Atomistic Simulations

Ju Li, Libor Kovarik

8 nm

Mishin, Acta Mater. 52 (2004) 1451 Ardell & Ozolins, Nature Mater. 4 (2005) 309

(NT) ensemble with two vacancies

Transition pathwaysobtained using

Nudged Elastic Band (NEB) method.

Henkelman & Jonsson, J. Chem. Phys. 113 (2000) 9901;

ibid 113 (2000) 9978.

I

I IC

0.44MPa m0.75

KG G

2D activation

3D activation

sorta too long

fN

kN

A new NEB methodconnecting to unstable final state

“Free-end” algorithm:

last nodeconstrained

to move only along

energy contour

T. Zhu, J. Li, A. Samanta, H.G. Kim, S. Suresh, “Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals,” PNAS 104 (2007) 3031.

Lu et al., Acta Mater.

53 (2005)2169.

dislocationtransmission?

Lu et al., Science 287 (2000) 1463; 304 (2004) 422.

*

activationvolume v

strain-ratesensitivity m

Uniaxial tension[Lu04]

Nanoindentation[Lu05]

Atomistic calculation

Diffusion-controlled processes

Bulk forest hardening

Comparison of yield stress, activation volume and strain-rate sensitivity between experimental measurements and atomistic calculation

Nano-twinnedCopper

~ 1 GPa

*700 MPa

780 MPa

32212 b

34424 b

036.0025.0

023.0013.0

31.0~ b ~ 1

31000100 b 005.00 bulk~ b

yield stress

* extracted from measured hardness as .3

HH

*

activationvolume v

strain-ratesensitivity m

Uniaxial tension[Lu04]

Nanoindentation[Lu05]

Atomistic calculation

Diffusion-controlled processes

Bulk forest hardening

Comparison of yield stress, activation volume and strain-rate sensitivity between experimental measurements and atomistic calculation

Nano-twinnedCopper

~ 1 GPa

*700 MPa

780 MPa

32212 b

34424 b

036.0025.0

023.0013.0

31.0~ b ~ 1

31000100 b 005.00 bulk~ b

yield stress

* extracted from measured hardness as .3

HH

First time atomistic calculation provides strain-rate sensitivity information, at experimentally realistic strain rate of ~10-4/s.

avg. shear stress = 750 MPa

initial equilibrium

free-end node

node 2

node 3

node 4

3initial saddlesupercellActivation volume is estimated by 100

Qb

G

constant supercellcalculation

saddle-point configuration

[112]/6[112]/6

pseudo-twinlayer

true-twinlayer

pure Ni column

half Ni column

push inpop out

slightly tilted viewred: Al black: Ni

Libor vacancy reorderingmechanism

Vacancy-aided reordering in 2-layer pseudo-twin long behind dislocations

For comparison,VNi migration barrier

in perfect Ni3Al is 1.24 eV.

shear stress = 900 MPa

Peter Sarosi

High Tensile Strength and Ductility of Cu with Nano-Sized Twins

Lu et al., Science 287 (2000) 1463; 304 (2004) 422.

Lu et al., Acta Mater.

53 (2005)2169.

dislocationtransmission?

B

,

log 3strain-rate sensitivity activation volume *

logT

k Tm v

m

Lu et al., Acta Mater. 53 (2005) 2169.

Like other nanocrystals, nanotwinned Cu shows increased strain-rate sensitivity (~0.03) and small activation volume (~12b3)

Can atomistic calculation provide strain-rate sensitivity (m) and activation volume (v*) information of experimental relevance?

stress

Act

ivat

ion

ener

gy Q

()

athermal threshold

ath

( )dQd

activation volume

0.7eV

0eV very likely to happen in 1s

very unlikely to happen in 1s

1 2

large 2

small thermal uncertainty

small 1

large thermal uncertainty

process 1

process 2

Stress-driven activated process

Larger meansthe activation is

more “collective”,less thermal

uncertainty & the process

more “athermal”.

point defect diffusion: ~0.02-0.1b3 forest dislocation cutting: ~103b3

J. Li, “The Mechanics and Physics of Defect Nucleation,” MRS Bulletin 32 (2007) 151-159.

= 252MPaQtms=0.67eV

Qabs=0.49eV

Qdes~5eV

In experiment, stress applied is uniaxial tension, not pure shear → Taylor factor M ≈ 3.1 to convert

shear stress to uniaxial stress : = M

int( , )True activation volume:

Q

We’ve computed tms≈79b3, abs≈des≈43b3

at = 252MPa.

* * *tms abs des

3 3

,

3

44 24

A conversion factor M/ between experimentally measured * and :

b b

vv v v