selective wet chemical etching of erosion resistant...
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Selective Wet Chemical Etching of Erosion Resistant Coatings
from Titanium Alloy Substrates:
Mechanism and Optimization
Rabib Chaudhury
Department of Chemical Engineering
McGill University
Montreal, Quebec, Canada
April 2013
Advisor: Professor Dimitrios Berk
A thesis submitted in partial fulfillment of the requirements
of the degree of Master of Engineering
© Rabib Chaudhury 2013
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Acknowledgments I would like to thank my advisor Professor Dimitrios Berk, whose guidance and patience
made this thesis possible. Ευχαριστώ! I would also thank our project partners at the Ecole
Polytechnique and in the industry in Montreal for their help and collaboration on this
project.
I would like to thank my lab-mates for making my research experience at McGill a
pleasant one. I would particularly like thanking lab-mate Pierre-Alexandre Pascone for
making me believe that I could when I thought I couldn’t. Undergraduate student Phi
Hung Vuong Nguyen should be thanked for his hard effort in helping run some
experiments relating to this project.
Samuel Bastien helped start this project in 2009. I would like to thank him for his
pioneering work. In addition, I would like to thank him for having the patience to answer
all of my annoying questions during my first few days (…months) on this project.
The support staff at the Department of Chemical Engineering should also be
acknowledged. I would like to thank Ranjan Roy, Gerald Lekyj, and Andrew Golsztajn
for their technical support and Jo-Ann Gadsby and Emily Musgrave for their
administrative support.
Research isn’t free. I would like to thank the Eugene Ulmer Lamothe fund for ensuring
that I didn’t need to moonlight as a waiter over the course of this project.
Finally, I would like to thank my loving parents. Just because I love them too.
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TABLE OF CONTENTS
ABSTRACT ..................................................................................................................................... 7 ABRÉGÉ ......................................................................................................................................... 2 1 INTRODUCTION .................................................................................................................... 3 2 OBJECTIVES .......................................................................................................................... 4 3 BACKGROUND AND LITERATURE REVIEW ............................................................... 5
3.1 PROPERTIES OF TITANIUM-BASED CERAMIC COATINGS .................................................... 5 3.2 REACTION MECHANISM ...................................................................................................... 6
3.2.1 The Role of Hydrogen Peroxide in Wet Chemical Etching ......................................... 6 3.2.2 Tracking Titanium From Coating to Solution ............................................................. 7 3.2.3 Formation of Coordination Complexes ....................................................................... 8
3.3 BACKGROUND ON SURROGATE MODELING ..................................................................... 10 3.3.1 Model Types ............................................................................................................... 13
3.3.1.1 Interpolation of Spatial Data (Kriging Models) ............................................................................... 13 3.3.1.2 Artificial Neural Networks (ANNs) ................................................................................................. 13 3.3.1.3 Least Squares – Support Vector Machine (LS-SVM) ...................................................................... 14
3.3.2 Model Evaluation ....................................................................................................... 15 3.3.3 Model Optimization (Genetic Algorithm) .................................................................. 16
4 METHODOLOGY ................................................................................................................ 18 4.1 EXPERIMENTAL SAMPLES AND SAMPLE HOLDERS .......................................................... 18
4.1.1 Flat Sample Holder .................................................................................................... 18 4.1.2 Sample Holder for Tension/Fatigue Samples ............................................................ 18
4.2 EXPERIMENTAL APPARATUS ............................................................................................ 19 4.3 SAMPLE PREPARATION AND EXPERIMENTAL RUNS ......................................................... 20
4.3.1 Sample Preparation ................................................................................................... 21 4.3.2 Experimental Runs ..................................................................................................... 21
4.4 ANALYTICAL METHODS ................................................................................................... 22 4.4.1 Calculating Etch Rates and Selectivity ...................................................................... 22 4.4.2 Measurement of Hydrogen Peroxide Concentration ................................................. 22
4.4.2.1 Quantification Method ..................................................................................................................... 22 4.4.2.2 Hydrogen Peroxide Sample Collection Method ............................................................................... 23
4.5 EXPERIMENTAL DESIGN ................................................................................................... 25 4.5.1 Box-Behnken Design of Experiment .......................................................................... 25 4.5.2 Full Factorial Design of Experiment ......................................................................... 26
4.6 SURROGATE MODELING (IMPLEMENTATION) .................................................................. 27 4.7 METHODOLOGY FOR KINETICS MODEL ............................................................................ 29
4.7.1 Determination of Etching Reaction Rate Laws ......................................................... 29 4.7.2 Determination of Temperature Dependence ............................................................. 30
5 RESULTS AND DISCUSSION ............................................................................................ 31 5.1 VERIFICATION OF WELL-MIXING ..................................................................................... 31 5.2 SELECTING A CARBOXYLIC SALT FOR ETCHING EXPERIMENTS ...................................... 33 5.3 HYDROGEN PEROXIDE STABILITY AND THE EFFECT OF EDTA ....................................... 34
5.3.1 Etching Experiments with Potassium Oxalate and Hydrogen Peroxide ................... 34 5.3.2 The Effect of EDTA on Temperature and Hydrogen Peroxide Stability ................... 38 5.3.3 Proposed Reaction Mechanism ................................................................................. 40
5.4 KINETICS AND OPTIMIZATION .......................................................................................... 42
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5.4.1 Box-Behnken Design of Experiment .......................................................................... 42 5.4.2 Full Factorial Design of Experiments ....................................................................... 47 5.4.3 Surrogate Modeling ................................................................................................... 48
5.4.3.1 First Modeling Iteration ................................................................................................................... 49 5.4.3.2 Second Modeling Iteration ............................................................................................................... 50
5.4.4 Kinetics ...................................................................................................................... 53 5.4.4.1 Determining Rate Laws .................................................................................................................... 53 5.4.4.2 Evaluating Temperature Dependence .............................................................................................. 62
5.5 A COMPARISON BETWEEN SURROGATE AND KINETIC MODELS ...................................... 65 5.6 MECHANICAL TESTING ..................................................................................................... 65
6 CONCLUSIONS AND RECOMMENDATIONS ............................................................... 66 7 REFERENCES ....................................................................................................................... 68 8 APPENDIX ............................................................................................................................. 70
A1. MATHEMATICAL EXPLANATION OF KRIGING ...................................................................... 70 A2. ADDITIONAL INFORMATION ON ARTIFICIAL NEURAL NETWORKS ..................................... 71
Biological Foundation ........................................................................................................... 71 Threshold Logic Units and Backpropagation of Errors ........................................................ 72
A3. THEORY OF EVOLUTION AND THE GENETIC ALGORITHM ................................................... 74 A4. SUMO FILES ........................................................................................................................ 75
Config File ............................................................................................................................. 75 Sample Data File ................................................................................................................... 75 Default File (Excerpt) ............................................................................................................ 76
A5. CALCULATION OF HYDROGEN PEROXIDE BEING IN EXCESS .............................................. 78 A6. ANOVA TABLES FOR BOX-BEHKEN DOE .......................................................................... 79 A7. ANOVA TABLES FOR FULL FACTORIAL DOE .................................................................... 80
9 APPENDIX REFERENCES ................................................................................................. 81
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List of Figures Figure 3-1. Comparison of drilling performance of TiN and TiAlN coated 6 mm drills in
34 CrNiMo6 [1] .......................................................................................................... 5 Figure 3-2. Addition/Elimination Mechanism for Nucleophilic Displacements at
Carbonyl Carbon by Hydrogen Peroxide Species [5] ................................................. 6 Figure 3-3. Coordination Complex Consisting of a Ligand (EDTA) and a Metal Ion (M).
Adapted from [18] ....................................................................................................... 9 Figure 3-4. Structure of a Peroxy Titanium Oxalate Complex ......................................... 10 Figure 3-5. SUMO Control Flow [20] .............................................................................. 11 Figure 3-6. SUMO Control Flow in Detail [20] ............................................................... 12 Figure 3-7. A Multi-Layered Feedforward Network [23] ................................................ 14 Figure 3-8. A Hyperplane Separating Two Classes of Data [24] ..................................... 15 Figure 3-9. The Genetic Algorithm Flowchart [25] .......................................................... 16 Figure 4-1. Sample Holder for Flat Specimens ................................................................ 18 Figure 4-2. Sample Wheel to Hold Tension and Fatigue Samples ................................... 19 Figure 4-3. Beaker Heater Experimental Set-Up .............................................................. 20 Figure 4-4. Percent Difference between Reference Method and Iced Method for Two
Etching Experiments ([H2O2]i =5.9 mol/L, [K2C2O4] = 0.225 mol/L, Ti = 75°C, 300 RPM) ......................................................................................................................... 24
Figure 4-5. Percent Difference between Reference Method and Pre-Mix Method for Two Etching Experiments ([H2O2]i =5.9 mol/L, [K2C2O4] = 0.225 mol/L, Ti = 75°C, 300 RPM) ......................................................................................................................... 25
Figure 5-1. Concentration of Hydrogen Peroxide in Different Locations of the Reactor Relative to the Concentration Obtained at Location 1 (C1) (T = 75°C [H2O2]i = 5.9 mol/L, [K2C2O4]i = 0.150 mol/L) .............................................................................. 32
Figure 5-2. The Effect of RPM Changes on the Etch Rate of the Coating ([H2O2]i =5.9 mol/L, [K2C2O4] = 0.150 mol/L, [EDTA] = 5e-3 mol/L, Ti = 75°C) ........................ 33
Figure 5-3. Etch Rates with Different Carboxylic Salts (T = 75 oC, [H2O2] = 2.9 M, 300 RPM, 20 minutes, (Potassium acetate is not visible because of very low values) ... 34
Figure 5-4. Temperature Increase Over the Course of a Full-Etch Experiment ([H2O2]i = 5.9 M, [K2C2O4] = 0.225 M, 300 RPM) ................................................................... 35
Figure 5-5. Average Decomposition of H2O2 (Ti = 70 C, [H2O2]i = 5.9 M, [K2C2O4] = 0.225 M, 300 RPM) .................................................................................................. 37
Figure 5-6. Average Temperature Comparison ([H2O2]i = 5.9 M, [K2C2O4] = 0.225 M, 300 RPM) .................................................................................................................. 38
Figure 5-7. Effect of EDTA on H2O2 Stability ([H2O2]i = 5.9 M, [K2C2O4] = 0.225 M, Ti = 70°C, 300 RPM) .................................................................................................... 40
Figure 5-8. Reaction Sequence for Titanium in the Wet Chemical Etching of TiAlN with Hydrogen Peroxide and Potassium Oxalate .............................................................. 41
Figure 5-9. Reaction Sequence of Titanium in the Wet Chemical Etching of TiAlN with Hydrogen Peroxide and Potassium Oxalate in the Presence of EDTA .................... 42
Figure 5-10. Quadratic Response Surface Model for Coated Etch Rates ......................... 44 Figure 5-11. Quadratic Response Surface Model for Uncoated Etch Rates ..................... 45
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Figure 5-12. Quadratic Response Surface Model for Selectivity ..................................... 46 Figure 5-13. Kriging Model of Selectivity (First Iteration), T = 75°C, 300 RPM ............ 49 Figure 5-14. Contour Plot for Artificial Neural Network Model, T = 75°C, 300 RPM ... 51 Figure 5-15. Contour Plot for LS-SVM Model, T = 75°C, 300 RPM .............................. 52 Figure 5-16. Least Squares Support Vector Machine Model for Selectivity (Second
Iteration), T = 75°C, 300 RPM ................................................................................. 53 Figure 5-17. Mass Lost (mg) vs. Time (min), Uncoated Samples, [H2O2] = 5.9 mol/L,
[K2C2O4] = 0.150 mol/L, T = 75°C, 300 RPM ......................................................... 54 Figure 5-18. Mass Lost (mg) vs. Time (min), Coated Samples, [H2O2] = 5.9 mol/L,
[K2C2O4] = 0.150 mol/L, T = 75°C, 300 RPM ......................................................... 55 Figure 5-19. Log plot of Etch Rate vs. Hydrogen Peroxide Concentration for Coated
Samples, [K2C2O4] 0.150 , T = 75°C, 300 RPM ........................................... 56 Figure 5-20. Log plot of Etch Rate vs. Potassium Oxalate Concentration for Coated
Samples, [H2O2] 5.9 , T = 75°C, 300 RPM ................................................... 56 Figure 5-21. Log plot of Etch Rate vs. Hydrogen Peroxide Concentration for Uncoated
Samples, , [K2C2O4] 0.150 , T = 75°C, 300 RPM ......................................... 57 Figure 5-23. Selectivity Based on Rate Laws Obtained at 75°C and 300 RPM ............... 60 Figure 5-24. Change of Selectivity with Respect to Hydrogen Peroxide Concentration at
Constant Potassium Oxalate Concentrations (0.075, 0.150, 0.225 mol/L), T = 75°C................................................................................................................................... 61
Figure 5-25. Change of Selectivity with Respect to Potassium Oxalate Concentration at Constant Hydrogen Peroxide Concentrations (2.9, 5.9, 8.8 mol/L), T = 75°C ......... 62
Figure 5-26. Arrhenius Plot for Coated Samples .............................................................. 62 Figure 5-27. Arrhenius Plot for Uncoated Samples .......................................................... 63 Figure 5-28. Selectivity as a Function of Hydrogen Peroxide Concentration and
Temperature at Fixed Potassium Oxalate Concentration (0.150 mol/L) .................. 64 Figure 5-29. (a) Slice of LS-SVM Model and (b) Slice of Kinetics Model at [K2C2O4] =
0.150 mol/L, T = 75°C .............................................................................................. 65 Figure 8-1. Structure of a Typical Neuron [2] .................................................................. 71 Figure 8-2. An Individual Node (TLU) within a Multi-Layered Feed-Forward Network
[3] .............................................................................................................................. 72 Figure 8-3. Supervised Learning of a Neural Network [4] ............................................... 73
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List of Tables Table 4-1. Factors for Box-Behnken DOE and Their Levels ........................................... 25 Table 4-2. Experimental Conditions for Box-Behnken DOE (Coded Values) ................. 26 Table 4-3. Full Factorial Factors and Levels .................................................................... 26 Table 4-4. Experimental Conditions for Full Factorial DOE (Coded Values) ................. 27 Table 4-5. Experimental Conditions Used for Surrogate Modeling ................................. 28 Table 4-6. Hydrogen Peroxide Concentrations (mol/L) for Fixed Potassium Oxalate
Concentration Experiments ....................................................................................... 30 Table 4-7. Potassium Oxalate Concentrations (mol/L) for Fixed Hydrogen Peroxide
Concentration Experiments ....................................................................................... 30 Table 5-1. Summary of Results from Box-Behnken DOE ............................................... 43 Table 5-2. Summary of Results from Full Factorial DOE ................................................ 47 Table 5-3. Summary of Seed Data Used for Surrogate Modeling .................................... 48 Table 5-4. Summary of All Calculated Reaction Orders .................................................. 58 Table 5-5. Summary of Calculated kUncoated and kCoated Values ........................................ 59 Table 8-1. ANOVA Results for Coated Etch Rates (Box-Behnken) ................................ 79 Table 8-2. ANOVA Results for Uncoated Etch Rates (Box-Behnken) ............................ 79 Table 8-3. ANOVA Results for Selectivity (Box-Behnken) ............................................ 79 Table 8-4. ANOVA Results for Coated Etch Rates (Full Factorial) ................................ 80 Table 8-5. ANOVA Results for Uncoated Etch Rates (Full Factorial) ............................ 80 Table 8-6. ANOVA Results for Selectivity (Full Factorial) ............................................. 80
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Abstract Titanium aluminum nitride (TiAlN) is a type of erosion resistant ceramic coating
that is applied to metal parts subject to high wear environments. Adding this
coating helps protect the underlying substrate from these adverse conditions.
Sometimes the coating layer must be removed and a new layer re-applied. The
overarching goal of this project is to successfully remove the TiAlN coating from
titanium alloy substrates through wet chemical etching. In meeting this goal, the
following objectives must be met: the process must be fast, selective (i.e. does not
adversely affect the underlying substrate), operate isothermally, and make use of
chemicals that are environmentally friendly. A combination of hydrogen peroxide,
potassium oxalate, and ethylenediaaminetetracetic acid (EDTA) was found to
accomplish the stated objectives. Hydrogen peroxide and potassium oxalate are
responsible for removing the coating and producing titanium metal ions in
solution. The role of EDTA is to form coordination complexes with these metal
ions so as to reduce their reactivity with hydrogen peroxide in solution. The
etching process was optimized for selectivity. A kinetic model was built using a
modified differential technique and Arrhenius plots. It was determined that
selectivity increases with increasing temperature and potassium oxalate
concentration while it decreases with increasing hydrogen peroxide concentration.
Sensitivity analysis shows that selectivity is much more prone to change with
changing hydrogen peroxide concentration. Surrogate modeling using a Least
Squares-Support Vector Machine model confirms the trends predicted by the
kinetic model except that selectivity seems to peak when varying potassium
oxalate concentration.
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Abrégé Titanium aluminum nitride (TiAlN) est un type de revêtement céramique résistant
à l'érosion qui est appliqué à des pièces métalliques soumises à des
environnements à forte usure. L'ajout de ce revêtement permet de protéger le
substrat de ces conditions défavorables. Parfois, la couche de revêtement doit être
retiré et une nouvelle couche réappliqué. L'objectif principal de ce projet est de
réussir à enlever le revêtement TiAlN à partir de substrats en alliage de titane par
‘wet chemical etching’. Pour atteindre cet objectif, les objectifs suivants doivent
être atteints: le processus doit être rapide, sélective (c'est à dire ne pas nuire au
substrat titanium), de s’opérer dans une manière isotherme, et faire usage de
produits chimiques qui sont respectueux de l'environnement. Une combinaison de
hydrogen peroxide, potassium oxalate et de l'acide ethylenediaaminetetracetic
(EDTA) a été trouvé pour atteindre les objectifs. Hydrogen peroxide et de
potassium oxalate sont responsables de l'élimination du revêtement et produire
des ions métalliques de titane en solution. Le rôle de l'EDTA est de former des
complexes de coordination avec ces ions métalliques de manière à réduire leur
réactivité avec le hydrogen peroxide en solution. Le processus a été optimisé
pour la sélectivité. Un modèle cinétique a été construit en utilisant une méthode
différentielle modifiée et des parcelles d'Arrhenius. Il a été déterminé que la
sélectivité augmente avec la température et la concentration de potassium oxalate
alors qu'il diminue quand la concentration de hydrogen peroxide augmente.
L'analyse de sensibilité montre que la sélectivité est beaucoup plus enclin à
changer avec la concentration de hydrogen peroxide. Modélisation de substitution
(Surrogate Modeling) en utilisant un modèle Least Squares-Support Vector
Machine confirme les tendances prédites par le modèle cinétique, sauf que la
sélectivité semble culminer en variant la concentration d'oxalate de potassium.
3
1 Introduction Erosion resistant coatings (coatings) are applied to metal parts such as tools and
engine blades that are subjected to conditions that cause wear and erosion. Adding
this ceramic layer is advantageous as it is expected that this layer will increase the
working life of the part. Examples of erosion resistant coatings include titanium
nitride (TiN) and titanium aluminum nitride (TiAlN). Of those two, TiAlN seems
to be preferable in terms of superior mechanical properties (Section 3.1).
The applied ceramic coating has to be replaced after long operation times as it is
also eventually eroded. In addition, coating procedures sometimes produce parts
that do not meet quality standards. In these cases, the coating must be completely
removed before a subsequent re-application. The stripping method must be
relatively fast, have high selectivity for the coating as opposed to the underlying
substrate and should be friendly to the environment. There exist several methods
to remove this coating such as plasma etching, laser ablation, and wet chemical
etching. The present research is part of a collaborative project with a research
group at Ecole Polytechnique in Montreal and several industrial partners. At
Ecole Polytechnique, dry methods such as plasma etching and laser ablation were
studied. At McGill, we study the wet chemical etching of titanium aluminum
nitride deposited on titanium alloy (Ti-6Al-4V) substrates.
This thesis is the continuation of the research conducted by Samuel Bastien from
September 2009-August 2011. His work with hydrogen peroxide/potassium
oxalate formulations is the foundation for the present work. Bastien found that
etch rates increased with increasing temperature and reactant concentrations.
Selectivity was found to increase with increasing temperature and potassium
oxalate concentration, but decreasing hydrogen peroxide concentration. The
present continuation of Bastien’s work involves the in depth study of the reaction
mechanism and kinetics as well as modeling and improving the selectivity.
4
The overarching goal for this project is to develop a process that is fast, selective,
operate isothermally, and be environmentally friendly. A fast removal process is
important for economic considerations. While we want to remove the coating in
an expedient manner, it is equally important to consider the effects of the reactive
mixture on the underlying titanium substrate; thus high selectivity is of equal if
not greater importance for the stripping process. Furthermore, isothermal
operation is important for constant reaction rates and safe operating conditions at
both laboratory and industrial scales. Although many powerful oxidizing agents
(e.g. hydrofluoric acid) exist for the removal, in this work we use hydrogen
peroxide, as is it a relatively benign substance. Using environmentally friendly
materials is also important since waste treatment will be less expensive in
industrial applications. We believe that etching using a combination of hydrogen
peroxide, potassium oxalate, and ethylenediaaminetetracetic acid (EDTA) can
meet all of these goals.
2 Objectives With the overall goals in mind, there are two primary objectives for the
continuation of Samuel Bastien’s work. The first objective is to investigate the
reaction mechanism for this process. By meeting this objective, we can
understand the role hydrogen peroxide and potassium oxalate in the wet chemical
etching process and by extension, exactly how EDTA helps maintain the system
at constant temperature.
The second objective is to optimize the selectivity of the process. This requires
the modeling of both the reaction strictly involving the TiAlN coating (coated
process) and the reaction involving strictly the underlying titanium alloy
(uncoated process). Accomplishing this goal requires building kinetic models
from both traditional chemical reaction engineering and non-conventional
machine learning techniques like surrogate modeling. The derived models will
help us develop a process that is both fast and selective.
5
3 Background and Literature Review In this chapter, some important background and literature references will be
reviewed in order to help place the results and discussion of the present work into
context. First, TiAlN’s apparent superiority over TiN will be addressed. In
Section 3.2, the titanium’s path from existing within the solid TiAlN coating to
solution will be examined. The role of coordination complexes in this work will
also be reviewed in Section 3.2. Finally, a full background on surrogate modeling
will be given in Section 3.3.
3.1 Properties of Titanium-Based Ceramic Coatings Historically, TiN coatings had been the standard in the tooling industry. TiAlN
coatings are a comparatively novel development in coating technology.
Preliminary results by Munz in 1986 showed that TiAlN has comparable
micromechanical properties to TiN while showing an increase in wear resistance
[1]. Figure 3-1 illustrates wear as a function of the number of drilled holes into a
steel sample (34 CrNiMo6) for both TiN coated and TiAlN coated drill bits. It is
clear from the figure that the TiAlN coated drill bit exhibits improved wear
resistance compared to the TiN coated bit since it was able to drill approximately
double (138 vs. 280) the number of holes.
Figure 3-1. Comparison of drilling performance of TiN and TiAlN coated 6 mm drills in 34 CrNiMo6
[1]
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3.2 Reaction Mechanism
3.2.1 The Role of Hydrogen Peroxide in Wet Chemical Etching It has been shown by Bonacchi, et al (2002) that a mixture of hydrogen peroxide
and potassium oxalate can successfully remove TiAlN coatings from metal
substrates [2]. As mentioned before, Bastien showed that the etch rates of both the
coating (TiAlN) and the substrate (Ti) are both positively correlated to hydrogen
peroxide and potassium oxalate concentrations. Selectivity, (Section 4.4.1)
seemed to be negatively correlated to hydrogen peroxide concentration while
being positively correlated to potassium oxalate concentration [3]. His
preliminary experiments showed that a mixture consisting solely of hydrogen
peroxide was not able to remove the coating. Similarly, potassium oxalate on its
own was not able to effectively remove the coating. It is believed that the
presence of the oxalate activates the hydrogen peroxide by the formation of a
peroxyacid (RC(O)OOH) [4]. The mechanism for the production of a peroxyacid
from hydrogen peroxide is as follows:
Figure 3-2. Addition/Elimination Mechanism for Nucleophilic Displacements at Carbonyl Carbon by
Hydrogen Peroxide Species [5]
The reaction illustrated in Figure 3-2 requires a strong acid catalyst in order to
ensure an adequate reaction rate. However, when an organic acid reactant itself is
particularly strong (formic or trifluoroperacetic), an additional acid catalyst is not
7
required since the organic acids themselves are able to catalyze the reaction [6].
Acids with similar pKa’s would also be able to self-catalyze the reaction. The
pKa’s of formic acid and trifluoroacetic acid are 3.75 and 0.50, respectively while
that of oxalic acid is 1.25 [7]. This could explain why hydrogen peroxide and the
oxalate group from potassium oxalate are able to etch samples without an
additional acid catalyst. It should also be noted that oxalate at slightly acidic pH
above 4 exists as a divalent ion [8]. As a result, using a potassium oxalate at an
acidic pH above 4 would be the same as using oxalic acid since the divalent
oxalate anion would be present in either case and would serve as the starting
material for the formation of a peroxy acid.
3.2.2 Tracking Titanium From Coating to Solution The coating to be removed from a titanium substrate consists of titanium,
aluminum, and nitrogen. Of these elements, it is important to track the path of
titanium from its location in the solid coating to in the solution as will be shown
in this section. Bonacchi, et al. showed that oxidation of Ti and Al takes place at
the surface, producing their respective oxides [2]. The overall oxidation of TiAlN
coating proceeds as follows [9]:
(3-1)
where x is the atomic fraction of Al in the coating and y is the nitrogen content of
the coating. It has also been shown in literature that metal oxides can be
reductively dissolved by the oxalate ion in acidic conditions [8]. If titanium
dioxide were reduced by the oxalate anion, the oxidation state of titanium would
go from +4 to +3. Titanium in this oxidation state is readily oxidized to titanium
(IV) [10]. In order for the reductive dissolution to occur, the oxalate anion is
oxidized to form carbon dioxide [11]:
(3-2)
8
It can be surmised that potassium oxalate reacts in a similar way in acidic
environments.
In the presence of titanium ions in their lower oxidation state (Ti3+), hydrogen
peroxide may play a role in the following manner [12]:
(3-3)
In this two-step process, titanium (III) is oxidized by hydrogen peroxide through a
free radical mechanism, producing titanium (IV) and hydroxide ions. In addition,
it has been shown that when the ratio of hydrogen peroxide to titanium (III) is
high, hydrogen peroxide itself is attacked by the OH radical [13]:
(3-4)
Titanium (IV) can react with hydrogen peroxide to form pertitanic acid [14]:
(3-5)
Pertitanic acid has a distinct yellow colour that can easily be observed visually.
Titanium (IV) can also form complexes with the radicals shown in Equation 3-4,
thereby stabilizing the radicals [13].
Hydrogen peroxide can also decompose spontaneously and exothermically
( , producing water and evolving oxygen gas [15]. This
disproportionation reaction occurs as follows:
(3-6)
3.2.3 Formation of Coordination Complexes In the previous section, a free radical mechanism for the exothermic
decomposition of hydrogen peroxide was shown. This reaction is undesirable,
9
because such a reaction may cause an increase in the temperature of the reacting
mixture. Binding the titanium cations in coordination complexes may effectively
prevent them from participating in these reactions (Equation 3-3); a study in
coordination complexes was done
Coordination complexes are the result of ionic interactions between a Lewis base
(ligand) and Lewis acid (acceptor) [16]. Titanium and aluminum ions are known
as type-a acceptors and form the most stable complexes with nitrogen, oxygen, or
fluorine atoms. A coordination number of a metal ion is defined to be the number
of donor atoms that surround it. Most transition metals have a coordination
number of 6. Such a coordination number leads to the formation of octahedral-
type bond geometry with the ligand [17]. Ethylenediaminetetraacetic acid
(EDTA) is therefore a useful ligand for chelating transition metal ions. EDTA,
when a fully ionized anion, has four oxygen and two nitrogen donor atoms that
would wrap around a metal ion producing a pseudo octahedral complex as shown
in Figure 3-3. Note how the donating atoms will wrap around the metal, forming
the octahedral structure.
Figure 3-3. Coordination Complex Consisting of a Ligand (EDTA) and a Metal Ion (M). Adapted from
[18]
As mentioned in Section 3.2.2 pertitanic acid is formed from titanium (IV) ions
and hydrogen peroxide. Kharkar and Patel showed that when in the presence of
excess hydrogen peroxide and oxalate anions, pertitanic acid can form a peroxy
titanium oxalate complex of the following structure [19]:
10
Figure 3-4. Structure of a Peroxy Titanium Oxalate Complex
As we can see from Figure 3-4, the coordination number of this complex is 6, too.
The authors proposed other coordination structures, but this one was deemed to be
most likely due to the fact that its coordination number is favorable with transition
metal ions. This complex is said to give off a distinct red-orange color when in
solution [14].
3.3 Background on Surrogate Modeling Within projects where resources are limited, obtaining a detailed understanding of
the experimental space over a relatively broad range of conditions may be
difficult. It is for this reason that surrogate modeling (SUMO) exists. The
software developed by Gorissen, et al. was developed in order to provide the user
a flexible and robust platform to approximate outputs when physically obtaining
these outputs is expensive or time consuming [20]. Given a seed data set derived
from an experimental design, SUMO is able to generate ‘simulated’ data based on
various parameters set by the user.
The control flow of SUMO is shown below in Figure 3-7:
11
Figure 3-5. SUMO Control Flow [20]
Given a physical data set and candidate sample points, simulations are performed
where the model and its parameters predict output values based on the patterns
found in the data set. These models are assessed based on an error measurement
equation set by the user. If the model reaches the target specification, then it is
returned. If the model does not reach the target, then the process is repeated using
different model parameters. A closer examination of the generate/update/assess
loop in Figure 3-5 will shed some light on what is actually happening.
12
Figure 3-6. SUMO Control Flow in Detail [20]
Experimental data are sent to the model “factory”. The purpose of the model
factory will be explained later. The user has already selected a model type (i.e.
Kriging, Artificial Neural Network, or Least-Squares Support Vector Machine) as
described in Section 3.3.1. In the first iteration, the model parameters are at some
default value. Simulated results are generated using candidate sample points in the
experimental space. This model is tested against the physical data points to
evaluate its accuracy. Based on the fitness of the model, its parameters are
optimized based on an algorithm that the user also selects. This optimization
occurs within the model builder. These new parameters are sent to the model
factory. The purpose of the model factory is to maintain separation between the
model and the model builder. This separation allows the programmer to design
model builders and model types independently so that one model builder could be
used for multiple model types.
13
3.3.1 Model Types
3.3.1.1 Interpolation of Spatial Data (Kriging Models) Kriging is a method of spatial prediction generally used in the mining industry. In
essence, a Kriging model takes a weighted average of neighbouring points in
order to estimate the value at a location where the value is not known. These
weights are the parameters to be optimized by the model builder. The best linear
prediction, i.e. the optimum weighting, is obtained when the mean square error of
the prediction is minimized [21]. A more rigorous approach is presented in the
Appendix A1.
3.3.1.2 Artificial Neural Networks (ANNs) The purpose of an artificial neural network is to recognize patterns within data
sets. Artificial neural networks have their roots in life sciences. Brains recognize
and analyse patterns through neural networks. With an artificial neural network,
one tries to replicate the networks observed in nature [22]. Examining this
biological process is a good place to start when describing the logic behind an
ANN (Appendix A2).
The digital analogue to this biological process is called a multi-layered feed
forward network. There are two outer layers within this network; the layers that
we can control. These are the input (Ni) and output (No) layers. For this project,
the input layer consists of the hydrogen peroxide concentration and the potassium
oxalate concentration and the output layer is selectivity. Between these two layers
there are an unknown number of hidden layers (Nh,i) that help build a relationship
between the input layer and the output layer. Figure 3-7 illustrates the way the
input layer and the output layer is connected.
14
Figure 3-7. A Multi-Layered Feedforward Network [23]
The premise of this type of network is that the output from any node, a.k.a.
threshold logic unit, at one layer is fed forward to the next layer. An output cannot
stay within the same layer and must move to the next, i.e. Nh,i has outputs that
feed only to Nh,i+1. One differentiation between artificial and actual neural
networks is that the connections between nodes have weights associated to them.
If the sum of these signals multiplied by their associated weights crosses a certain
threshold, the node will send out a signal to the nodes to which it is connected.
For more information on how each individual node works and how an ANN
“teaches itself,” refer to Appendix A2.
3.3.1.3 Least Squares – Support Vector Machine (LS-SVM) Like a neural network, a support vector machine is also a pattern recognition
model. Unlike the neural network, however, there is no system of nodes and
layers such as those shown in Figure 3-7. A support vector machine is a type of
linear classifier [24]. In other words, the data is separated into two sub-classes.
Ideally these two classes will be completely separable and distinct from one
another, but this is rarely the case in the real world. The purpose of a support
vector machine is to generate a hyperplane that would maximize the distance
between said hyperplane and the closest data points from either subclass. An
example of this separation is shown in Figure 3-8.
15
Figure 3-8. A Hyperplane Separating Two Classes of Data [24]
For this project, a least-squares support vector machine (LS-SVM) was used in
favour of a traditional SVM. The major difference between the two model types is
that an LS-SVM requires the solving of a set of linear equations while a
traditional SVM requires convex quadratic programming, making LS-SVM easier
to run.
3.3.2 Model Evaluation There are multiple methods to evaluate a model’s accuracy. In the present work,
the root relative squared error was used. A root relative squared error takes the
error of the projected value of a case versus its target value and compares it to the
error that would be generated if the simplest case were to be taken (the average).
This is illustrated by the following equation.
(3-7)
The value predicted (Pij) by the model in iteration i for experimental condition j
(e.g. 2.9 M hydrogen peroxide and 0.150 M potassium oxalate) is compared
against the physically obtained value at the same condition (Tj). This value is then
divided by the error that would be observed by the simplest predictor possible: the
arithmetic mean of the results from n experimental conditions . In theory, a
root relative squared error of 0 would be ideal, as it would imply that the
16
predicted values match the physically obtained values exactly. A root relative
squared error of greater than 1 would be undesirable; as this would imply that the
model is worse at predicting data than just the average of all the physically
obtained data points.
3.3.3 Model Optimization (Genetic Algorithm) The method for model parameter optimization is the genetic algorithm based on
Darwin’s theory of evolution (Appendix A3). The following figure provides a
visual look at what the genetic algorithm does [25].
Figure 3-9. The Genetic Algorithm Flowchart [25]
We start with model parameters at some default value and we want to use the
genetic algorithm to optimize these parameters. An initial “population” of random
values is created and evaluated for their fitness. The ones that seem to be best
17
within the population are pooled. These candidates are then mated, i.e. their
binary codes are crossed over. If the optimal solution is found, then the process
stops. If not, then these offspring are the evaluated for their fitness and the cycle
continues until an optimal solution is found. The primary advantage of crossing
over is that the good qualities of both “parents” can be sent to their offspring,
thereby increasing the likelihood of obtaining an optimal solution.
18
4 Methodology
4.1 Experimental Samples and Sample Holders
4.1.1 Flat Sample Holder Our industrial partners sent flat titanium alloy samples coated with TiAlN (coated
samples) and uncoated titanium alloy (Ti-6Al-4V) samples to us. Samples were
coated on both sides. In order to keep these samples stationary within the reactor,
a polytetrafluoroethylene (PTFE) sample holder was designed by Sam Bastien [3]
for ease of use and to ensure minimal fluid flow obstruction within the reactor.
Figure 4-1 shows a sample holder (white) with an uncoated flat specimen.
Figure 4-1. Sample Holder for Flat Specimens
4.1.2 Sample Holder for Tension/Fatigue Samples Samples for tension and fatigue testing were not flat. Rather, they were cylindrical
in shape and were threaded on either end. While the middle portion of these
samples was coated, the threaded portions were not. In order to accommodate this
sample geometry, a new sample holder was designed in January 2012. A circular
sample “wheel” was designed so that multiple samples could be etched
simultaneously. This was done for both timesaving and quality control reasons.
19
Figure 4-2. Sample Wheel to Hold Tension and Fatigue Samples
Figure 4-2 shows the sample wheel used to hold up to eight samples. Each hole on
the wheel was threaded so that samples could be screwed into place. The opposite
threaded end of the sample was topped with a threaded PTFE cap. In order help
protect the uncoated threads from exposure to the reactive mixture, the threaded
portions of each sample was first covered with PTFE tape.
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&Figure 4-3. Beaker Heater Experimental Set-Up
4.3 Sample Preparation and Experimental Runs In this section, the methods employed to clean and weigh experimental samples
before and after any etching experiment will be reviewed. In addition, a typical
experimental run will be described in Section 4.3.2.
21
4.3.1 Sample Preparation Samples were cleaned before and after every etching experiment. The sample was
first rinsed under tap water and soap. The samples were then rinsed with acetone
so as to remove any water insoluble impurities existing on the surface of the
sample. Finally the samples were rinsed with reverse osmosis water. The samples
were then dried in an oven at 80°C for three hours. After the drying procedure,
samples were weighed using an electronic balance accurate up to 0.1 mg. Samples
were ultimately placed in plastic sealable bags for storage.
4.3.2 Experimental Runs Given a fixed solution volume of 750 mL, required molar concentration, and
assuming that the density of hydrogen peroxide is 1 g/L, the required volume of a
50% W/W stock solution can be calculated. This calculated volume of stock
solution was added to an appropriate amount of reverse osmosis water such that
the total volume always equaled 750 mL. The required amounts of potassium
oxalate and EDTA powders were obtained using an electronic balance accurate up
to 1 mg. The solution was then poured into a 1 L beaker.
The beaker containing the etching solution was first pre-heated on a hot plate up
to the reaction temperature. Once the desired temperature was reached, the beaker
was transferred to the apparatus as indicated in Figure 4-3 and a pH probe was
then inserted in order to obtain an initial pH reading. A 2 mL sample was drawn
from the solution for the eventual quantification of the hydrogen peroxide
concentration (Section 4.4.2.1). The experimental sample was then inserted into
the etching solution as shown in Figure 4-3. Over the course of the experimental
run, temperature was monitored. Depending on the type of experiment, 2 mL
hydrogen peroxide samples were either taken at regular intervals (Section 5.3) or
simply at the end of the experiment (all other sections). At the end of the
experiment, the sample was removed and rinsed thoroughly with reverse osmosis
water. The sample was then placed in storage. Once all replicates for a particular
experimental condition were completed, all relevant samples were taken from
storage and cleaned, dried, and weighed in the method described in Section 4.3.1.
22
4.4 Analytical Methods
4.4.1 Calculating Etch Rates and Selectivity Etching experiments were run at a variety of different ranges of reactant
concentration and temperature. The etching rate for coated and uncoated samples
was defined to be the amount of mass lost from the sample per unit area, per unit
time ( ). The lost mass was obtained by the weight difference between the
cleaned and dried samples before and after each etching experiment. Since the
hydrogen peroxide and potassium oxalate in solution were in large excess
compared to the amount of coating, the etching rate is considered constant over
the course of the reaction. All of the mass lost from coated samples was attributed
to the coating, i.e. none of the underlying substrate was removed as care was
taken to make sure that the reaction time was short enough.
The selectivity (S) is defined to be the ratio between the etch rate obtained under
given conditions with a coated sample (rC) and the etch rate obtained under the
same conditions with an uncoated sample solely comprising titanium alloy (rU).
(4-1)
4.4.2 Measurement of Hydrogen Peroxide Concentration
4.4.2.1 Quantification Method Hydrogen Peroxide reacts with excess Potassium Iodide (KI) in the presence of an
ammonium molybdate catalyst ((NH4)6Mo7O24·4H2O) to produce triiodide ions
(I3-). These ions can then be subsequently titrated with a standard thiosulfate
solution (S2O32-). Five mL of a solution consisting of 1.4x10-4M ammonium
molybdate and concentrated sulfuric acid was mixed in an Erlenmeyer flask with
0.2 g of KI. A small volume (0.1 mL) of hydrogen peroxide drawn using a
micropipette from the reactive mixture was then weighed and placed into the flask
yielding a distinctly brown solution. Sodium thiosulfate of known normality (N)
23
was then added drop wise using an automated titrator until the solution was clear
and exhibited no colour. Given the volume of thiosulfate (V) and the mass of
hydrogen peroxide solution (W) added to the Erlenmeyer flask, the experimental
concentration of hydrogen peroxide was calculated from:
(4-2)
4.4.2.2 Hydrogen Peroxide Sample Collection Method Due to the time requirements of a titration, it was no longer possible to take a
sample, run it immediately, and return to the etching experiment for the next time
point. Taking hydrogen peroxide samples periodically over the course of an
etching experiment required a change to the established method. In addition, the
fact that samples are taken at temperatures significantly above room temperature
meant that there was a risk that samples taken early on during the experiment
would continue to react inside the glass vial, thereby returning an inaccurately low
concentration value once titrated. Two different sample-taking methods were
tested and compared to a reference method:
1. Reference Method: Taking a series hydrogen peroxide samples over the
course of the etching experiment and placing them in glass vials. These
samples were stored at room temperature until they were all titrated after
the end of an etching experiment.
2. Iced Method: Same as the reference method, but samples were stored in
an ice bath instead of at room temperature. It was assumed that cooling
down the samples would help mitigate the degradation of hydrogen
peroxide inside the glass vial.
3. Pre-Mix Method: Sodium thiosulfate and potassium iodide were mixed
and placed into Erlenmeyer flasks before the start of an etching
experiment. It was assumed that immersing the hydrogen peroxide sample
in this pre-made solution would quench any reaction involving hydrogen
peroxide.
24
Figure 4-4 shows the percent difference between the reference method and the
iced method for two separate etching experiments. Storing the samples in ice
seems to have an effect on stabilizing hydrogen peroxide.
Figure 4-4. Percent Difference between Reference Method and Iced Method for Two Etching
Experiments ([H2O2]i =5.9 mol/L, [K2C2O4] = 0.225 mol/L, Ti = 75!C, 300 RPM)
Figure 4-5 illustrates the percent difference between reference method and pre-
mix method samples from two identical etching experiments. As with the iced
samples, the general trend again is that storing the hydrogen peroxide samples at
room temperature seems to cause the hydrogen peroxide concentration to be lower
when compared to an alternative method. Both alternatives produced similar
results, and the pre-mix method was chosen to be added to the standard operating
procedure for hydrogen peroxide concentration measurements.
25
Figure 4-5. Percent Difference between Reference Method and Pre-Mix Method for Two Etching
Experiments ([H2O2]i =5.9 mol/L, [K2C2O4] = 0.225 mol/L, Ti = 75!C, 300 RPM)
4.5 Experimental Design
4.5.1 Box-Behnken Design of Experiment A three-level, three-factor Box-Behnken design of experiment (DOE) was used in
order to examine the response surface. The three responses tested for were coated
etch rate, uncoated etch rate, and selectivity. The three factors were: hydrogen
peroxide concentration, potassium oxalate concentration, and EDTA
concentration. Table 4-1. Factors for Box-Behnken DOE and Their Levels
Factors
Levels Hydrogen Peroxide Concentration (mol/L)
Potassium Oxalate Concentration (mol/L)
EDTA Concentration (mol/L)
-1 2.9 0.075 2.70E-03 0 5.9 0.150 5.00E-03
+1 8.84 0.225 6.80E-03
Since both coated and uncoated responses were to be tested, the experiments
outlined in the following table had to be run twice: once with a coated sample and
once with an uncoated sample. The conditions in Table 4-2 are presented with
their coded values for readability. All experiments were conducted at 75!C and
agitated at 300 RPM.
26
Table 4-2. Experimental Conditions for Box-Behnken DOE (Coded Values)
Experiment ID
Hydrogen Peroxide Concentration (mol/L)
Potassium Oxalate Concentration (mol/L)
EDTA Concentration (mol/L)
1 -1 -1 0 2 +1 -1 0 3 -1 +1 0 4 +1 +1 0 5 -1 0 -1 6 +1 0 -1 7 -1 0 +1 8 +1 0 +1 9 0 -1 -1
10 0 +1 -1 11 0 -1 +1 12 0 +1 +1 13 0 0 0 14 0 0 0 15 0 0 0
4.5.2 Full Factorial Design of Experiment Following the Box-Behnken DOE, a two-level, two-factor Full Factorial DOE
was completed based on the results from the Box-Behnken experiments. As with
the Box-Behnken DOE, the three responses were coated etch rate, uncoated etch
rate, and selectivity. The two factors were hydrogen peroxide and potassium
oxalate concentration. Table 4-3. Full Factorial Factors and Levels
The experimental conditions as required by the Full Factorial DOE are
summarized in Table 4-4. Again, each condition was run for both coated and
Factors Level Hydrogen Peroxide
Concentration (mol/L) Potassium Oxalate Concentration (mol/L)
-1 2.9 0.100 +1 4.4 0.150
27
uncoated samples. Since the Full Factorial experiments are a direct consequence
of the results from the Box-Behnken DOE, the Experiment ID numbering
continues from the end of the Box-Behnken experiments. Table 4-4. Experimental Conditions for Full Factorial DOE (Coded Values)
Experiment ID
Hydrogen Peroxide Concentration (mol/L)
Potassium Oxalate Concentration (mol/L)
16 -1 -1
-1 -1
17 +1 -1
+1 -1
18 -1 +1
-1 +1
19 +1 +1
+1 +1
All experiments were run at 75°C, 300 RPM, and a constant concentration of
EDTA of 2.7x10-3 mol/L. As implied in Table 4-4, all experiments were run in
duplicate.
4.6 Surrogate Modeling (Implementation) Implementing SUMO on a Matlab platform requires the creation or modification
of three files. Firstly a file telling SUMO what we are running and from where to
read the data must be created: the data file (prepared by user). The data file will
read the experimental data from a file containing strictly the experimental
conditions and their results. A physical experimental data set comprising a Box-
Behnken as well as a factorial experimental design was used (Table 4-5). As
such, all data was obtained at 75°C and 300 RPM.
28
Table 4-5. Experimental Conditions Used for Surrogate Modeling
Hydrogen Peroxide Concentration (mol/L)
Potassium Oxalate Concentration (mol/L)
2.9 0.075 2.9 0.225 2.9 0.150 2.9 0.100 4.4 0.100 4.4 0.150 5.9 0.075 5.9 0.225 5.9 0.150 8.8 0.075 8.8 0.225 8.8 0.150
The default file (came with software) is essentially the “control centre” of SUMO.
Here, changes are made to all relevant settings such as model type, model
optimization, error measurement, sample selection algorithms, and any other
aspect that could be changed within the SUMO framework. Once all of these files
are configured properly, running SUMO from Matlab requires simply typing ‘go’
within the Command Window. Copies of all three files are included within
Appendix A4. The model types that were used were: Kriging, Artificial Neural
Network, and the Least Squares-Support Vector Machine. These models were
optimized using a genetic algorithm and evaluated using the root relative squared
error formula. Further information on the different model type, optimizer, and
evaluator is available in Section 3.3.
The results from experiments conducted at the conditions outlined in Table 4-5
were inputted into each of the four models and an optimal point was found. The
concentration ranges for potassium oxalate and hydrogen peroxide for this data set
is the same as the range outlined in the previous section. The conditions. The
29
optimal point was to be physically tested and its result subsequently added to the
existing data set. This new data set was then run with the same three model types
and a new optimal point was found. This iterative process continued until the new
optimum was within the same region as the previous one. The reason for using
more than one model type was to investigate if all model types would converge to
one unique optimum within the experimental space.
4.7 Methodology for Kinetics Model
4.7.1 Determination of Etching Reaction Rate Laws From previous experiments, it was determined that etch rates from both coated
and uncoated samples are directly related to the concentrations of both hydrogen
peroxide and potassium oxalate in solution. As a result, the following two rate
laws are proposed.
(4-3)
(4-4)
Exponential factors α, β, γ, and θ are unknown. The natural logarithm was
applied to both equations 4-3 and 4-4. The exponential factors were then solved
by running experiments as outlined in Table 4-6 and Table 4-7. The conditions
in each table were run in triplicate for both coated and uncoated samples. All
experiments were conducted at 75 °C and at an agitation rate of 300 RPM for
25 minutes.
30
Table 4-6. Hydrogen Peroxide Concentrations (mol/L) for Fixed Potassium Oxalate Concentration Experiments
[H2O2]
[K2C2O4] 0.150
2.9 4.4 5.9 8.8
Table 4-7. Potassium Oxalate Concentrations (mol/L) for Fixed Hydrogen Peroxide Concentration Experiments
[K2C2O4]
[H2O2] 5.9
0.075 0.100 0.150 0.225
4.7.2 Determination of Temperature Dependence We assume that the reaction rate constants for both the uncoated and coated
etching processes, kU and kC respectively follow the Arrhenius relationship.
(4-5)
Where A is the pre-exponential factor, Ea is the activation for the reaction, R is the
universal gas constant, and T is the temperature of the system. Experiments were
run with temperatures ranging from 55°C to 85°C with the hydrogen peroxide
concentration fixed at 2.9 and the potassium oxalate concentration fixed at
0.150 . Experiments were run in duplicate for both coated and uncoated
samples. All experiments were run at 300 RPM. Data from these experiments
were used to create Arrhenius plots, which were then used to evaluate temperature
dependence.
31
5 Results and Discussion
5.1 Verification of Well-Mixing Two sets of preliminary experiments were performed to determine if the reactor
operated under perfectly mixed conditions and if the rotational speed of the
impeller had an effect on the etching rate.
In the first set, hydrogen peroxide samples were taken at three different locations
within the reactor after the end of the experiment:
1. Near the coated sample
2. Near the impeller
3. A location diametrically opposed to the coated sample.
Two experiments were performed at stir speeds of 50 and 450 RPM. All
experiments were completed at 75°C with initial concentrations of 5.9 mol/L
hydrogen peroxide and 0.150 mol/L potassium oxalate. Figure 5-1 illustrates how
the concentration of hydrogen peroxide varied in different locations of the reactor.
Locations 2 and 3 were compared to that of location 1 (C1). At both high and low
speeds, there is very little variability in the hydrogen peroxide concentration at the
different locations indicating that there are no observable concentration gradients
within the reactor.
32
Figure 5-1. Concentration of Hydrogen Peroxide in Different Locations of the Reactor Relative to the Concentration Obtained at Location 1 (C1) (T = 75!C [H2O2]i = 5.9 mol/L, [K2C2O4]i = 0.150 mol/L)
The second set of experiments investigated the effect of the rotation speed of the
impeller on etch rate. All experiments were performed at the same conditions as
the first set of experiments as outlined above. The three tested mixing rates were
50, 300, and 450 RPM. If the etch rate varies greatly with mixing speed, it
indicates that the external mass transfer coefficient in the system is increasing as
well. This result is indicative of a system under mass transfer control rather than
kinetic control. Figure 5-2, shows that the etch rate does not vary significantly
over different mixing speeds.
33
Figure 5-2. The Effect of RPM Changes on the Etch Rate of the Coating ([H2O2]i =5.9 mol/L, [K2C2O4]
= 0.150 mol/L, [EDTA] = 5e-3 mol/L, Ti = 75!C)
It was observed that the etch rates obtained at 50 RPM were slightly higher than
those obtained at higher speeds. One-way analysis-of-variance on this data set
with a null hypothesis that rotation speed will not affect etch rate produced a p-
value of 0.17. If we were to set the critical p-value at 0.05, the null hypothesis is
not rejected. Therefore, we cannot conclude that the mixing speed affects etch
rate, and as a consequence our system is under kinetic control.
5.2 Selecting a Carboxylic Salt for Etching Experiments In Section 3.2.1, a mechanism for the formation of peroxyacids from hydrogen
peroxide and carboxylic acids/salts was introduced. Three carboxylic salts with
varying structures were chosen for testing: potassium formate, potassium acetate,
and potassium oxalate. As Figure 5-3 illustrates, potassium formate (KCO2H) and
potassium acetate (KCH3CO2) produce etch rates that are significantly lower than
that of potassium oxalate at the same initial concentration. The etch rate with
potassium acetate is lower compared to that of potassium formate. This result can
be explained by the fact that the acetate anion has an extra methyl group while
such a relatively bulky group does not hinder the formate anion.
34
Potassium oxalate, on the other hand, at the same concentration produced a much
higher etch rate than the other two. It is postulated that the extra carboxylic
functional group oxalate group may be the cause of higher observed etch rates. In
order to test this, the initial concentration of potassium oxalate was reduced by
one half to 0.113 M in order to make the molarity of the carboxylic groups equal
to that of the formate and acetate salts. The potassium oxalate salt produced
higher etch rates despite the fact that its initial concentration was half of those of
the formate and acetate salts. Based on the results from these experiments, it was
verified that potassium oxalate is the preferred carboxylic salt for etching
experiments.
Figure 5-3. Etch Rates with Different Carboxylic Salts (T = 75 oC, [H2O2] = 2.9 M, 300 RPM, 20
minutes, (Potassium acetate is not visible because of very low values)
5.3 Hydrogen Peroxide Stability and the Effect of EDTA
5.3.1 Etching Experiments with Potassium Oxalate and Hydrogen Peroxide
With potassium oxalate and hydrogen peroxide selected as the preferred reactants
as outlined in the previous section, the next step was to conduct ‘full-etch’
experiments using hydrogen peroxide (5.9 mol/L) and potassium oxalate (0.225
mol/L) to remove all of the coating from a given sample. Although this
formulation enabled the complete removal of the coating, the temperature of the
35
reacting solution was not stable within the reactor and it kept increasing as shown
in Figure 5-4. .
Figure 5-4. Temperature Increase Over the Course of a Full-Etch Experiment ([H2O2]i = 5.9 M,
[K2C2O4] = 0.225 M, 300 RPM)
From an initial temperature of 70!C, the etching process results in an increase of
almost 30!C. The experiment was stopped just before the reactor temperature
reached 100!C for safety reasons. Because there were no other contributing
factors to temperature increase, it was evident that there was an exothermic
reaction occurring within the reactor.
It was not clear from the temperature data only whether the exothermic reaction
was a direct result of the oxidation of the coating on the sample or a reaction
occurring in solution. In order to determine the origin of the exothermic reaction,
the sample was removed from the reactor at a set time and left out of the reactor
for 15 minutes. The temperature within the reactor continued to increase even
though the sample – and hence the TiAlN coating – was absent from the system.
This indicated that the reaction that was causing the temperature increases was
36
occurring as a homogenous reaction within the solution and not from the
heterogeneous coating removal process.
One of the possible reasons for this increase in temperature is that hydrogen
peroxide is being reduced by titanium ions in solution as outlined in Section 3.2.2.
Figure 5-5 illustrates the decomposition of hydrogen peroxide over time. The
concentrations have been normalized in order to illustrate better the magnitude of
hydrogen peroxide decomposition. Relative to the amount of coating on a sample,
the amount of hydrogen peroxide within the system is in great excess. A
calculation for this is shown in the appendix. The concentration of hydrogen
peroxide should decrease in the order of less than 5% of its initial concentration if
all the TiALN coating were to be removed; however it is clear from Figure 5-5
that the decrease in hydrogen peroxide concentration is much greater than 5%.
Over the course of the experiment, the hydrogen peroxide concentration decreases
almost 35% from its initial concentration. In addition, the rate of hydrogen
peroxide decomposition increases significantly at the 40-minute mark. From the
30 to 45 minute mark, the hydrogen peroxide concentration decreases at a rate of
0.003 mol/L/min. From the 45 to 65 minute mark, hydrogen peroxide decreases at
an average rate of approximately 0.02 mol/L/min. From 65 minutes onwards, the
rate of decomposition only increases. An inspection of Figure 5-4 shows that the
rate of temperature increase also seems to spike at the 40-minute mark. This
synchronicity indicates that hydrogen peroxide participates in the oxidation of
titanium (III). As mentioned in Section 3.2.2, hydrogen peroxide spontaneously
decomposes in an exothermic process (Equation 3-3). As titanium (III) is oxidized
exothermically, the temperature within the system goes up. This increase in
temperature will then favour both the oxidation of titanium (III) as well as the
spontaneous decomposition of hydrogen peroxide. In this runaway situation
where hydrogen peroxide is being consumed exothermically in two different
ways, a significant decrease in hydrogen peroxide concentration can be expected.
37
Figure 5-5. Average Decomposition of H2O2 (Ti = 70 C, [H2O2]i = 5.9 M, [K2C2O4] = 0.225 M, 300
RPM)
A control group of experiments with 5.9 M hydrogen peroxide and 0.225 M
potassium oxalate in the absence of any coated or uncoated sample showed that
the temperature remains constant at 75OC. These reactant concentrations were
deemed high enough that if there were any decomposition, it would be detectable.
Titanium (III) ions in solution give off a “reddish violet” colour [26]. The
predominant colour observed in solution during these experiments was yellow
with a slight green tinge. This yellowish colour is indicative of the formation of
pertitanic acid from titanium (IV) and hydrogen peroxide (Section 3.2.2). This
indicated that it was indeed the titanium (III) ions in solution that was contributing
to the consumption of hydrogen peroxide while also forming titanium (IV). The
newly formed titanium (IV) then further consumed the hydrogen peroxide to form
pertitanic acid. In Section 3.2.3, the potential of forming a peroxy titanium oxalate
complex was reviewed. The distinctive red-orange color of this complex was not
observed. It is, however, possible that this type of complex is being formed, but at
a dilute concentration such that its color is not visible to the naked eye.
38
5.3.2 The Effect of EDTA on Temperature and Hydrogen Peroxide Stability
In order to prevent the decomposition of hydrogen peroxide, the titanium (III)
ions that are released into solution can be chelated using EDTA. Section 3.2.3
gives information on coordination complexes and why EDTA is a good choice for
transition metal ions like titanium (III). As the role EDTA’s in the process was to
“bind” metal ions, it was added in excess of what was stiochiometrically required
(Appendix A5). The concentration of EDTA used was 6.8 x 10-3 M for all
experiments.
Figure 5-6. Average Temperature Comparison ([H2O2]i = 5.9 M, [K2C2O4] = 0.225 M, 300 RPM)
Figure 5-6 illustrates in the average temperature over time for experimental runs
in the presence and absence of EDTA. Each point is the average reactor
temperature taken at the prescribed time for four identical runs. The addition of
EDTA had a clear effect on the temperature stability within the reactor. Starting
from approximately the 30-minute point and onwards, the two curves start to
diverge. While the rate of temperature increase in the no-EDTA runs gets steadily
39
higher over time, the respective rate for EDTA runs is relatively constant. There
was more variability observed in the no-EDTA runs when compared to runs done
with EDTA because a runaway situation as the one observed in the absence of
EDTA runs is inherently more subject to error than the relatively stable system
seen with EDTA. In both cases, the samples were completely etched of the
coating and while it did take slightly longer by approximately 7 minutes in the
EDTA runs, the overall change in temperature was 6°C as opposed to the 30°C
observed in the no-EDTA runs.
Verifying that EDTA enhanced hydrogen peroxide stability over the course of the
etching was necessary in order to validate the theory that hydrogen peroxide was
reacting in the way proposed in the previous section. Figure 5-7 shows how the
addition of EDTA stabilizes hydrogen peroxide in the system. Each data point is
the average normalized concentration of hydrogen peroxide taken at the
prescribed time for four identical runs. The concentration normalized to the initial
concentration of hydrogen peroxide in the reactor, i.e. 5.9 M while the time is
normalized to the overall run time, i.e. 65 minutes for runs with EDTA and 55
minutes for runs without EDTA. Normalizing the reaction time was done so that
both curves would start and end at the point. In essence, the x-axis describes the
“reaction progress” with 0 being the start of the run and 1 being the point where
the coating is completely removed.
40
Figure 5-7. Effect of EDTA on H2O2 Stability ([H2O2]i = 5.9 M, [K2C2O4] = 0.225 M, Ti = 70!C, 300
RPM)
Experiments completed without EDTA show a sharp decrease in hydrogen
peroxide concentration after a reaction progression of approximately 0.7. At that
identical point in reaction progression, the samples with EDTA produced
hydrogen peroxide concentrations that were not significantly different from the
initial concentration. It was observed that the average hydrogen peroxide
concentration did drop to about 3% from its initial concentration. A slight drop
was expected, however because Hydrogen peroxide is consumed in the etching
process and given the amount of coating on the sample; a 3% drop is reasonable.
5.3.3 Proposed Reaction Mechanism Based on experimental and literary evidence, we propose the following reaction
sequence for Titanium in the wet chemical etching of TiAlN with hydrogen
peroxide and potassium oxalate.
41
Figure 5-8. Reaction Sequence for Titanium in the Wet Chemical Etching of TiAlN with Hydrogen
Peroxide and Potassium Oxalate
We start with TiAlN on the sample. In step 1, the titanium in the coating will be
oxidized to form titanium dioxide (Equation 3- 1). In step 2, titanium dioxide will
be reductively dissolved in the presence of divalent oxalate ions yielding titanium
(III) ions in solution. In this step, oxalate is oxidized to form carbon dioxide
(Equation 3-2). In step 3, titanium (III) ions will decompose hydrogen peroxide
through a free radical mechanism producing titanium (IV) ions (Equation 3-4). In
the presence of hydrogen peroxide, titanium (IV) will react to form the
experimentally observed yellow pertitanic acid in step 4 (Equation 3-5). Pertitanic
acid in the presence of hydrogen peroxide and oxalate can form peroxy titanium
oxalate complexes (step 5). This last step has not been confirmed visually. It is for
this reason that the final step is outlined in red in Figure 5-8.
Based on experimental results, the EDTA is confirmed to help stabilize hydrogen
peroxide in the presence of titanium (III) ions. When EDTA is present in the
system, the etching process will proceed as follows:
42
Figure 5-9. Reaction Sequence of Titanium in the Wet Chemical Etching of TiAlN with Hydrogen
Peroxide and Potassium Oxalate in the Presence of EDTA
Like the sequence proposed in Figure 5-8, TiAlN is oxidized to form titanium
dioxide, which is then reductively dissolved to form titanium (III) ions. The key
difference between the two sequences occurs at step 3. Without EDTA, the
titanium (III) would be oxidized by hydrogen peroxide. In the presence of EDTA,
titanium (III) will form an octahedral or pseudo-octahedral coordination complex
with EDTA, thereby eliminating its role in decomposing hydrogen peroxide. The
presence of EDTA will stabilize the concentration of hydrogen peroxide in the
system as well as keep the reactor temperature controlled at its set point.
5.4 Kinetics and Optimization
5.4.1 Box-Behnken Design of Experiment In Section 4.5.1 the experimental conditions for a three-level, three-variable Box-
Behnken DOE was outlined. The results of this series of experiments are outlined
in the table below.
43
Table 5-1. Summary of Results from Box-Behnken DOE
Experiment ID
Etch Rate Coated (mg/hr/cm2)
Etch Rate Uncoated (mg/hr/cm2)
Selectivity
1 6.23 0.67 9.36 2 8.67 2.09 4.16 3 6.13 0.71 8.67 4 19.08 5.23 3.65 5 7.69 0.66 11.72 6 15.09 2.73 5.53 7 5.50 0.59 9.28 8 15.02 2.53 5.93 9 10.20 1.57 6.48
10 16.47 2.18 7.55 11 7.17 1.15 6.24 12 16.36 1.60 10.24 13 12.33 1.40 8.8 14 12.59 1.54 8.17 15 13.07 1.45 9.01
Three-way ANOVA was performed to test the significance of the dependent
variables and their interactions to either the coated etch rate, the uncoated etch
rate, or the selectivity. The tables in their entirety can be found in Appendix A6.
In general, a p-value (Prob>F) of less than 0.05 implies a significant effect. From
inspecting all three tables, it seems that hydrogen peroxide has a significant effect
on all responses. A change in hydrogen peroxide concentration should
significantly affect the coated etch rate; the uncoated etch rate, or the selectivity.
In a similar fashion, potassium oxalate concentration is also significant. The
EDTA concentration does not seem to affect the coated etch rate or selectivity at a
significant level. In addition, its relation to the uncoated etch rate (p = 0.0128),
while being significant, is comparatively much larger than the p-values for
hydrogen peroxide or potassium oxalate concentration (0.0008 and 0.0024,
respectively). While ANOVA gave us an idea of what effects were potentially
significant, concrete conclusions (i.e. rejecting terms in regression analysis) were
44
not made from ANOVA alone. The reason for this action is that these tables
represent 15 data points in a relatively large experimental space.
The next step in analyzing the data from Table 5-1 was to perform regression with
full quadratic terms and interactions. The result from running this regression was
then plotted on a three-dimensional plot with the three axes representing one of
the independent variables. The dependent variable (response) at each point on this
set of axes was shown in color-based scale. Areas on the three-dimensional plot
that show a red-like color mean that the response is relatively high. Areas in blue
imply that the response is relatively low.
Figure 5-10. Quadratic Response Surface Model for Coated Etch Rates
As Figure 5-10 illustrates, the etch rate for coated samples seems to be
independent of EDTA concentration while being positively correlated to both
potassium oxalate and hydrogen peroxide concentration. This is evident by the
fact that the color goes towards red at higher reactant concentrations (the x-y
plane) while remaining unchanged in either x-z or y-z planes.
45
Figure 5-11. Quadratic Response Surface Model for Uncoated Etch Rates
Much like coated etch rates, uncoated etch rates also seem to be unaffected by
EDTA concentrations while being affected by hydrogen peroxide and potassium
oxalate concentrations. The lowest etch rates are observed at low concentrations
of hydrogen peroxide. This is evidenced by the deep blue color displayed at these
concentrations on Figure 5-11. In contrast, the color displayed at the same area on
Figure 5-10 exhibit a lighter blue color (higher rates by comparison). This
apparent difference in color is important when considering the next figure.
46
Figure 5-12. Quadratic Response Surface Model for Selectivity
Since maximizing selectivity is one of the key goals in this project, the area
bounded by hydrogen peroxide concentrations 2.9 mol/L to 4.4 mol/L and
potassium oxalate concentrations 0.100 mol/L to 0.150 mol/L was of particular
interest as this is the area where the highest selectivites seem to occur. This should
be clear by examining Figure 5-10 and Figure 5-11.
In addition to providing an optimal area of selectivity for further investigation,
results from the Box-Behnken DOE showed that the concentration of hydrogen
peroxide and potassium oxalate are significant factors in determining selectivity.
When comparing their respective p-values (0.0076 vs. 0.0421), it seems as though
the system is more sensitive to hydrogen peroxide than to potassium oxalate
concentration. This observation will be discussed in more depth in Section
5.4.4.1.
47
5.4.2 Full Factorial Design of Experiments As mentioned in the previous section, the Box-Behnken DOE provided us with an
area in the experimental space to explore further. This area is defined to be
hydrogen peroxide concentrations bounded by 2.9 and 4.4 mol/L and potassium
concentrations bounded by 0.100 mol/L and 0.150 mol/L. A two-level, two-factor
Full Factorial DOE was run with the aforementioned concentration values acting
as maxima and minima. The results from this series of experiments are shown in
the following table. Table 5-2. Summary of Results from Full Factorial DOE
Experiment ID
Etch Rate Coated (mg/hr/cm^2)
Etch Rate Uncoated (mg/hr/cm^2)
Selectivity
16 6.61 0.66 10.03 5.56 0.63 8.79
17 9.08 1.08 8.41 8.65 1.16 7.42
18 5.54 0.77 7.19 7.15 0.71 10.06
19 9.79 1.02 9.59 12.20 1.26 9.65
Two-way ANOVA was performed with this data set. For all ANOVA tables from
the Full Factorial DOE, please refer to Appendix A7. As with the Box-Behnken
DOE, the hydrogen peroxide concentration was shown to have a significant effect
on the etch rates of both coated and uncoated samples (p<0.05). Potassium oxalate
concentration was not significant, however. This result seems to agree with those
of the Box-Behnken DOE. For that DOE, p-values for potassium oxalate
concentration, while being significant, were relatively higher than those for
hydrogen peroxide. When investigating a considerably smaller concentration
range, it would be reasonable to observe a previously significant term lose its
significance.
The ANOVA for selectivity showed that no terms were significant. Based on the
selectivity values outlined in Table 5-2, this result is not surprising. Over the four
48
different experimental conditions, selectivity does not vary enough to draw any
conclusions as to where the optimum may lie. The concentration ranges were too
narrow to produce significant differences in selectivity.
5.4.3 Surrogate Modeling Data from the Box-Behnken and Full Factorial DOEs was used as the seed data
for surrogate modeling. Despite being a three-factor design, using the data from
the Box-Behnken DOE was deemed appropriate since EDTA had no significant
effect on selectivity. This conclusion is evident from inspecting the ANOVA table
for selectivity from this DOE (Appendix A6). In cases where the same
concentration of hydrogen peroxide and potassium oxalate, but a different
concentration of EDTA was run, the selectivity results were averaged.
Duplicate/triplicate measurements were also averaged because SUMO does not
read multiple measurements at the same condition; it would only read the first
value given at that condition and ignore the rest. The following table outlines the
results used for modeling the process.
Table 5-3. Summary of Seed Data Used for Surrogate Modeling
Hydrogen Peroxide Concentration (mol/L)
Potassium Oxalate Concentration (mol/L)
Selectivity
2.9 0.075 9.36 2.9 0.225 8.67 2.9 0.150 10.5 2.9 0.100 9.41 4.4 0.100 7.92 4.4 0.150 9.62 5.9 0.075 6.36 5.9 0.225 8.90 5.9 0.150 8.67 8.8 0.075 4.16 8.8 0.225 3.65 8.8 0.150 5.73
49
5.4.3.1 First Modeling Iteration The first modeling iteration was done with the initial data set as described in the
previous section. The most accurate model type, based on root relative squared
error was the Kriging model.
Figure 5-13. Kriging Model of Selectivity (First Iteration), T = 75!C, 300 RPM
Similar to an empirically derived model, the trend from this model indicates that
selectivity decreases with increasing hydrogen peroxide concentration. Unlike the
empirical model, this model shows a different trend for potassium oxalate
concentration. Selectivity seems to go up with increasing potassium oxalate
concentration, but then hits a peak. After this peak, the selectivity goes down with
increasing potassium oxalate concentration. Upon inspection of Figure 5-13, the
optimum seemed to occur at a physically tested point at a low concentration of
hydrogen peroxide as expected (2.9 mol/L) and a mid-range concentration of
potassium oxalate (0.150 mol/L). It should be noted that all three models showed
this point to be the optimum. It should also be noted that there was a largely
unexplored area of the experimental space between 2.9 and 4.4 mol/L hydrogen
peroxide and between 0.150 and 0.200 mol/L potassium oxalate where the
expected selectivity (based on the models) was almost as high as the potential
50
optimum. Despite the fact that a physical point was potentially an optimum, there
was a risk of missing a true optimum located within the unexplored range.
Therefore another iteration was done with a new physical data point at 4.4 mol/L
hydrogen peroxide and 0.200 mol/L potassium oxalate.
5.4.3.2 Second Modeling Iteration The additional data point as described above was physically tested and the
selectivity under these conditions was determined to be 8.55, which was lower
than the predicted value of approximately 10. With this additional point, the
second iteration of model running produced the same optimum point as the first
iteration. This time, the best model in terms of root relative squared error was the
artificial neural network. While the neural network model did provide the best fit,
the reason for this accuracy must be addressed. Neural networks that used
supervised learning methods have a tendency to overfit. When a model overfits, it
will be very accurate at fitting known data (hindsight), but will be poor at
predicted new data (foresight). Despite the mathematical accuracy, the model
itself may not accurately describe the physical process. This becomes clear when
examining the contour plot for the Artificial Neural Network Model (Figure
5-14). The data points are denoted by the black dots. The selectivity at any given
condition is shown by the color displayed at that point. The model tends to move
exactly with the data, thereby generating a very accurate fit, but it is apparent that
such a model will not be good at predicting selectivity for simulated conditions.
51
Figure 5-14. Contour Plot for Artificial Neural Network Model, T = 75!C, 300 RPM
Upon completion of the second modeling iteration, the model that provided a
good fit along with discernible trends was the least-squares support vector
machine model (LS-SVM). The contour plot for the LS-SVM model (Figure
5-15) shows that trends for hydrogen peroxide and potassium oxalate are easily
identifiable. This model may not have the hindsight of the neural network, but
predications based on this model would be made with more confidence.
52
Figure 5-15. Contour Plot for LS-SVM Model, T = 75!C, 300 RPM
As stated in Section 3.3.1.3, the nature of any SVM model is to classify the
physical data into two subclasses. Based on the LS-SVM model (Figure 5-16),
selectivity clearly decreases with increasing hydrogen peroxide concentration.
This trend is common amongst all models, however. The potassium oxalate trend
is that selectivity increases with increasing potassium oxalate concentration up to
0.150 mol/L and then proceeds to decrease with increasing potassium oxalate
concentration. This trend was not observable in both Kriging and Artificial Neural
Network models for the second iteration. While trends may or may not be
observable depending on the model type, the local optimum remains the same for
all models: a low concentration of hydrogen peroxide (2.9 mol/L) and a mid-range
concentration (0.150 mol/L) of potassium oxalate.
53
Figure 5-16. Least Squares Support Vector Machine Model for Selectivity (Second Iteration), T = 75!C,
300 RPM
5.4.4 Kinetics
5.4.4.1 Determining Rate Laws
Verification of the Kinetics Model
The key assumption in this model is that the etch rate must be constant over the
course of the experiment. First, all reactions were operated under isothermal
conditions. This was verified by taking thermocouple readings during each
experimental run. The temperature in the reactor never deviated from the set
point of 75 !C by more than 1!C over the course of any experiment.
As the dissolved reactants are in large excess compared to the material to be
etched (Appendix A5), their concentrations are constant over time. Also because
the reactant concentrations and temperature are not varying, the etch rate should
be constant. Figure 5-17 illustrates how the mass of an uncoated sample decreased
over time at a constant etch rate.
54
Figure 5-17. Mass Lost (mg) vs. Time (min), Uncoated Samples, [H2O2] = 5.9 mol/L, [K2C2O4] = 0.150
mol/L, T = 75!C, 300 RPM
The same kind of experiment was run with coated samples. Figure 5-18
illustrates how the amount of mass lost for coated samples varied over time
showing that there is some lag time before the rate of removal increases. This can
be attributed to the presence of an oxide layer that must first be removed before
the erosion resistant coating is exposed to the reactants. After approximately 30
minutes, visual inspection of the sample indicated that the coating had been nearly
removed in its entirety. This observation would explain why the rate seems to
level off after 30 minutes. In the case of the kinetics model experiments, the time
scale for the reactions were such that there would be coating remaining on the
sample when it was to be removed from the reactor. The thickness of the coating
on the sample is not uniform, so a small amount of underlying substrate was
typically exposed to the system. From these data, it can be concluded that the etch
rate for coated samples could be considered constant up to the point at which
nearly all of the coating has already been removed. While it was desired to run
these experiment with multiple replicate measurements, the quantities of both
coated and uncoated samples were always limited. As a result, only single
measurements were taken.
55
Figure 5-18. Mass Lost (mg) vs. Time (min), Coated Samples, [H2O2] = 5.9 mol/L, [K2C2O4] = 0.150
mol/L, T = 75!C, 300 RPM
Derivation of Rate Laws from Kinetic Model
The reaction orders in equations 4-3 and 4-4 are determined by plotting the
natural logarithm of the etch rates against the natural logarithm of the
concentration of one of the reactants while the other reactant concentration is held
constant. Figure 5-19 illustrates the effect of the concentration of hydrogen
peroxide on the etching rate of a coated sample at a potassium oxalate
concentration of 0.150 mol/L.
56
Figure 5-19. Log plot of Etch Rate vs. Hydrogen Peroxide Concentration for Coated Samples, "#$%$&'(!
!)*+,)! , T = 75!C, 300 RPM
The slope of the line as calculated by linear regression gives us the value of X
(0.599). Similarly the value of *&(4+&5%'4*+%2&5P&$4D*+,&4&0*$*H4/&.H#'&1*')&
G4/P*+,&#-4H4'%&(#+(%+'/4'*#+&4'&4&8*-%2&hydrogen peroxide concentration of 5.9
mol/L (Figure 5-20) resulting in a value of Y of 0.319.
Figure 5-20. Log plot of Etch Rate vs. Potassium Oxalate Concentration for Coated Samples, "-$&$(! !
,*.! /!T = 75!C, 300 RPM
57
A series of experiments with identical initial conditions was then conducted on
uncoated samples to determine the values of Z&69B9:A&4+2&[ (0.264) (Figure 5-21
and Figure 5-22).
Figure 5-21. Log plot of Etch Rate vs. Hydrogen Peroxide Concentration for Uncoated Samples, ,
"#$%$&'(! !)*+,)! , T = 75!C, 300 RPM
Figure 5-22. Log Plot of Etch Rate vs. Potassium Oxalate Concentration for Uncoated Samples, "-$&$(!
!,*.! /!T = 75!C, 300 RPM
The results illustrated by Figure 5-22 show that the value for [ is 0.264. Table
5-4 summarizes the orders of the reactions obtained from all four sets of
experiments.
58
Table 5-4. Summary of All Calculated Reaction Orders
Order Associated With: Value
α Hydrogen Peroxide Concentration on Coated Samples 0.599
β Potassium Oxalate Concentration on Coated Samples 0.319
γ Hydrogen Peroxide Concentration on Uncoated Samples 1.16
θ Potassium Oxalate Concentration on Uncoated Samples 0.264
With the orders known, the reaction rate constants can be calculated. These values
for the reaction rate constants are calculated with 99% confidence. The 99%
confidence interval for kc is approximately sixty times larger than that of ku, but
proportionately only three times larger. There is clearly more variability in the
data used to calculate kc, and by extension, α and β. However, the reason for the
99% confidence interval for kc being proportionately larger than that of ku is
more due to the high level of consistency in the data obtained from the uncoated
samples rather than the variability of the data obtained from the coated samples.
Table 5-5 summarizes the results from these calculations. The calculations have
shown that the value of kC to be 9.79 +/- 0.35 and the value
of kU to be 0.42 +/- 5.5*10-3 . These values for the reaction
rate constants are calculated with 99% confidence. The 99% confidence interval
for kc is approximately sixty times larger than that of ku, but proportionately only
three times larger. There is clearly more variability in the data used to calculate
kc, and by extension, α and β. However, the reason for the 99% confidence
interval for kc being proportionately larger than that of ku is more due to the high
level of consistency in the data obtained from the uncoated samples rather than
the variability of the data obtained from the coated samples.
59
Table 5-5. Summary of Calculated kUncoated and kCoated Values
Experimental Conditions Calculated k values
[H2O2]
kU
kc
[K2C2O4] = 0.150
2.9 0.42 9.48 4.4 0.43 10.12 5.9 0.42 10.28 8.8 0.42 9.99
[K2C2O4]
[H2O2] = 5.9
0.075 0.41 9.23
0.100 0.42 10.03
0.150 0.42 9.85
0.225 0.41 9.37
Average 0.42 9.79
99% CI 5.5*10-3 0.35
Analysis of Selectivity based on Kinetics Model
With the rate constants obtained experimentally the selectivity of the system can
be obtained from Equation 4-1:
(5-1)
Equation (5-1) was plotted within the experimental concentration ranges and is
illustrated in Figure 5-23.
60
Figure 5-23. Selectivity Based on Rate Laws Obtained at 75!C and 300 RPM
By examining Figure 5-23 and Equation 5-1, it can be seen that the selectivity of
the system is highly sensitive to hydrogen peroxide concentration. This
experimental model also indicates that the selectivity has a slight positive
correlation to potassium oxalate concentration. An optimum selectivity would be
observed at the lowest tested concentration of hydrogen peroxide and highest
tested concentration of potassium oxalate.
Sensitivity analysis was performed by taking the partial derivative of Equation 5-1
with respect to one reactant concentration while keeping the other constant
(Equations 5-2 and 5-3). For simplicity, the uncertainties in the reaction rate
constants are not taken into account.
(5-2)
(5-3)
Concentrations of hydrogen peroxide and potassium oxalate in Figure 5-24 and
Figure 5-25 are denoted by [H2O2] and [K2C2O4], respectively. Figure 5-24
61
shows how selectivity will vary with varying hydrogen peroxide concentration at
constant potassium oxalate concentration. We can see that the selectivity is more
sensitive to a change in concentration at lower concentrations of hydrogen
peroxide compared to higher concentrations. Figure 5-25 illustrates how
selectivity will change with respect to potassium oxalate concentration at constant
hydrogen peroxide concentration. Similar to the trend observed in Figure 5-24,
selectivity is more sensitive to change at lower concentrations of potassium
oxalate. As we approach higher concentrations of potassium oxalate, the curves
appear to level off.
In addition, it does not seem as though a change in potassium oxalate
concentration will lead to significant change selectivity with respect to hydrogen
peroxide concentration. This is evident from inspection of Figure 5-24 in that
despite varying potassium oxalate concentration from its minimum to maximum
value, the corresponding curves (i.e. selectivities) are very close to each other.
Conversely, from Figure 5-25 we can see that a change in hydrogen peroxide
concentration from its minimum to maximum value at a given concentration of
potassium oxalate will significantly change the observed selectivity.
Figure 5-24. Change of Selectivity with Respect to Hydrogen Peroxide Concentration at Constant
Potassium Oxalate Concentrations (0.075, 0.150, 0.225 mol/L), T = 75!C
62
Figure 5-25. Change of Selectivity with Respect to Potassium Oxalate Concentration at Constant
Hydrogen Peroxide Concentrations (2.9, 5.9, 8.8 mol/L), T = 75!C
5.4.4.2 Evaluating Temperature Dependence Please refer to Section 4.7.2 for the methodology for this set of experiments.
Experiments run on coated samples yielded the Arrhenius plot as illustrated in
Figure 5-26.
Figure 5-26. Arrhenius Plot for Coated Samples
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From Figure 5-26, the activation energy of the coated etching process was
determined to be 79.2 . Experiments were run at the same conditions using
titanium alloy samples. Data from this series of experiments were used to generate
an Arrhenius plot for uncoated samples (Figure 5-27).
Figure 5-27. Arrhenius Plot for Uncoated Samples
The activation energy for the uncoated etching process was determined to be
58.4 . From both Arrhenius plots, the pre-exponential factors were also
determined. With expressions for the reaction constants specified as functions of
temperature, it is now possible to state the rate laws for the coated and uncoated
etching processes as functions of temperature, hydrogen peroxide concentration,
and potassium oxalate concentration:
(5-4)
(5-5)
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By applying equation (4-1) to these updated rate laws and fixing the potassium
oxalate concentration at 0.150 , we obtain a plot of Selectivity as a function of
hydrogen peroxide concentration and temperature (Figure 5-28).
Figure 5-28. Selectivity as a Function of Hydrogen Peroxide Concentration and Temperature at Fixed
Potassium Oxalate Concentration (0.150 mol/L)
The trends in Figure 5-28 suggest that selectivity will increase with increasing
temperature and decreasing hydrogen peroxide concentration. That higher
temperatures favour higher selectivities is explained by the fact that the activation
energy for the coated etching process is higher than that of the uncoated etching
process. As observed with the Kinetic Model, the system is sensitive to hydrogen
peroxide concentration regardless of temperature. The lower the hydrogen
peroxide concentration, the higher the observed selectivity. With these two trends
in mind, it follows that the best selectivity will be observed at the lowest
concentration of hydrogen peroxide and the highest experimental temperature.
Referring to Figure 5-28, the highest selectivity was observed at said conditions
(
65
5.5 A Comparison between Surrogate and Kinetic Models Figure 5-29 shows a comparison in selectivity behaviour versus hydrogen
peroxide concentration between the LS-SVM model from the Surrogate Modeling
toolbox (a) and the Kinetics Model (b). The main difference between the two
models is that the Kinetics model will have selectivity go down faster at lower
concentrations of hydrogen peroxide while the LS-SVM model indicates a near
constant rate of selectivity decrease. The kinetics model also seems to suggest
higher selectivities than those proposed by the LS-SVM model. Of course, this
result may be due to the fact that the kinetics model provides an ideal picture of
the process while the LS-SVM model directly classified experimentally obtained
data.
Figure 5-29. (a) Slice of LS-SVM Model and (b) Slice of Kinetics Model at [K2C2O4] = 0.150 mol/L, T =
75!C
5.6 Mechanical Testing It should be noted that the sample holder described in Section 4.1.2 was used to
produce samples for fatigue and tension testing. Results from these tests are not
available at this time.
66
6 Conclusions and Recommendations It has been shown that potassium oxalate is the superior organic salt in
comparison to other organic salts such as potassium formate or potassium acetate.
At the same molar concentration, the etch rate obtained was significantly higher
with potassium oxalate. When the number of anions was matched (i.e. half the
original concentration of potassium oxalate), it the resultant etch rate was still
higher.
The pathway for titanium in the TiAlN etching process has also been elucidated
from both experimental and literary findings. Titanium will first be oxidized by a
peroxyacid to form titanium (IV) dioxide. Divalent oxalate anions will reductively
dissolve titanium (IV) oxide to produce titanium (III) ions. Titanium (III) will
catalyze the decomposition of hydrogen peroxide via a free radical mechanism,
giving us titanium (IV) ions. Titanium (IV) can then react with hydrogen peroxide
to give us the yellow coloured pertitanic acid. Pertitanic acid has been shown in
literature to form peroxy titanium oxalate complexes, but this has not been
confirmed by our experiments.
The decomposition of hydrogen peroxide is an exothermic process that results in a
runaway temperature situation when samples are to be completely etched. Adding
a complexing agent such as EDTA to the reactive mixture prior to inserting the
coated sample averts this undesirable situation.
Through Box-Behnken and Full Factorial experimental designs, it has been shown
that hydrogen peroxide has a significant effect on the etch rates for the coating as
well as the substrate. Potassium oxalate was also shown to be significant, but less
than hydrogen peroxide.
67
Using a modified differential approach as well as generating Arrhenius plots
helped produce fully specified rate laws for both coated and uncoated processes.
These laws are functions of hydrogen peroxide concentration, potassium oxalate
concentration, and reactor temperature. Analysis of these rate laws shows that
selectivity increases with increasing temperature, increasing potassium oxalate
concentration, and decreasing hydrogen peroxide concentration. Sensitivity
analysis shows that selectivity is more sensitive to changes in hydrogen peroxide
concentration than potassium oxalate concentration.
The Least-Squares Support Vector Machine was selected as the best surrogate
model for selectivity. It indicates that the optimum selectivity will increase with
decreasing hydrogen peroxide concentration. Selectivity seems to peak as a mid-
range concentration (0.150 mol/L) of potassium oxalate regardless of hydrogen
peroxide concentration.
While potassium oxalate seems to be the preferred choice, etching with other
organic salts besides the ones tested here as well as oxalic acid should be done. In
addition, experiments with different initial pH’s should be attempted in order to
get a better idea of its effect on etch rates and selectivity.
68
7 References [1] Munz, W.D., Titanium aluminum nitride films: A new alternative to TiN
coatings. J. Vac. Sci. Technol. A., 1986. 4 (6): pp. 2717-2725. [2] Bonacchi, D., et al., Chemical stripping of ceramic films of titanium
aluminum nitride from hard metal substrates. Surface and Coatings Technology, 2003. 165: pp. 35-39.
[3] Bastien, S. Selective Chemical Stripping of Thin Film Coatings Using Hydrogen Peroxide and Potassium Oxalate. McGill University MEng Thesis, 2011.
[4] Strukul, G. Catalytic Oxidations with Hydrogen Peroxide as Oxidant. Kluwer Academic Publishers, 1992, p. 74.
[5] Strukul, op.cit., p. 62 [6] Strukul, op.cit., p. 22 [7] Gokel, G.W. Dean’s Handbook of Organic Chemistry (2nd Edition).
McGraw Hill, 2004. [8] Mukherjee, A., et al., Dissolution Stutdies on TiO2 with Orgnics.
Chemosphere, 2005. 61: pp. 585-588. [9] Panjan, P., et al., Oxidation behavior of TiAlN coatings sputtered at low
temperatures. Vacuum, 1999. 53: pp. 127-131. [10] Greenwood, N.N., Earnshaw, A., Chemistry of the Elements. Pergamon
Press, 1984, p. 1116. [11] Davies, G., Watkins, K.O., Inner-Sphere Mechanisms of Oxidation.
Stoichiometry and Kinetics of the Cobalt (III) Oxidation of Oxalic Acid in Acid Perchlorate Solution. Inorganic Chemistry, 1970. 9: pp. 2735-2739.
[12] Ardon, M. Oxygen, Elementary Forms and Hydrogen Peroxide. W. A. Benjamin, Inc., 1965, p. 89.
[13] Takakura, K., Ranby, B., Studies of Free-Radical Species from the Reactions of Titanium (III) Ions and Hydrogen Peroxide. Journal of Physical Chemistry, 1968. 72: pp. 164-168.
[14] Eisenberg, G. Colorimetric Determination of Hydrogen Peroxide. Industrial and Engineering Chemistry, 1943. 15: pp. 327-328.
[15] Baker, C. (2007). Decomposing Hydrogen Peroxide. Royal Society of Chemistry. Retrieved January 25, 2013, from http://www.rsc.org/Education/EiC/issues/2007May/ExhibitionChemistry.asp
[16] Greenwood, op.cit., p. 1060.
69
[17] Greenwood, op.cit., p.1072-1074. [18] Greenwood, op.cit., p. 1073, fig. 19.5. [19] Kharkar, D.P., Patel, C.C., Peroxy Titanium Oxalate. Proceedings of the
Indian Academy of Sciences, Section A, 1956. 44: pp. 287-306. [20] Gorissen, D., et al., A Surrogate Modeling and Adaptive Sampling
Toolbox for Computer Based Design. Journal of Machine Learning Research., 2010. 11: pp. 2051-2055.
[21] Hartman, L., Hossjer, O., Fast Kriging of Large Data Sets with Gaussian Markov Random Fields. Computational Statistics and Data Analysis, 2007. 52: pp. 2331-2349.
[22] Rios, D. (n.d.). The Biological Model. Learning Artificial Neural Networks. Retrieved December 1, 2012, from http://www.learnartificialneuralnetworks.com/#Biological
[23] Rios, D. (n.d.). Multi-layer feed-forward networks. Learning Artificial Neural Networks. Retrieved December 1, 2012, from http://www.learnartificialneuralnetworks.com/backpropagation.htmlSuykens, J., et al. Least-Squares Support Vector Machines. World Scientific, 2002, p. 30.
[24] Sivanandam, S.N., Deepa, S.N., Introduction to Genetic Algorithms. Springer, 2008, p. 32.
[25] Greenwood, op.cit., p. 1089.
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8 Appendix
A1. Mathematical Explanation of Kriging This is an excerpt from a paper written by Hartman and Hossjer [1].
71
A2. Additional Information on Artificial Neural Networks
Biological Foundation The neuron is divided basically into its three major parts: the soma, the axon, and
the dendrites. The soma can be considered the central component of the neuron
because it houses the nucleus of the cell. From the soma extend dendrites.
Multiple dendrites branch from the soma and from each branch results further
branching. The axon also extends from the soma, but unlike dendrites, only one
axon exists for each soma. Signals to the soma are received through the dendrites
while signals from the soma are transmitted via the axon. Although there is only
one axon per soma, the axon does branch out at the axon terminal so that a signal
from one soma can be received by multiple dendrites. Based on this input/output
structure, one can define the synapse to be the connection of one neuron’s axon
terminal branch to another neuron’s dendrite branch. When the sum of all the
signals received at the soma is high enough, a pulse is generated and is
transmitted through the axon to a synapse.
Figure 8-1. Structure of a Typical Neuron [2]
72
Threshold Logic Units and Backpropagation of Errors A node in an ANN is also referred to as a threshold logic unit. Each node receives
multiple signals (Wj,i) from nodes from another level and each signal is multiplied
by the associated weight (xj) between the nodes of interest.. A higher weight
implies a stronger relationship between nodes. Weights can range from -1
(inhibitory) to +1 (excitatory). The sum of these weight-signal products is
subjected to the activation function of the node. The purpose of the activation
function is to scale the node’s output to a value between 0 and 1. One such
function is the sigmoid function. The output signal is then sent to nodes at the
next level.
Figure 8-2. An Individual Node (TLU) within a Multi-Layered Feed-Forward Network [3]
Neural networks of the type shown here teach (i.e. optimize) themselves by a
process known as back-propagation of errors. This is a supervised learning
method where the value produced by the model is compared against a known
quantity. The difference between the produced value and reference value is the
error and it is this error that is minimized.
73
Figure 8-3. Supervised Learning of a Neural Network [4]
Within this type of learning, only the weights between nodes are modified. The
network itself, i.e. the way the nodes are connected, or the activation functions
within each node do not change.
74
A3. Theory of Evolution and the Genetic Algorithm Darwin’s theory of evolution is predicated upon the ability of offspring to inherit
trait from their parents and that mutation in these traits is possible. Traits that are
ultimately beneficial for the individual make it more likely that he/she would
reproduce and carry that trait forward into the next generation. Individuals
without these traits, or worse yet, traits are ultimately detrimental to that
individual given their surroundings make this individual less likely to reproduce
and carry these detrimental traits forward. Therefore, in an isolated system, the
population will eventually display only these beneficial traits, as only these traits
will exist within the gene pool. Changes within the gene pool would then occur
through mutation as well as through genetic crossover.
From the above description, it is clear that this type of selection process can be
applied to optimization problems. The parallels are quite simple. A chromosome
can be regarded as a string of binary code and a genotype can be regarded as a
certain sequence within that string.
75
A4. SUMO Files
Config File
Sample Data File
76
Default File (Excerpt)
77
78
A5. Calculation of Hydrogen Peroxide Being in Excess
Of titanium, aluminum, and nitrogen, titanium has the highest molecular weight.
Therefore the most conservative possible estimate of the molar mass of TiAlN
would be that it was three parts pure titanium (143.7 g/mol). The lowest tested
concentration of hydrogen peroxide was 2.9 mol/L. At the solution volume of 750
mL, there would be 2.2 mol of hydrogen peroxide in solution. If one mol of
hydrogen peroxide were responsible for removing one mol of TiAlN, there would
have to be more than 312 grams of coating on the sample for hydrogen peroxide
to be a limiting reactant. Since there is much less than 312 g of coating on each
sample, it is therefore safe to assume that hydrogen peroxide is in excess.
79
A6. ANOVA Tables for Box-Behken DOE Notes:
X1: Hydrogen peroxide concentration
X2: Potassium oxalate concentration
X3: EDTA Concentration
Table 8-1. ANOVA Results for Coated Etch Rates (Box-Behnken)
Table 8-2. ANOVA Results for Uncoated Etch Rates (Box-Behnken)
Table 8-3. ANOVA Results for Selectivity (Box-Behnken)
80
A7. ANOVA Tables for Full Factorial DOE Notes:
X1: Hydrogen peroxide concentration
X2: Potassium oxalate concentration
Table 8-4. ANOVA Results for Coated Etch Rates (Full Factorial)
Table 8-5. ANOVA Results for Uncoated Etch Rates (Full Factorial)
Table 8-6. ANOVA Results for Selectivity (Full Factorial)
81
9 Appendix References
[1] Hartman, L., Hossjer, O., Fast Kriging of Large Data Sets with Gaussian Markov Random Fields. Computational Statistics and Data Analysis, 2007. 52: pp. 2331-2349
[2] Introductory Psychology Image Bank. McGraw Hill Higher Education. Retrieved December 1, 2012, from http://www.mhhe.com/socscience/intro/ibank/set1.htm
[3] Rhode, C. (2010). An Introduction to Neural Networks: The Perceptron. Lower Columbia College. Retrieved December 3, 2012, from http://lowercolumbia.edu/students/academics/facultypages/rhode-cary/intro-neural-net.htm
[4] Rios, D. (n.d.). Multi-layer feed-forward networks. Learning Artificial Neural Networks. Retrieved December 1, 2012, from http://www.learnartificialneuralnetworks.com/backpropagation.html