Elimination or Significant Reduction of the Effects of StressConcentrators by Nanosizing

Collaborators:P. Deymier, MSE, Univ. of ArizonaE. Enikov, AME, Univ. of ArizonaC. Haynie, CEEM, Univ. of Arizona

Central Theme: When spatial dimensions are below a material specific one, which most likely is in the nanometer range, stress concentrators become insignificant.

Molecular Dynamics results and design of experiments

10,000 layers of alternating metal/polymer.Each layer is 20-30nm thick. Courtesy: Sigma Tech. Intl., Inc.

Components with Nanodimensional Structure

Technologies presently exist, and are becoming more efficient, in producing components of nanodimenions (nanolaminates, nanoflakes, nanofibers, comb, etc.)

Nano-composite for energetic pigmentapplications. Courtesy: Sigma Tech. Intl., Inc.

One Potential Important Future application: Hydrogen storage by adsorption, where intentional surfaces, pores …(STRESS CONCENTRATORS) increase the surface area.

Future Technologies

The mechanical integrity is paramount, and insensitivity to defects is a reliability design dream come true – stress concentrators are ubiquitous

Nature Knows

Courtesy: Gao et al, 2003, Proc.Nat. Acad. Sci.

The basic building components in many biological materials remarkable for their properties are at the nanoscale (mineral/organic).

Why the Nanoscale ??

Stress Concentrators

Nano stress concentrators (NSCs) here indicate defects such as impurities, inclusions, cracks, pores;

defects other than NSCs, e.g. dislocations, are also addressed yet they are considered part of the “bulk” material

Examples: from roughness of substrate, impurities, pores, inclusions

In biological materials NSCs are trapped proteins within mineral crystals during biomineralization. Consistency in these materials is remarkable.

σ

σ h

1.0

h

/f th

Griffith criterion for a cracked crystal

Theoretical strength for a perfect crystal

(a) (b)

Crack

hcr

Size Effects – Since Galileo Galilei and Leonardo da Vinci

/f a E h

Considering for a brittle material:1J/m2, E=100GPa, th=E/30] and

we obtain hcr = 30nm

Note on Hall-Petch effects

Yield strength of electroplated Cu thin films as a functionof film thickness t. In the plot of these nanoindentationexperimental results, sizing to ~200nm, the yield stresswas assumed as the 1/3 of the hardness. Courtesy of Volinsky and Gerberich, 2003, Microel. Engr. Journal.

Size Effects: Well Studied

Insensitivity to NSCs has not been speculated,Plus difficulties in studying (experimental and simulation)

Koehler, 1970: a structure comprised of alternating layersof two suitable metals exhibits a resistance to plastic deformationthat would be greater than that expected from a homogenous alloyof the two.

Below Certain Nanoscales: More than Size Effects

Strength

Thickness

NSC

dia

met

er

Strength

Thickness

NSC

dia

met

er

Expected Behavior – Insensitivity to Defects

For NSC diameter = ½ thickness hcr

Side views

strain

stre

ss (

Pa)

0.025 0.05 0.075 0.1 0.125 0.15

1109

2109

3109

4109

5109

3D views

MD Simulations (EAM) – Cu Crystal with a NSC Pulled in (001)

Over 2,000,000 atoms

Many slip planes

High strain rate

Non periodic BC

side views

0.025 0.05 0.075 0.1 0.125 0.15

-1109

1109

2109

3109

4109

5109

strain

Stre

ss (

Pa)

3Dviews

MD Simulations (EAM) – Cu Crystal w/o NSC Pulled in (001)

Over 2,000,000 atoms

Two slip planes

High strain rate

Non Periodic BC

(111) slip planes form

0.025 0.05 0.075 0.1 0.125 0.15-1109

1109

2109

3109

4109

5109

0.025 0.05 0.075 0.1 0.125 0.15

-1109

1109

2109

3109

4109

5109

strainstrain

stre

ss (

Pa)

stre

ss (

Pa)

(a) (b)small systemwith NSC

large system with same NSC

large system,no NSC

small system, no NSC

Insensitivity to the NSCs

Large system: 28.88x28.88x28.88 nm3 (over 2,000,000 atoms) 3.0x3.0x0.4 nm3 NSC

Small system: 18.05x18.05x18.05 nm3 (~ 500,000 atoms) 3.0x3.0x0.4 nm3 NSC

0.06 0.08 0.1 0.12 0.14 0.16

2500

5000

7500

10000

12500

15000

strain

N

without NSC

with NSC

Why the Insensitivity ?

Total number of atomistic defects, N, versus strain for the small Cu(001) system with and without NSC. Plot was obtained from atom positions at five strain levels during deformation.Role of Surfaces: ratio surface/volume ~ 1/a important for small a

If, on average, the energy required for

forming each atomistic defect is constant,

this explains insensitivity of the material to NSCs

With NSC

Without NSC

External surfaces start dominating as atomistic defect initiation sites

Surfaces – large system, high strain rate, non periodic BC

With NSC

Without NSC

External surfaces start dominating as atomistic defect initiation sites

Surfaces, small system, high strain rate, non periodic BC

With NSC, side views

Loaded surfaces start dominating as atomistic defect initiation sitesfor two large (infinite) lateral dimensions (periodic BC). NSCsstimulate the clustering of atomistic defects.

Surfaces, small system, high strain rate, periodic BC

Without NSC, side views

Slower Strain Rates – Non Periodic BC

Large System Small System

Number of Atomistic Defects Versus Strain,(one realization, even though process is statistical)

0.06 0.08 0.1 0.12 0.14

5000

10000

15000

20000

25000

0.04 0.06 0.08 0.1 0.12

5000

10000

15000

20000

25000

30000

Strain Strain

N N

With NSC

Without NSC

Without NSC

With NSC

Slow strain rate, large system, no NSC and 2 NSC sizes (3 curves)

Slow strain rate, small system, no NSC and 1 large NSC

0.025 0.05 0.075 0.1 0.125 0.15

-2109

-1109

1109

2109

3109

0.025 0.05 0.075 0.1 0.125 0.15

-2109

-1109

1109

2109

3109

4109

Slower Strain Rates – Non Periodic BC

Strain

Strain

Str

ess

(Pa)

Str

ess

(Pa)

Surprise: Slower Strain Rates – Periodic BC

Large System Small System

Number of Atomistic Defects Versus Strain.NSCs stimulate the clustering of atomistic defects.

0.06 0.08 0.1 0.12 0.14 0.16 0.18

5000

10000

15000

20000

25000

30000

35000

0.04 0.06 0.08 0.1 0.12

20000

40000

60000

80000

100000

Strain Strain

N

N

Without NSC

With NSC With NSC

Without NSC

0.025 0.05 0.075 0.1 0.125 0.15-1109

1109

2109

3109

4109

5109

6109

Slow strain rate, large system, no NSC and 2 NSC sizes (3 curves)

0.025 0.05 0.075 0.1 0.125 0.15

-2109

2109

4109

6109

Slow strain rate, small system, no NSC and 1 NSC

Slower Strain Rates – Periodic BC

Strain

Strain

Str

ess

(Pa)

Str

ess

(Pa)

Without NSC

Without NSC

With NSC

With NSC 1

With NSC 2

Slower strain rate, non periodic BC

Large system with NSC

Large system, no NSC

Slower strain rate, non periodic BC – side views

Large system with NSC

Large system, no NSC

Slower strain rate, periodic BC

Large system with NSC

Large system, no NSC

Atomistic defects cluster at the loading surfaces

Slower strain rate, periodic BC – side views

Large system with NSC

Large system, no NSC

Atomistic Defects cluster at the loading surfaces

Experiments

Nanoindentation: not appropriate for this workThe very local indenter, which introduces a NSC, interacts strongly with pre-existing NSCs; two samples(films of different thickness) are unlikely to have the same NSCs positioned near the indenter in a similar fashion.

Experiments

(Left) SPM 2.5x2.5 μm2 image of metal nanotubes, (right) higher magnification SPM image. The diameter of the metal tubes is about 40nm and the thickness about 10nm.

2.5 m

Def

lect

ion

(load

)

Probe’s Vertical Position (displacement)

(a) (b)

(c)

The SPM probe is pushed on the metal tubes lying on a flat wafer. Height image using contact mode (low resolution) after load is imposed by Force Volume SPM. (a) 1x1μm, (b) 500x500nm; the marked area (red ellipse) was damaged during the Force Volume SPM. (c) Typical force displacement curve. Limitations …. force volume SPM.

Experiments

SPM Probe

Membrane

WaferSpin-on Glass, Etched after Film Deposition

TOP VIEW (Partial): ARRAY OFCYLINDRICAL HOLES IN WAFER

SIDE VIEW: ONE HOLE AND MEMBRANE

SPM Probe

Membrane

WaferSpin-on Glass, Etched after Film Deposition

TOP VIEW (Partial): ARRAY OFCYLINDRICAL HOLES IN WAFER

SIDE VIEW: ONE HOLE AND MEMBRANE

Membrane tests

Smooth Probe

Wafer Wafer

Au/Al film

9 MD cells

Force

SPM probe FEM domain

SIDE VIEW

TOP VIEW (not to scale)

Cr bonding

Schematic of the membrane problem. Nine MD cells are coupled to FEs discretizing the rest of the film. The handshake region coupling the MD and FE regions is wavelet-based, filtering high frequencies that create unrealistic reflections at the interface.

Simulation of Experiments

Simulation Issues

-The MD-FE interface (not resolved – dispersion issues) use a wavelet-based absorbing interphase

- Propagation of atomistic defects in the FE domain use kMC (kinetic Monte Carlo) as intermediate technique to avoid artificial dislocation pileup Has been tested (Frantziskonis & Deymier, 2000)

Conclusions

For Cu subjected to tensile strain, the critical dimensions for the effects of NSCs are larger than the examined (up to) 28.8nm. Multiscale simulations are necessary to identify critical dimensions and also examine slower strain rates.

The spatial pattern of atomistic defects that develops during straining is different for a system with NSCs than one without NSCs. Yet, the number of atomistic defects (number of atoms with modified coordination number) seems to be independent of the NSCs. Samples larger than critical tend to cluster atomistic defects.

Surfaces are instrumental in initiating atomistic defects. Surface Effects, also instrumental at macro-scales, are beneficial at nano-scales, i.e. they eliminate the effects of stress concentrators.

Strain rate (1 order of magnitude difference) does not alter the conclusions

Computer power and experimental difficulties of the past did not allow one to even speculate that such a (materials processing and reliability) dream may be true!