with experiment

durations of (a) 1min, (b) 5 min, (c) 10 min, and (d) 30 min. Note that the attack bands are become less uniform as the corrosion is allowed to continue for longer times.......................................................................................................................... 68

Figure 29: Crevice holds of 35 µm gap with 0.6 V (SCE) hold potential with experiment

durations of (a) 1min, (b) 5 min, (c) 10 min, and (d) 30 min. Note that the attack bands are become less uniform as the corrosion is allowed to continue for longer times.......................................................................................................................... 70

Figure 30: Crevice holds of 93 µm gap with 0.6 V (SCE) hold potential with experiment

durations of (a) 1min, (b) 5 min, (c) 10 min, and (d) 30 min. The blue arrows indicate areas within the variable region that show signs of chemistry and/or potential changes. Note that the attack bands are straighter than the ones from smaller gaps. ............................................................................................................. 72

Figure 31: Crevice holds of 153 µm gap with 0.6 V (SCE) hold potential with

experiment durations of (a) 10minand (b) 30 min. The blue arrows indicate area that displayed evidence of changes in chemistry during corrosion. Note the straight attack bands............................................................................................................... 74

Figure 32: A 395 µm crevice held at 0.6V (SCE) for 30 mins. The entire surface

passivated and showed no signs of active corrosion................................................. 75 Figure 33: x2 vs. g and x vs. g plots of the average xcrit values from the crevice

experiments. Average values were obtained by taking the midpoint of the given xcrit range.......................................................................................................................... 76

Figure 34: (a) xcrit ranges for 14, 35, 93, and 153 µm crevice gaps from the experimental

crevice runs. Notice that the range decreases with increasing gap (b) a close-up of the 14 µm crevice gap data showing the increase in the range of xcrit with time. ..... 78

Figure 35: The movement of xcrit as a function of potential for a crevice gap of 35 µm for

hold potentials (SCE) of (a) 500 mV, (b) 525 mV, and (c) 600 mV. ....................... 79 Figure 36: The range of xcrit as a function of potential for a crevice gap of 35 µm for hold

potentials of 500 mV, 525 mV, and 600 mV (SCE)................................................ 80

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Figure 37: Morphology of the attack band shown by confocal laser scanning images for (a) front of attack band, (b) middle of attack band, and (c) rear of attack band. ...... 81

Figure 38: (a) Morphology of the passive region by confocal laser scanning images. (b)

Morphology of passive attack in the variable region. (c) Morphology of active attack in the variable region revealing the facet structure. ....................................... 82

Figure 39: (a) Suspected active corrosion in variable region of Ni200 crevice sample and

(b) etched surface of Ni200 polished surface, where the grain boundaries are visible. Comparing the two shows that the possible active region is indeed due to active corrosion because of the faceted structure in both images. ...................................... 84

Figure 40: (a) a 93 µm gap crevice after 30 minutes of active corrosion, the close-up

image is that of a section of the variable region where there is a transition between active and passive corrosion morphology. A focused-ion beam was used to cut out a section along the transition line. Notice the highly faceted structure in the active region, whereas the passive region has very little attack. The surface was tilted 45 º to allow the cutout interior to be viewed. (b) a magnified image of the cut out area rotated 30 º counter-clockwise. Individual grains are visible along the cutout wall by their difference in grayscale. Comparing the position of these grains with the attack above, it is shown that the active corrosion does preferentially attack grain facets. ........................................................................................................................ 86

Figure 41: Technique used to determine xcrit from the output of CREVICERv2. Ecrit is

determined from the electrochemical boundary condition and the potential distribution in the crevice is used to find the distance down the length of the crevice where the potential is equal to Ecrit. .......................................................................... 88

Figure 42: xcrit

2 vs. gap plot of DeJong’s six electrochemical boundary conditions, with larger gap sizes used than in DeJong’s experiments. The curves lose linearity when the gap increases past 100 µm. ................................................................................. 89

Figure 43: (a) The double bump boundary condition was examined at gaps of 20, 60,

200, and 500 µm. The 200 and 500 µm gaps have results that deviate from the linear behavior seen at smaller gaps. (b) Crevice potential distributions of the four gaps and the resulting distance down th length of the crevice where Ecrit is reached. (c) Crevice current distributions for each gap. When the active corroding region reaches the crevice tip at the two large gaps, the current distribution is distorted causing the scaling law plot (a) to deviate from linearity......................................... 91

Figure 44: xcrit vs. total crevice current for each of the six boundary conditions. ........... 93 Figure 45: xcrit vs. electrochemical power density for each of the six boundary

conditions.................................................................................................................. 94 Figure 46: xcrit vs. Ecrit for each of the six boundary conditions....................................... 95

xiv

Figure 47: Measured electrochemical boundary condition of Ni200 in 0.5 H2SO4 (blue) and the corresponding mathematical fit (pink). Ecrit ws determined to be 0.244 V (SCE)......................................................................................................................... 97

Figure 48: (a) Potential distributions from CREVICERv2 for gaps ranging from 14 –395

µm. The 395 µm gap near reach Ecrit and passivated at the onset. (b) Corresponding current distributions for each gap size, notice that the 395 µm gap exhibits very low current indicating passive corrosion onely. .............................................................. 99

Figure 49: xcrit

2 vs. gap and xcrit vs, g plots for the Skinny boundary condition (DeJong) and for the experimentally determined polarization behavior. In both the Skinny and the experimental case, the region at small gaps is more linear for the xcrit

2 vs. gap plots than the xcrit vs, g plots. .................................................................................. 101

Figure 50: (a) Potential distributions produced by CREVICERv2 for hold potentials of

0.5, 0.525, and 0.6 V (SCE). (b) Corresponding current distributions. As the applied potential is increase, the active region moves deep into the crevice.......... 102

Figure 51: (a) Comparison of the xcrit

2 vs. g plots for the results obtained experimentally and from CREVICERv2. (b) Comparison of the xcrit vs. g plots for the results obtained experimentally and from CREVICERv2. Both plots show excellent agreement between model and experimental data. ................................................. 104

Figure 52: Comparison of experimental and CREVICERv2 results of varying hold

potential. The model predicts a linear behavior which is not seen in the experimental results. ............................................................................................... 105

Figure 53: Pickering’s[17] (a) 50-hour and (b) 150-hour corrosion profiles. (c)

Mathematical representations of both profiles that were coded into CREVICERv2 as part of the geometric boundary condition. The original crevice gap was 0.3 mm. 107

Figure 54: (a) Comparison of the effect of gap profile and additional current density

provided by the increase in surface area in the actively corroding region. (ON = extra surface area is taken into account, OFF = extra surface is NOT area taken into account). (b) Close-up of where the potential distributions cross Ecrit. ................. 110

Figure 55: (a) Comparison of the effect of solution conductivity (nickel concentration)

over the region of greatest attack (gray area) and the increase in active surface area for the 50-hour profile. (b) Comparison of the effect of solution conductivity (nickel concentration) and increase in active surface area for the 150-hour profile. Nickel concentration of the solution can be seen to have a much greater effect on xcrit than does the increase in active surface area. (ON = extra surface area is taken into account, OFF = extra surface is NOT area taken into account).............................. 112

Figure 56: Comparison of xcrit

2 vs. gap and xcrit vs. gap plots for the experimental and model results, along with the results predicted by Pickering’s Equation 7. ........... 123

xv

Figure 57: Comparison of the experimental and model results, along with the results predicted by Pickering’s Equation 7 for variable hold potentials. The model and Pickering’s results are in excellent agreement, whereas the experimental data do not correspond as well................................................................................................... 125

Figure 58: From Pickering[17], the inset shows the current fluctuation when the crevice

is flushed with fresh solution. ................................................................................. 131 Figure 59: From Pickering[17], the electrochemical behavior of nickel in sulfuric acid

scanned in both directions. Pickering chose the ‘Pasive to Active’ curve with Epass = 108 mV as the boundary condition modeled. ......................................................... 132

Figure 60: From Pickering[10], the electrochemical behavior of nickel in (a) 0.5 M

H2SO4, (b) 0.5 M H2SO4 + sat. NiSO4, and (c) 0.01 M H2SO4 + sat. NiSO4. ........ 133 Figure 61: Schematic of capillary vs. natural convective forces inside a corroding crevice

(assuming unit thickness into the page). Active corrosion causes density gradients to form leading to a stratified solution. The denser solution will tend to flow out of the crevice due to the increase in the force of gravity pulling down. ..................... 138

Figure 62: Examination of the competing forces within two volumes of solution, one

containing 0.5 M H2SO4 and the other containing 0.5 M H2SO4 + saturated NiSO4 for variable crevice gaps. The volume height is 0.1 cm and the width is 0.7 cm. Notice that in the region of interest (gaps < 400 µm), the upward capillary forces are dominant over the downward forces due to gravity................................................ 140

Figure 63: Schematic of a dense volume of solution (assuming unit thickness into the

page) with lighter solution volumes above and below and the corresponding capillary and gravity forces acting on each (h = height of solution volume). ....... 141

Figure 64: Former with gold lines laid evaporated down within the crevice region to

allow for conductivity changes to monitored during active corrosion. .................. 149 Figure 65: Schematic of a microfabricated crevice with an array of individually

addressable electrodes............................................................................................. 150

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LIST OF SYMBOLS

a .............................................................................................................. fit parameter []

b .............................................................................................................. fit parameter []

c .............................................................................................................. fit parameter []

Ci ............................................................................ concentration of species i [mol/m3]

Ci∇~ .......................................................gradient of concentration of species i [mol/m4]

d .............................................................................................................. fit parameter []

Di ....................................................................................... diffusivity of species i [m2/s]

e............................................................................................................... fit parameter []

Ecorr .................................................................... open circuit or corrosion potential [V]

Ecrit .................................................. potential at point of maximum current density [V]

Epass .......................................................................... primary passivation potential [V]

Esurf ................................................ applied potential to the boldly exposed surface [V]

F ................................................................................ Faraday’s constant 96,487 [C/eq]

g .............................................................................................................. fit parameter []

G ............................................................................................................ crevice gap [m]

g ......................................................................... acceleration due to gravity 980[cm/s2]

h .............................................................................................................. fit parameter []

h ............................................................................... height of a volume of solution [m]

h(x,y) .................................................................... height of a crevice at point (x,y) [m]

i .............................................................................................................. fit parameter []

i ....................................................................current density across an interface [A/m2]

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I .................................................................. total current flowing out of the crevice [A]

IR ..........................................................................................................voltage drop [V]

IR* .................................critical voltage drop required for stable crevice corrosion [V]

j .............................................................................................................. fit parameter []

J el~ ...............................................................................................electrical flux [C/m2-s]

J i~ ............................................................................flux vector of species i [mol/m2-s]

k .............................................................................................................. fit parameter []

l .............................................................................................................. fit parameter []

L ..................................................................................................... length of crevice [m]

Lc ................................distance from mouth of crevice to region of severest attack [m]

NA ...............................................................................Avogadro’s number [atoms/mol]

Q .....................................................................................................electrical charge [C]

R ............................................................................ total crevice solution resistance [Ω]

Rcap ................................................................................................... capillary radius [m]

RRMS .........................................................................roughness root mean squared [µm]

t .......................................................................................................................... time [s]

ui................................................................. mobility constant for species i [m2-mol/J-s]

v~ ............................................................................ velocity vector of the solution [m/s]

w ........................................................................................................ .crevice width [m]

Xp ....................... distance from the crevice mouth to the region of severest attack [m]

x ......................................................................................... distance into the crevice [m]

xpass ..................... distance from the crevice mouth to the region of severest attack [m]

xcrit ............ distance from mouth of crevice to the beginning of the severest attack [m]

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x0 ............................................................................................................ fit parameter []

y0 ............................................................................................................ fit parameter []

zi ............................................................................charge number for species i [eq/mol]

φs ................................................................................................... solution potential [V]

φ s∇~ .........................................................................gradient in solution potential [V/m]

φ s2~∇ ............................................................ LaPlacian of the solution potential [V/m2]

γ .............................................................................................. surface tension [dyne/cm]

κ ....................................................................................... solution conductivity [Ω-m]-1

ρ....................................................................................................................................... solution density [grams/cm3]

σ ....................................................................................... solution conductivity [Ω-m]-1

ABREVIATIONS

FIB .....................................................................................................Focused Ion Beam

HER ................................................................................ Hydrogen Evolution Reaction

LSM ....................................................................................Laser Scanning Microscope

ORR ................................................................................... Oxygen Reduction Reaction

RTU ..........................................................................................................Ready To Use

SCE ....................................................................................Saturated Calomel Electrode

TCA ........................................................................................................ trichloroethane

TCE ..................................................................................................... trichloroethylene

CHAPTER 1. INTRODUCTION

Corrosion can be described as the degradation of metal by dissolution in an

aggressive solution. Corrosion can lead to the deterioration of the metal’s surface, which

in turn can lessen the metal’s aesthetic value, or even its performance in a structural

sense. Localized corrosion is a type of corrosion that happens at discrete sites. That is,

only small regions on the metal surface undergo significant metal dissolution. However,

the mass loss at these sites can be quite high and occur in a short amount of time.

Crevice Former

Crevice Substrate

Boldly Exposed Surface GL

Figure 1: A schematic of a crevice formed by a former and substrate.

Crevice corrosion is a specific type of localized corrosion. It involves the creation

of an occluded region at a particular site on the metal surface by a crevice former (Figure

1). The former can be metal or non-metal. The occluded region can then develop its own

chemistry and potential distributions that are substantially different from those of the bulk

solution, causing an aggressive environment to be created. A classic example is what

happens when a washer is tightened down on a pole of a swing set that is left out in the

open weather. When the washer and pole are pressed together, they create a restricted

region that can now hold rainwater. With time, the occluded region develops a solution

environment into which metal from the washer and pole are dissolved. After a period of

2

time, enough mass loss has occurred to one or both of the pieces to cause mechanical

failure.

Many models have been developed to explain the mechanisms to which govern

crevice corrosion. Two of the most important models are the Critical Crevice Solution

(CCS) model and the Critical Potential Drop (IR*) model. The CCS model was first

developed by Fontana and Greene[1] and later couched numerically for stainless steel in

seawater by Oldfield and Sutton[2-4]. It is primarily concerned with how the restricted

geometry of a crevice restricts the mass transport of species into and out of the occluded

region resulting in a solution chemistry that is much different than the bulk solution.

When the solution becomes sufficiently aggressive, the onset of crevice corrosion begins.

The (IR*) model by Pickering[5-10] focuses on how the restricted geometry causes

potential drops within the solution of the occluded site. At locations where the potential

falls to a critical value, the resulting anodic current density causes high levels of metal

dissolution within the crevice. Both models have been shown to predict crevice corrosion

well for some systems while also failing to account for the results from a variety of

others.

The Cathodic Focusing (CF) model, developed by Stewart[11], attempted to bring

the CCS and IR* models together. In brief, if a crevice is undergoing active corrosion

near its mouth producing an outward flow of current, the potential deep within a crevice

drops near to the open circuit potential. At this location, the cathodic and anodic

reactions cancel each other. However, if the active corrosion at the mouth of the crevice

requires more cathodic current density, cathodic reactions such as the Hydrogen

3

Evolution Reaction (HER) or the Oxygen Reduction Reaction (ORR), can begin to

dominate deep in the crevice causing an alkalizing effect.

Stewart developed a two spatial dimensional and temporal model for the

examination of crevice corrosion – called CREVICER. Later, DeJong[12] significantly

improved the speed of the solver routine used by CREVICER resulting in CREVICERv2.

This program will be discussed in more detail later.

No matter which model is chosen, comparisons to experimental or practical cases

are made difficult for two main reasons. First, practical crevices have gaps that are on the

scale of 0.1 – 10 µm. Computational models can be developed to examine crevices at

this size but well-controlled crevices cannot be manufactured for experimental testing

using current machining techniques available to this author, which have a tolerance of

±13 µm. Second, in order to decrease computation time to an acceptable level, the

geometry of the modeled crevice has to be idealized. The crevice is assumed to have a

constant gap height, width, and length. With the standard machining techniques available

to the author, perfectly flat surfaces cannot be fabricated.

A solution which enabled the modeled results to be directly compared with those

from experiments was devised by DeJong[12]. Semiconductor microfabrication

techniques were modified to create crevice formers and substrates that produced ideal

dimensions that could be reproduced accurately. Also, since the semiconductor industry

deals with structures on the micron scale, crevice heights were reliably reproduced which

came close to the scale seen in practical cases.

4

CHAPTER 2. BACKGROUND

2.1 Modeling

2.1.1 Motivations for Modeling

Modeling of engineering principles and phenomena has expanded over the last 20

years in large part because of the advances in computers. Computers have facilitated the

solving of mathematical problems that are too complicated (or impossible) to be done by

hand. Today, the use of computational modeling has become one of the fastest growing

subjects in all of engineering because of its many advantages.

One advantage of employing computational models is their ability to fill in the

holes of experimental data. For example, perhaps due to time restraints or the lack of

technology to collect data in a given set of parameters, the behavior of an alloy may not

be known for every environment it encounters. Modeling can be used to expand the

existing knowledge to encompass a whole myriad of circumstances that the alloy may

encounter. To do this experimentally would require an enormous amount of data to be

taken that could be time prohibitive.

Models are also valuable because of their predictive ability. Before an

experiment is ever run, a model can determine the results that are expected, and use this

information to improve the experimental design. Another common use of models is that

of life prediction. That is, how long a certain part will stay functional under a given set

of conditions.

5

The ability to separate parameters that in practice cannot be separated is one of

the major advantages of modeling. The implementation of “virtual experiments” with

only a subset of the experimental parameters (which cannot be replicated in the

laboratory) can be used to gain insight into how inseparable parameters affect one

another.

2.1.2 Governing Equations

The modeling of the corrosion behavior of a crevice requires the knowledge of its

electrochemical potential and chemical environment. The model’s goal is to predict how

the distribution of these parameters will change over time and space. There are three

governing equations used in the modeling of corrosion used to solve theses parameters.

This section briefly outlines these equations which are described in more detail by

Stewart[11].

The first governing equation is the mass transport equation that specifies the flux

of chemical species in the crevice. This equation is expressed as:

φ siiiiiii C u F z - C D - v C = J ∇∇ ~~~~ (1)

Where:

J i~ is the flux vector of species i [mol/m2-s]

Ci is the concentration of species i [mol/m3]

v~ is the velocity vector of the solution [m/s]

Di is the diffusivity of species i [m2/s]

6

∇Ci~ is the gradient of concentration of species i [mol/m4]

zi is the charge number for species i [eq/mol]

F is Faraday’s constant 96,487 [C/eq]

ui is the mobility constant for species i [m2-mol/J-s]

∇φ s~ is the gradient in solution potential [V/m]

The first term on the right-hand side of this equation governs the movement of

chemical species due to convective forces in the solution. Convective transport occurs

when the flowing movement of the electrolyte displaces chemical species.

The second term describes the movement of chemical species by diffusion.

Diffusion occurs spontaneously when a concentration gradient exists in the solution. The

species move to minimize the gradient in a spontaneous fashion.

The third term governs movement of charged species due to migration. Migration

is due to a potential gradient that exists within the solution. As with diffusion, the

charged species (or ions) in solution will move spontaneously to minimize the potential

gradient.

The second governing equation often used in modeling crevice corrosion is based

on the conservation of charge. It describes the accumulation of electrical charge in the

crevice:

i - h - = t

h se φκ

ρ 2~∇∂

∂ (2)

7

Where:

h is the height of the volume [m]

t

e

∂∂ ρ

is the time rate of change of the density of electric charge in

solution [C/m3-sec]

κ is the solution conductivity [Ω-m]-1

φ s2~∇ is the LaPlacian of the solution potential [V/m2]

i is the current density across an interface [A/m2]

The flux of charge out of the volume and the generation of charge inside the

solution determine the amount of electrical charge in solution. The first term on the

right-hand side of the equation describes the flux of electrical charge (current) out of a

volume of solution.

Because charge cannot accumulate in solution, generation is due only to current

across an interface (i.e., wall of a crevice). The second term expresses the generation of

charge. When the crevice is at steady state, the rate of change of electrical charge (the

left-hand side of Equation 2) is zero, and this equation can be readily used to solve for the

potential distribution in the crevice.

The third governing equation used in crevice corrosion models is that of charge

neutrality within the solution:

0 = C z iii

∑ (3)

8

Where:

zi is the charge number for species i [eq/mol]

Ci is the concentration of species i [mol/m3]

This last equation is used to combat some of the mathematically feasible, but

physically impossible, situations that arise from assumptions made in the derivation of

the first two governing equations. The effects of diffusion potential, due to potential

differences cause by the variations in diffusion rates among different ions, were ignored

in the derivation of the mass transport equation. Therefore, charge separations between

ions in solution are mathematically feasible, but physically impossible. To eliminate this

consequence, one of the species is used as a charge neutralizer. That is, its concentration

distribution throughout the solution is not determined by the first two governing

equations. Rather, its concentration for a given region of solution is determined solely by

the need to balance charge within that region.

2.1.3 Common Simplifications

As a crevice corrosion model becomes more complex, it becomes more difficult

to solve. Therefore, many assumptions are made in order to simplify the governing

equations described above. The goal is to remove factors that do not play a strong role in

the mechanisms of crevice corrosion, but not to eliminate too many factors causing the

model to lose its predictive behavior. Only a few assumptions are described below. A

much more detailed examination of these assumptions are made by Stewart[11].

9

The simplifying assumptions commonly made in crevice corrosion models fall

into five different categories, as defined by Stewart[11]:

1. Elimination of Some Thermodynamic Variables: Because most experiments

are performed at a constant temperature and pressure, the effects of changes

to these are often ignored.

2. Simplifying Chemistry Effects: Dilute solution theory is usually assumed;

the diffusivity and mobility of a species is independent of its concentration.

The precipitation and accumulation of corrosion products is often ignored.

3. Simplifying Potential Effects: As described above, the diffusion potential is

usually ignored in most models and charge neutrality is maintained by

specific species, not through the first two governing equations.

4. Ignoring Some Temporal Effects: Whereas changes of species concentration

over time may be accounted for, the changes in electrode kinetics or

generation rates with time are often ignored. The use of a single

electrochemical polarization behavior is often used throughout a model. This

study examines some of the problems associated with this practice. Some

models also assume chemical reaction are in equilibrium at all times, or also

called steadystate.

5. Simplifying Geometry: As mentioned earlier, models assume that a crevice

has ideal dimensions. However, this is often not the case of practical

crevices that often have variations in geometry throughout.

10

2.1.4 Numerical Methods for Solving

Once the governing equations have been formulated, a method for solving the

equations quickly and easily is required. One way is to solve the equations analytically.

Although this method yields an exact solution, many simplifications must be made. Most

important is the need to simplify the boundary conditions. However, the degree of

simplification required may cause the model to lose its ability to be directly compared to

any practical case.

Another choice for solving the governing equations is to use a numerical method.

The three most popular methods for numerical solving are the finite difference method

(FD), the boundary element method (BEM), and the finite difference method (FEM).

Finite difference modeling involves dividing the region of interest into a grid of

points, expressing the governing differential equations as difference equations at each

point, and solving the difference equations to determine an approximate solution of the

governing equations. Finite difference methods are simple to code, but clumsy when

applied to complex geometries. They are most often used for the temporal aspect of a

model.

Boundary element models translate the differential equations across the crevice

volume into integral equations over the surface enclosing the volume and solve these

integral equations by dividing up the surface into elements. The main drawback of

boundary element models is that they are most useful when the geometry of interest has a

low surface-to-volume ratio. This method is rarely used because most occluded regions

do not meet this requirement.

11

Finite element models divide the region of interest into simple geometric shapes

(such as triangles), build equations for the value of the variable of interest at each node

on each shape, and then solve the equations for all of the nodes simultaneously. Finite

element models have the advantage that they can represent complex geometries well.

FEM was the chosen method by Stewart to be implemented within the occluded model

CREVICER, which was used in this study.

2.2 CREVICERv2

2.2.1 Overview

CREVICER is a two-dimensional computational model for mass transport in

occluded regions which was developed at the University of Virginia by Stewart[11]. The

model maps the spatiotemporal chemical and potential fields within a crevice in two

dimensions, taking into account diffusion, migration, and generation of species. One key

characteristic of the model is its ability to use a wide range of boundary conditions.

In CREVICER, second-order partial differential equations are used to describe the

governing equations for the chemical concentration and potential fields within the

crevice. This approach allows the equations to be easily solved using a finite element

method. The equation for a concentration field is:

y)(x,J + C y)(x,u F zy)h(x, + C y)(x,Dy)h(x, = tCy)h(x, iiiiii

i ~~~~ 2 ∇∇∇∂

∂ φ (4)

Where:

12

h(x,y) is height at point (x,y) [m]

Ci is the concentration of species i [mol/m3]

Di is the diffusivity of species i [m2/s]

∇Ci~ is the gradient of concentration of species i [mol/m4]

zi is the charge number for species i [eq/mol]

F is Faraday’s constant 96,487 [C/eq]

ui is the mobility constant for species i [m2-mol/J-s]

∇φ s~ is the gradient in solution potential [V/m]

J i~ is the flux vector of species i [mol/m2-s]

The equation for the potential field in the crevice is:

y)(x,J + y)h(x, - = tQy)h(x, el

~~ 2φκ ∇∂∂

(5)

Where:

h(x,y) is height at point (x,y) [m]

Q is charge in Coulombs [C]

κ is the conductivity [(Ω-m)-1]

φ s2~∇ is the LaPlacian of the solution potential [V/m2]

J el~ is the electrical flux [C/m2-s]

13

The assumption of charge neutrality (Equation 3) is also used in CREVICER. At each

time step, species concentration fields are determined using Equation 4 for n-1 species.

The concentration field for the nth species set such that at each point in the crevice charge

neutrality is maintained.

2.2.2 Improvements

As part of an M.S. thesis, DeJong[12] made significant improvements to

CREVICER. The routine that solved the matrix of equations was optimized which

resulted in almost an order of magnitude increase in speed. CREVICER’s capabilities

were also expanded to include homogenous aluminum reactions. This addition allowed

effects of the hydrolysis of aluminum ions on the the chemistry of the occluded region to

be included. Finally, a Graphical User Interface (GUI) was designed to facilitate in the

creation of a crevice to be modeled. This GUI allowed users without intimate knowledge

of the code itself to use CREVICER. After these changes, the model was renamed

CREVICERv2.

2.3 Scaling Laws

2.3.1 Definition

A scaling law describes the effect of crevice geometry on the corrosion behavior

(concentration, potential, and attack gradients) of an occluded region. For corrosion

conditions to remain constant as crevice geometry is changed, the potential and chemical

distributions must remain constant on a normalized length scale. A scaling law is a factor

14

of two geometric measures of a crevice that must be maintained as the scale of a crevice

is altered. For example, the two most common scaling laws are L/G and L2/G where L =

either the length of the crevice or the distance between the crevice mouth and the site of

greatest attack (xcrit), and G = the crevice gap (Figure 2). Previous work of other groups

will be briefly reviewed below, whereas a more detailed review of scaling laws can be

found in the M.S. thesis by DeJong[12].

Length (L)

Width (w)

Gap (G)

Crevice Mouth

xcrit

Figure 2: Schematic of an ideal crevice indicating the crevice gap, width, and length dimensions.

2.3.2 Previous Work

For crevices in which there is negligible current generated at the tip and one or

both of the crevice flanks have a constant active current density over the entire surface

area, the scaling factor Lc2/G, where Lc is the crevice length and G is the crevice gap, has

been shown by Turnbull[13] and Psaila-Dombrowski[14] to be the correct one.

15

Modeling by Gartland[15] and Watson and Postlethwaite[16] showed that the

scaling factor Xp2/G held true when the crevice wall was passive until the distance into

the crevice Xp was reached where active corrosion took over. This finding was important

because no longer was the entire crevice length considered, but only the region that

remained passive.

In work performed by Xu and Pickering[5], Xp2/G was also shown to be the

correct scaling law. However, their work also suggested that if the passive current is

negligible when compared to the current in the active region, the scaling law is reduced to

Xp/G, as described by:

wGIX

EE pcritsurf κ

=− )( (6)

Where:

Xp is the distance from the mouth of the crevice to the region of

greatest attack [m]

κ is the solution conductivity [(ohm-m)-1]

w is the width of the crevice [m]

G is the crevice gap [m]

Esurf is the surface hold potential [V vs. SCE]

Ecrit is the potential at which the critical current density is reached

[V vs. SCE]

I is the total crevice current [A]

16

Chemistry changes within the crevice were not considered and the voltage drop down the

length of the crevice was determined to be the dominant mechanism for crevice

corrosion. In brief, the distance from the mouth of the crevice to the beginning of the

region of active corrosion, xcrit (also called xpass by Pickering[17]), is determined by the

potential drop down the length of the crevice due to the solution resistance and the

current flowing out of the crevice. If a piece of metal in a particular solution exhibits

passive corrosion above a certain potential, while below that potential the metal

undergoes active corrosion, the system is said to display an active/passive behavior.

Therefore, if the boldly exposed surface is polarized to a high potential in the passive

region the surface will only undergo light corrosion. Within the crevice however, the

restricted geometry can cause the potential to drop into the region of active corrosion.

The distance down the crevice at which critical potential is reached is xcrit. The critical

potential (Epass), as defined by Pickering[17], is the potential at which the current density

reaches 0.05 mA/cm2 during the transition from passive to active behavior. In this study,

the critical potential (Ecrit) is defined as the potential at which the current density reaches

its peak just after the active/passive transition where active corrosion begins. This

potential drop theory, also called the IR* theory will be explored throughout this study

and is illustrated in Figure (3).

17

IR*

Ecorr

Esurf

Ecrit

i (A/cm2)

E (V

vs.

SC

E) Active

Region

PassiveRegion

HERCrevice

Substrate

CreviceFormer

CreviceMouth

x = xcrit

x = 0

x = L

G

Figure 3: Schematic illustrations of the crevice corrosion attack on the crevice wall (left), and E(x) distribution and resulting I(x) current densities on the crevice wall (right). Adapted from Pickering[6].

In modeling by DeJong[12, 18], it was shown that the correct scaling law for active

corrosion controlled by the IR* mechanism was xcrit2/G. The system of interest was

nickel in 0.5 H2SO4, a system that exhibits active/passive behavior. As with the work by

Xu and Pickering[5], only initial potential distributions were considered. No chemistry

changes allowed within the crevice. Six electrochemical boundary conditions described

mathematically were examined by DeJong as to their affect on the position of the active

region on the crevice wall. Figure 4 shows these six boundary conditions. All six of the

18

boundary conditions had the same peak current of 10 mA/cm2. However, the basic

shape, potential at which the peak current was reached, Ecrit, and the passive current

density were varied. Using each of the six boundary conditions, one-dimensional models

were performed for a crevice length of 0.7 cm with crevice gaps ranging from 10 – 150

µm.

From the resulting potential distributions, the value of xcrit was determined based

on the value of Ecrit of the boundary condition used. xcrit2/G and xcrit/G were both plotted

and can be seen in Figure 5. From the plots, it was determined that the scaling law

xcrit2/G was the correct one based on the linearity exhibited at gaps < 100 µm, which is

the scale on which practical crevices exist, whereas the xcrit/G plots exhibited no such

linearity. DeJong suggested that the reason for loss of linearity of the xcrit2/G plots at

larger gaps was due to the active region nearing the crevice tip, which altered the current

produced by the crevice, thereby changing the value of xcrit. DeJong also suggested that

modeling crevices at larger gaps would likely provide some insight to this phenomenon.

The effect of larger gaps was a major part of this study and will be examined further.

19

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Potential (V vs. SCE)

Log

I (A

/cm

2 )

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Potential (V vs. SCE)

Log

I (A

/cm

2 )

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Potential (V vs. SCE)

Log

I (A

/cm

2 )

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Potential (V vs. SCE)

Log

I (A

/cm

2 )

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Potential (V vs. SCE)

Log

I (A

/cm

2 )

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Potential (V vs. SCE)

Log

I (A

/cm

2 ) Normal

Shifted

Ipass↑

Skewed

Skinny Double Bump

Figure 4: Six different boundary conditions used by DeJong to investigate scaling laws[12].

20

NormalShiftedIpass↑

Skewed SkinnyDouble Bump

0

1

2

3

4

5

6

0 40 80 120

Gap (µm)

X crit

(mm

)

160

0

5

10

15

20

25

30

35

0 40 80 120 160

Gap (µm)

X crit

(mm

)

Figure 5: xcrit2 vs. G and xcrit vs. G plots from DeJong[12] of the six boundary conditions.

21

2.4 Microfabrication

In the microfabrication industry, because such a high priority has been given to

the goal of producing devices on the micron scale, with extreme reproducibility, several

fabrication techniques have become standards. Techniques such as lithography, surface

cleaning, and laying down metal lines by evaporation are just a few.

The use of microfabrication techniques to examine corrosion mechanisms has had

little exposure. In related work by Alkire[19, 20], 304 stainless steel specimens were

polished and spin coated with photoresist. In the earlier study[19], a chrome mask was

used to expose a 100 µm diameter circle in the center of the sample. The photoresist was

then developed to remove the resist from the exposed area leaving only the small circle of

bare steel exposed. It was then possible to examine the corrosion behavior of single MnS

inclusions within this site. In the later study[20], this technique was improved. Again

polished 304 stainless steel samples were coated with photoresist. However, instead of a

single circle, a chrome mask with a grid of 121 squares (100 µm on a side) was used.

MnS inclusions were then identified within a certain region using this grid. An additional

layer of photoresist was applied and a chrome mask with only one of the squares was

used to expose the desired region. This allowed for specific inclusions to be identified

and examined.

In work by Wall and others[21], photolithography techniques were used to create

small Cu defects on the surface on aluminum. An aluminum sample was coated with

photoresist and then copper was deposited onto the surface using electron-beam metal

evaporation. Specific Cu regions were then created by a metal liftoff technique that

22

removed Cu at predetermined sites. The effects of having a noble metal (Cu) on an

aluminum surface during active pitting were examined.

In recent work by DeJong[12, 18], microfabrication techniques were used to create

crevices with rigorously defined geometry on the micron scale. In the study, pressing of

a former and a substrate together (both of which were built upon silicon wafers) formed

the crevice. The former defined the height of the crevice, whereas nickel was evaporated

down onto the substrate piece to create a 4 x 7 mm electrode. A detailed description of

the microfabrication steps used can be found in the M.S. thesis by DeJong[12]. Figures 6

and 7 are schematics, taken form DeJong’s work, of the fabrication process used to create

the crevice formers and substrates respectively.

siliconsilicon dioxidephotoresist 1

a)

c)

b)

d)

e)

Figure 6: Process for fabricating crevice formers. a) Step 2, wet oxidation. b) Step 3, photolithography. c) Step 4, oxide etch. d) Step 5, photoresist removal. e) Step 6, silicon etching.

23

siliconsilicon dioxidephotoresist 1photoresist 2nickel

a)

c)

b)

d)

e)

Figure 7: Process for fabricating crevice substrates. a) Step 2, wet oxidation. b) Step 3 and Step 4, two-layer photolithography. c) Step 5, oxide etch. d) Step 6, metal evaporation. e) Step 7, metal lift-off.

DeJong encountered difficulties during the fabrication process of both the

formers and the substrates that limited the ability to directly compare the results to those

predicted by modeling. One of the difficulties was the inability to fabricate substrates

with enough metal thickness to allow for long experiments to be performed. The metal

dissolved completely away before the experiment completed. Also, during dicing of the

substrates, the electrode metal began to peel off creating a jagged edge at the mouth of

the crevice. High former surface roughness was also a difficulty encountered.

24

Many of the techniques used by DeJong were the basis for this current study.

Improvements were made to these existing techniques and others were created which

allowed for improved performance of the crevices and experimental and modeling results

to be directly compared. These improvements will be discussed in later sections.

2.5 Convection and Surface Tension

2.5.1 Definitions

As described earlier, convection is the movement of species due to solution flow.

Examination of the mass transport equation (1) indicates that the concentration of a

particular molecule, and the velocity of the solution describe convection. As described

by Voss[22], fluid convection can be driven by either pressure or density differences

throughout a solution. Pressure driven flows are directed from regions of high

hydrostatic pressures towards regions of lower pressures. An example of this effect is

when solution is forced out a crack due to ‘pumping action’ during corrosion fatigue. As

the crack becomes smaller, the pressure within the crack increases above that of the

outside solution causing solution to flow out of the crack.

Density-driven flow occurs when gravity forces act on denser regions of the

solution causing them to flow downward relative to solutions of less density beneath

them. This type of convection will be a major topic throughout this study.

Surface tension is the force that a solution applies at the interface with a surface.

It is a fixed material property that does not depend on the interfacial surface type (e.g.

metal or plastic). Also called surface energy, its units are energy per unit length

25

(dyne/cm and mN/m are the most common). Surface tension causes water to rise in a

tube placed into a glass of water, or in the case of this study, the acid solution to wick up

into the crevice even though only the mouth of the crevice is held below the solution’s

surface. This phenomenon is called capillary rise[23].

Equilibrium is reached between the weight of the solution being held in the tube

above the solution’s surface and the pressure the solution is applying to the sides of the

tube (Figure 8).

ρgh

capRγ2

Capillary withRadius = Rcap

ρgh

capRγ2

Capillary withRadius = Rcap

Figure 8: A schematic of how capillary forces and gravity acting on a solution volume reach equilibrium at a certain height.

26

From Glover[23], the equilibrium for capillary rise for a hemispherical surface can

be described by:

ghRcap

ργ=

2 (6)

Where: γ is the surface tension [dyne/cm]

Rcap is the radius of the tube [cm]

ρ is the density of the solution [gram/cm2]

g is the acceleration due to gravity [cm/s2]

h is the height the solution rises within the tube [cm]

As seen from the equation, if the surface tension is increased, the height of the

solution in the straw is also increased. As well, if the density of a solution is changed, the

height will also be affected. Rearranging the equation, the equilibrium height of the

liquid can be determined:

gRh

cap ργ2

= (7)

2.5.2 Corrosion Consequences

As discussed earlier, convection is rarely considered in most corrosion

experiments. The one main exception is that of cracks which exhibit changes in size

through mechanical stress. If the two sides of a crack are continually subjected to

periodic pressing and pulling forces, the crack will take in and push out solution causing

convective flow to occur. Turnbull[24-26] developed models to account for this type of

27

convection seen in corrosion fatigue cracks. In the work by Psaila-Dombrowski[14] a

model was also developed to account for solution flow due to convection in stress-cracks

of light water reactors.

In work that closely follows this study, Pickering and others[5, 10, 16, 17, 27, 28]

have examined the crevice corrosion behavior of nickel in sulfuric acid. The crevice

corrosion of this system was determined to be solely a function of the IR* theory. That

is, no solution changes were responsible for the initiation of corrosion. The rationale

behind this was that as a crevice undergoes active corrosion, nickel ions are dissolved

into the crevice solution and cause the density of that solution region to increase. Gravity

then pulls down on the denser solution causing it to flow out of the crevice mouth.

Pickering refers to this as natural convection. The critical assumption is that this

convective flow keeps the solution within the crevice equal to that outside the crevice,

which in turn prevents changes in solution chemistry from altering the electrochemical

behavior of the system.

One goal of this study was to examine the assumption that natural convection

keeps the solution chemistry constant during active corrosion. At large gaps (300 µm) as

used by Pickering, this assumption may be true, but at smaller gaps that more closely

resemble those seen in practical cases, this assumption was shown to deviate. In this

study the competing roles of natural convection and surface tension are examined.

28

CHAPTER 3. THESIS OBJECTIVES

(1) Improve upon the microfabrication techniques used to by DeJong in previous

studies[12, 18] to create rigorously defined crevice geometries that will allow

extended crevice corrosion experiments to be performed. Improvements to

the surface roughness of the former and increase in the nickel thickness of the

substrates were top priorities.

(2) Examine the change in the physical chemistry properties of 0.5 M H2SO4 as a

function of NiSO4 concentration. Specifically, how variation in nickel

concentration affects the solution conductivity, density, and surface tension.

(3) Regress data taken from DeJong’s previous study on scaling laws and to

determine how the defining characteristics of the six boundary conditions used

in the study affected the determined values of xcrit.

(4) Determine the origin of the loss of linearity at large gaps in the results of

DeJong on scaling laws.

(5) Investigate how the increase in surface area and nickel concentration within

the crevice due to active corrosion affect the value of xcrit.

(6) Compare experimental and predicted results (from CREVICERv2) for the

dependence of xcrit on gap size, experiment duration, and hold potential.

29

(7) Examine the effects of the competing forces of natural convection and surface

tension on the attack morphology as a function of experiment duration and

gap size.

30

CHAPTER 4. EXPERIMENTAL PROCEDURES

4.1 Microfabrication

Semiconductor device manufacturing techniques were used to create the crevice

former and substrate which when assembled together made a crevice. The formers

defined the crevice gap while the substrates provided a metal electrode surface for

crevice corrosion experiments. All fabrication steps, with the exception of polishing,

were performed at the Semiconductor Device Laboratory, a class 10,000 clean room

located in the Department of Electrical Engineering at the University of Virginia. The

crevice formers and one type of crevice substrate were built on 2-inch diameter, 300 ± 25

µm thick silicon wafers from Virginia Semiconductor (Fredericksburg, VA). The wafers

were doped with boron (a p-type dopant) to achieve a resistivity of less than 0.1 Ω-cm.

The low resistivity was chosen to allow electrical connections to be made to the back of

the substrate. The other type of crevice substrates were built on top of 0.0575-inch thick

Ni200 (Goodfellows Corp.) alloy that had been wet polished to 1200 grit. The Ni200

alloy has a nickel concentration of greater than 99.5%. The complete chemical

composition can be found in Table 1 that was performed by Wah Chang, Inc. (Albany,

OR). The fabrication steps are summarized below; detailed run sheets can be found in

Appendix A.

Table 1: Chemical composition of Ni200

Ni C Mn Fe S Si C 99.625 0.0715 0.2150 0.0116 0.0002 0.073 0.0037

31

4.1.1 Crevice Formers

Step 1: Initial Wafer Cleaning: The following procedure is an abbreviated RCA

cleaning as detailed in the literature∗. The wafers were consecutively dipped in boiling

acetone and boiling methanol for 5 minutes each. The wafers were spin-cleaned

sequentially using ethanol, trichloroethane (TCA), methanol, and then blown dry with

nitrogen gas. The purpose of the various solvents is to remove surface residues. Wafers

were then dipped into buffered oxide etch solution (10 parts ammonium fluoride, 1 part

hydrofluoric acid by volume) and rinsed with flowing distilled water to remove the native

oxide. Each wafer was examined under an optical microscope. If residue still remained

on the wafer surface, the procedure was repeated.

Step 2: Photolithography: Following the initial cleaning, NANO SU-8 negative

photoresists (MicroChem, Newton, MA.) of various viscosities were used to pattern the

geometry of the crevice formers and create a range of photoresist heights. Each type of

SU-8 photoresist requires specific photolithography parameters that can be found in

Appendix A. Wafers were spin-coated with the photoresist and baked on 55ºC and 90ºC

hotplates to set the photoresist. Bake times varied with type of SU-8 used. The wafers

were allowed to cool on a flat surface for 30 minutes. A chrome-glass mask (Nanofilm,

Inc., Westlake Village, CA.) with four individual former patterns was placed on top of

the wafer to define the 4 x 7 mm crevice areas. The wafer was then exposed to UV

radiation. The wafers were baked and again allowed to cool. The photoresist was

developed using NAON XP-SU-8 developer, whereby the mask pattern was transferred

to the wafer.

∗ The RCA cleaning is a series of baths and rinses designed to remove surface residue from silicon wafers. It is a standard used throughout the microfabrication industry developed by the RCA Corporation.

32

Step 3: Dicing: Two protective layers of AZP4210 photoresist (Clariant

International, Ltd., Muttenz, Switzerland) were applied to the patterned wafers for

protection during dicing. The wafers were diced using a Disco DAD-2H/6T automatic

dicing saw to separate the individual formers. The protective photoresist was completely

removed using AZ developer. Each wafer yielded 4 individual formers.

Step 4: Final Cleaning and Photoresist Height Measurement: After dicing, each

individual former was spin-cleaned using consecutive rounds of ethanol, TCA, and

methanol. The patterned photoresist height was measured using a Tencor Alpha-Step

200 contact profilometer which has a resolution of 5 nm.

4.1.2 Crevice Substrates

4.1.2.1 Silicon Wafers

Step 1: Initial Wafer Cleaning: As was the case with the crevice formers, the

abbreviated RCA cleaning was used.

Step 2: Metal Evaporation: Cleaned wafers were loaded into a metal evaporator.

The sample chamber was pumped down to ~5.0 x 10-7 Torr over a 5 hour period. First, a

140 Å adhesion layer of chromium was evaporated onto the wafer. A 400 Å layer of

nickel was evaporated on top of that. A set of wafers were set aside for potentiodynamic

scans which skipped steps 2, 3, and 4, and went directly to the electroplating step.

Step 2: Photolithography: After metal evaporation, the wafers were cleaned using

the abbreviated RCA clean procedure. Only SU-8-10 negative photoresist was used to

pattern the geometry of the crevice substrate. Wafers were spin-coated with the

33

photoresist and baked on 55ºC and 90ºC hotplates to set the photoresist. Bake times vary

with type of SU-8 used. The wafers were allowed to cool for 30 minutes. A chrome-

glass mask (Nanofilm, Inc.) with four individual former patterns was placed on top of the

wafer to define the 4 x 7 mm crevice areas. The wafer was then exposed to UV radiation.

The wafers were baked and again allowed to cool. The photoresist was developed using

XP-SU-8 developer, whereby the mask pattern was transferred to the wafer.

Step 3: Dicing: As was the case with the formers, two protective layers of

AZP4210 photoresist was applied to each wafer. The wafers were diced to separate the

individual substrates. Each wafer yielded two individual substrates as illustrated in

Figure (9).

Contact

Electrode(4 x 10 mm)

SU-8Photoresist

Figure 9: Schematic of individual crevice substrate after dicing.

34

Step 5: Cleaning and Photoresist Height Measurement: Each individual substrate

was spin-cleaned using consecutive rounds of ethanol, TCA, and methanol. The

patterned photoresist height was measured using a Tencor Alpha-Step 200 contact

profilometer.

Step 6: Electroplating: The clean substrates were placed backside down on a

clean glass slide with melted G-wax spread over its surface. The wax served the purpose

of adhering the substrate to the slide and electrical isolating the backside of the wafer.

The glass slide was loaded into an electroplating holder called a “mousetrap” (Figure 10).

A gold contact was lowered onto the contact patch of the substrate. Both the contact and

the outer substrate edges were coated with trichloroethylene (TCE) diluted G-wax using a

toothpick. This procedure served to define the desired substrate area exposed for

electroplating. The mousetrap was connected to the negative lead of the electroplater,

while a piece of high purity nickel was attached to the positive lead to act as the anode.

Both the mousetrap and the anode were placed into the nickel-plating solution that

consisted of 500 mL of nickel sulfamate (RTU) and 5 mL of nickel “S” semi-bright

additive brightener (Technic Inc., Cranston, RI.). The bath temperature was maintained

at 45 ˚C throughout the plating. An agitator (Arrow Engineering) was used to keep the

plating solution stirring during the plating process. The electroplater was set to produce a

15 mA (55 mA/cm2 for 0.28 cm2 area) current with a 10 V limit. Current was applied for

20 – 30 minutes. After 3 substrates had been plated the solution was replaced with a

fresh batch.

35

Figure 10: The ‘mousetrap’ used during the electroplating step to make electrical contact on the wafer.

Step 7: Final Cleaning and Electroplated Metal Height Measurement: After

electroplating, each individual substrate was spin-cleaned using consecutive rounds of

ethanol, TCA, and methanol. The patterned electroplated nickel profile was measured

across the width of the substrate using the profilometer. The known height of the

surrounding photoresist allowed for the determination of the metal height.

4.1.2.2 Ni200 Plate

Step 1: Polishing: Ni200 2 x 2 inch plates were cut into four 1 x 1 inch pieces for

use in potentiodynamic testing. Samples to be used in crevice assembly experiments

were further milled down to 17 x 21 mm. A six-inch piece of nickel ribbon was attached

to one side of the potentiodynamic scan samples using silver conductive adhesive

(Electron Microscope Sciences). The milled samples had no wires connection made to

them. Each sample was mounted in Epo-Thin Epoxy (Buehler) with one of the faces

exposed at the bottom of the mount. The samples were wet polished to a 1200 grit

finish. The samples for potentiodynamic testing were set aside while the samples for

36

crevice substrates were removed from the epoxy by heating the mounts with a heat gun

until the epoxy became soft. Figure 11 shows a polished sample later used in a crevice

experiment (before patterning), as well as, a polished sample still in its mount which was

used for potentiodynamic scans.

a) b)

Ni Ribbon

Figure 11: a) Polished sample of Ni200 to be used as a crevice substrate; b) Polished sample mounted in epoxy for use in potentiodynamic experiments. The nickel ribbon was attached to the sample before the sample was covered in epoxy to allow for an electrical connection to be made.

Step 2: Initial Cleaning: As with the crevice formers and previous wafer

substrates, an abbreviated RCA cleaning was used to remove surface residue.

Step 3: Photolithography: SU-8-5 and SU-8-50 negative were used to pattern the

geometry of the crevice formers and create two different photoresist heights. Each

sample was spin-coated with the photoresist and baked on 55ºC and 90ºC hotplates to set

the photoresist. Bake times vary with type of SU-8 used. The samples were allowed to

cool for 30 minutes. A chrome-glass mask (Nanofilm, Inc.) with four individual former

patterns was placed on top of the sample to define the 4 x 7 mm crevice areas. The

37

sample was then exposed to UV radiation. The samples were baked and again allowed to

cool. The photoresist was developed using XP-SU-8 developer, whereby the mask

pattern was transferred to the sample. Each sample contained two substrate areas.

Step 4: Final cleaning and Photoresist Height Measurement: Each sample was

spin-cleaned using consecutive rounds of ethanol, TCA, and methanol. The patterned

photoresist height was measured using a Tencor Alpha-Step 200 contact profilometer.

4.1.3 Experimental Setup

4.1.3.1 Crevice Assembly

Patterned silicon and Ni200 substrates were affixed to a 3 x 3 inch piece of

Plexiglas using Dow Corning vacuum grease. The grease held the substrate in place and

electrically isolated the back of the substrate. A crevice former was placed with the

patterned side down onto the substrate area. Two optical microscopes, one with a top-

down view and one with a side-view were used to align the crevice former over the

substrate area. The goal was to match the photoresist boundaries of both the former and

the substrate so that a gap of continuous height was created throughout the crevice. A

smaller piece of Plexiglas was placed on top of the former and held down with nylon

screws that connected the two pieces of Plexiglas.

An electrical connection to the substrate was made by connecting six inches of 0.1

mm diameter Premion (99.998% pure) platinum wire to the pattern-defined substrate

contact patch using conductive adhesive. The entire assembly was vertically aligned in

the corrosion-testing cell. Only the very bottom of the crevice former was allowed to

38

touch the surface of the acid solution. Capillary action drew the solution up into the

crevice. This position was maintained throughout the experiment to prevent current from

being able to leak out from the sides of the crevice. The platinum wire was connected to

the working lead of the potentiostat. A platinum-niobium mesh and a saturated calomel

electrode were used as the counter and the reference electrode respectively. Before each

test, the open circuit potential of the crevice was allowed to stabilize. Stabilization was

defined as having occurred when the open circuit potential varied by only ±1 mV over a

5-minute period. Stabilization took between 30 minutes and 4 hours. A schematic of the

corrosion-testing cell can be seen in Figure 12.

39

CreviceAssemblyCrevice

Assembly

Former

Substrate

Crevice Tip OpenTo Air

Crevice Tip OpenTo Air

Substrate

SolutionWicking

Figure 12: A schematic of the crevice assembly. Only the crevice mouth was placed into the solution. The solution wicked up the entire crevice length due to capillary action.

4.1.3.2 Potentiodynamic Scans

Both electroplated wafers and polished Ni200 samples were used in polarization

scans. The Ni200 samples were able to be loaded directly into a standard flat-cell,

whereas the wafers had to be strengthened or they would break during placement into

the cell. The un-patterned, but electroplated, wafers had a 6-inch piece of nickel ribbon

attached to the back using conductive adhesive to allow connection to the working lead

on the potentiostat. Epoxy was used to attach a 1 x 1 inch piece of Plexiglas to the

backside of the wafer. A 1-cm2 knife-edge gasket was used to define the electrode area

40

exposed to the electrolyte. The attached nickel ribbon was connected to the working

lead, a platinum-niobium mesh was connected to the counter lead, and a calomel

electrode was used as a reference electrode. Before each test, the open circuit potential

was allowed to stabilize. Scans were performed over the range of –0.1 V vs. open

circuit potential to 1.0 V (SCE) with a scan rate of 2 mV/sec. Solutions containing 0.5

M or 0.01 M H2SO4 with varying NiSO4 concentrations (between zero and 3.5 M

saturation) were used. After the scan was completed, the Ni200 samples were wet

polished to 1200 grit for reuse while the wafers were rotated to an un-corroded region

and run again.

4.1.3.3 Equipment

All electrochemical experiments were performed using either an EG&G Versastat

or an EG&G model 273 potentiostat. A Dell 333 MHz computer controlled the Versastat

and the 273. Scribner Associates CorrWare v2.3f electrochemical analysis software was

used to run the experiments.

Solution conductivity measurements were made using a YSI Model 3200

conductivity meter with a YSI Model 3252 conductivity cell with a cell constant K = 1.0

cm-1. Solution pH measurements were taken with a Corning pH/ion analyzer model 350.

The analyzer was calibrated using standard, buffered solutions with pH values of 2.0, 3.0,

4.0, and 6.0. Electrolyte surface tension values were taken using a Kruss Tensiometer

model K-12 using the platinum plate technique. Electrolyte density measurements were

taken by measuring the mass of 1 mL (cm3) with a Denver Instrument Precision Balance

41

M220D. The electrolyte was drawn using an Epindorf pipette to ensure accurate solution

volume.

4.1.4 Crevice Assembly Experiments

Crevice experiments were performed in 0.5 M H2SO4 solution. After each

experiment, the cell was emptied, rinsed with de-ionized water, and refilled with fresh

acid solution. Formers with 7.3, 28.0, 74.3, and 86.5 µm gap sizes were used. Diced

wafer pieces 301.5 µm thick were used in conjunction with the 86.5 µm formers to create

extra large gaps of ~400 µm. The wafer pieces were placed along either side of the

substrate electrode and the former was placed on top of these pieces so that the former’s

SU-8-covered feet rested on top of the wafer pieces. The SU-8 patterned on the

substrates also added ~7 µm to the total crevice gap, resulting in final crevice gaps of

~14, 35, and 93 µm. Substrates with SU-8-50 spun on them (~79 µm) were combined

with the 74.3 µm formers to create crevice gaps of ~153 µm. Experiments were run for 1,

5, 10, and 30 minutes with potentiostatic hold potentials in the range of 0.5 to 0.6 V

(SCE).

Metallography was performed on a 1 x 1 inch sample of Ni200 plating which had

been wet polished to 1200 grit. The surface was etched using equal parts of concentrated

acetic acid, concentrated nitric acid, and distilled water[29]. A Zeiss 510 LSM (laser

scanning microscope) and a FEI 200 FIB (focused-ion beam) were used to examine the

attack morphology.

42

4.2 Modeling

All modeling experiments were performed on a Dell 610 Workstation with dual

Intel Xeon processors and 2 GB of RAM. CREVICERv2, created by Stewart[11] and

DeJong[12], was used to model the crevice corrosion experiments. The same finite

element solver routine was used throughout the experiments, whereas the author

programmed new materials, reactions, and geometries.

4.2.1 Scaling Law Investigation Follow-up

New experiments and regression of previous data were performed on the scaling

law investigations by DeJong[12, 18], as discussed in Section 2.3.2.

4.2.1.1 Effect of Larger Gap Sizes

Crevice gap values of 20 to 600 µm were run for each one of the six DeJong

electrochemical boundary conditions as discussed in Section 2.3.2. The same code from

the DeJong experiments was used which included the 0.184 (ohm-cm)-1 solution

conductivity (0.428 M H2SO4), 10-8 sec pseudo-electrical time step, and a convergence

limit of 0.002. The same finite element mesh with 350 nodes down the length of the

crevice (0.7 cm) with a greater concentration of nodes at the crevice mouth was also

used. (At the crevice mouth, the distance between nodes was 0.02 µm and increased

gradually to 50 µm at the crevice tip). Only the crevice gap was varied. The initial

potential distribution was the desired output. The setup routine of CREVICERv2 used by

the author can be found in Appendix B.

43

4.2.1.2 Investigation of Boundary Condition Characteristics

The key characteristics of each of the six DeJong electrochemical boundary

conditions were examined as to their relationship with xcrit. The characteristics examined

were: 1) Ecrit – the potential at which the peak current density is reached; 2) xcrit – the

distance down the depth of the crevice where Ecrit is reached (20 µm gap); the xcrit values

obtained from a 20 µm crevice where chosen because they lay in the linear portion of the

xcrit2 vs. G plot; 3) Itot – the total current flowing out of the crevice; 4) power density (PD)

– the area under the electrochemical boundary condition curve between –0.3 and 0.8 V

(SCE), with 1 x 10-5 A/cm2 used as the lower current boundary.

4.2.2 Crevice Corrosion Experiments

4.2.2.1 Comparisons to Experiments on Microfabricated Crevices

CREVICERv2 was used to model the initial potential and current distributions

down the length of the crevice. The potentiodynamic scan of Ni200 in 0.5 H2SO4

described in Section 4.1.3.2 was mathematically fitted and coded into CREVICERv2.

Crevices with gaps of 14, 35, 93, 153, and 395 µm were chosen for direct comparison

with results from the microfabricated crevice experiments. The potentiostatic hold

potential at the crevice mouth was +600 mV. The pseudo-electrical time step was set to

10-7.

44

4.2.2.2 Effect of Crevice Area and Electrolyte Conductivity on xcrit

CREVICERv2 was used to examine crevices with more complicated crevice

geometries. Gap profiles from Abdulsalam and Pickering[17] were digitized and fitted

using mathematical equations. The gap profiles of interest were at time = 0, where the

crevice has a uniform gap of 300 µm, time = 50 hours, and time = 150 hours. The effect

of the larger crevice area (due to profile curvature) on the potential distribution was

examined. The same Ni / 0.5 M H2SO4 boundary condition used to compare the

microfabricated crevices was also used here.

The effect of varying the electrolyte conductivity directly over the beginning of

the region of greatest attack was also examined. The solution conductivity between 0.05

and 0.15 cm down the length of the crevice was varied to coincide with the measured

conductivity (Section 2.3.1.3.3) from adding 0.2 M, 1.1 M, and saturated (3.5 M) NiSO4.

The code written by the author used in this and the previous section can be found in

Appendix B.

45

CHAPTER 5. RESULTS

5.1 Microfabrication

5.1.1 Formers

As in semiconductor processing, silicon wafers were used as the foundation for

the crevice formers. A patterned chrome-glass mask was designed as to yield four

formers from one wafer. The mask design can be seen in Figure 13. As listed in Table 2,

varying types of SU-8 photoresist were patterned onto the wafers to create the crevice

sidewalls and to control gap height (Figure 14a and 14c). Former gap sizes of 7.3, 16.4,

28.0, 74.3, and 86.5 µm were created using this technique with a maximum ±2%

difference in height down the length of the former. Figure 15 is a secondary electron

image taken after cutting through some of the SU-8 using a Focused Ion Beam (FIB).

4 mm

8 mm

0.4 mm

4 mm

8 mm

0.4 mm

Figure 13: The mask used to pattern the crevice formers. The dark regions on the mask define the crevice walls.

46

Table 2: Former heights determined by SU-8 type and spin coater speed.

Former SU-8 Type Spin Speed (rpm) SU-8 Height (µm) FJ-1 5 1800 7.3 FJ-2 10 1800 16.4 FJ-3 25 1800 28.0 FJ-4 50 1800 74.3 FJ-5 50 1600 86.5

This new fabrication technique differs significantly from the one used by

DeJong[12, 18]. In DeJong’s technique, the bulk silicon was patterned and etched to a

specific depth (Figure 14b and 14d). Vertical sidewalls were achieved by choosing an

etchant that preferentially etched the crystal orientations that were not part of the vertical

sidewalls. This kept the etchant from etching under the patterned areas. However, this

resulted in a significant roughness along the former flank. As seen in Figure 14e and 14f,

the old (DeJong) former had a roughness value twice that of the new type of former.

The new former fabrication technique was also faster than the old one. Without

the need to etch silicon, one of the major steps could be skipped in the new technique

saving time and supplies.

47

NEW OLD

Thermal Oxide

Silicon Wafer

Photoresist

a) b)

f)

Silicon Wafer

c) d)

e)

RRMS (1.640 µm)RRMS (0.874 µm)

Figure 14: Comparison of old and new former fabrication techniques. (a) and (b) schematics of new and old former, (c) and (d) images of new and old formers, (e) and (f) comparison of former surface roughness using a confocal laser scanning microscope. Notice that the new former has a roughness that is half of the one from the old technique.

48

SU-8

Silicon

Damage CausedBy FIB

Silicon Wafer

ExaminedRegion

SU-8

Figure 15: Image of the SU-8 on a former cut away using a focused-ion beam.

5.1.2 Substrates

5.1.2.1 Silicon Wafer Based

A new microfabrication technique was also developed to build the crevice

substrates. Schematics and photographs in Figure 16 compare the resulting substrates

created using this new technique and the one used by DeJong[12, 18]. A 140 Å layer of

chrome was evaporated onto a two-inch wafer, followed by a 400 Å layer of nickel. The

chrome acted as an adhesion layer between the nickel and the silicon. The smaller nickel

thickness (as opposed to 600 Å as used by DeJong) prevented the nickel layer from

49

peeling away from the wafer as seen in a sample fabricated by DeJong in Figure 17. SU-

8-10 photoresist was spun onto the wafer. Two substrate designs (Figure 18) were

patterned onto the wafer. The pattern created an exposed substrate area of 4 x 10 mm

with vertical sidewalls ~17 µm high. A small contact patch was added to the substrate

design to allow an electrical connection during experiments.

50

Evaporated NickelThermal Oxide

NEW OLD

Silicon WaferEvaporated Chromium

Photoresist

Silicon Wafer

a) b)

c) d)

Electrode

Contact

Electroplated Nickel

Figure 16: Comparison of substrates fabricated from the old and new techniques. (a) Schematic of new substrate, electroplated nickel thickness of ~17µm; (b) Schematic of old substrate, evaporated nickel thickness 0.4 µm max; (c) Image of new substrate with a 7 x 10 mm electrode and electrical contact patch; (d) Image of old substrate, electrical connection was made by adhering a platinum wire to its back.

51

JaggedEdge

Crevice Mouth

Figure 17: The jagged edge of a substrate fabricated using the old technique. The new technique improved upon this by coating the substrate with protective photoresist layers before dicing.

4 mm

10 mm

2.75 mm

4 mm

2.5 mm

4 mm

10 mm

2.75 mm

4 mm

2.5 mm

Figure 18: The mask design used to pattern the electrode area and contact patch onto the substrates.

52

The contact patch was also used as an electrical connection during nickel plating.

The new nickel-plating technique yielded nickel thickness of ~17 µm which matched the

difference in height created by the photoresist when defining the electrode area. The

length of plating time was determined to be 23 minutes at 55 mA/cm2 to achieve this

thickness. This is a vast improvement over the 0.6 µm maximum nickel thickness

achieved by DeJong using metal evaporation. The greater nickel thickness resulted in an

electrochemical behavior that more closely resembled that of Ni200 (a high purity nickel

alloy used in later experiments) as indicated in Figure 19. Figure 20 shows a profile scan

across the width (4 mm) of a finished substrate. Notice that the thickness of the nickel

increases towards the sidewalls on an average of 4 µm. Figure 21 is a secondary electron

image taken after a section of the plated nickel / SU-8 photo resist interface was cut away

using an FIB. The substrates yielded from this new technique are listed in Table 3.

Chemical composition analysis was attempted on the plated nickel at Motorola’s Process

and Materials Characterization Lab (Mesa, AZ), but was inconclusive due to equipment

problems during the analysis.

Table 3: Statistics of silicon-based substrates.

Si Based Substrate

SU-8-5 Height (µm) ± 0.5 – 1.0

Plated Ni Height Range (µm)

Resulting Extra Gap Range (µm)

SJ-1a 17.31 11.3 – 7.8 9.5 – 6.0 SJ-1b 17.30 10.0 – 7.0 7.5 – 10.4 SJ-2a N/A Broke dicing -- SJ-2b N/A Broke dicing -- SJ-3a 17.02 Broke dicing -- SJ-3b 16.93 17.0 – 13.0 4.0 – 0.0 SJ-4a 16.87 15.9 – 11.5 5.3 – 1.0 SJ-4b Flaw in SU-8 -- --

SJ-5a -> 6b Scratched during photolithography

-- --

SJ-7a 15.21 15.2 – 10.7 4.5 – 0 SJ-7b 16.43 18.4 – 13.4 +3 -> -2

53

SJ-8a 15.67 15.7 – 11.5 4.1 – 0 SJ-8b 16.35 12.8 – 9.75 6.7 – 3.6 SJ-9a 15.66 15.6 – 10.6 4.8 – 0 SJ-9b 16.11 16.7 – 12.5 +4.2 -> -1 SJ-10a 15.69 16.7 – 12.5 +3.2 -> -1 SJ-10b Flaw in SU-8 -- -- SJ-11a 15.71 20.7 – 15.0 +1 -> -5 SJ-11b 16.26 18.3 – 13.0 +2.9 -> -2 SJ-12a 15.99 16.0 – 11.5 4.2 - 0 SJ-12b 15.99 17.5 – 13.1 +2.9 -> -1.5 SJ-13a 16.56 16.6 – 12.6 4 – 0 SJ-13b 16.33 17.3 – 12.1 +4.2 ->-1 SJ-14a 15.17 15.2 – 10.8 4.4 – 0 SJ-14b 15.30 15.3 – 11.2 4.1 – 0 SJ-15a 15.70 15.1 – 10.9 4.8 – 0.6 SJ-15b 16.18 16.7 – 11.8 +4.4 -> -0.5 SJ-16a 15.48 14.9 – 10.4 4.9 – 0.5 SJ-16b 15.42 17.9 –11.6 +2.7 -> -2.5 SJ-17a 16.08 No Nickel plated -- SJ-17b 16.36 No Nickel plated --

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-8 -7 -6 -5 -4 -3 -2 -1 0Log Current Density (A/cm2)

Pote

ntia

l (V

vs. S

CE) Ni 200 alloy

8.7 µm Ni Substrate0.3 µm Ni Substrate

Figure 19: Comparison of the electrochemical behavior of an old substrate with only 0.3 µm nickel thickness, a new substrate with 8.7 µm of electroplated nickel, and Ni200. Notice the behavior of the thicker nickel is more comparable to Ni200 than the thin nickel substrate.

54

SU-8 SU-8

Electroplated Nickel

Note: X vs. Y scale = 1000:1

Figure 20: A profilometer scan of a silicon-based substrate across the electrode width after electroplating. Note the x-axis is 1000 times the scale that the y-axis.

55

Electroplated Nickel

Silicon Wafer

SU-8

ExaminedRegion

SU-8

Figure 21: Image of a cross-section of a silicon-based substrate after electroplating. The area was exposed using a focused-ion beam.

Wafers for polarization scans were also fabricated in the same manner except no

photoresist was applied. Using the plating specs for the patterned substrates produced

less than 2 µm nickel plate thickness on these wafers. Since these wafers had an area to

be plated which was 5.06 cm2 (compared with 0.28 cm2 on the patterned substrates) the

plating current was increased to 100 mA (19.8 mA/cm2). With these plating specs, a

plated nickel thickness of ~17 µm was achieved on the un-patterned wafers (Table 4).

56

Table 4: Un-patterned silicon wafers with electroplated nickel for potentiodynamic testing.

Wafer Plating Duration (min)

Plating Current (mA)

Plated Nickel Thickness (µm)

WJ-1 23 15 1.6 WJ-2 30 15 1.8 WJ-3 Broken -- -- WJ-4 30 15 2.0 WJ-5 60 15 4.5 WJ-6 20 100 12 WJ-7 20 100 17 WJ-8 20 100 20 WJ-9 20 100 10

WJ-10 25 100 14 WJ-11 25 100 18 WJ-12 23 100 20 WJ-13 25 100 21

5.1.2.2 Ni200-Based Substrate

Crevice substrates were also made using Ni200 plates. Figure 22 is a picture from

a Confocal Laser Scanning Microscope (LSM) showing a Ni200 surface after polishing.

The average roughness (RRMS = standard deviation) measured by the LSM was ±0.104

µm. SU-8 was spun onto the plate and patterned using the same substrate mask used with

the silicon based substrates. Unlike the silicon-based substrates, either SU-8-5 or SU-8-

50 was used to define the electrode and contact areas. The thickness of the different

photoresists added to the final gap size when the substrate was combined with a crevice

former. Table 5 list the substrates fabricated by this process.

57

Table 5: Ni200-based substrate statistics.

Ni200 Substrate SU-8-5 Height (µm)

SP-1 No SU-8 applied SP-2 SU-8 removed completely SP-3 7.30 SP-4 7.30 SP-5 8.70 SP-6 7.50 SP-7 7.13 SP-8 7.01 SP-9 6.75

SP-10 7.26 SP-11 7.17 SP-12 7.21 SP-13 7.18 SP-14 8.63 SP-15 7.33 SP-16 7.43 SP-17 7.47 SP-18 7.61 SP-19 7.28 SP-20 7.43 SP-21 7.44 SP-22 7.14

SP-23** SU-8 cracked SP-24** 79.2 SP-25 7.5

SP-26** 79.1 ** SU-8-50 used, spun at 1600 rpm for 30 secs

58

(RRMS 0.104 µm)

50 µm

Figure 22: The surface of a Ni200 sample after polishing to 1200 grit.

5.1.3 Electrochemistry of Substrates

5.1.3.1 Silicon-Based

Potentiodynamic scans of the electroplated wafers in 0.5M H2SO4, 0.5 M H2SO4

+ 3 M NiSO4, and 0.01 M H2SO4 + 3 M NiSO4 are shown in Figure 23 and listed in

Table 6. The first scan on a particular wafer always produced a critical current density

that was higher (100 mA/cm2) and a more noble passivation potential, Ecrit, than

expected. The passive current also varied by up to two orders of magnitude from sample

to sample. As to be discussed at greater detail later, the microfabricated substrates

therefore were not used in this study.

59

Table 6: Potentiodynamic scans performed on nn-patterned wafers with electroplated nickel

Wafer Run [H2SO4] (M)

[NiSO4] (M)

Ecorr (V vs. SCE)

12 1 0.5 0 -0.314 12 2 0.5 0 -0.311 11 2 0.5 0 -0.358 8 2 0.5 0 -0.309 9 5 0.5 3.0 -0.296

10 2 0.01 3.0 -0.455

Figure 23: Polarization behavior of silicon-based electroplated nickel substrates. Notice the lack of reproducibility in peak and passive current densities for different substrates in 0.5 m H2SO4. The lack of reproducibility ultimately led to these substrates being replaced with the Ni200 substrates.

5.1.3.2 Ni200 Based

Potentiodynamic scans of polished Ni200 samples were carried out in 0.5 and

0.01 M H2SO4 with a range of NiSO4 concentrations ranging from zero to saturated.

60

Table 7 lists the potentiodynamic scans that were performed. As shown in Figure 24, the

passive current remained constant with a value of ~2x10-5 mA/cm2 from run to run. This

is in sharp contrast to the results seen with the silicon-based substrates. However, the

peak current varied depending upon the concentration of NiSO4. At concentrations less

than 0.028 M, the curve had a reproducible double bump shape with a peak current of

7.745 (± 0.212) mA/cm2 at the 0.244 V (SCE) bump, a passive current of 3.281 (± 0.135)

x 10-2 mA/cm2 at 0.6 V (SCE), and an open circuit potential of –0.222 (± 0.002) V

(SCE)*. (Only the curve for zero Ni2+ is shown in Figure 24). However, the shape of the

curve altered when the concentration of NiSO4 reached 0.028 M. The second peak at

0.088 V began to dominate and rise in potential and peak current. At a NiSO4

concentration of 0.295 M the curve no longer has a double bump shape.

* The passive current, peak current, and open circuit potential values given are averages with standard deviations taken from 10 different scans with nickel concentrations ranging from zero to 10-2 M.

61

DoubleBumps

Figure 24: Potentiodynamic scans of Ni200 substrates in 0.5 m H2SO4 with various concentrations of NiSO4. The electrochemical behavior remains constant until the NiSO4 concentration increases above 0.028M, where an increase in peak current density and a loss of the double bump shape is lost.

5.1.4 Physical Chemistry of Electrolytes

The conductivity of each solution, used during the above potentiodynamic scans,

was measured and is shown in Table 7. Figure 25 illustrates of how solution conductivity

is a function of NiSO4 concentration. At low values (<0.01 M), increasing NiSO4

concentration corresponded in a weak increase in solution conductivity. However, at

values greater than 0.01 M, solution conductivity decreased with increasing NiSO4

concentration. The measured conductivity value 0.1891 (ohm-cm)-1, for the 0.5 M H2SO4

without NiSO4, agreed with values from the literature[10, 17, 27].

62

Table 7: Potentiodynamic scans performed on Ni200 samples in 0.5 H2SO4 with variable NiSO4 concentration, and physical chemistry measurements of each solution.

Substrate

[H2SO4] (M)

[NiSO4] (M)

Ecorr (V vs. SCE)

Conductivity(ohm-cm)-1

Density (g/cm3)

Surface Energy

(dyne/cm) NI-2 0.5 0 -0.235 0.1891 1.0314 72.76 NI -7 0.5 10-5 -0.217 0.1892 -- -- NI -5 0.5 10-4 -0.238 0.1893 -- -- NI -3 0.5 10-3 -0.226 0.1899 -- --

-- 0.5 0.00118 -- -- 1.0315 72.56 NI -4 0.5 10-2 -0.225 0.1906 1.0403 72.74 NI -7 0.5 0.028 -0.215 0.1870 1.0452 72.57 NI -7 0.5 0.094 -0.210 0.1805 1.0473 72.64 NI -7 0.5 0.118 -0.181 0.1788 1.0499 72.94 NI -7 0.5 0.295 -0.204 0.1544 1.0746 73.11 NI -7 0.5 0.589 -0.180 0.1455 1.1192 73.18 NI -7 0.5 1.178 -0.216 0.1211 1.1902 73.45 NI -7 0.5 1.767 -0.221 0.0947 1.2792 75.92 NI -7 0.5 Saturated -0.228 0.0760 1.3654 78.10 NI -3 0.01 Saturated -0.310 0.0495 -- --

0.00

0.05

0.10

0.15

0.20

0.25

0.00001

0.0001

0.0010.01

0.1 1 10

[Ni2+] (M)

Con

duct

ivity

(ohm

-cm

)-1

Figure 25: Conductivity as a function of nickel concentration.

63

The pH of each solution was also measured. All of the solutions had a pH of 0.5

except the one with 0.01 M H2SO4 that had a pH of 2.2. These values correspond to

values from the literature[10].

Density and surface energy measurements were taken from solutions containing

0.5 M H2SO4 and varying NiSO4 concentration from zero to saturated. The solution

density increased with increasing NiSO4 concentration. The surface energy increased

slowly with NiSO4 concentration until saturation at which point the surface energy value

reach a maximum. The values can be found in Table 7.

5.2 Microfabricated Crevice Experiments

The assembly of a substrate and a particular former allowed varying crevice gaps

to be created for testing. Figure 26a shows a picture of an 86 µm former face-down on a

Ni200 substrate. Figure 26b is a close-up view of the crevice sidewall formed by the SU-

8 on the former. Table 8 lists the substrates and formers used in each run and the

resulting values of xcrit, the measured distance down the crevice length from the crevice

mouth to the first line of severe attack. Because the experiments produced attack bands

that were not always perpendicular to the length of the crevice, the maximum and

minimum values of xcrit were recorded.

64

b)

a) Former

Substrate Nickel Electrode

Substrate SU-8

CreviceMouth

Nickel Electrode

Substrate SU-8

Former SU-8

FormerSilicon Wafer

93 µmCrevice

Figure 26: (a) 86 µm former face-down on a Ni200 substrate; (b) a close-up view of the crevice sidewall formed by the SU-8 on the former. The edge of the SU-8 on the substrates is the pink dashed line. It is hard to see due to the surface of the substrate being highly reflective.

65

Table 8: Results of crevice hold experiments with variable gap, experimental duration, and hold potential.

Substrate Former Total Gap (µm)

Run Time (min)

Hold Potential (V vs. SCE)

Ecorr (V vs. SCE)

Xcrit range (mm)

SP-7a FJ-5 93.7 30 0.600 -0.203 3.21 – 3.45 SP-7b FJ-5 93.7 30 0.600 -0.203 1.96 – 2.10 SP-9a FJ-3 34.8 30 0.600 -0.131 1.95 – 2.74 SP-9b FJ-3 34.8 30 0.600 -0.131 1.26 – 1.46 SP-10a FJ-1 14.6 1 0.600 -0.153 0.96 – 1.20 SP-10b FJ-1 14.6 1 0.600 -0.153 0.62 – 1.12 SP-11a FJ-5 93.7 1 0.600 -0.204 2.30 – 2.33 SP-11b FJ-5 93.7 1 0.600 -0.204 2.36 – 2.40 SP-12a FJ-5 93.7 10 0.600 -0.159 2.55 – 2.77 SP-12b FJ-5 93.7 10 0.600 -0.159 2.29 – 2.34 SP-13a FJ-3 35.2 1 0.600 -0.167 1.11 – 1.40 SP-13b FJ-3 35.2 1 0.600 -0.167 1.78 – 2.08 SP-14a FJ-1 15.9 5 0.600 -0.221 1.00 – 1.50 SP-14b FJ-1 15.9 5 0.600 -0.221 0.25 – 0.85 SP-15a FJ-1 14.6 10 0.600 -0.187 0.51 – 1.13 SP-15b FJ-1 14.6 10 0.600 -0.187 0.31 – 0.98 SP-16a FJ-1 14.7 30 0.600 -0.160 1.03 – 2.34 SP-16b FJ-1 14.7 30 0.600 -0.160 0.27 – 1.77 SP-17a FJ-3 35.5 10 0.600 -0.207 1.34 – 2.23 SP-17b FJ-3 35.5 10 0.600 -0.207 0.82 – 1.04 SP-18a FJ-3 35.6 5 0.600 -0.217 1.32 – 2.41 SP-18b FJ-3 35.6 5 0.600 -0.217 2.40 – 2.54 SP-19a FJ-5 94.7 5 0.600 -0.219 3.00 – 3.34 SP-19b FJ-5 94.7 5 0.600 -0.219 2.76 – 2.77 SP-21b FJ-3 35.4 5 0.500 -0.158 1.25 – 1.32 SP-22b FJ-3 35.1 5 0.525 -0.112 1.82 – 2.17 SP-24a FJ-4 153.5 30 0.600 -0.228 3.69 – 3.74 SP-24b FJ-4 153.5 30 0.600 -0.228 3.60 – 3.74 SP-25a FJ-5 395** 30 0.600 -0.142 Passivated SP-26a FJ-5 153.4 10 0.600 -0.202 3.53 – 3.66

**301.5µm spacer used between the substrate and the former to achieve the 395 µm gap

Each crevice sample examined showed the same general trend of having three

separate regions down the length of the crevice: passive, active, and etched (or varying)

as seen in Figure 27 (sample SP-7a). The passive region begins at the crevice mouth and

continues until active corrosion begins which is xcrit. The active region is the band of

greatest attack where active corrosion has taken place. The variable attack region begins

after the attack band and continues down the length of the crevice. This region has

variable amounts of attack based on time, gap, and hold potential. Also, the variable

66

attack region is sometimes not uniform across the width of the crevice. As seen in Figure

27, there can be seen pockets of passive, lightly etched, and active corrosion spread

throughout this region.

Crevice Mouth

PassiveRegion

Variable AttackRegion

1 mm

35 µm gap+0.6V hold

ActiveRegion

Figure 27: An example of a corroded crevice substrate with a 35 µm gap held at +0.6 V (SCE) for 30 mins. Notice the three distinct regions of morphology, passive, active, and variable.

5.2.1 Effect of Gap Size and Experiment Duration on xcrit

Figure 28 shows the results of pressing a 7.3 µm former (~14 µm total crevice

gap) onto a series of Ni200 substrates and varying the experiment duration between 1, 5,

10, and 30 minutes with a hold potential of 0.6 V (SCE). Crevice samples with the same

hold times are true replicates in that they were performed at the same time on the same

piece of Ni200. (Each sample had two substrates patterned on it). At t = 1 min, the

67

attack band is a simple curved line across the width of the crevice. The maximum and

minimum values of xcrit are 0.62 and 1.20 mm respectively. As the run duration is

increased, the attack band shape becomes less uniform. At t = 30 min, values of xcrit vary

significantly across the crevice width with an xcrit range of 0.27 – 2.34 mm.

68

Attack Band

Crevice Mouth

Max xcrit

Min xcrit

1 mm

1 mm

1 mm

1 mm

1 mm

1 mm

1 mm

1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 min

5 min

10 min

30 min

a)

b)

d)

c)

1 min

5 min

10 min

30 min

a)

b)

d)

c)

Gap = 14 µm 0.6 V vs. SCE hold potential

Figure 28: Crevice holds of 14 µm gap with 0.6 V (SCE) hold potential with experiment durations of (a) 1min, (b) 5 min, (c) 10 min, and (d) 30 min. Note that the attack bands are become less uniform as the corrosion is allowed to continue for longer times.

Figure 29 shows the results of pressing a 16.4 µm former (~35 µm total crevice

gap) onto a series of Ni200 substrates and varying the experiment duration between 1, 5,

10, and 30 minutes with a hold potential of 0.6 V (SCE). At t = 1 min and 5 min, the

69

attack band is a well defined curved line across the width of the crevice. A lack of attack

ahead and behind the attack band can be seen. The maximum and minimum values of

xcrit are 1.11 and 2.08 mm respectively. At t = 10 min the attack band is still a simple

curve. Little attack is seen in front of the attack band, but the region behind the attack

band has undergone noticeable corrosion. At t = 30 min, the attack band begins to lose

its uniform shape and the values of xcrit vary across the crevice width with an xcrit range of

1.26 – 2.74 mm. The regions in front and behind the attack band have undergone even

more noticeable corrosion.

70

Crevice Mouth

1 mm

1 mm

1 mm

1 mm

1 mm

1 mm

1 mm

1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 min

5 min

10 min

30 min

a)

b)

d)

c)

1 min

5 min

10 min

30 min

a)

b)

d)

c)

Gap = 35 µm 0.6 V vs. SCE hold potential

Figure 29: Crevice holds of 35 µm gap with 0.6 V (SCE) hold potential with experiment durations of (a) 1min, (b) 5 min, (c) 10 min, and (d) 30 min. Note that the attack bands are become less uniform as the corrosion is allowed to continue for longer times.

Figure 30 shows the results of pressing a 86.5 µm former (~93 µm total crevice

gap) onto a series of Ni200 substrates and varying the experiment duration between 1, 5,

71

10, and 30 minutes with a hold potential of 0.6 V (SCE). At t = 1 min. the attack band is

straight across the width of the crevice. A lack of attack ahead and behind the attack

band can be seen. The maximum and minimum values of xcrit are 2.30 and 2.44 mm

respectively. At t = 5 min the attack band remains straight and has become more defined

as a dark band surrounded by lighter areas. Little attack is seen in front of the attack

band, but the region behind the attack band has undergone noticeable corrosion. Also

seen behind the attack band are areas that vary in color at the same crevice depth. At t =

10 min, the band of greatest attack is very distinguishable as a much darker region than

the lighter corrosion around it. Behind the attack band, the contrast between intermittent

darker and lighter areas has increased. At t = 30 min, the attack band is still fairly

straight across the width of the crevice with an xcrit range of 1.96 – 3.45. (This large

variation is due mostly to the two samples having significantly different depths of

greatest attack.) Behind the attack band, significant active corrosion has taken place,

however, intermittently mixed with areas of little attack. In front of the attack band still

showed little evidence of corrosion.

72

Crevice Mouth

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 mm1 mm

1 min

5 min

10 min

30 min

a)

b)

d)

c)

1 min

5 min

10 min

30 min

a)

b)

d)

c)

Gap 93 µm 0.6 V vs. SCE hold potential

Figure 30: Crevice holds of 93 µm gap with 0.6 V (SCE) hold potential with experiment durations of (a) 1min, (b) 5 min, (c) 10 min, and (d) 30 min. The blue arrows indicate areas within the variable region that show signs of chemistry and/or potential changes. Note that the attack bands are straighter than the ones from smaller gaps.

Formers with a 74.3 µm height were pressed onto two Ni200 substrates with SU-

8-50 thickness of ~79.2 and 79.1 µm resulting in crevice gaps of 153.5 and 153.4 µm.

73

The crevices were held at 0.6 V (SCE) for 10 (SP-26) and 30 (SP-24) min. Sample (SP-

26) was damaged during crevice assembly and only one of the electrodes (side a) was

used. As seen in Figure 31, the line of greatest attack is very straight with an xcrit range

of 3.53 – 3.74 mm over all three electrode areas. The attack band is the dark region right

after the sharp line of light attack. Little attack is seen ahead of the attack band while

significant corrosion has occurred behind. Pockets of passive corrosion can be seen

centered across the crevice width with signs of significant corrosion along the sidewalls

deep into the crevice. Also, the amount of active attack in the variable region of the

sample held for 10 min (Figure 31a) was much less that the amount seen in the ones held

for 30 min (Figure 31b).

74

1 mm1 mm

1 mm1 mm

10 min

30 min

1 mm1 mm

a)

b)

30 min

Gap = 153 µm 0.6 V vs. SCE hold potential

Figure 31: Crevice holds of 153 µm gap with 0.6 V (SCE) hold potential with experiment durations of (a) 10minand (b) 30 min. The blue arrows indicate area that displayed evidence of changes in chemistry during corrosion. Note the straight attack bands.

Figure 32 shows the results of pressing an 86.5 µm former, along with 301.5 µm

sidewall spacers, together with a Ni200 substrate (7.5 µm SU-8 thickness) to create a

crevice gap of 395 µm. The crevice was held at 0.6 V (SCE) for 30 min. Little or no

attack is seen down the length of the crevice.

75

1 mm1 mm

Crevice Mouth

Gap = 395 µm 0.6 V vs. SCE hold potential

Figure 32: A 395 µm crevice held at 0.6V (SCE) for 30 mins. The entire surface passivated and showed no signs of active corrosion.

The average experimental xcrit

2 and xcrit values at time = 1 min for crevice gaps of

14, 35, and 93 µm are compared in Figure 33a and b. The average xcrit2 and xcrit values

taken from the runs with 153 µm gaps had an experiment run time of 10 min. In both

cases, xcrit and xcrit2 increase with increasing gap size in a monotonic fashion.

76

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 20 40 60 80 100 120 140 160 180

Gap (microns)

Xcrit

(mm

)

0.0

4.0

8.0

12.0

16.0

0 20 40 60 80 100 120 140 160 180

Gap (microns)

Xcrit

2 (mm

2 )

b)

a) 0.6 V vs. SCE hold potential

0.6 V vs. SCE hold potential

Figure 33: x2 vs. g and x vs. g plots of the average xcrit values from the crevice experiments. Average values were obtained by taking the midpoint of the given xcrit range.

77

The range of xcrit for each run is shown in Figure 34a. The plot indicates a trend

of increasing xcrit range with decreasing gaps size. At small gaps, increasing run time

also resulted in an increase in the range of xcrit (Figure 34b).

a)

0.0

1.0

2.0

3.0

4.0

5.0

0 5 10 15 20 25 30 35

Time (min)

Xcrit

(mm

)

14 micron gap 35 micron gap 93 micron gap 153 micron gap

0.6 V vs. SCE hold potential

b)

78

0.0

0.5

1.0

1.5

2.0

2.5

0 5 10 15 20 25 30 35

Time (min)

Xcrit

(mm

)±0.12

±0.25

±0.31

±0.66

±0.25±0.30 ±0.36

±0.75

0.6 V vs. SCE hold potential14 µm gap

Figure 34: (a) xcrit ranges for 14, 35, 93, and 153 µm crevice gaps from the experimental crevice runs. Notice that the range decreases with increasing gap (b) a close-up of the 14 µm crevice gap data showing the increase in the range of xcrit with time.

5.2.2 Effect of Potential on xcrit

To test the effect of potential on xcrit, a 28.0 µm crevice former was pressed

against four Ni200 substrates to create a crevice gap of 35 µm. One sample was held at

0.5 V, one at 0.525 V, and two at 0.6 V (SCE) for 5 minutes. Figure 35 illustrates the

movement of xcrit as a function of hold potential (only one example of a 0.6V hold is

shown). The crevice held at 0.5 V (SCE) had the smallest average xcrit (1.29 mm) with a

range of 1.25 – 1.32 mm. The crevice held at 0.525 V had a larger average xcrit (2.00

mm) with a range of 1.82 – 2.17. One of the samples held at 0.6V had the highest

average xcrit (2.47 mm) with a range of 2.40 – 2.54 mm. The other sample held at 0.6 V

had an average xcrit of 1.87 mm that is less than the value taken from the crevice held at

79

0.525 V. The measured range was 1.32 – 2.41 mm. The average xcrit and its

corresponding range can be seen in Figure 36.

+500 mV

+525 mV

+600 mV

xcrit

xcrit

xcrit

1 mm1 mm

1 mm1 mm

1 mm1 mm

Crevice Mouth

a)

b)

c)

Gap = 35 µm

Figure 35: The movement of xcrit as a function of potential for a crevice gap of 35 µm for hold potentials (SCE) of (a) 500 mV, (b) 525 mV, and (c) 600 mV.

80

0

0.5

1

1.5

2

2.5

3

0.475 0.500 0.525 0.550 0.575 0.600 0.625

Potential (V vs. SCE)

Xcrit

(mm

)

Gap = 35 µm

Figure 36: The range of xcrit as a function of potential for a crevice gap of 35 µm for hold potentials of 500 mV, 525 mV, and 600 mV (SCE).

5.2.3 Attack Morphology

Figures 37 and 38 are a series of images down the length of sample SP-7a (93 µm

gap, +0.6 V (SCE) hold potential, 30 experiment duration) that examine the ranging

morphology found within the crevice. Figure 37a is a magnified image of the transition

from the passive region into the attack band. The image indicates that little attack occurs

in the passive region, in contrast to the active region that shows that active corrosion has

taken place.

81

CreviceMouth

(a) Front ofAttack Band

(b) Middle ofAttack Band

(c) Rear ofAttack Band

1 mm

50 µm 50 µm 50 µm

Passive Active VariablePassive Active Variable

Figure 37: Morphology of the attack band shown by confocal laser scanning images for (a) front of attack band, (b) middle of attack band, and (c) rear of attack band.

Figure 37b is a magnified image of the middle of the attack band. This shows

severe attack by the rough topography and the multifaceted surfaces.

82

(b) (Variable)Passive Attack

CreviceMouth

1 mm

(c) (Variable)Active Attack

(a) Passive Attack

Passive Active VariablePassive Active Variable

50 µm 50 µm 50 µm

Figure 38: (a) Morphology of the passive region by confocal laser scanning images. (b) Morphology of passive attack in the variable region. (c) Morphology of active attack in the variable region revealing the facet structure.

The transition from attack band to the variable region is shown in Figure 37c. A

sharp contrast can be seen at the transition point in that the attack band is a very rough

surface while after the transition little or no attack is seen.

83

The differences in the amount of attack in the varying region can be seen by

further examination of Figure 38. Figure 38b shows an area deep into the crevice that has

undergone some light etching. At the same crevice depth, Figure 38c shows an area that

has undergone active corrosion. Figure 38a shows an area in the passive region with little

or no attack that is much like the light etching seen in the variable region.

A Ni200 sample polished to 1200 grit was lightly etched (using equal parts of

water, concentrated acetic acid, and concentrated nitric acid) to enable the examination of

the grain boundaries. Figure 39b is an image (x50) of the etched surface. The grain

boundaries are seen as straight lines between 10 - 50 µm in length. The same grain

boundary sizes are seen in Figure 39a showing an area that is believed to have undergone

active corrosion past the region of the attack band.

84

a)Corroded Surface

b)Etched Surface

50 µm50 µm

Figure 39: (a) Suspected active corrosion in variable region of Ni200 crevice sample and (b) etched surface of Ni200 polished surface, where the grain boundaries are visible. Comparing the two shows that the possible active region is indeed due to active corrosion because of the faceted structure in both images.

Figure 40a shows an area in the variable region where both active and passive

corrosion are taking place. Figure 40a is a picture taken after a section along the

transition between active and passive corrosion was cut out using a focused-ion beam

(FIB). The surface was tilted 45º so that the interior of the cut could be examined.

85

Figure 40b is a magnified image of Figure 40a which has been rotated 45º counter-clock

wise. Along the vertical wall of the cut, grain boundaries can been seen by the

differences in gray scale intensity between grains. In the active region, whole facets of

grains have dissolved away, whereas only the grain boundaries have light attack in the

passive region. Farther into the passive region, the attack on the grain boundaries is

much less.

86

Crev ice Mouth PassiveAttack

ActiveAttack

a)

b)

GrainBoundary

GrainBoundary

Figure 40: (a) a 93 µm gap crevice after 30 minutes of active corrosion, the close-up image is that of a section of the variable region where there is a transition between active and passive corrosion morphology. A focused-ion beam was used to cut out a section along the transition line. Notice the highly faceted structure in the active region, whereas the passive region has very little attack. The surface was tilted 45 º to allow the cutout interior to be viewed. (b) a magnified image of the cut out area rotated 30 º counter-clockwise. Individual grains are visible along the cutout wall by their difference in grayscale. Comparing the position of these grains with the attack above, it is shown that the active corrosion does preferentially attack grain facets.

87

5.3 Modeling

5.3.1 Scaling Law Investigation Follow-up

The previous work by DeJong[12] demonstrated that the shape of the systems

electrochemical boundary condition (polarization curve) for the nickel / 0.5M H2SO4

system affected the scaling laws. The boundary conditions used in this study were

discussed in Section 2.3.2 and are shown in Figure 4.

DeJong determined the expected depth of greatest attack, xcrit, by the method

illustrated in Figure 41. The potential at which the polarization curve reached a

maximum current density, Ecrit, was measured on each polarization curve. However, in

the case of the double bump boundary condition (Figure 4), Ecrit was determined by

DeJong to be the more noble peak of the double bump. This is comparable to the

definition used by this author where Ecrit is at the start of the more noble double bump,

which corresponds to the beginning of the region of active attack. The potential

distribution down the length of the crevice was determined using CREVICERv2. The

depth at which Ecrit was reached equaled xcrit. These criteria were applied to each of the

six boundary conditions at gaps ranging from 1.5 to 150 µm. As stated by DeJong, the

scaling law plots of xcrit2 vs. gap (Figure 42) were linear for gaps ranging from 1.5 to 100

µm. However, for gaps larger than 100 µm, linearity was lost.

88

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Potential (V vs. SCE)

Log

I (A

/cm

2 )

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.002 0.004 0.006 0.008 0.01

Position (m)

Pote

ntia

l (V

)

Ecrit

xcrit

Figure 41: Technique used to determine xcrit from the output of CREVICERv2. Ecrit is determined from the electrochemical boundary condition and the potential distribution in the crevice is used to find the distance down the length of the crevice where the potential is equal to Ecrit.

5.3.1.1 Effect of Larger Gap Sizes

The same model run by DeJong was used to examine the behavior of the scaling

law factors at gaps larger than 100 µm. Gaps ranging up to 600 µm were studied for each

89

of the six electrochemical boundary conditions and the resulting xcrit’s were measured.

Figure 42 is a plot of xcrit2 vs. gap for all 6 boundary conditions updated with larger gap

sizes. The figure illustrates that linearity is indeed lost when the gap size is increased

past 100 µm for all boundary conditions.

0

5

10

15

20

25

30

35

40

45

50

0 100 200 300 400 500 600 700 800

Gap (µm)

X crit

2 (mm

)

Shifted

Normal

Skewed

Double Bump

Ipass↑Skinny

Figure 42: xcrit

2 vs. gap plot of DeJong’s six electrochemical boundary conditions, with larger gap sizes used than in DeJong’s experiments. The curves lose linearity when the gap increases past 100 µm.

This loss of linearity was examined more closely. The Double Bump boundary

condition was chosen for further study due to its similarity to the experimentally

measured polarization curve having a similar shape (Figure 24). Figure 43a shows that

two gaps in the linear range (20 and 60 µm) and two outside the linear range (200 and

500 µm) were chosen for this examination. Figure 43b shows the potential distributions

90

of each of these gaps and the corresponding current distributions, Figure 43c. The

current distribution plots show that curves for the two smaller gaps have a complete

double bump shape which resembles the boundary condition. However, the two larger

gaps have current distributions that do not have the complete shape of the boundary

condition. The current distribution for the 200 µm gap has the first bump but the second

bump is distorted, whereas the 500 µm gap plot has lost its second bump entirely.

91

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.002 0.004 0.006 0.008Crevice Depth X (m)

Pote

ntia

l (V

vs S

CE)

Ecrit for Double Bump

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.002 0.004 0.006 0.008Crevice Depth X (m)

Pote

ntia

l (V

vs S

CE)

Ecrit for Double Bump

0

0.2

0.4

0.6

0.8

1

1.2

0 0.002 0.004 0.006 0.008

Crevice Depth X (m)

Curr

ent D

ensi

ty (A

/m2 )

Crev ice Bottom

0

0.2

0.4

0.6

0.8

1

1.2

0 0.002 0.004 0.006 0.008

Crevice Depth X (m)

Curr

ent D

ensi

ty (A

/m2 )

Crev ice Bottom

0

5

10

15

20

25

30

35

40

0 100 200 300 400 500 600 700 800

Gap (µm)

X crit

2 (mm

2 )

Passivation

0

5

10

15

20

25

30

35

40

0 100 200 300 400 500 600 700 800

Gap (µm)

X crit

2 (mm

2 )

Passivation20 µm gap60 µm gap200 µm gap500 µm gap

20 µm gap60 µm gap200 µm gap500 µm gap

20 µm gap60 µm gap200 µm gap500 µm gap

a)

b) c)

Eapp = 0.3 V vs. SCE

Figure 43: (a) The double bump boundary condition was examined at gaps of 20, 60, 200, and 500 µm. The 200 and 500 µm gaps have results that deviate from the linear behavior seen at smaller gaps. (b) Crevice potential distributions of the four gaps and the resulting distance down th length of the crevice where Ecrit is reached. (c) Crevice current distributions for each gap. When the active corroding region reaches the crevice tip at the two large gaps, the current distribution is distorted causing the scaling law plot (a) to deviate from linearity.

92

5.3.1.2 Investigation of Boundary Condition Characteristics

Several defining characteristics of each boundary condition were compared to one

another to see if any correlation with x was seen. Table 9 lists all of the characteristics

for each boundary condition.

crit

Table 9: Characteristics of DeJong’s boundary conditions.

Boundary Condition

E (V vs. SCE) crit I (mA) tot Power Density (Watts/cm ) 2

X (20 µm gap) crit(mm)

Normal 0 0.322 0.503 1.34 Double Bump 0.075 0.392 0.742 0.80 Skinny 0 0.201 0.202 2.08 Skew 0.05 0.328 0.518 1.09 Ipass↑ 0 0.414 0.596 1.21 Shifted -0.05 -0.05 0.333 0.503 1.56

Figure 44 shows that as Itot increases, xcrit decreases. However, the point

corresponding to the Ipass↑ boundary condition does not follow this trend. Even though

it has the highest Itot value (2.84 mA), it does not have the smallest corresponding xcrit.

The Shifted point also does not follow this trend, but to a lesser extent.

93

0.0

0.5

1.0

1.5

2.0

2.5

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Total Crevice Current, Itot (mA)

X crit

(mm

)

Shifted

Normal

Skewed

Double Bump

Skinny

Ipass↑

Figure 44: xcrit vs. total crevice current for each of the six boundary conditions.

Figure 45 indicates that as power density is increased, xcrit decreases. Again

however, there are points that do not follow the trend. The points corresponding to the

Normal and Skewed boundary conditions have power densities that are about the same as

the Shifted boundary condition, but their xcrit values are significantly smaller.

94

0.0

0.5

1.0

1.5

2.0

2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Electrochemical Power Density (W/cm2)

X crit

(mm

)

Shifted

Normal

Skewed

Double Bump

Skinny

Ipass↑

Figure 45: xcrit vs. electrochemical power density for each of the six boundary conditions.

Figure 46 shows that as the value of Ecrit increases, xcrit decreases. As with the

other plots, there is a point that does not follow the trend. In this case, the Skinny

boundary condition has an Ecrit value of 0.0 V (SCE) that is the same as the Normal and

the Ipass↑ boundary conditions. While the Normal (1.34 mm) and Ipass↑ (1.30 mm)

boundary conditions produce very similar xcrit values, the Skinny produced a much higher

xcrit (2.08 mm).

95

0.0

0.5

1.0

1.5

2.0

2.5

-0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

Ecrit (V vs. SCE)

X crit

(mm

)

ShiftedNormal

Skewed

Double Bump

Skinny

Ipass↑

Figure 46: xcrit vs. Ecrit for each of the six boundary conditions.

5.3.2 Crevice Corrosion Experiments

CREVICERv2 was used to model the nickel / 0.5 M H2SO4 system and to

compare these results with the ones obtained experimentally. Figure 47 shows the

experimentally obtained polarization curve from substrate NI-2 (Table 7, Figure 24) with

its double bump shape. An Ecrit of 0.244 V (SCE) was determined from the data to be the

beginning of the active nose (corrosion). This curve was fit mathematically to a series of

high order polynomial, exponential, and sigmoidal equations using SigmaPlot 2000TM

(the overlaid curve in Figure 47). The equations used were:

96

10th Order Polynomial

1110987654320 lxkxjxixhxgxexdxcxbxaxyy +++++++++++= (8)

Modified 2 Parameter Exponential Decay

+= cxb

aey (9)

3 Parameter Sigmoidal

bxx

e

ay )0(

1−−

+= (10)

Where:

y is the current density in [A/m2]

x is the potential in [V vs. SCE]

y0, x0, a, b, c, d, e, g, h, i, j, k, l are fit parameters

Each region that was fit had to have an R2 value > 0.999 to qualify. The fit parameters

were coded into CREVICERv2 to define the electrochemical boundary condition and can

be found in Table (10).

97

Table 10: Fit parameters used to mathematically describe the polarization curve in Figure (47).

Potential Range

(V vs. SCE)

> 0.750 0.400 0.750

0.306 0.400

0.250 0.306

-0.100 0.250

-0.235* -0.100

Equation Type

(Order)

Poly (3)

Poly (3)

Modified Exponential

Decay

Sigmoidal Poly (11)

Poly (10)

y0 -0.0007 0.0003 - - 0.0049 0.0938 x0 - - - 0.2726 - - a 0.0029 -0.0013 2.57358e-5 0.0076 0.034 -3.7514 b -0.0037 0.0019 0.1126 -0.0098 0.2811 61.1780 c 0.0016 -0.0009 -0.2617 - -1.6702 453.6162 d - - - - -40.2348 874.5814 e - - - - 100.9172 -7526.3694 g - - - - 1628.2576 -35029.2485 h - - - - -1058.3561 101206.0435 i - - - - -38833.3098 1075895.0779 j - - - - -73116.8588 2834226.9535 k - - - - 1166188.391 2585682.6718 l - - - - -2152169.6822 -

*Below –0.235 V(SCE), which is Ecorr, the current density was set to 0.

Potential (V vs. SCE)

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

Log

i (A

/cm

2 )

1e-6

1e-5

1e-4

1e-3

1e-2

1e-1Ecrit = 0.244 V vs. SCE

Figure 47: Measured electrochemical boundary condition of Ni200 in 0.5 H2SO4 (blue) and the corresponding mathematical fit (pink). Ecrit ws determined to be 0.244 V (SCE).

98

5.3.2.1 Effect of Crevice Gap on xcrit

Table 11 list the results from model runs with crevice gaps of 14, 35, 93, 153, and

395 µm. The crevice mouth was held at 0.6 V (SCE). The initial potential and current

distributions were the outputs of interest (Figure 48a and b). The plots indicate that xcrit

moved deeper into the crevice as the gap increased. With a 395 µm gap size, the

potential did not drop below Ecrit (0.244 V (SCE)) in the 7 mm crevice, therefore, active

corrosion did not take place within the crevice. This effect is illustrated in Figure 48b by

the very low current density observed down the length of the crevice.

Table 11: Results of crevice holds modeled by CREVICERv2.

Gap (µm) Hold Potential (V vs SCE)

Xpass (mm) Xpass2 (mm2)

5 0.6 0.55 0.30 14 0.6 0.83 0.69 25 0.6 1.12 1.26 35 0.6 1.33 1.76 35 0.525 0.86 0.74 35 0.5 0.77 0.59 50 0.6 1.59 2.52 75 0.6 1.98 3.90 93 0.6 2.26 5.12 106 0.6 2.49 6.20 130 0.6 2.89 8.35 153 0.6 3.54 12.51 395 0.6 N/A N/A

99

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007

Crevice Depth (m)

Pote

ntia

l (V

vs. S

CE)

0.E+00

1.E-03

2.E-03

3.E-03

4.E-03

5.E-03

6.E-03

7.E-03

8.E-03

9.E-03

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007

Crevice Depth (m)

Cur

rent

Den

sity

(A/c

m^2

)

395 µm

153 µm

93 µm

14 µm

395 µm

153 µm93 µm14 µm

a)

b)

Ecrit = 0.244 V

35 µm

35 µm

Figure 48: (a) Potential distributions from CREVICERv2 for gaps ranging from 14 –395 µm. The 395 µm gap near reach Ecrit and passivated at the onset. (b) Corresponding current distributions for each gap size, notice that the 395 µm gap exhibits very low current indicating passive corrosion onely.

100

Figures 49a and b are plots of xcrit2 vs. gap and xcrit vs. gap respectively. The xcrit

2

vs. gap plot is linear below gap sizes of ~100 µm with an R2 = 0.998. The same region

on the xcrit vs. gap has a slightly lower R2 value of 0.983. The scaling factor of DeJong’s

Skinny boundary condition, which has a much thinner active nose (~75 mV) than the one

used in this model (~400 mV), was plotted on the same graphs to contrast the difference

between the two boundary conditions. The xcrit2 vs. gap plot for the Skinny is even more

linear below gap sizes of ~100 µm with an R2 = 0.9996. Again, the same region on the

xcrit vs. gap for the Skinny boundary condition has a slightly lower R2 value of 0.9875

indicating less linearity.

101

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

0 20 40 60 80 100 120 140 160 180

Gap (microns)

Xcrit

2 (mm

2 )

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 20 40 60 80 100 120 140 160 180

Gap (microns)

Xcrit

(mm

)

R2 = 0.9980

R2 = 0.9996

R2 = 0.9875

R2 = 0.9830

Skinny

ExperimentalModel Fit

Skinny

ExperimentalModel Fit

Figure 49: xcrit2 vs. gap and xcrit vs, g plots for the Skinny boundary condition (DeJong) and for the

experimentally determined polarization behavior. In both the Skinny and the experimental case, the region at small gaps is more linear for the xcrit

2 vs. gap plots than the xcrit vs, g plots.

5.3.2.2 Effect of Potential on xcrit

Figures 50a and b are the resulting potential and current distributions for a 35 µm

gap with the crevice mouth held at 0.6, 0.525, and 0.5 V (SCE). The results are listed in

102

Table 11. The value of xcrit was shown not to increase greatly between 0.5 and 0.525 V

(0.77 and 0.86 mm), but did significantly increase (1.33 mm) when the hold potential was

increased to 0.6 V.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007

Crevice Depth (m)

Pote

ntia

l (V

vs. S

CE)

0.E+00

1.E-03

2.E-03

3.E-03

4.E-03

5.E-03

6.E-03

7.E-03

8.E-03

9.E-03

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007

Crevice Depth (m)

Cur

rent

Den

sity

(A/c

m^2

)

0.600 V

0.500 V

a)

b)

0.600 V

0.500 V

Ecrit = 0.244 V

0.525 V

0.525 V

Figure 50: (a) Potential distributions produced by CREVICERv2 for hold potentials of 0.5, 0.525, and 0.6 V (SCE). (b) Corresponding current distributions. As the applied potential is increase, the active region moves deep into the crevice.

103

5.3.2.3 Comparisons to Experiments on Microfabricated Crevices

Figure 51 compares the results from the experiments on microfabricated crevices

to the results from CREVICERv2. The plots of xcrit2 vs. gap and xcrit vs. gap (Figures 51a

and b) show good agreement between the experimental and model results. However, the

plot of xcrit vs. varying potential (Figure 52) does not indicate a clear correlation between

the experimental and model results.

104

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0 20 40 60 80 100 120 140 160 180

Gap (microns)

X crit

2 (mm

2 )

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 20 40 60 80 100 120 140 160 180

Gap (microns)

X crit

(mm

)

a)

b)

Model

Experimental Model

0.6 V vs. SCE Hold

0.6 V vs. SCE Hold

Experimental

Figure 51: (a) Comparison of the xcrit2 vs. g plots for the results obtained experimentally and from

CREVICERv2. (b) Comparison of the xcrit vs. g plots for the results obtained experimentally and from CREVICERv2. Both plots show excellent agreement between model and experimental data.

105

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.475 0.500 0.525 0.550 0.575 0.600 0.625

Potential (V vs. SCE)

Xcrit

(mm

)

Experimental

Model

Figure 52: Comparison of experimental and CREVICERv2 results of varying hold potential. The model predicts a linear behavior which is not seen in the experimental results.

5.3.2.4 Effect of Crevice Area and Electrolyte Conductivity on xcrit

Gap profiles after 50 and 150 hours of active corrosion of two crevices substrates

from Abdulsalam and Pickering[17] were digitized and fit mathematically to a series of

linear and exponential equations using SigmaPlot 2000TM. The equations used were:

Linear

axyy += 0 (11)

Exponential Decay

bxaeyy −+= 0 (12)

106

Exponential Growth

bxaeyy += 0 (13)

Where:

y is the penetration depth [mm]

x is the distance down the length of the crevice mouth [mm]

Y0, a, b are fit parameters

Table (12) lists the fit parameters used for the 50-hour profile, while Table (13) lists the

fit parameters for 150-hour profile. Images of the profiles can be seen in Figure 53a and

b. The resulting digitized plots are in Figure 53c. The gap size at time = 0 was 300

µm[17].

Table 12: Fit parameters for Pickering’s 50-hour profile.

(x) Distance Down Crevice

(mm)

< 1.22 2.5355 1.22

4.1865 2.5355

7.00 4.1865

Equation Type Not altered

Exponential Decay

Exponential Growth Linear

y0 - 2.287 2.2121 0.0003429 a - 40.1953 0.0056 - b - 3.4381 1.0571 -

Table 13: Fit parameters for Pickering’s 150-hour profile.

(x) Distance Down Crevice

(mm)

< 1.15 2.5192 1.15

6.3178 2.5192

7.00 6.3178

Equation Type Not altered Exponential Decay Linear Linear y0 - 1.9098 1.5028 2.432939 a - 1214.372 0.1607 0.0121 b - 6.2201 - -

107

50 hr

-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.0

0 2 4 6 8 10

Penetration Depth (mm)

Pene

trat

ion

Dept

h (m

m)

150 hr

a) b)

c)

Figure 53: Pickering’s[17] (a) 50-hour and (b) 150-hour corrosion profiles. (c) Mathematical representations of both profiles that were coded into CREVICERv2 as part of the geometric boundary condition. The original crevice gap was 0.3 mm.

108

The mathematical equations used to fit the profiles were also used to account for

the increase in surface area due to the curved surface of the heavily attacked region. The

derivative was taken of each equation. The derivative of an equation defines the tangent

to the curve at that specific x-value (depth down the length of the crevice). By entering

an x-value, the slope of the curve at that point is obtained. Using the Pythagorean

theorem, the slope can be used to find the vector magnitude between two x-values.

Therefore, if the absolute value of the slope were equal to 1 (no change in gap size

between the two points) the vector magnitude would be equal to 1. However, if the slope

has an absolute value greater than 1 (it can never be less than 1) then the magnitude will

be some number larger than 1. The greater the difference between the gap values at each

point, the larger the magnitude. This magnitude vector was calculated for each element

and the result was multiplied to each element’s surface area. This approach allowed the

increase in surface area due to a curved penetration profile to be taken into account. The

code for this routine can be found in Appendix B.

The effect of the 50 and 150-hour profiles and their corresponding increases in

surface area can be seen in the potential distributions in Figure 54a. Figure 54c is a

close-up of where the potential distributions cross Ecrit (0.244 V (SCE)). The resulting

xcrit values are tabulated in Table 14. Because the larger gap sizes caused a decrease in

resistance (R) down the length of the crevice, the criteria for stable crevice corrosion (IR

> IR*) was no longer met. Therefore, IR* had to be decreased to cause stable corrosion

to occur within the crevice. IR* was decreased by holding the crevice mouth at a lower

hold potential of 0.342 V (SCE), compared with 0.6 V (SCE) from earlier experiments.

Since IR* = Esurf – Ecrit, in this case IR* became 0.98 V (0.342 – 0.244 V).

109

Table 14: Results of crevice experiments modeled by CREVICERv2 with area compensation, solution conductivity, and profile as variables.

Hold Potential (V vs. SCE)

Profile Area Compensation

[Ni++] Near Crevice

Mouth (M)

σ Near Crevice Mouth

(ohm-cm)-1

Xcrit (mm)

0.342 300 um OFF 0 0.1891 1.25 0.342 50 hr OFF 0 0.1891 1.15 0.342 50 hr ON 0 0.1891 1.11 0.342 150 hr OFF 0 0.1891 1.11 0.342 150 hr ON 0 0.1891 1.02 0.342 50 hr ON 0.1 0.1745 1.14 0.342 50 hr ON 1.0 0.1203 0.86 0.342 50 hr ON Saturated 0.0704 0.40 0.342 150 hr ON 0.1 0.1745 1.07 0.342 150 hr ON 1.0 0.1203 0.82 0.342 150 hr ON Saturated 0.0704 0.39

110

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007

Crevice Depth (m)

Pote

ntia

l (V

vs. S

CE)

0.2

0.21

0.22

0.23

0.24

0.25

0.26

0.27

0.28

0.29

0.3

0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.001 0.0011 0.0012 0.0013 0.0014

Crevice Depth (m)

Pote

ntia

l (V

vs. S

CE)

a)

b)

300 µm

150 hr, Area ON

50 hr, Area ON

300 µm150 hr, Area ON

50 hr, Area ON

Ecrit = 0.244 V

1.02 mm

1.11 mm

1.15 mm

1.25 mm

50 hr, Area O FF

50 hr, Area O FF

150 hr, Area OFF

150 hr, Area OFF

Figure 54: (a) Comparison of the effect of gap profile and additional current density provided by the increase in surface area in the actively corroding region. (ON = extra surface area is taken into account, OFF = extra surface is NOT area taken into account). (b) Close-up of where the potential distributions cross Ecrit.

111

Figures 55a and b show the effect of adding various concentrations of NiSO4 to

the crevice between x = 0.5 and x = 1.5 mm (i.e., the beginning of the region of greatest

attack). This simulated an increase in nickel ions due to active corrosion centered on xcrit.

The conductivity values measured are listed in Table 7. Both figures show that

increasing the nickel ion concentration near the crevice mouth decreased the value of xcrit.

The more concentrated the nickel ions, the smaller xcrit became.

112

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007

Crevice Depth (m)

Pote

ntia

l (V

vs. S

CE)

a)

b)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007

Crevice Depth (m)

Pote

ntia

l (V

vs. S

CE)

50 hr, Area O FF

50 hr, Area ON

50 hr, Area On, 0.1 M NiSO4

50 hr, Area On, 1.0 M NiSO4

50 hr, Area On, Sat. NiSO4

Ecrit = 0.244 V

Region of Variable

Conductivity

150 hr, Area OFF

150 hr, Area ON

150 hr, Area On, 0.1 M NiSO4

150 hr, Area On, 1.0 M NiSO4

150 hr, Area On, Sat. NiSO4

Ecrit = 0.244 V

Region of Variable

Conductivity

Figure 55: (a) Comparison of the effect of solution conductivity (nickel concentration) over the region of greatest attack (gray area) and the increase in active surface area for the 50-hour profile. (b) Comparison of the effect of solution conductivity (nickel concentration) and increase in active surface area for the 150-hour profile. Nickel concentration of the solution can be seen to have a much greater effect on xcrit than does the increase in active surface area. (ON = extra surface area is taken into account, OFF = extra surface is NOT area taken into account).

113

CHAPTER 6. DISCUSSION

6.1 Performance of Microfabricated Formers and Substrates

The use of microfabrication techniques was demonstrated to be a viable method

of creating crevices ideal in geometry and on the scale of crevices found in practical

cases. The techniques originally designed by DeJong were used as a starting point and

many of their shortcomings were remedied during this study.

The use of SU-8 to define the height of a crevice former allowed for the crevice

gap to be rigorously controlled with a ±2% difference in gap height down the length of

the former. Because the surface of the silicon wafer was not etched away, the original

smoothness of the surface as purchased was left intact. Comparing figures 14e and 14f it

can be seen that the roughness of a new former surface is half that of one made with the

old technique. At large gaps (>75 µm), the small variations (from the original technique)

may not affect the results but at smaller crevice gaps (especially <10 µm) the variation

becomes a significant percentage of the total gap height. The crevice then loses its ideal

geometry and the ability to directly and confidently compare experimental results to

modeling results is decreased.

In the previous technique, the crevice substrates created were also in need of

improvements. The maximum nickel thickness of 0.6 µm from the old metal evaporation

technique limited the time in which an experiment could be performed since the nickel in

the active regions would be corroded completely away in minutes. The development of

an electroplating technique increased the nickel thickness to ~17 µm. Greater thickness

could be achieved only with longer plating times. In Figure 19 it can be seen that the

114

thicker plated nickel sample has a polarization behavior that more closely resembles that

of a Ni200 sample, which is 99.6% nickel. It has an open circuit value of –0.225 V

(SCE) and an active nose width of about 550 mV (at 0.1 mA/cm2), which are in line with

those observed for Ni200. The active nose is also centered on 0.1 V (SCE) as seen in the

Ni200 case. This similar electrochemical behavior is in sharp contrast to the substrate

from the earlier technique, which has an active peak only 200 mV (at 0.1 mA/cm2) wide

and 300 mV lower than the one seen in Ni200. The open circuit potential was also 150

mV lower than Ni200. Furthermore, the scan could not be completed because the thin

nickel layer had already completely corroded at 0.0 V (SCE). The need for

electrochemical similarity is so that results from this work can be directly compared to

the work by Pickering and others[5, 10, 17, 27, 28, 30].

Experimental difficulties did arise with the electroplated nickel. As seen in a

profile scan across an electroplated crevice (Figure 20), the nickel surface is not

completely flat. In most cases this variation was about ±2 µm. As with the formers, this

variation may not be important at larger gaps but may become significant at smaller gaps.

This bowl-shaped profile arises from the edges of the electrode having access to more

plating current than the center of the electrode. The idea of overplating the electrode and

polishing the surface flat was rejected because of the concern that SU-8 would be unable

to withstand the mechanical strain of a chemical-mechanical polisher. While the nickel

would polish to a flat surface, the SU-8 would be torn completely off, thereby exposing

layer of evaporated nickel underneath.

The electrochemical behavior of the electroplated nickel, while comparable to

Ni200, was different in several ways. Although the active nose was the same width, it

115

was an order of magnitude higher than the one seen from Ni200. Also, the characteristic

double bump shape of nickel in 0.5 M H2SO4 system as seen by Pickering and others[10,

17, 27, 31] was absent. As seen in Figure 23, the electrochemical behavior did not remain

constant from sample to sample. First, when the samples were potentiodynamically

tested, the transition from active to passive corrosion was 400 mV higher than the ones

seen by the aforementioned groups. Some samples took multiple scans to achieve a

reasonable transition value. The resulting passive current from sample to sample differed

by three orders of magnitude. Originally, it was believed that a film from the SU-8,

which was not completely removed during developing, was the cause of these problems.

However, this was shown to not be the case due to the reproducible results from the

Ni200 samples that were also coated with SU-8. Although a chemical analysis of the

electroplated samples was not available, it is believed that some kind of surface film from

the plating process was the cause of these anomalies. The lack of reproducibility of

electrochemical behavior ultimately led to the electroplated samples to be replaced by

Ni200 samples.

For Ni200 substrates, SU-8 was patterned onto a polished sample and developed.

The SU-8 provided an insulator between the nickel and the crevice former sidewalls.

This prevented sub-crevices from being formed during the experiment, unlike if a former

was placed directly onto bare metal. The SU-8 also showed excellent adhesion to the

nickel surface as evidenced by the absence of attack seen underneath the SU-8 on any of

the samples (Figures 28 thru 31). The polished surface also was flatter than the

electroplated surface with an RRMS of only 0.104 µm in contrast to the nickel height

variation of 4 µm seen across the width of the electroplated samples.

116

The electrochemical behavior of the Ni200 samples also showed excellent

reproducibility with regards to the shape and size of the active nose, as well as the

passive current density, as seen in Figure 24. The effect of increasing Ni2+ concentration

on the electrochemical behavior of this system was also examined. Figure 24 shows a

series of scans with varying Ni2+ concentration as listed in Table 7. There was no change

in the shape of the scan until a Ni2+ concentration of 0.028 M was reached. At this

concentration, both active peaks increased in magnitude slightly. The lower peak became

raised in potential as well. The width of the active nose also decreased. However, the

active/passive transition potential Ecrit remained the same. As the Ni2+ concentration

increased further, the lower peak continued to increase in magnitude and rise further in

potential. At a Ni2+ concentration of 0.295 M, the double bump shape completely

disappeared and the active nose became even smaller in width. At saturation of Ni2+, the

entire active nose rose in potential. (Due to the sharp shape of the top of the active nose,

this is believed to be an effect of IR losses in solution.) The importance of the effects of

Ni2+ concentration at values greater than 0.028 M is that the electrochemical boundary

condition may change over time as the crevice actively corrodes. The estimation of

amount of attack at a given time will be affected and may differ from the one predicted

using the original boundary condition.

The advantages that have been discussed of using Ni200 as a substrate base can

also be extended to the examination of any alloy or element. The quality of adherence of

the SU-8 to the surface of the metal will be critical. Also, the SU-8 should not be

attacked by the solution. This ability to apply SU-8 at alloy surfaces opens up the

117

possibility of studying many different systems that undergo crevice corrosion using this

technique.

A disadvantage of using engineering alloy plates as substrates is that

independently addressable electrodes are not possible. One of the main reasons behind

the use of electroplating was that the electrode area metal could be patterned into many

sections to allow for individual measurements to be made of each section. This design

would allow the current and potential distributions to be examined spatially inside of a

crevice undergoing active corrosion.

6.2 Physical Chemistry of Electrolytes

The physical properties of an electrolyte within a crevice are important in the

study of crevice corrosion. For one, solution conductivity plays a major role in the

potential distributions down a crevice. Density and surface tension are also important

properties, which as shown below, can affect the flow of solution within a crevice.

The solution conductivity was examined for a number of 0.5 M H2SO4 solutions

with varying Ni2+ concentration. The conductivity measured for 0.5 M H2SO4 was

0.1891 (ohm-cm)-1 at 25 ºC. As seen in Figure 25, as the Ni2+ concentration increased,

the solution conductivity also increased. A maximum conductivity of 0.1906 (ohm-cm)-1

was reached at a Ni2+ concentration of 10-2 M. As the concentration of ions increased,

the amount of charge that the solution can transfer also increases making the solution

more conductive. This increase in conductivity from 0.1891 to 0.1906 (ohm-cm)-1

follows the dilute solution theory, which assumes that the number of ions is so small

when compared with all the molecules in a given volume that the ions never interact with

one another. However, at higher concentrations the ions begin to interact. This reduces

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the mobility of the ions, and consequently, the conductivity[32]. As seen in Figure 25,

when the Ni2+ concentration was increased above 10-2 M, the conductivity began to

decrease until a minimum value of 0.0760 (ohm-cm)-1 was reached at Ni2+ saturation.

Solution conductivity is a significant variable in crevice corrosion. Gartland[33,

34] accounted for conductivity changes in a model of the crevice corrosion behavior of

Fe-Ni-Cr-Mo alloys in chloride solutions. The equivalent conductance based on dilute

solution theory was modified to include the effect of solution viscosity on conductivity.

As the ion concentration increased, the electrophoretic effect became significant.

Gartland describes this effect as each moving ion carries a “cloud” of solvent molecules

with it. As the ion concentration increases, the forces acting on these ions also increase

due to the accompanying “clouds”. Gartland accounted for this viscosity change by

fitting the curve of experimentally determined ionic strength versus equivalent

conductance values for various solutions. The function was then incorporated as an

additional factor in determining conductance. The importance of this is that when

modeling crevice corrosion, the potential drop due to solution resistance can be

calculated using the dilute solution theory only for low concentrations of solute.

However, in areas of active corrosion, the ion concentration may increase so much that

the solution becomes less conductive, thereby causing an increase in potential drop,

whereas dilute solution theory would predict a decrease in potential drop. Since the

model used in this study did not account for viscosity effects, other methods were used,

which are discussed in greater detail in Section 6.4.2.

The surface tension was measured for 0.5 M H2SO4 with varying Ni2+

concentrations. The surface tension (energy) varied slightly as the Ni2+ concentration

119

was increased. Above 0.094 M NiSO4, the surface tension began to rise slowly until a

maximum of 78.10 dyne/cm was reached at Ni2+ saturation. Since surface tension affects

how a solution moves along a surface, it affects solution flow within a crevice. This

effect is examined in Section 6.4.3.

The density of solution was also measured for 0.5 M H2SO4 with varying Ni2+

concentrations. As expected, the density increased with increasing Ni2+ concentration as

seen in Table 7. The density of 0.5 M H2SO4 increased by 33% when it was saturated

with NiSO4. As mentioned earlier, differences in density throughout a solution cause

convection by gravity. This is also discussed in more detail in Section 6.4.3.

6.3 Scaling Law Investigation Follow-Up

6.3.1 Investigation of Boundary Condition Characteristics

The examination of DeJong’s six boundary conditions was expanded to included

how several key characteristics were related to xcrit. Figure 44 indicates that as the total

crevice current (Itot) increased, xcrit decreased for most cases. However, the existence of

outlying points, which did not follow this trend, did not allow conclusions to be drawn

involving only Itot. The same can be seen in Figures 45 and 46 for the effect of

electrochemical power density and Ecrit on the resulting value of xcrit. As both

characteristics increased, the resulting xcrit value decreased. However, outlying points in

both cases also did not allow any general statement to be made with respect to the

relationship each has with xcrit. What this study showed was that there is no one clear

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characteristic that can predict xcrit. Therefore, a combination of these factors plays a role

in the location of active corrosion within a crevice.

6.3.2 Effect of Larger Gap Sizes

The scaling law investigations by DeJong demonstrated for a variety of

electrochemical boundary conditions there exists a linear relationship between xcrit2 and

gap size. However, at larger gaps, linearity was lost. In this study, closer examination of

the double bump case showed that the finite crevice depth was the cause of this (Figure

43). As Ecrit moved deeper and deeper into the crevice with increasing gap size, the

active area of the crevice flank also moved deeper into the crevice. At gaps greater than

100 µm, the active area reached the tip of the crevice. Figure 43c indicates that when the

active region reached the tip, the current distribution lost it double bump shape thereby

affecting the value of xcrit. In essence, the active corrosion began to “feel” the crevice tip.

Therefore, not only does the crevice gap affect xcrit, but the crevice length does as well.

Xu and Pickering[5] developed an analytical solution for xcrit (xpass) with the crevice

length as one of its variables. Abdulsalam and Pickering[27] simplified this model by

checking that the aspect ratio of crevice length over gap (L/G) was greater than the

critical value required for stable corrosion to take place. The crevice length was then

replaced by the crevice width as a variable. Later, Abdulsalam and Pickering[17]

simplified this model even further by assuming that if the passive current was negligible

compared to the peak current, the solution for xcrit became:

121

IEEwa

x critsurfcrit

)( −=

κ (14)

Where:

xcrit is the distance from the mouth of the crevice to the region of

greatest attack [m]

κ is the solution conductivity [(ohm-m)-1]

w is the width of the crevice [m]

a is the crevice gap [m]

Esurf is the surface hold potential [V vs. SCE]

Ecrit is the potential at which the critical current density is reached

[V vs. SCE]

I is the total crevice current [A]

However, this study indicates that even when stable corrosion is provided for by

(L/G) > (L/G)crit, the crevice length can only being ignored as long as the active region

does not come near the crevice tip. Comparison of the experimental and modeling results

obtained in this study are compared with those predicted by Equation 14 using the crevice

current predicted by CREVICERv2 (Table 15). As can be seen in Figure 56, the

modeling results from this study closely match those calculated using Pickering’s

solution. These results indicate that Pickering’s solution also compensates for the finite

crevice depth through the non-monotonic behavior of the total crevice current as a

function of gap. However, examination of Figure 56 indicates that Pickering’s solution

deviates from results from this study at gaps < 10 µm. Because Pickering’s solution is

122

based upon the scaling law being xcrit/G and shows a linear behavior at large gaps, the

prediction of the critical aspect ratio (L/G)crit may not hold true at smaller gaps, where the

xcrit2/G scaling law seems to be the correct choice.

Table 15: Results from applying Pickering’s model to the crevice current modeled by CREVICERv2.

Gap (µm) Total Crevice Current (pA)

Hold Potential (V vs SCE)

Xpass (mm) Xpass2 (mm2)

5 7.98 0.6 0.01 0.000105 14 0.276 0.6 0.83 0.69 25 0.368 0.6 1.11 1.24 35 0.435 0.6 1.32 1.73 35 0.435 0.525 1.04 1.08 35 0.435 0.5 0.95 0.90 50 0.518 0.6 1.58 2.50 75 0.625 0.6 1.97 3.86 93 0.676 0.6 2.25 5.07

106 0.701 0.6 2.48 6.14 130 0.732 0.6 2.91 8.46 153 0.686 0.6 3.65 13.3

*For each gap the solution conductivity was 0.184 (ohm-cm)-1 and the crevice width was 25 µm.

123

0.02.04.06.08.0

10.012.014.0

0 50 100 150 200

gap (microns)

x crit

2 (mm

)

0.00.51.01.52.02.53.03.54.0

0 50 100 150 200

gap (microns)

x crit

(mm

)

Experimental

Model

Experimental

ModelPickering’s

a)

b)

Pickering’s

Figure 56: Comparison of xcrit2 vs. gap and xcrit vs. gap plots for the experimental and model results,

along with the results predicted by Pickering’s Equation 7.

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6.4 Comparison of Model and Experimental Results

6.4.1 Potential Effects on xcrit

As described previously, the IR* theory states that for stable corrosion to take

place, IR > IR*, where IR* = Esurf – Ecrit. Therefore, the amount of voltage drop within

the crevice must be greater than the difference between the surface hold potential and the

potential at which the active corrosion takes place. So if the surface hold potential is

increased, either I or R must be increased to maintain stable crevice corrosion. Assuming

the current and solution conductivity stay the same, the only way to increase the IR drop

is to increase the distance between the anode and cathode resulting is a greater resistance.

In this study, three crevices with gaps of 35 µm were held at 0.5, 0.525, and 0.600 V vs.,

SCE for 5 minutes. From Figure 35, it can be seen that the value of xcrit does indeed

increase with increased hold potential. However, when these data are compared to that

predicted by CREVICERv2 (Figure 32) the experimental xcrit was continually larger. The

reason behind this discrepancy may be that the 35 µm gap size was too small which

caused deviations in xcrit as seen for the 14 and 35 µm gaps previously (Figures 28 and

29). A larger range of examined hold potentials may also be helpful. Using Equation 14,

the experimental and predicted data from this study can be compared to the work by

Pickering. The resulting xcrit values are listed in Table 15. As can be seen in Figure 57,

the xcrit values predicted by CREVICERv2 and the Pickering equation are almost

identical. This agreement supports the idea that the IR* theory holds true for increasing

hold potential as stated by Pickering.

125

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.475 0.500 0.525 0.550 0.575 0.600 0.625

Potential (V vs. SCE)

Xcrit

(mm

)

Experimental

Pickering’s

Model

Figure 57: Comparison of the experimental and model results, along with the results predicted by Pickering’s Equation 7 for variable hold potentials. The model and Pickering’s results are in excellent agreement, whereas the experimental data do not correspond as well.

6.4.2 Gap, Area, and Electrolyte Effects on xcrit

The measured parameters used in the microfabricated crevice experiments were

carried over and used as boundary conditions in the modeling experiments. The

parameters included electrochemical behavior, solution conductivity, hold potential (0.6

V vs. SCE), and crevice geometry. The potential distribution down the length of the

crevice was the desired output. From this, the beginning of the region of greatest attack,

xcrit, was determined. Unlike the microfabricated crevice experiments, where the value of

xcrit was taken at time = 1 min (10 min for gap = 153 µm), the model results were based

upon the initial potential distribution. (The reason for this is that in order to visually

observe a surface change on the experimental crevice, some corrosion needed to have

taken place, therefore, the run time was increased to 1 min). Figure 51 compares the

126

results predicted by the model and those obtained experimentally. The experimental data

are in excellent agreement with that predicted by the model. The effect of larger gaps

(>100 µm), where the scaling law becomes nonlinear, was also observed in the

experimental results. This indicates that the active corrosion region came into contact

with the tip of the crevice. In Figure 31 evidence of active corrosion can be seen near the

crevice tip of the corroded 153 µm gap microfabricated crevice. These experimental

results, coupled with the modeling results, support the idea that the crevice “felt” the

crevice tip with a gap of 153 µm.

Further examination of Figure 51 indicates that the neither the xcrit2/g or the xcrit/g

seems to fit the experimental data better than the other. One explanation could be that the

extreme width of the active nose (~400 mV) makes the difference undetectable. As seen

in Figure 49 for gaps <100 µm, the case of the experimentally measured boundary

condition is very linear for xcrit2/G (R2 = 0.998) and somewhat less linear for xcrit/G

(0.983). This is also seen with the Skinny boundary condition where the plot of xcrit2/G

(0.9996) is more linear than that of xcrit/G (0.9875). While the R2 values show that all

four cases display linearity, visual inspection throughout the range of 5 – 100 µm gap

indicates that the xcrit/G fits are not as good as the ones from xcrit2/G. This is most

apparent for the Skinny case. The xcrit/G plot has a definite curve to it, whereas the

xcrit2/G plot follows the fitted line point for point. This suggests that for a system with a

thinner active nose, the xcrit2/G scaling law would be more predictable that the xcrit/G one.

Since the nickel / 0.5 M H2SO4 system has a wide active nose, experimental

measurements may not show a definite scaling law.

127

The effect of increased area in the active region due to dissolution has also been

investigated. In earlier work, Pickering and others[5, 10, 17] have stated that xcrit (which

they call xpass) moves towards the mouth of the crevice during stable crevice corrosion in

the nickel / 0.5 M H2SO4 system. They indicated that the movement towards the mouth

was due to an increase in current because the region of active corrosion has increased in

surface area due to metal dissolution. Because there is more area, more total current is

produced. The IR* model then predicts that a shorter path length between anode and

cathode is needed for stable crevice corrosion. Figure 50 compares the resulting xcrit

values from a set of models involving penetration profiles taken from Pickering’s own

work[17] using this study’s electrochemical boundary condition1. Profiles taken after 50

and 150 hours were compared along with the initial case (t = 0) where the entire crevice

had a gap of 300 µm. The 150-hour profile had a maximum gap of 1430 µm (1130 µm

penetration + 300 µm original gap), whereas the 50-hour profile’s largest gap was 986

µm (686 µm penetration + 300 µm original gap) as shown in Figure 53a. Figure 54b is a

close-up of the region where the potential distributions cross Ecrit (0.244 mV vs. SCE). It

can be seen that when the current from the extra area was included (ON) for both

profiles, xcrit decreased from its value for when the area was unaccounted for (OFF).

This result would seem to support Pickering’s theory, however, the increase in gap size in

the active region without the corresponding area compensation also moved xcrit towards

the mouth. This result conflicts with the IR* theory which states that a larger gap

decreases resistance between the anode and cathode, thereby increasing the necessary

1 The boundary condition measured by Pickering was replaced for the one from this study because of the inability to create a mesh that matched the crevice length (0.1cm) and allowed CREVICERv2 to converge.

128

distance between them to achieve enough resistance to have IR > IR*, thereby stable

corrosion takes place.

An explanation for this discrepancy is that the decreased resistance of larger gaps

increases the “throwing power” of the system. That is, more distance is required for the

same amount of potential drop to occur and thus, more current can be thrown deeper into

the crevice. The potential will remain in the active region for a greater distance down the

crevice and increase the total crevice current coming out of the crevice. The increased I,

combined with the same R, decreases the necessary distance between anode and cathode

to achieve IR > IR*, thereby decreasing xcrit. In Figure 54b, the movement of xcrit toward

the mouth supports this idea as active corrosion penetrates deeper into the metal. As can

be seen from Table 14, the value of xcrit decreased by 8 % when the initial 300 µm gap

was replaced with the 50-hour profile. The value of xcrit decreased by another 3 % when

the 50-hour profile was replaced by the 150-hour profile which had even deeper

penetration (increased gap) at the active site. This indicates that the profile of the crevice

plays as important role in the movement of xcrit.

The effects of changes in electrolyte conductivity were also examined and

compared to the effect of area changes during stable crevice corrosion. Ignoring any

convection, as active corrosion takes place, the crevice solution above the beginning of

the area of greatest attack would increase in Ni2+ concentration, although this will be

moderated by diffusion.

As shown in Figure 25, the solution conductivity increased slightly until Ni2+

concentration reached 0.01 M, then significantly dropped as the Ni2+ concentration

approached saturation. Figure 55 shows how changing the conductivity over the area of

129

greatest attack (x = 0.5 – 1.5 mm) affects the crevice potential distribution for both the 50

and 150-hour profile used earlier. As seen earlier, compensating for the increase in

surface area moved xcrit towards the mouth only slightly. Keeping the area compensation

ON, 0.1 M NiSO4 was added to the solution above the active area. This decreased the

conductivity in that region from 0.184 to 0.1788 (ohm-cm)–1. The value of xcrit actually

increased slightly for both: 1.11 to 1.14 mm for the 50-hour profile; 1.02 to 1.07 mm for

the 150-hour profile. The reasons for this are unclear.

When the Ni2+ concentration was increased to 1.0 M ((0.121 (ohm-cm)–1), xcrit

decreased significantly for both profiles: 1.14 to 0.86 mm for the 50 hour profile and 1.07

to 0.86 mm for the 150 hour profile. When the Ni2+ concentration was increased to

saturation (0.076 (ohm-cm)–1)), xcrit decreased even more significantly from 0.86 to 0.40

mm for the 50 hour profile and from 0.82 to 0.39 mm for the 150 profile. This shows that

changes in crevice solution chemistry have drastic effects on xcrit. In comparison, the

profiles used here are examples of extreme crevice corrosion. That is, the large

penetration depths increased the available surface area and therefore, the total crevice

current. However, even at extremes, the area compensation caused only a decrease in xcrit

of approximately 5%. When the solution was saturated with Ni2+, an extreme chemical

change, xcrit decreased by approximately 65%. Therefore, the chemical changes caused

an order of magnitude more change in xcrit than the area compensation effects did.

As mentioned in Section 6.2, CREVICERv2 uses the dilute solution theory to

calculate solution conductivity. However, this method will over estimate the

conductivity at high concentrations of Ni2+ where the conductivity is seen to decrease due

ion-ion interaction. Therefore, to simulate the lower conductivities associated with

130

higher Ni2+ concentration, the concentrations of H+ and SO42- were lowered, whereas the

Ni2+ concentration was left at its initial value of zero. Because only the initial potential

distribution was of interest, the actual species’ concentrations within the solution were

not as important as the resulting conductivity.

Pickering and others[5, 10, 17, 27, 28] have repeatedly assumed that no chemistry

changes take place within their corroding crevices due to natural convection. As Ni2+

ions are dissolved into solution they cause an increase in density. This density difference

allows gravity to pull the heavier metal containing solution out of the bottom of the

crevice, thereby keeping the chemistry constant within the crevice because bulk solution

is drawn into replace it. The assumption of sufficient natural convection will be

examined more closely in Section 6.4.3; here the chemistry changes themselves will be

examined.

In one set of experiments, Pickering[17] flushed a crevice with fresh 0.5 M H2SO4

as it was undergoing stable crevice corrosion. As the Figure 58 indicates, the measured

current oscillated with the flushing action. Pickering stated that the current was seen to

decrease when the crevice was flushed, proving that there was no accumulate of Ni2+

ions. The rationale was that Ni2+ ions cause the active peak to decrease according to their

scans. Therefore, if Ni2+ ions were in the crevice and they were flushed out, the measured

current would go up, not down as was seen. The ‘Passive to Active’ polarization scan as

seen in Figure 59, was chosen to be the defining electrochemical boundary condition for

their system with a peak current of ~5 mA/cm2. They refer to Figure 60 which is shows

the effect of Ni2+ on the polarization curve[10]. This figure shows that the addition of

Ni2+ lowers the peak current to ~3 mA/cm2. This change is not that drastic, especially

131

taking into account that the same graph gives a peak current density, with no Ni2+ added,

of ~14 mA/cm2. This value conflicts with the assumed critical current density of ~5

mA/cm2 from Figure 59. Because the data from these two graphs do not correspond well,

it may be unwise to draw any conclusions from them. If the polarization scans taken in

this study are considered instead, an increase in Ni2+ concentration would cause the active

nose to increase as opposed to decreased (as seen in Pickering’s curve) If there was

nickel in solution, flushing it out would cause the total current to drop, as was seen by

Pickering. Therefore, the statement by Pickering that there was no accumulation of Ni2+

ions within the crevice may be called into question. In contrast, the polarization curves in

Figure 24 support the assertion that there was accumulation of Ni2+ ions as shown by the

decrease in total current after flushing.

Figure 58: From Pickering[17], the inset shows the current fluctuation when the crevice is flushed with fresh solution.

132

Figure 59: From Pickering[17], the electrochemical behavior of nickel in sulfuric acid scanned in both directions. Pickering chose the ‘Pasive to Active’ curve with Epass = 108 mV as the boundary condition modeled.

133

Figure 60: From Pickering[10], the electrochemical behavior of nickel in (a) 0.5 M H2SO4, (b) 0.5 M H2SO4 + sat. NiSO4, and (c) 0.01 M H2SO4 + sat. NiSO4.

6.4.2 Attack Morphology

Each sample that underwent stable crevice corrosion was shown to have three

distinct regions of attack: passive, active, and variable as seen in Figure 27. The passive

region had potentials that were more noble than the active nose and underwent very light

attack, if any. The active region corresponded to where the potential of the active nose

was reached along the wall of the crevice. In this region, a wide band of attack was seen.

Deeper into the crevice, the variable region was seen. In this region both passive and

active attack was seen at the same depth within the crevice. Each of these regions will be

examined more closely.

134

The passive region can easily be identified by its smooth surface. Figure 38a

demonstrates how little attack is seen in the passive region, with the 3-D LSM image

indicating a very flat surface. The small marks seen on the image are probably the result

of preferential attack at scratches or inclusions. Examination of the series of images for

crevices held for different times and potential, and for varying gap size shows that the

passive region remains free of attack for all cases except those of the smaller (14 and 35

µm) gaps at 10 and 30 min hold times. The reason for this difference at small gaps will

be discussed in detail later.

The active region can be identified visually as a dark band across the width of the

crevice. The dark color is due to nickel sulfate gathering at the surface[10, 17, 27, 35]. On

closer inspection (Figure 37b), the attack band has an extremely rough surface. However,

the surface seems to have some regularity to it, in that the corroded edges are straight.

Figure 39 compares a suspected active region with a metallographically etched surface of

Ni200. The etched surface also shows these straight lines, which according to Van der

Voort[29], are the grain boundaries. This result would indicate that during active

corrosion, the grain boundaries of the grain facets are being preferentially corroded.

Pickering and Frankenthal[36] indicated that this same faceted structure was a feature of

active dissolution from a film-free surface for iron and stainless steels. Pickering and

others[27] also reported faceted surfaces in the regions of active corrosion attack in the

nickel / 0.5 M H2SO4 system.

The variable region showed some very interesting results. Many of the crevices

showed evidence of both active and passive attack beyond the active region. Figure 40a

was taken after a section between two visually different areas was cut out using a

135

focused-ion beam. It can be seen that the area on the right (Figure 40a) did indeed

undergo active corrosion due to the faceted structure. The area on the left has some light

attack at the grain boundaries but the surface remained relatively flat. This result

indicates that passive corrosion had taken place. Figure 40b is a close up of this area

rotated 30 degrees counter-clockwise. Along the cut out wall, the grains themselves can

clearly be seen due to their different tints. Comparing these grains with the morphology

of the surface, one can see that the attack is definitely at the facet edges. Also, the

difference between active and passive attack is that in the passive region, only the grain

boundaries were attacked, while in the active region, whole facets of the grains had been

completely dissolved away. Evidence of this variable attack can be seen after 5 minutes

within a crevice with a gap of 93 µm. The arrows in Figure 30 indicate the regions of

variable attack. It can be seen that the boundaries between these areas become more

pronounced over time. Therefore, something is causing changes in potential or solution

composition above the corrosion band.

The attack of the passive region at small gaps and the variable corrosion seen

above the attack band both point to a breakdown in the assumed constant chemistry

conditions. Convection, or lack there of, may be the cause. One of Pickering and

coworkers[5, 10, 17, 27] canons for the IR* theory is that natural convection at all gap sizes

pulls all of the metal ions out of the crevice and this keeps the crevice solution

composition constant and equal to the bulk composition. This allows the assumption that

no chemistry changes happen within the crevice during corrosion to be made. However,

the presence of the variable attack region in this study would indicate that significant

chemical changes are occurring and lingering with the crevice. If the solution over the

136

attack band accumulated Ni2, its density would increase according to Table 7. The denser

solution would then have a stronger gravitational force pulling it down. If this solution

moved down the crevice in a straight band across the crevice width, you would expect no

changes in the morphology of attack. However, it can be seen in Figure 34a, that as the

crevice gap is reduced, the range of xcrit increases. That is, the band of active attack loses

it straightness and begins to blur and distort and seen in Figure 28 with the 14 µm gap.

The blurring of the attack band would indicate that the solution is not moving

down uniformly. At the larger gaps, the variable attack regions would indicate that as

heavier solution moves down the crevice, lighter solution is taking its place. However,

the distinct boundaries of active and passive attack, as seen in Figures 30 and 31, indicate

that non-uniform convective currents develop within a corroding crevice. That is, the

regions of passive attack directly above the attack band would indicate that the potential

has dropped below the active nose region producing less attack. The areas of greater

attack above the attack band would indicate that Ni2+ is accumulating in these regions.

The rationale is that at low Ni2+ concentrations, the solution becomes more conductive

and increases its throwing power. Therefore, the active nose increased the amount of

area it occupied along the crevice wall causing active corrosion deeper into the crevice.

When the Ni2+ concentration became larger than 0.028 M, the boundary condition

switched, as seen in Figure 24, to one with a sharper, but larger active nose. This change

in boundary condition caused the active band to expand deeper into to crevice, but for

only a shorter distance due to the increase in IR drop pushing the potential below the

active nose.

137

While uneven convection partially explains the anomalies seen in the attack

morphology, the reason for the non-uniformity needs to be examined closer. Looking at

the results from crevices with 93 µm gaps and potential hold times greater than one

minute in Figure 30, as mentioned above, visually different areas of attack can be seen

within the variable region. The attack bands perpendicular to the width of the crevice

indicate that convection was not uniform above the active region. The reason for this

may be explained by surface tension and solution density differences throughout the

crevice solution. When stable crevice corrosion occurs, Ni2+ ions are dissolved into the

solution over the active region and their concentration increases (Figure 61). As

indicated from density and surface energy measurements of 0.5 M H2SO4 with varying

Ni2+ concentration (Table 7), the density and the surface energy increased with increasing

NiSO4 concentration. Although the previous mentioned studies[5, 10, 17, 27, 28] consider

natural convection by density differences, they do not consider the influence of surface

tension on solution flow. In this case, surface tension forces work to counteract natural

convection.

138

Gap

CreviceMouth

StratifiedCreviceSolution

( )hgρ

Gap21

2γ

Former Substrate

ActiveCorrosion

Figure 61: Schematic of capillary vs. natural convective forces inside a corroding crevice (assuming unit thickness into the page). Active corrosion causes density gradients to form leading to a stratified solution. The denser solution will tend to flow out of the crevice due to the increase in the force of gravity pulling down.

Equation 6 can be expanded from a one-dimensional case (where the units are

force per unit area), to a three-dimensional case (force), by multiplying the left side by

the height and width of the column and the right side by the gap and width of the column

giving:

139

ghGwR

hw

cap

ργ=

2 (15)

Where:

γ is the surface tension [dyne/cm]

Rcap is the radius of the tube (G/2) [cm]

ρ is the density of the solution [gram/cm2]

g is the acceleration due to gravity [cm/s2]

h is the height the solution rises within the tube [cm]

G is the crevice gap (2*Rcap) [cm]

w is the height the solution rises within the tube [cm]

It can be seen that as gap size is decreased, the capillary force (left side of Equation 15) is

increased. At the same time, the volume of solution within the crevice is decreased; thus,

the force pulling the solution down due to gravity (right side of Equation 15) is

decreased. Using Equation 15, Figure 62 examines the capillary and gravity forces acting

on a volume of 0.5 M H2SO4 and a volume of 0.5 M H2SO4 + saturated NiSO4 (0.7 cm

crevice width and 0.1 cm column height for each) for a range of crevice gaps. It can be

seen that for gaps in the range of this study (<400 µm), the capillary forces are orders of

magnitude higher than the forces due to gravity (note the logarithmic scale). Therefore,

surface tension is dominant over gravity. This leads to a stratified solution within the

crevice.

140

0 .0 1

0 .1

1

10

10 0

10 0 0

10 0 0 0

10 0 0 0 0

0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1

Gap (cm)

Forc

e (d

yne)

Upward Capillary Force(acid w/ sat. Ni2+)

Downward Gravity Force (acid)

Downward Gravity Force(acid w/ sat. Ni2+)

Region of Interest

Upward Capillary Force(acid)

Figure 62: Examination of the competing forces within two volumes of solution, one containing 0.5 M H2SO4 and the other containing 0.5 M H2SO4 + saturated NiSO4 for variable crevice gaps. The volume height is 0.1 cm and the width is 0.7 cm. Notice that in the region of interest (gaps < 400 µm), the upward capillary forces are dominant over the downward forces due to gravity.

Consider the case in which if two volumes of nickel-free acid solution are placed

above and below a volume of acid saturated with nickel ions (Figure 63). The more dense

volume of solution would, due to gravity, tend to move below the lower lighter volume.

However, for the crevice gaps of interest to crevice corrosion, the volumes will remain

where they are due to the dominating capillary forces. This stratification leads to an

unstable system described by the Kelvin-Helmholtz instability[37] theory. Basically, if a

heavy solution rests above a light one, the criteria for instability is met, and any

disturbance (e.g., vibration) will create ‘internal gravity waves’ between the solutions. At

specific sites on these waves, the system becomes so unstable that the heavier solution

will flow down towards the mouth by convection, whereas the lighter solution will move

141

upwards everywhere else to counterbalance this flow. These sites of instability have

become ‘convection channels’ in the terminology used in this thesis.

Capillary Forces

LightSolution

LightSolution

Gravity Force

Gap

h

h

h

HeavySolution

Figure 63: Schematic of a dense volume of solution (assuming unit thickness into the page) with lighter solution volumes above and below and the corresponding capillary and gravity forces acting on each (h = height of solution volume).

These convection channels would cause the solution to develop non-uniform

chemistry changes across its width, in turn, causing non-uniform potential distributions as

well. This would result in an uneven band of attack. At gaps of 14 µm (Figure 28), this

is exactly what has been seen. At short times, the attack band is relatively straight. As

the hold is increased, the bands become more and more bent. This effect can be also seen

142

in Figure 34b. As the hold time was increased, the range of xcrit also increased (Figures

28 – 31) indicating that the band of attack became less uniform.

Not only did hold time affect convection, but also the gap size did as well. As the

gap increased, its capillary force decreased, whereas its force due to gravity increased.

This would cause solution to flow easier down the crevice. This flow in turn would allow

the attack band to stay more uniform by minimizing chemical changes. Examinations of

the images with increasing gap support this theory. As seen in Figure 34a, as the gap

sized increased, the range of xcrit decreased. It can also be seen that as hold time is

increased, the convection channels become more prominent because of the sharper

boundaries between active and passive corrosion in the variable regions.

Examination of the samples with 153 µm gaps (Figure 31), indicate another

interesting feature of the attack morphology of the variable region. At both 10 and 30

min hold times, active attack can be seen to have taken place along the edges of the

crevices. This result can be explained by surface tension differences across the width of

the crevice. Down the middle of the crevice length, there are only two walls on which

the solution can apply capillary pressure. However, there are three at the crevice edges.

The extra side increases the capillary force the solution in at the edges and allows heavier

solutions to remain at larger heights as opposed to the regions in the center of the crevice.

Therefore, Ni2+ concentrations would rise at the edges during active corrosion causing the

greater attack seen due to the increase in throwing power or the enlargement of the active

nose of the boundary condition.

143

CHAPTER 7. CONCLUSIONS

The objectives of this study, which were introduced in Chapter 3, have been

accomplished. Microfabrication techniques have been improved and new ones designed

which facilitated the creation of crevices with gap sizes similar to those found in practical

cases. The crevices fabricated were used to elicit information on the mechanisms of

crevice corrosion and the factors that affect them for the nickel / H2SO4 system. The

occluded geometry model, CREVICERv2, was used to predict the initial potential

distributions and attack profiles of crevice corrosion experiments that mirrored the ones

performed experimentally. Predicted and experimental results were found to agree very

well. The roles of finite crevice depth, crevice area changes, solution conductivity

differences, and convection were also illuminated during this study.

The specific achievements of this study were:

(1) Microfabrication: Formers with specific gaps were created using new

microfabrication techniques that improved on the ones used previously. Former

roughness was significantly decreased by the elimination of bulk silicon etching

and the shortened the fabrication time making it more efficient. The smallest

crevice gap possible with this new technique is 7 µm determined by the least

viscous photoresist used. Metal substrate thickness was increased by over an

order of magnitude through the design and implication of a new electroplating

technique that allowed for longer experiments. The same pattering techniques

used to create the silicon based crevice formers and substrates were applied to a

high nickel concentration alloy Ni200 and shown to produce excellent results.

144

This technique has great potential because it can be applied to any alloy for

crevice corrosion testing purposes.

(2) Physical Chemistry Characteristics of the Electrolyte: Changes in the

conductivity of 0.5 M H2SO4 were found to be very small at low values of nickel

concentration. However, when nickel concentration was increased past 0.1 M, the

conductivity began to decrease substantially until the minimum was reached at

saturation. Surface tension was also a weak function of nickel concentration at

low values but was found to slowly increase as nickel concentration was

increased.

(3) Effect of Finite Crevice Depth on Scaling Laws: At gaps greater that 100 µm

and a crevice length of 7 mm, the xcrit2/gap scaling law was found to deviate from

linearity in both experimental and modeling results. The finite crevice depth was

determined to be the cause. The analytical model used by Pickering[17] also

predicted the value of xcrit correctly at large gaps. However, since it is based upon

the scaling law being xcrit/gap and shows a linear behavior at large gaps, the

prediction of the critical aspect ratio (L/G)crit, may not hold true at smaller gaps,

where the xcrit2/gap scaling law seems to be the correct choice.

(4) Effect of Boundary Condition Characteristics on xcrit: None of the

characteristics of six boundary conditions were determined to be the sole

determinant of the depth of greatest attack, xcrit. The results indicate that a

combination of one or more of total crevice current, Itot, the potential at which the

peak current was reached, Epass, and the electrochemical power density determines

xcrit.

145

(5) Effect of Surface Area and Electrolyte Composition on xcrit: The resulting

increase in current from the increase in surface area due to active corrosion was

determined to have little effect on the depth of greatest attack, xcrit. However, the

increase in nickel concentration over the attack area exhibited a significant affect

on xcrit at nickel concentrations greater than 1.0 M.

(6) Comparison of Experimental and Predicted Results: The values of xcrit as a

function of gap obtained from the microfabricated crevices and those predicted by

CREVICERv2 were shown to be in excellent agreement. This demonstrates the

ability of microfabricated crevices to be used to probe crevice corrosion scaling

laws by allowing direct comparisons of experimental and modeling results. The

predicted values with potential as a variable did not show the same quality of

agreement. The reason for this is unknown.

(7) Role of Convection and Surface Tension: The effect of electrolyte surface

tension was shown to have an increasing affect on the attack morphology as the

crevice gap was decreased. As gaps became smaller, the attack morphology

became less uniform across the width of the crevice. As gap size was increased,

natural convection due to density differences within the crevice solution played an

increasing role in the attack morphology. Larger gaps were shown to have much

straighter bands of attack, although distinct convection channels could be visually

identified due to differences in the degree of attack. Also, the channels also

became more prominent the longer corrosion was allowed to continue. Therefore,

it was determined that natural convection does not completely keep the crevice

solution free of Ni2+ ions and that chemistry changes can occur within the crevice.

146

As a result, the IR* theory can no longer be the only mechanism which controls

corrosion at small gaps.

147

CHAPTER 8. FUTURE WORK

Experiments:

Crevice Holds: Perform crevice holds in 0.5 M H2SO4 + saturated NiSO4 to examine the

effects of keeping the crevice Ni2+ concentration constant throughout the experiment.

Expand the range of hold potentials and gap size to examine their effect on xcrit.

Polarization Data: Collect more polarization behavior data as a function of nickel

concentration. Perhaps perform potential holds to examine the steady-state current

density at various potentials and nickel concentrations.

Modeling:

Perform Real Time Experiments: Examine the effect of chemistry changes within an

actively corroding crevice as a function of time. The results could then be compared with

experimental results with variable hold times. Nickel concentrations could then be

determined as a function of time and space.

Improve Solution Conductivity Method: The dilute solution theory of conductivity used

by CREVICERv2 has been shown to be insufficient in accounting for the decrease in

conductivity at high solute concentrations. Another factor such as viscosity needs to be

incorporated into the calculation of conductivity to match the values seen experimentally.

148

Microfabrication:

Improvements to Formers: Additional patterning on the former surface would allow for

the effect of sub crevices to be examined. pH and specific ion sensors incorporated into

the former would provide valuable information within a crevice. Also, using lines of a

noble metal, such as gold, to act as conductivity electrodes along the formers surface

could illicit valuable information about chemistry changes with an actively corroding

crevice. Figure 64 is an image of a preliminary sample of this. Notice the pads outside

of the crevice area for use as electrical connections to a conductivity meter. The use of

clear glass as a foundation for crevice formers would allow visual observation of an

actively corroding crevice. This could lead to a better understanding of the role of

convection channels.

149

SU-8

Gold LinesElectrical

Contact Pad

Figure 64: Former with gold lines laid evaporated down within the crevice region to allow for conductivity changes to monitored during active corrosion.

Improvements to Substrates: The electrochemistry of the electroplated metal needs to be

improved in terms of reproducibility of the resulting electrochemical behavior. Perhaps

looking into other types of plating solutions and the chemical analysis of the current

plated nickel would improve upon this. Performance of the electroplated metal is

important to be able to produce substrates that have individually addressable electrodes

(Figure 65). These substrates would allow for the spatial resolution of potential and

current distributions within a crevice undergoing stable corrosion.

150

electricalconnection

SiO2

1.25 mm

1 cm

0.1-10 µm

Si

1 cm

oxide

Figure 65: Schematic of a microfabricated crevice with an array of individually addressable electrodes.

151

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156

APPENDIX A: MICROFABRICATION PROCESSING SHEETS

Process sheet: RCA clean

1. Dip wafer in TCE for 3 min.

2. Dip wafer in acetone for 3 min.

3. Dip wafer in methanol for 3 min.

4. Rinse wafer in DI water for for 1 min.

5. Dip wafer in NH4OH/H2O2/H2O (1:1:5) for 12 minutes. Maintain temperature of solution at

75-80 °C.

6. Rinse wafer in DI water for 1 min.

7. Dip wafer in 10:1 BOE for 15 sec.

8. Rinse wafer in DI water for 25 sec. Do not dry.

9. Immediately dip wafer in HCl/H2O2/H2O (1:1:6) for 12 minutes. Maintain temperature of solution

at 75-80 °C.

10. Rinse wafer in flowing DI water for 2 min.

11. Blow-dry with nitrogen gun.

12. Inspect wafer under a bright light and microscope. If wafer does not appear clean, repeat steps 1-

12

157

Process sheet: Abbreviated RCA clean

1. Dip wafer in boiling acetone for 5 min

2. Dip wafer in boiling methanol for 5 min.

3. Place wafer on spinner.

4. Spray for 5 sec. with ethanol.

5. Spray for 5 sec. with TCA.

6. Spray for 5 sec. with methanol.

7. Repeat steps 2-4 two more times.

8. Blow-dry with nitrogen gun.

9. Dip wafer in 10:1 BOE for 15 sec.

10. Rinse wafer in flowing DI water for 2 min.

11. Blow-dry with nitrogen gun.

12. Inspect wafer under a bright light and microscope. If wafer does not appear clean, repeat steps 1-

12.

158

Process sheet: Metal evaporation

1. Load wafers on sample holders, place in evaporator chamber.

2. Change the glass slide on the chamber lid.

3. Make sure the crystal health is over 80 – change if not.

4. Make sure there is enough metal in the crucible – add more if not.

5. Close the vent valve.

6. Turn the mechanical pump on.

7. Open the rough valve.

8. Wait for the pressure at TC2 (inside the chamber) to drop to 8 Pa.

9. Close the rough valve.

10. Open the hi-vac valve.

11. Pressure should drop rapidly.

12. Close the mechanical pump breaker.

13. Wait until pressure is in the 10-6 range (several hours). (Turn filament on to check pressure)

14. Turn water on – valves behind chamber counter-clockwise.

15. On the power supply, turn the main breaker on, the key lock on, and the high voltage on.

16. Turn the turret source to the proper place (usually Cr first for adhesion layer).

17. Turn the gun filament on.

18. Record the pressure in the logbook.

19. On the film deposition controller, select Film # and Set Process # (same as the turret number for the

metal).

20. Scroll through and check the settings against the reference sheet located near the evaporator.

21. Set the desired deposition thickness (turn the key to unlock the program to set the thickness).

22. Make sure the shutter is set to auto.

23. Press start. Record everything in the logbook.

24. Turn gun filament off.

25. Wait 5 min before switching sources to next metal.

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26. Repeat 17-25 for each layer.

27. Turn gun filament, high voltage, key lock, main breaker, and water off in reverse order.

28. Wait 5 min before venting chamber.

29. Turn the pressure filament off.

30. Close the hi-vac valve.

31. Open the vent valve.

32. When vented, open the chamber and remove the wafers.

33. Repeat steps 5-12 to pump chamber back down before leaving station.

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Process sheet: Photolithography Mask Cleaning

1. Place mask into holder.

2. Remove any residual photoresist with a swab soaked in acetone.

3. Place mask in elevated temperature mask cleaning bath for 15 min.

4. Place mask in distilled water rinse bath for 15 min with continuing water flow.

5. Blow-dry w/ nitrogen gun.

6. Place mask in 107ºC oven for 20 min.

7. Blow-dry with nitrogen gun.

8. Remove mask from holder and place it in its container to cool for 30 min.

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Process sheet: Photolithography for crevice formers and substrates

1. Place wafer (or metal sample) on spinner.

2. Spray for 5 sec. with ethanol.

3. Spray for 5 sec. with TCA.

4. Spray for 5 sec. with methanol.

5. Repeat steps 2-4 two more times.

6. Blow-dry with nitrogen gun.

7. Place wafer on 160 °C hot plate for 15 min to dehydrate.

8. Put wafer back in its holder and let cool for 10 min.

9. Place wafer on photoresist spinner.

10. Test vacuum, bring spinner up to 6000 rpm.

11. Blow dry wafer with nitrogen gun for 30 sec at 6000 rpm.

12. Spin certain SU-8: begin at 1200rpm then gradually increase speed to 1800rpm in 5 seconds. The total

spinning time is 30 seconds.

13. Soft-bake on hot plates: 55°C 90°C 55°C

SU-8-5 30 sec 15 min 30 sec SU-8-10 1 min 25 min 1 min SU-8-25 1.5 min 35 min 1.5 min SU-8-50 2 min 50 min 2 min

14. Relax wafer at room temperature on a flat place for 20 min.

15. Place chrome glass mask on the mask holder/vacuum chuck on the exposure machine.

16. Turn on the mask vacuum.

17. Place the wafer on the tray and push it in.

18. Raise the wafer with the lever on the left and adjust the stage height so that the mask just touches the

wafer when the lever is about ¾ turned.

19. Look through the microscope, focus on the mask, and adjust the wafer so that the mask pattern is

centered on the wafer.

20. Turn the lever completely, slide the bar forward, and press the white button to set the vacuum.

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21. Set the exposure time to appropriate sec. Power (mJ/cm2) λ~365 nm Exposure Time

SU-8-5 200 20 sec SU-8-10 400 40 sec SU-8-25 800 60 sec SU-8-50 1600 2 min

22. Press the green button to start the exposure.

23. After the exposure is complete, slide the bar back, turn the lever back the other way (lowering the

wafer), and remove the wafer and the mask from the exposure machine.

24. Post Exposure Bakes: 55°C 90°C 55°C

SU-8-5 30 sec 15 min 30 sec SU-8-10 1 min 25 min 1 min SU-8-25 1.5 min 35 min 1.5 min SU-8-50 2 min 50 min 2 min

25. Develop in SU-8 developer (NANO XP-SU-8): Dip Rinse

SU-8-5 10 sec 15 sec SU-8-10 20 sec 25 sec SU-8-25 70 sec 70 sec SU-8-50 100 sec 80 sec

26. Look at the pattern under low light in the microscope. If the pattern is unclear, either expose the

photoresist longer or rinse the wafer in acetone for several minutes until the photoresist is removed and

repeat steps 1-25.

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Process sheet: Dicing

1. Place patterned wafer on photoresist spinner.

2. Test vacuum, bring spinner up to 6000 rpm.

3. Blow dry wafer with nitrogen gun for 30 sec at 6000 rpm.

4. Spin on AZ4210 photoresist for 30 sec at 3000 rpm.

5. Soft bake: 55°C 90°C 55°C 30 sec 15 min 30 sec

6. Place wafer in exposure machine (for more detail see above).

7. Set exposure switch to flood.

8. Expose for 25 sec.

9. Repeat steps 4 – 8. (AZ4210 layer used to protect SU-8 during dicing)

10. Mount wafer on top of large scrap silicon wafer using melted black wax.

11. Use either S2045 or S2035 dicing blade.

12. Clean inner ring of blade with swab and isopropyl alcohol.

13. At dicing machine: turn on water and compressed air using the yellow handles on the white pipes to

the left of the dicing saw.

14. Turn on the main breaker, lamp, TV and camera (switches to right of saw).

15. Open lid and attach blade.

16. Place holder against blade and tighten using the tool stored on top of the saw.

17. Place the safety cover over the blade and holder and tighten screws. Make sure the nozzle points to the

right.

18. Push ‘spindle on’ on display – should read 30,000 rpm.

19. Allow saw to warm up for ½ - 1 hour.

20. Open lid and place mounted wafer on stage.

21. Press ‘vacuum’ and ‘setup’ to auto-align the blade.

22. Use ‘shift’ to scroll through the settings – make necessary changes.

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23. Make sure z-index is set to desired distance above the stage (approximately 0.050 is the height of two

wafers)

24. Use ‘jog/scan’ to align blade in the proper location for a cut.

25. Press ‘semi-auto’.

26. Press the button with an arrow pointed upward and to the right to begin a cut.

27. Once the cut has begun, press ‘jog/scan’ to get out of the semi-auto mode so that the blade stops after

one cut.

28. Repeat steps 15-18 until all cuts have been made.

29. Press ‘spindle off’ perform steps 3-8 in reverse order to power down.

30. In clean room: remove diced wafer pieces from holder by melting wax on 120°C hot plate, discard

scrap diced pieces.

31. Rinse former or substrate in TCE to remove black wax.

32. Place sample into AZ 400K 1:4 DI developer for 4 minutes or until AZ photoresist is completely

removed.

33. Rinse in running distilled water for 2 minutes.

34. Take diced samples into clean room and perform a spin clean (ethanol, TCE, and methanol repeated

three times while wafer is on spinner).

35. Blow-dry with nitrogen gun.

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Process sheet: Substrate Electroplating

1. Place a glass side in boiling acetone for 5 minutes.

2. Place slide in boiling methanol for 5 minutes.

3. Blow-dry with nitrogen gun.

4. Place in container with arrow indicating the cleaned end.

5. Record the SU-8 height around the defined electrode area of the substrate using the Tencor

profilometer.

6. Place substrate on spinner.

7. Spray for 5 sec. with ethanol.

8. Spray for 5 sec. with TCA.

9. Spray for 5 sec. with methanol.

10. Repeat steps 2-4 two more times.

11. Blow-dry with nitrogen gun.

12. Place cleaned glass slide on 120°C hot plate.

13. Melt black wax on one end of slide covering an area just larger than a substrate.

14. Place substrate on 50°C hotplate for 30 sec.

15. Move substrate to 90°C hotplate for 1 min.

16. Place substrate on glass slide (still on the 120°C hotplate) on top of black wax (photoresist side

up) with the electrode area closest to the end of the slide.

17. Position substrate using toothpicks.

18. Move slide to 90°C hotplate for 1 min.

19. Place slide on 50°C hotplate for 30 sec.

20. Place the slide into the mousetrap; the end without the substrate goes first.

21. Bring the gold contact down onto the contact patch until it just touches.

22. Turn ½ more to apply slight pressure to contact.

23. Coat the contact and the exposed edges of the substrate with black wax diluted with TCE.

24. Dry under heating lamps for 45 minutes.

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25. Mix 350 mL of plating solution with 3 mL of brightener.

26. Heat plating solution to 45°C using hot water bath.

27. Place anode plate (nickel) into 1 M HCl for 10 minutes to clean.

28. Place anode into solution and hook to red lead of the electroplater.

29. On the electroplater readout, set source to 15 mA (or 100 mA if plating a entire wafer), and set V

limit to 10 V.

30. Dip substrate into 1m HCl for 1 min, then rinse with 3 beakers of distilled water.

31. Blow-dry with nitrogen gun.

32. Plug green cathode wire into mousetrap.

33. Place substrate into plating solution so its face is parallel to the anode.

34. Start the agitator.

35. Let the substrate sit for 1 min.

36. Turn on electroplater by turning switch on blue box to the appropriate anode position.

37. Plate for 20 – 25 min.

38. Remove substrate from solution and rinse in 3 beakers of distilled water.

39. Plating solution can be used for one more plating run, then replace.

40. Remove wax from contact using TCE.

41. Remove glass slide from mousetrap.

42. Place slide on 50°C hotplate for 30 sec.

43. Move slide to 90°C hotplate for 1 min.

44. Move slide to 120°C hotplate and remove substrate from wax using toothpicks.

45. Place substrate in TCA for 5 min to remove all of the wax.

46. Blow-dry with nitrogen gun.

47. Measure plated nickel thickness using the profilometer using the know height of the surrounding

SU-8 to calculate.

48. Spray for 5 sec. with ethanol.

49. Spray for 5 sec. with TCA.

50. Spray for 5 sec. with methanol.

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51. Repeat steps 2-4 two more times.

52. Blow-dry with nitrogen gun.

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APPENDIX B: CODE ADDITIONS TO CREVICERv2

Chemtest.cpp #include <iostream.h> #include <fstream.h> #include <time.H> #ifndef __STRING_H #include <string.h> #endif #include <math.h> #ifndef __TCHEM_H #include "tchem.H" #endif #ifndef __TASPECIE_H #include "taspecie.H" #endif #ifndef __TALLSPEC_H #include "tallspec.H" #endif #ifndef __TMATERIA_H #include "tmateria.H" #endif #ifndef __TBARRELM_H #include "tbarrelm.H" #endif #ifndef __SOLVER_H #include "solver.H" #endif int gap_correct = 0; int area_correct = 0; // 0 = off // 1 = Pickering's 50 hr profile // 2 = Pickering's 150 hr profile // 3 = Simple staggered gap //This function reads the ANSYS-generated test fields to get //the mesh information (Node number, Node position, Node connectivity) void setup(TSolutionVolume *els[3250],int *iNumOfElements, NodeInfo *nodes[6500],int *iNumOfNodes,TAllSpecies *crc)

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//setup int count1, count2, dum, nodenumber, iNumUsedNodes, temp; long double x,y,z,newY,ymax,xmax; int next; char dumch; int i,j,k,elnumber; double r; double y0, a, b, avgY = 0; double gap = 20e-6; // gap is the height, or z-coordinate, of the crevice double temp_gap = 0; TASpecies *foo; TChemistry *initchem; TMaterial *mat; TMaterial *matedge; TMaterial *tip; mat = new TNickel(crc); matedge = new TMaterial(crc); //tip = new TNickel_Edge(crc); tip = new TMaterial(crc); // Fill crc with the species that will be in this crevice foo = new TSO4mm(); crc->AddSpecies(foo); foo = new THp(); crc->AddSpecies(foo); foo = new TNipp(); crc->AddSpecies(foo); foo = new TO2(); crc->AddSpecies(foo); foo = new TElectrical(); crc->AddSpecies(foo); foo = new TTemperature(); crc->AddSpecies(foo); foo = new TPressure(); crc->AddSpecies(foo); // Set the initial chemistry initchem = new TChemistry(); initchem->AddSpecies("H+",428,0); initchem->AddSpecies("Ni++",0,0); initchem->AddSpecies("SO4--",214,0); initchem->AddSpecies("O2",0.55,0); initchem->AddSpecies("temperature",298,1);

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initchem->AddSpecies("pressure",1e5,1); initchem->AddSpecies("electrical",-0.2,0); // Open files for input and output, read in mesh information ifstream nofile("novar350",ios::in); cout << "read files now" << endl; count1 = 0; nodenumber = 0; next = nofile.peek(); while(next != EOF) while (next == ' ') // move past all of the spaces nofile.get(dumch); next = nofile.peek(); if ((next == '0') || (next == '1') || (next == '2') || (next == '3') || (next == '4') || (next == '5') || (next == '6') || (next == '7') || (next == '8') || (next == '9')) // this line is not a waste line nofile >> temp >> x >> y >> z; nofile.ignore(256, '\n'); // ignore the rest of the line nodes[count1] = new NodeInfo; nodes[count1]->chem = new TChemistry(initchem); nodes[count1]->oldchem = new TChemistry(initchem); nodes[count1]->dbX = x; nodes[count1]->dbY = y; nodes[count1]->dbZ = z; nodes[count1]->iUsed = 0; // initialize to 'not used' nodes[count1]->iNodeId = temp; count1++; //find the largest y and x values //will be used to define the active sides later if (y > ymax) ymax = y; if (x > xmax) xmax = x; else nofile.ignore(256,'\n'); // ignore the entire line if // it is a waste line next = nofile.peek(); nodenumber = count1; // save the total number of nodes read // now open and pass through "elements" twice, // once to see which nodes are used, // and a second time to create the elements

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ifstream elfile("elvar350",ios::in); next = elfile.peek(); while(next != EOF) while (next == ' ') // move past all of the spaces elfile.get(dumch); next = elfile.peek(); if ((next == '0') || (next == '1') || (next == '2') || (next == '3') || (next == '4') || (next == '5') || (next == '6') || (next == '7') || (next == '8') || (next == '9')) // this line is not a waste line elfile >> elnumber >> dum >> dum >> dum >> dum >> i >> j >> k; elfile.ignore(256, '\n'); // ignore the rest of the line nodes[i-1]->iUsed = 1; nodes[j-1]->iUsed = 1; nodes[k-1]->iUsed = 1; else elfile.ignore(256, '\n'); // ignore the entire line if // it is a waste line next = elfile.peek(); // Renumber the nodes sequentially iNumUsedNodes = 0; for (count1=0;count1<nodenumber;count1++) if (nodes[count1]->iUsed !=0) nodes[count1]->iNodeId = iNumUsedNodes; iNumUsedNodes++; // Go though "elements" again, this time creating TSolutionVolumes ifstream el2file("elvar350",ios::in); ofstream outelem("elements.txt",ios::out); temp = 0; next = el2file.peek(); while(next != EOF) while (next == ' ') // move past all of the spaces el2file.get(dumch); next = el2file.peek(); if ((next == '0') || (next == '1') || (next == '2') || (next == '3') || (next == '4') || (next == '5') || (next == '6') || (next == '7') || (next == '8') || (next == '9')) // this line is not a waste line el2file >> elnumber >> dum >> dum >> dum >> dum >> i >> j >> k; el2file.ignore(256, '\n'); // ignore the rest of the line //***** for penetration profile correction purposes

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avgY = (nodes[i-1]->dbY + nodes[j-1]->dbY + nodes[k-1]->dbY)/3; if (gap_correct == 0) temp_gap = gap; //pickering's 50 hour profile if (gap_correct == 1) if (avgY <= 0.00122) //near crevice mouth temp_gap = gap;//do nothing else if ((avgY > 0.00122) && (avgY <= 0.0025355)) y0 = 2.3250 - 0.038; a = 40.1953; b = 3.4381; temp_gap = gap - ((y0 + a * exp(-b * (avgY * 1000))) - 3)/1000; else if ((avgY > 0.0025355) && (avgY <= 0.0041865)) y0 = 2.2121; a = 0.0056; b = 1.0571; temp_gap = gap - ((y0 + a * exp(b * (avgY * 1000))) - 3)/1000; else if (avgY > 0.0041865) temp_gap = gap + 0.0003429; //pickering's 150 hour profile if (gap_correct == 2) if (avgY < 0.00115) //near crevice mouth temp_gap = gap;//do nothing else if ((avgY >= 0.00115) && (avgY < 0.0025192)) y0 = 1.9098; a = 1214.372; b = 6.2201; temp_gap = gap - ((y0 + a * exp(-b * (avgY * 1000))) - 3)/1000; else if ((avgY >= 0.0025192) && (avgY < 0.0063178)) y0 = 1.4266 + 0.0762;

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a = 0.1607; temp_gap = gap - ((y0 + a * (avgY * 1000)) - 3)/1000; else if (avgY >= 0.0063178) y0 = 2.4057 + 0.027239; a = 0.0121; temp_gap = gap - ((y0 + a * (avgY * 1000)) - 3)/1000; //simple gap if (gap_correct == 3) // if (avgY < 0.00115) //near crevice mouth if (avgY < 0.0012) //near crevice mouth temp_gap = 300e-6;//do nothing // else if ((avgY >= 0.00115) && (avgY < 0.0025192)) else if ((avgY >= 0.0012) && (avgY < 0.0025)) temp_gap = 1500e-6; // else if ((avgY >= 0.0025192) && (avgY < 0.0063178)) else temp_gap = 1000e-6; /* else if (avgY >= 0.0063178) else if (avgY >= 0.0025) temp_gap = 800e-6; */ //********** els[elnumber-1] = new TSolutionVolume(nodes[i-1],nodes[j-1], nodes[k-1],temp_gap,mat,matedge,matedge,matedge,crc); outelem << (elnumber-1) << " " << nodes[i-1]->iNodeId << " " <<

nodes[j-1]->iNodeId << " " << nodes[k-1]->iNodeId << " " << avgY << " " << temp_gap << endl;

temp++; else el2file.ignore(256, '\n'); // ignore the entire line if // it is a waste line next = el2file.peek(); ///////////////////////////////////////////////////////////////////////// // This section condenses the array of nodes and keep only those used // Can't do this earlier b/c have to keep old numbering system // until elements are created

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///////////////////////////////////////////////////////////////////////// for(count1=0;count1<iNumUsedNodes;) if(nodes[count1]->iUsed == 0) // This method works only because // ANSYS generates sequentially numbered // nodes (although an excess) delete(nodes[count1]); for(count2=count1;count2<(nodenumber-1);count2++) nodes[count2] = nodes[count2+1]; else count1++; /////////////////////////////////////////////////////////////////////////// // This section defines the boundary conditions for the relevant shape // It sets the potential and/or gradients at some of the nodes /////////////////////////////////////////////////////////////////////////// double ix,iy,jx,jy,kx,ky,top,bottom,left,right; cout << "Nodes " << iNumUsedNodes << endl; cout << "Using boundary conditions for Test1" << endl; for(count1=0;count1<iNumUsedNodes;count1++) if (nodes[count1]->dbY < .000001) //crevice opening (y=0) nodes[count1]->oldchem->SetConcentration("electrical",0.6); // setting potential at crevice opening to // value in the passive region nodes[count1]->chem->SetConcentration("electrical",0.6); // setting potential at crevice opening to // value in the passive region nodes[count1]->oldchem->SetFixed("electrical",1); // the potential for this node is fixed nodes[count1]->chem->SetFixed("electrical",1); // the potential for this node is fixed nodes[count1]->oldchem->SetConcentration("H+",428); // setting H+ at crevice opening to bulk condition nodes[count1]->chem->SetConcentration("H+",428); // setting H+ at crevice opening to bulk condition nodes[count1]->oldchem->SetFixed("H+",1); // the concentration for this node is fixed nodes[count1]->chem->SetFixed("H+",1); // the concentration for this node is fixed nodes[count1]->oldchem->SetConcentration("SO4--",214); // setting SO4-- at crevice opening to bulk condition nodes[count1]->chem->SetConcentration("SO4--",214); // setting SO4-- at crevice opening to bulk condition nodes[count1]->oldchem->SetFixed("SO4--",1); // the concentration for this node is fixed nodes[count1]->chem->SetFixed("SO4--",1);

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// the concentration for this node is fixed nodes[count1]->oldchem->SetConcentration("Ni++",0); // setting Ni++ at crevice opening to bulk condition nodes[count1]->chem->SetConcentration("Ni++",0); // setting Ni++ at crevice opening to bulk condition nodes[count1]->oldchem->SetFixed("Ni++",1); // the concentration for this node is fixed nodes[count1]->chem->SetFixed("Ni++",1); // the concentration for this node is fixed nodes[count1]->oldchem->SetConcentration("O2",0.44); // setting O2 at crevice opening to bulk condition nodes[count1]->chem->SetConcentration("O2",0.44); // setting O2 at crevice opening to bulk condition nodes[count1]->oldchem->SetFixed("O2",1); // the concentration for this node is fixed nodes[count1]->chem->SetFixed("O2",1); // the concentration for this node is fixed //From LAD's evans code in nisi /* else // set initial potential distribution as a slant newY = ((-10)*nodes[count1]->dbY) + 0.35; nodes[count1]->oldchem->SetConcentration("electrical",newY); nodes[count1]->chem->SetConcentration("electrical",newY); */ //setting tip to active for(count1=0;count1<temp ;count1++) ix = els[count1]->i->dbX; iy = els[count1]->i->dbY; jx = els[count1]->j->dbX; jy = els[count1]->j->dbY; kx = els[count1]->k->dbX; ky = els[count1]->k->dbY; //tip if((iy == ymax) && (jy == ymax)) els[count1]->ijmat = tip; if((iy == ymax) && (ky == ymax)) els[count1]->ikmat = tip; if((jy == ymax) && (ky == ymax)) els[count1]->jkmat = tip; // Assign the proper values for the number of nodes and elements

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*iNumOfElements = temp; *iNumOfNodes = iNumUsedNodes; // setup void main(void) // main int count, count1, count2; int i,j,k,stable; double temp2, temp3; int done = 0; double residual; TAllSpecies crc; TSolutionVolume *els[3250]; int iNumOfElements; int iNumOfNodes; NodeInfo *nodes[6500]; char nm[20]; char name[20];; double kt, th, tempd; TSpeciesName neutname; long double time; setup(els, &iNumOfElements, nodes, &iNumOfNodes, &crc); // Calls setup double Niflux[3250]; char fluxfile[20]; int count3; double press, temper, avgpot, avgy, newflux, pendepth, newi, el_area; double multi = 0; double slope = 0; double a, b ; for(count3=0;count3<iNumOfElements;count3++) Niflux[count3] = 0; cout << "to main" << endl; count2=0; count1=0; //*****START CHEMICAL LOOP for(count2=1;count2<2;count2++) // loop through number of timesteps // Copy the new values to the old to prepare for the next timestep SetOldChem(nodes,iNumOfNodes); cout << "Time period " << count2 << " found" << endl; done = 0; // set flag for electrical finished to FALSE cout << "Starting ELECTRICAL" << endl; sprintf(name,"electrical"); time = 1e-8; // set delta t for electrical

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kt = 1; th = 1; stable = 1; // check for Peclet stability // cout << iNumOfElements << endl; for(count=0;count<iNumOfElements;count++) // initialize elements for electrical stable = stable && els[count]->SetConstants(name,kt,th); if (!stable) cout << "Ooops not stable" << endl; cout << "Kt= " << els[0]->Kt << " Kx= " << els[0]->Kx << " Ky= " << els[0]->Ky << " Mx= " << els[0]->Mx << " My= " << els[0]->My << " " << els[0]->currentspecies << endl; count1 = 0; //reset to get out of loop if needed //**************************************** //*****START ELECTRICAL LOOP while(done != 1) // loop until stable E-I SetOldChem(nodes,iNumOfNodes); cout << "Entering SOLVE" << endl; Solve(els,iNumOfElements,nodes,iNumOfNodes,time,name); cout << "Just back from SOLVE" << endl; residual = AvgDifference(nodes,iNumOfNodes); if (residual < .002) // typically .1 done = 1; // have convergd to stable E-I cout << "residual = " << residual << endl; cout << "Time period " << count2 << " electrical found" << endl; sprintf(nm, "el%d.txt", count2); Print(iNumOfNodes,nodes,nm,name); cout << nm << endl; else cout << "residual = " << residual << endl; sprintf(nm, "b%d.txt", count1); // Print(iNumOfNodes,nodes,nm,name); cout << nm << endl; count1++; if (count1>200) done = 1; sprintf(nm, "b%d.txt", count1); Print(iNumOfNodes,nodes,nm,name); // reinitialize the variables for(count=0;count<iNumOfElements;count++) els[count]->SetConstants(name,kt,th);

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//************************************************************* time = 0.1; // set delta t for chemical kt = 1; th = 0.5; //***Ni++ sprintf(name,"Ni++"); cout << "starting " << name << endl; stable = 1; for(count=0;count<iNumOfElements;count++) // initialize elements for copper stable = stable && els[count]->SetConstants(name,kt,th); if (!stable) cout << "Ooops not stable " << name << endl; cout << "Entering SOLVE" << endl; Solve(els,iNumOfElements,nodes,iNumOfNodes,time,name); cout << "Time period " << count2 << " " << name << " found" << endl; sprintf(nm, "Ni_%d.txt", count2); Print(iNumOfNodes,nodes,nm,name); cout << nm << endl; sprintf(fluxfile, "NiFlux_%d.txt", count2); ofstream outflux(fluxfile,ios::out); for(count3=0;count3<iNumOfElements;count3++) temper = els[count3]->avgchem->GetConcentration("temperature"); press = els[count3]->avgchem->GetConcentration("pressure"); avgpot = (els[count3]->i->chem->GetConcentration("electrical") + els[count3]->j->chem->GetConcentration("electrical") + els[count3]->k->chem->GetConcentration("electrical"))/3; avgy = (els[count3]->i->dbY + els[count3]->j->dbY + els[count3]->k->dbY)/3; //pickering's 50 hour profile if (area_correct == 1) //need derivative of curve fit to morphology to get slope //need to add a function to chemtest that will also adjust the gap //according to the fitted curve if (avgy <= 0.00122) //near crevice mouth slope = 0; else if ((avgy > 0.00122) && (avgy <= 0.0025355)) a = 40.1953; b = 3.4381; //derivative of exp decay y = y0 + a*exp(-bx) slope = -a * b * exp(-b * (avgy * 1000)); else if ((avgy > 0.0025355) && (avgy <= 0.0041865)) a = 0.0056;

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b = 1.0571; //derivative of exp decay y = y0 + a*exp(bx) slope = a * b * exp(b * (avgy * 1000)); else if (avgy >= 0.0041865) slope = 0; else slope = 0; //using a^2 + b^2 = c^2 (multi) assuming side b is = 1 //where slope = b(rise)/a(run) multi = sqrt((slope * slope) + 1); //pickering's 150 hour profile else if (area_correct == 2) //need derivative of curve fit to morphology to get slope //need to add a function to chemtest that will also adjust the gap //according to the fitted curve if (avgy < 0.00115) //near crevice mouth slope = 0; else if ((avgy >= 0.00115) && (avgy < 0.0025192)) a = 1214.372; b = 6.2201; //derivative of exp decay y = y0 + a*exp(-bx) slope = -a * b * exp(-b * (avgy * 1000)); else if ((avgy >= 0.0025192) && (avgy < 0.0063178)) //derivative of linear fit y = y0 + ax slope = 0.1607; else if (avgy >= 0.0063178) //derivative of linear fit y = y0 + ax slope = 0.0121; //using a^2 + b^2 = c^2 (multi) assuming side b is = 1 //where slope = b(rise)/a(run) else slope = 0; multi = sqrt((slope * slope) + 1); else multi = 1;

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newi = //gives current density in A/cm^2 multi * els[count3]->mat->GetNetCurrentDensity(els[count3]

->avgchem,avgpot,temper,press,multi) / 10000; newflux = //gives flux in mol/cm^2-s multi * els[count3]->mat->GetChemicalFlux(name,els[count3]

->avgchem,avgpot,temper,press) / 10000; Niflux[count3] = Niflux[count3] + newflux*time; el_area = els[count3]->A; el_area = el_area * 10000; // m^2 -> cm^2 // penetration depth = i(A/cm^2)*A.W. A.W. = 58.69 grams / mole // ------ rho = 8.9 grams / cm^3 // rho*n*F // flux = i / nf (mol/cm^2-s) // pd = flux * A.W. / rho (cm/s) // pd (microns) = pd (cm) * 1000 pendepth = Niflux[count3] * 58.69 / 8.9 * 1000; //gives microns of penetration depth

outflux << count3 << " " << avgy << " " << Niflux[count3] << " " << pendepth << " " << newi << " " << el_area << " " << endl;

//***H+ sprintf(name,"H+"); cout << "starting " << name << endl; stable = 1; for(count=0;count<iNumOfElements;count++) // initialize elements for hydrogen stable = stable && els[count]->SetConstants(name,kt,th); if (!stable) cout << "Ooops not stable " << name << endl; cout << "Entering SOLVE" << endl; Solve(els,iNumOfElements,nodes,iNumOfNodes,time,name); cout << "Time period " << count2 << " " << name << " found" << endl; sprintf(nm, "H_%d.txt", count2); // Print(iNumOfNodes,nodes,nm,name); cout << nm << endl; //***O2 sprintf(name,"O2"); cout << "starting " << name << endl; stable = 1; for(count=0;count<iNumOfElements;count++) // initialize elements for oxygen stable = stable && els[count]->SetConstants(name,kt,th); if (!stable)

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cout << "Ooops not stable " << name << endl; cout << "Entering SOLVE" << endl; Solve(els,iNumOfElements,nodes,iNumOfNodes,time,name); cout << "Time period " << count2 << " " << name << " found" << endl; sprintf(nm, "O2_%d.txt", count2); // Print(iNumOfNodes,nodes,nm,name); cout << nm << endl; //***SO4- sprintf(name,"SO4--"); cout << "starting " << name << endl; NeutralizeChargeSO4(nodes, iNumOfNodes, &crc); cout << "Time period " << count2 << " " << name << " found" << endl; sprintf(nm, "SO4_%d.txt", count2); cout << "made it" << endl; // Print(iNumOfNodes,nodes,nm,name); cout << nm << endl; // end of count2 loop // main

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Fem.cpp /**************************************************************************** TSolutionVolume: This is the constructor for this class. This procedure should only be called once. => memory leak via avgchem Also => Big problems if nodes have different numbers of species 07/24/01 modified by Jason Lee to include area correction for penetration profiles ****************************************************************************/ TSolutionVolume::TSolutionVolume(NodeInfo *nodei, NodeInfo *nodej, NodeInfo *nodek, double height, TMaterial * material, TMaterial * ij, TMaterial * ik, TMaterial * jk, TAllSpecies * allspecies) double iY, jY, kY, avgY; //for use w/ area correction i = nodei; // Grab pointers to vertices for later use j = nodej; k = nodek; int area_correction = 0; // 0 = off // 1 = Pickering's 50 hr profile // 2 = Pickering's 150 hr profile // initialize the pointer to avgchem to ensure proper number of species avgchem = new TChemistry(i->chem); // load avgchem with the right species // Set the value of avgchem to the proper average of the nodal values SetChemistry(); crc = allspecies; mat = material; ijmat = ij; ikmat = ik; jkmat = jk; theta = 1; // Set the degree of explicitness(0) or implicitness(1) Kt = 0; // This really should always be 1 if the diff eq is in std form Kx = 1; // Diffusion terms Ky = Kx; // Hard to envision aqueous system where Kx!=Ky (liquid crystal) Kxy = 0; Mx = 0; // Migration terms My = 0; P = 0; // Find bi,bj,bk ci,cj,ck and A based on coordinates of vertices // ?? Move to separate procedure if element splitting is required // Formulas pulled from Allaire, p.41 ?? bi = j->dbY - k->dbY; // these 6 terms used in Bx, also to find A

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bj = k->dbY - i->dbY; bk = i->dbY - j->dbY; ci = k->dbX - j->dbX; cj = i->dbX - k->dbX; ck = j->dbX - i->dbX; A = (bi*cj - bj*ci)/2; avgY = (i->dbY + j->dbY + k->dbY)/3; if (area_correction == 1) area_multi = Get50hrAreaCorrection(avgY); else if (area_correction == 2) area_multi = Get150hrAreaCorrection(avgY); else area_multi = 1; Lij = sqrt(bk*bk + ck*ck); Lik = sqrt(bj*bj + cj*cj); Ljk = sqrt(bi*bi + ci*ci); h = height; //height of crevice in meters // find the width and height of element // there are probably better ways of finding the derivates wrt x,y dX = fabs(ci); if (dX < fabs(cj)) dX = fabs(cj); if (dX < fabs(ck)) dX = fabs(ck); dY = fabs(bi); if (dY < fabs(bj)) dY = fabs(bj); if (dY < fabs(bk)) dY = fabs(bk); /************************************************************************ Get50hrAreaCorrection: 08/08/01 by Jason Lee This function adjusts the area of the element based upon the increase in area due to metal dissolution based upon a fitted curve to the shape of the attacked region.

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The derivative is then taken to get the slope of the tanget /************************************************************************/ double TSolutionVolume::Get50hrAreaCorrection(double avgY) double multi = 0; double slope = 0; //need derivative of curve fit to morphology to get slope //need to add a function to chemtest that will also adjust the gap //according to the fitted curve double a, b ; //pickering's 50 hour profile if (avgY <= 0.00122) //near crevice mouth slope = 0; else if ((avgY > 0.00122) && (avgY <= 0.0025355)) a = 40.1953; b = 3.4381; //derivative of exp decay y = y0 + a*exp(-bx) slope = -a * b * exp(-b * (avgY * 1000)); else if ((avgY > 0.0025355) && (avgY <= 0.0041865)) a = 0.0056; b = 1.0571; //derivative of exp decay y = y0 + a*exp(bx) slope = a * b * exp(b * (avgY * 1000)); else if (avgY >= 0.0041865) slope = 0; else slope = 0; //using a^2 + b^2 = c^2 (multi) assuming side b is = 1 //where slope = b(rise)/a(run) multi = sqrt((slope * slope) + 1); return(multi); /************************************************************************ Get150hrAreaCorrection: 07/19/01 by Jason Lee This function adjusts the area of the element based upon the increase in area due to metal dissolution based upon a fitted curve to the shape of the attacked region. The derivative is then taken to get the slope of the tanget

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/************************************************************************/ double TSolutionVolume::Get150hrAreaCorrection(double avgY) double multi = 0; double slope = 0; //need derivative of curve fit to morphology to get slope //need to add a function to chemtest that will also adjust the gap //according to the fitted curve double a, b ; //pickering's 150 hour profile if (avgY < 0.00115) //near crevice mouth slope = 0; else if ((avgY >= 0.00115) && (avgY < 0.0025192)) a = 1214.372; b = 6.2201; //derivative of exp decay y = y0 + a*exp(-bx) slope = -a * b * exp(-b * (avgY * 1000)); else if ((avgY >= 0.0025192) && (avgY < 0.0063178)) //derivative of linear fit y = y0 + ax slope = 0.1607; else if (avgY >= 0.0063178) //derivative of linear fit y = y0 + ax slope = 0.0121; else slope = 0; //using a^2 + b^2 = c^2 (multi) assuming side b is = 1 //where slope = b(rise)/a(run) multi = sqrt((slope * slope) + 1); return(multi);

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Tmateria.cpp TNickel::TNickel(TAllSpecies * allspecies) /********************************************************************** TNickel(): Constructor for class material used for copper plating on gold **********************************************************************/ crc = allspecies; PDS = new TPDS(crc); // PDS = new TPickering_Act_to_Pass(crc); // PDS = new TPickering_Pass_to_Act(crc); double TNickel::GetChemicalFlux(TSpeciesName name,TChemistry *chemistry, double E, double T, double P) /********************************************************************** 10/20/98 GetChemicalFlux : Returns the chemical flux [mol/(m^2-s)] of species "name"for the test material in solution "chemistry" at "potential". CONVENTIONS: Fluxes >0 produce species Fluxes <0 consume species **********************************************************************/ double flux; flux = PDS->GetFluxOfSpecies(name,chemistry,E,T,P); return(flux); double TNickel::GetChemicalFlux(TSpeciesName name,TChemistry *chemistry, double E, double T, double P, double area_correct) /********************************************************************** 10/20/98 GetChemicalFlux : Returns the chemical flux [mol/(m^2-s)] of species "name"for the test material in solution "chemistry" at "potential". CONVENTIONS: Fluxes >0 produce species Fluxes <0 consume species **********************************************************************/ double flux; flux = area_correct * PDS->GetFluxOfSpecies(name,chemistry,E,T,P);

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return(flux); double TNickel::GetNetCurrentDensity(TChemistry *chemistry, double E, double T, double P) /********************************************************************** 10/20/98 GetNetCurrentDensity : Returns the total electrical flux [A/m^2] for the material in solution "chemistry" at "potential". CONVENTIONS: Currents > 0 are ANODIC Currents < 0 are CATHODIC **********************************************************************/ double net; net = PDS->GetCurrentDensity(chemistry,E,T,P); return(net); double TNickel::GetNetCurrentDensity(TChemistry *chemistry, double E, double T, double P, double area_correct) /********************************************************************** 10/20/98 GetNetCurrentDensity : Returns the total electrical flux [A/m^2] for the material in solution "chemistry" at "potential". CONVENTIONS: Currents > 0 are ANODIC Currents < 0 are CATHODIC **********************************************************************/ double net; net = area_correct * PDS->GetCurrentDensity(chemistry,E,T,P); return(net); TNickel_Edge::TNickel_Edge(TAllSpecies * allspecies) /********************************************************************** TNickel(): Constructor for class material used for copper plating on gold **********************************************************************/ crc = allspecies; PDS = new TPickering_Edge(crc); double TNickel_Edge::GetChemicalFlux(TSpeciesName name,TChemistry *chemistry, double E, double T, double P)

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/********************************************************************** 10/20/98 GetChemicalFlux : Returns the chemical flux [mol/(m^2-s)] of species "name"for the test material in solution "chemistry" at "potential". CONVENTIONS: Fluxes >0 produce species Fluxes <0 consume species **********************************************************************/ double flux; flux = PDS->GetFluxOfSpecies(name,chemistry,E,T,P); return(flux); double TNickel_Edge::GetNetCurrentDensity(TChemistry *chemistry, double E, double T, double P) /********************************************************************** 10/20/98 GetNetCurrentDensity : Returns the total electrical flux [A/m^2] for the material in solution "chemistry" at "potential". CONVENTIONS: Currents > 0 are ANODIC Currents < 0 are CATHODIC **********************************************************************/ double net; net = PDS->GetCurrentDensity(chemistry,E,T,P); return(net);

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Treactio.cpp TPDS::TPDS(TAllSpecies * allspecies) /********************************************************************** TPDS: This function is the constructor for this class This class represents the potentiodynamic scan for nickel in H2SO4 Written 10/20/98 by Lisa DeJong - Revised 7/17/01 by Jason Lee for Ni200 2 mV/sec scan **********************************************************************/ environment = allspecies; double TPDS::GetFluxOfSpecies(TSpeciesName name, TChemistry * chemistry, double E, double T, double P) /*********************************************************************** GetFluxOfSpecies() : This function returns the flux of species name. It is a virtual function and can be redefined. RETURNS: The chemical flux in mol/(m^2-s) inet [A/m^2] N(X) = ---- v(X) --------------- nF [eq/mol]-[C/eq] ***********************************************************************/ double flux; int stochcoeff, n; stochcoeff = 1; // stoichometric coefficient for Ni++ in Ni -> Ni++ + 2e- n = 2; // number of e transferred in Ni -> Ni++ + 2e- if (StringsEqual(name,"Ni++")) flux = (GetCurrentDensity(chemistry,E,T,P)*stochcoeff)/(n*F); else flux = 0; return(flux); double TPDS::AnodicCurrentDensity(TChemistry * chemistry, double E, double T, double P) /*********************************************************************** AnodicCurrentDensity: This function calculates the anodic current density of the reaction. This function calculates the anodic current density based on potential The following are polynomial fits of PDS of Ni200 in 1N H2SO4 with a scan rate of 2mV/sec.

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Last modified by Jason Lee 07/17/01 ***********************************************************************/ long double ia, current, areascale; //current in A/cm^2 long double x0,y0,a,b,c,d,e,g,h,i,j,k,l = 0.0; //parameters for up to a 12th polynomial fit //no 'f' because already a defined variable in Sigma //Plot which was used to fit the curves if (E > 0.750) y0 = -0.0007; a = 0.0029; b = -0.0037; c = 0.0016; current = y0 + a*E + b*pow(E,2) + c*pow(E,3); else if ((E > 0.400) && (E <= 0.750)) y0 = 0.0003; a = -0.0013; b = 0.0019; c = -0.0009; current = y0 + a*E + b*pow(E,2) + c*pow(E,3); else if ((E > 0.306) && (E <= 0.400)) a = 2.57358e-5; b = 0.1126; c = -0.2617; current = a * exp(b /(E + c)); //exponential decay else if ((E > 0.250) && (E <= 0.306)) a = 0.0076; b = -0.0098; x0 = 0.2726; current = a / (1 + exp(-(E - x0)/b)); //sigmodial else if ((E > -0.100) && (E <= 0.250)) y0 = 0.0049; a = 0.034; b = 0.2811; c = -1.6702; d = -40.2348; e = 100.9172; g = 1628.2576; h = -1058.3561; i = -38833.3089; j = -73116.8588;

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k = 1166188.3912; l = -2152169.6822;

current = y0 + a*E + b*pow(E,2) + c*pow(E,3) + d*pow(E,4) + e*pow(E,5) + g*pow(E,6) + h*pow(E,7) + i*pow(E,8) + j*pow(E,9) + k*pow(E,10) + l*pow(E,11);

else if ((E > -0.235) && (E <= -0.100)) y0 = 0.0938; a = 3.7514; b = 61.1780; c = 453.6162; d = 874.5814; e = -7526.3694; g = -35029.2485; h = 101206.0435; i = 1075895.0779; j = 2834226.9535; k = 2585682.6718;

current = y0 + a*E + b*pow(E,2) + c*pow(E,3) + d*pow(E,4) + e*pow(E,5) + g*pow(E,6) + h*pow(E,7) + i*pow(E,8) + j*pow(E,9) + k*pow(E,10);

else current = 0; // below Ecorr = -0.235V areascale = 10000; // polarization curve was given in A/cm^2 - // this converts to A/m^2 ia = current * areascale; return(ia); double TPDS::CathodicCurrentDensity(TChemistry * chemistry, double E, double T, double P) /*********************************************************************** CathodicCurrentDensity: This function calculates the cathodic current density of the reaction. ***********************************************************************/ double ic; // current ic = 0; return(ic); TLAD_PDS::TLAD_PDS(TAllSpecies * allspecies) /********************************************************************** TPDS: This function is the constructor for this class This class represents the potentiodynamic scan for nickel in H2SO4 Written 10/20/98 by Lisa DeJong - Simulated potentiodynamic curves of Ni/1N H2SO4 system Used by LAD for scaling law studies

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**********************************************************************/ environment = allspecies; double TLAD_PDS::GetFluxOfSpecies(TSpeciesName name, TChemistry * chemistry, double E, double T, double P) /*********************************************************************** GetFluxOfSpecies() : This function returns the flux of species name. It is a virtual function and can be redefined. RETURNS: The chemical flux in mol/(m^2-s) inet [A/m^2] N(X) = ---- v(X) --------------- nF [eq/mol]-[C/eq] ***********************************************************************/ double flux; int stochcoeff, n; stochcoeff = 1; // stoichometric coefficient for Ni++ in Ni -> Ni++ + 2e- n = 2; // number of e transferred in Ni -> Ni++ + 2e- if (StringsEqual(name,"Ni++")) flux = (GetCurrentDensity(chemistry,E,T,P)*stochcoeff)/(n*F); else flux = 0; return(flux); double TLAD_PDS::AnodicCurrentDensity(TChemistry * chemistry, double E, double T, double P) /*********************************************************************** AnodicCurrentDensity: This function calculates the anodic current density of the reaction. JSL's simulated PDS ***********************************************************************/ double ia, exponent, areascale; double mu, sigma, mutwo, downshift, proportion, beta, alpha, gamma, x_shift; double pi = 3.14159; /*Skewed_________________________________________________________________________________________ beta = 0.1; alpha = 2; gamma = 1; downshift = -5; //K2 proportion = 0.815; //K1 x_shift = 0.15; exponent = proportion/((pow(beta, alpha))*gamma)*(pow(x_shift - E, alpha-1))*exp((E - x_shift)/ beta) + downshift;

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//_______________________________________________________________________________________________*/ /*Double Bump____________________________________________________________________________________ mu = 0.075; mutwo = -0.075; sigma = 0.06; downshift = -5; //K2 proportion = 0.425; //K1 exponent = proportion/(sigma*pow(2*pi,0.5))*exp(-1*pow(E-mu,2)/(2*pow(sigma,2))) + proportion/(sigma*pow(2*pi,0.5))*exp(-1*pow(E-mutwo,2)/(2*pow(sigma,2)))+ downshift; //_______________________________________________________________________________________________*/ //Skinny_________________________________________________________________________________________* mu = 0.0; sigma = 0.04; downshift = -5; //K2 proportion = 0.3; //K1 exponent = proportion/(sigma*pow(2*pi,0.5))*exp(-1*pow(E-mu,2)/(2*pow(sigma,2)))+downshift; //_______________________________________________________________________________________________*/ /*Normal_________________________________________________________________________________________ mu = 0.0; //Changed parameters JSL 07/17/00 sigma = 0.1; downshift = -5; //K2 proportion = 0.75; //K1 exponent = proportion/(sigma*pow(2*pi,0.5))*exp(-1*pow(E-mu,2)/(2*pow(sigma,2)))+downshift; //_______________________________________________________________________________________________*/ /*Ipass 3.0_________________________________________________________________________________________ mu = 0.0; //Changed parameters JSL 07/17/00 sigma = 0.1; downshift = -5; //K2 proportion = 0.75; //K1 if (E >= 0.09)

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exponent = -3.0; else exponent = proportion/(sigma*pow(2*pi,0.5))*exp(-1*pow(E-mu,2)/(2*pow(sigma,2)))+downshift; //_______________________________________________________________________________________________*/ /*Ipass 2.5_________________________________________________________________________________________ mu = 0.0; //Changed parameters JSL 07/17/00 sigma = 0.1; downshift = -5; //K2 proportion = 0.75; //K1 if (E >= 0.06) exponent = -2.5; else

exponent = proportion/(sigma*pow(2*pi,0.5))*exp(-1*pow(E-mu,2)/ (2*pow(sigma,2)))+downshift;

//___________________________________________________________________________________*/ /*Shifted_____________________________________________________________________________ mu = -0.05; sigma = 0.1; downshift = -5; //K2 proportion = 0.75; //K1 exponent = proportion/(sigma*pow(2*pi,0.5))*exp(-1*pow(E-mu,2)/(2*pow(sigma,2)))+downshift; //___________________________________________________________________________________*/ areascale = 10000; // polarization curve was given in A/cm^2 - // this converts to A/m^2 ia = pow(10,exponent)*areascale; return(ia); double TLAD_PDS::CathodicCurrentDensity(TChemistry * chemistry, double E, double T, double P) /*********************************************************************** CathodicCurrentDensity: This function calculates the cathodic current density of the reaction. ***********************************************************************/

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double ic; // current ic = 0; return(ic); TPickering_Act_to_Pass::TPickering_Act_to_Pass(TAllSpecies * allspecies) /********************************************************************** TPDS: This function is the constructor for this class This class represents the potentiodynamic scan for nickel in H2SO4 Active to passive scan from Abdulsalam, Pickering Corrosion Science Vol 41 (1999) pp 351 - 375, fig 2 Written by 7/21/01 by Jason Lee **********************************************************************/ environment = allspecies; double TPickering_Act_to_Pass::GetFluxOfSpecies(TSpeciesName name, TChemistry * chemistry, double E, double T, double P) /*********************************************************************** GetFluxOfSpecies() : This function returns the flux of species name. It is a virtual function and can be redefined. RETURNS: The chemical flux in mol/(m^2-s) inet [A/m^2] N(X) = ---- v(X) --------------- nF [eq/mol]-[C/eq] ***********************************************************************/ double flux; int stochcoeff, n; stochcoeff = 1; // stoichometric coefficient for Ni++ in Ni -> Ni++ + 2e- n = 2; // number of e transferred in Ni -> Ni++ + 2e- if (StringsEqual(name,"Ni++")) flux = (GetCurrentDensity(chemistry,E,T,P)*stochcoeff)/(n*F); else flux = 0; return(flux); double TPickering_Act_to_Pass::AnodicCurrentDensity(TChemistry * chemistry, double E, double T, double P) /*********************************************************************** AnodicCurrentDensity: This function calculates the anodic current density of the reaction. This function calculates the anodic current density based on potential ***********************************************************************/

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double ia, current, areascale; //current in A/cm^2 long double x0,y0,a,b,c,d,e,g,h,i,j,k,l = 0.0; //parameters for up to a 12th polynomial fit //no 'f' because already a defined variable in Sigma //Plot which was used to fit the curves if(E >= 0.5929) y0 = 7.27988e-6; a = 6.8459e-13; b = 17.4595; current = y0 + a*exp(b*E); else if ((E >= 0.2156) && (E < 0.5929)) y0 = 8.03446e-6; a = 0.00063988; b = 15.657; current = y0 + a*exp(-b*E); else if ((E > 0.1957) && (E < 0.2156)) y0 = 0.001064; a = -0.00479399; current = y0 + a*E; else if ((E > 0.1759) && (E <= 0.1957)) y0 = 0.0164156; a = -0.0832204; current = y0 + a*E; else if ((E >= 0.1560) && (E <= 0.1759)) y0 = 0.00230371; a = 0.0387031; b =0.734442; c = -2.72277; d = -62.3967; e = 215.904; g = 1330.18; h = -6027.96;

current = y0 + a*E + b*pow(E,2) + c*pow(E,3) + d*pow(E,4) + e*pow(E,5) + g*pow(E,6) + h*pow(E,7);

else if ((E >= -0.1021) && (E < 0.1560)) y0 = 0.00235446; a = 0.0407448; b = 0.65821;

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c = -3.26665; d = -42.2201; e = 189.096; current = y0 + a*E + b*pow(E,2) + c*pow(E,3) + d*pow(E,4) + e*pow(E,5); else if ((E >= -0.1589) && (E < -0.1021)) y0 = 0.00476228; a = 0.0278034; current = y0 + a*E; else if ((E >= -0.1901) && (E < -0.1589)) y0 = 0.00235809; a = 0.0128581; current = y0 + a*E; else if ((E > -0.2014) && (E < -0.1901)) y0 = 0.000228221; a = 0.0010775; current = y0 + a*E; else if ((E >= -0.2695) && (E <= -0.2014)) y0 = -3.43604e-6; a = 0.000827228; b = 20.0421; current = y0 + a * exp(b * E); else current = 0; // below Ecorr = -0.2695V areascale = 10000; // polarization curve was given in A/cm^2 - // this converts to A/m^2 ia = current * areascale; return(ia); double TPickering_Act_to_Pass::CathodicCurrentDensity(TChemistry * chemistry, double E, double T, double P) /*********************************************************************** CathodicCurrentDensity: This function calculates the cathodic current density of the reaction. ***********************************************************************/ double ic; // current

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ic = 0; return(ic); TPickering_Pass_to_Act::TPickering_Pass_to_Act(TAllSpecies * allspecies) /********************************************************************** TPDS: This function is the constructor for this class This class represents the potentiodynamic scan for nickel in H2SO4 Passive to active scan from Abdulsalam, Pickering Corrosion Science Vol 41 (1999) pp 351 - 375, fig 2 Written by 7/21/01 by Jason Lee **********************************************************************/ environment = allspecies; double TPickering_Pass_to_Act::GetFluxOfSpecies(TSpeciesName name, TChemistry * chemistry, double E, double T, double P) /*********************************************************************** GetFluxOfSpecies() : This function returns the flux of species name. It is a virtual function and can be redefined. RETURNS: The chemical flux in mol/(m^2-s) inet [A/m^2] N(X) = ---- v(X) --------------- nF [eq/mol]-[C/eq] ***********************************************************************/ double flux; int stochcoeff, n; stochcoeff = 1; // stoichometric coefficient for Ni++ in Ni -> Ni++ + 2e- n = 2; // number of e transferred in Ni -> Ni++ + 2e- if (StringsEqual(name,"Ni++")) flux = (GetCurrentDensity(chemistry,E,T,P)*stochcoeff)/(n*F); else flux = 0; return(flux); double TPickering_Pass_to_Act::AnodicCurrentDensity(TChemistry * chemistry, double E, double T, double P) /*********************************************************************** AnodicCurrentDensity: This function calculates the anodic current density of the reaction. This function calculates the anodic current density based on potential ***********************************************************************/

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double ia, current, areascale; //current in A/cm^2 long double x0,y0,a,b,c,d,e,g,h,i,j,k,l = 0.0; //parameters for up to a 12th polynomial fit //no 'f' because already a defined variable in Sigma //Plot which was used to fit the curves if (E >= 0.6723) a = 1.09075e-8; b = 8.3916; current = a * exp(b * E); else if ((E >= 0.2752) && (E < .6723)) y0 = 1.64711e-7; a = 4.76594e-6; current = y0 + a*E; else if ((E >= 0.1078) && (E < 0.2752)) y0 = 1.79941e-6; a = 0.0406103; b = 63.4199; current = y0 + a * exp(-b * E); else if ((E >= 0.0369) && (E < 0.1078)) a = 0.05; b = 103.7694; current = a * exp(-b * E); else if ((E >= -0.1816) && (E < 0.0369)) y0 = 0.00419155; a = 0.111484; b = 0.357812; c = -172.801; d = -4844.87; e = 8271.95; g = 2.06725e6; h = 3.44614e7; i = 2.58869e8; j = 9.4618e8; k = 1.36467e9;

current = y0 + a*E + b*pow(E,2) + c*pow(E,3) + d*pow(E,4) + e*pow(E,5) + g*pow(E,6) + h*pow(E,7) + i*pow(E,8) + j*pow(E,9) + k*pow(E,10);

else if ((E >= -0.2496) && (E < -0.1816)) a = 979.037; b = 70.3302;

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current = a * exp(b * E); else current = 0; // below Ecorr = -0.2496V areascale = 10000; // polarization curve was given in A/cm^2 - // this converts to A/m^2 ia = current * areascale; return(ia); double TPickering_Pass_to_Act::CathodicCurrentDensity(TChemistry * chemistry, double E, double T, double P) /*********************************************************************** CathodicCurrentDensity: This function calculates the cathodic current density of the reaction. ***********************************************************************/ double ic; // current ic = 0; return(ic); TPickering_Edge::TPickering_Edge(TAllSpecies * allspecies) /********************************************************************** TPDS: This function is the constructor for this class This class represents the potentiodynamic scan for nickel in H2SO4 Passive to active scan from Abdulsalam, Pickering Corrosion Science Vol 41 (1999) pp 351 - 375, fig 2 Written by 7/25/01 by Jason Lee **********************************************************************/ environment = allspecies; double TPickering_Edge::GetFluxOfSpecies(TSpeciesName name, TChemistry * chemistry, double E, double T, double P) /*********************************************************************** GetFluxOfSpecies() : This function returns the flux of species name. It is a virtual function and can be redefined. RETURNS: The chemical flux in mol/(m^2-s) inet [A/m^2] N(X) = ---- v(X) --------------- nF [eq/mol]-[C/eq] ***********************************************************************/ double flux;

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int stochcoeff, n; stochcoeff = 1; // stoichometric coefficient for Ni++ in Ni -> Ni++ + 2e- n = 2; // number of e transferred in Ni -> Ni++ + 2e- if (StringsEqual(name,"Ni++")) flux = (GetCurrentDensity(chemistry,E,T,P)*stochcoeff)/(n*F); else flux = 0; return(flux); double TPickering_Edge::AnodicCurrentDensity(TChemistry * chemistry, double E, double T, double P) /*********************************************************************** AnodicCurrentDensity: This function calculates the anodic current density of the reaction. This function calculates the anodic current density based on potential ***********************************************************************/ double ia, areascale; areascale = 10000; ia = 1.9157 * areascale; //9.5785 A/cm^2 return(ia); double TPickering_Edge::CathodicCurrentDensity(TChemistry * chemistry, double E, double T, double P) /*********************************************************************** CathodicCurrentDensity: This function calculates the cathodic current density of the reaction. ***********************************************************************/ double ic; // current ic = 0; return(ic);