Simulation: Powerful tool for Microscale Materials Design and Investigation

Dr. Xining Zang ME 138/ME238

Prof. Liwei Lin Professor, Dept. of Mechanical Engineering Co-Director,

Berkeley Sensor and Actuator Center The University of California, Berkeley, CA94720

e-mail: lwlin@me.berkeley.edu http://www.me.berkeley.edu/~lwlin

Time Scale and Length Scale

Modeling and Simulation Modeling: describes the classical scientific method of formulating a simplified imitation of a real situation with preservation of its essential features In other words, a model describes a part of a real system by using a similar but simpler structure

Simulation: putting numbers into the model and deriving the numerical end-results of letting the model run on a computer. A simulation can never be better than the model on which it relies.

Computational Materials Science

Micro scale Meso scale Atomic scale Electron scale

Experiments

Materials Science Question

Model System

Simulation

Result Analysis

Theory

https://www.mgi.gov/subcommittee-materials-genome-initiative-smgi

Materials Genome Initiative

https://mgi.nist.gov/

The Materials Genome Initiative is amulti-agency initiative designed to create anew era of policy, resources, andinfrastructure that support U.S. institutionsin the effort to discover, manufacture, anddeploy advanced materials twice as fast, ata fraction of the cost.

Advanced materials are essential toeconomic security and human well being,with applications in industries aimed ataddressing challenges in clean energy,national security, and human welfare, yet itcan take 20 or more years to move amaterial after initial discovery to themarket. Accelerating the pace of discoveryand deployment of advanced materialsystems will therefore be crucial toachieving global competitiveness in the21st century.

Materials Project Harnessing the power of supercomputingand state of the art electronic structuremethods, the Materials Project providesopen web-based access to computedinformation on known and predictedmaterials as well as powerful analysistools to inspire and design novelmaterials.

Dr. Kristin Persson (LBNL) Prof. Gerbrand Ceder

Molecular Dynamics Key: Newton second law & Hamiltonian

Sir William Rowan Hamilton (1805-1865 Ireland).

Sir Isaac Newton (1643-1727 England)

Molecular Dynamics• Using the information gained from r, v and application

of the forces:

• Initial positions are advanced towards a lower energy state.

• Through some time step delta t

• New positions are obtained.

• New velocities are obtained

• REPEAT.

• This is repeated as many times as is needed to obtained equilibrium.

MD for mechanical properties

Young’s ModulusYoung’s Modulus

Yield Strength Yield Strength

Interface structure Interface structure

Dislocation-interface interactionDislocation-interface interaction

An example: ultralow elastic modulus

10μm

GPanm

10~20nm thickness, one order decrease)

Mechanical propertyNanocrystalline softening

Has been limitedly studied in typical FCC metal Cu/Ti etcGrain boundary dominated sliding > dislocation strengthening 2D stress field

Reverse Hall-PeigeNeed to be tested out

Nature 391, 561-563 (5 February 1998) International Journal of Solids and StructuresVolume 49, Issue 26, 15 December 2012, Pages 3942-3952

Why atomistic simulation?

A.Misra, M.J,Demkowicz,et,al JOM,2008 April

from • Hall-petch

to• Single dislocation• Nanocrystalline softening?

thickness

Dislocation

outline

Simulation process outline

Calculation details

Interface structure

Dislocation-interface interaction

Methodology

Results and discussion

Difficulties and questions

Simulation process outline

interface construction

relaxation [quenching MD]

calculation certain properties

Interface structure

interface

Coherent ——transparent

Semi-coherent——half-transparent

Incoherent interface ——opaque

examples

Cu-Ni (Fcc-Fcc) {Medyanik 2009}{Rao 2000}

Cu-Ag(Fcc-Fcc) {Hoagland 2002}Cu-Nb(Fcc-Bcc)

{Wang, 2008} {Wang, 2008}

KS

KS1

KS2

KSmin

plane strain adjoining atom layer

Incoherent Cu-Nb

|| , ||Cu Nb Cu Nb （111） （110） 110> 111>

Kurdjumov–Sachs (KS)

Cu and Nb slabs translate

minimize the energy

Positions of Cu and Nb not relaxed

perfect Cu and Nb

M.J.Demkowicz, Jour.Necluar.Mater.372(2008)

KS1

a strained monolayer

3 Cu, 2 Nb 1 Nb

homogeneous in-plane deformation

KS2

Requires– Direction of the monolayer rows A||1– The rows C || Nb– d(A) is chosen such that s(C)=s(Nb)– d(C) is chosen such that s(A)=s(Nb)

M.J.Demkowicz, Jour.Necluar.Mater.372(2008)

Results– 1 atoms less per 188 atoms– Energy per atom to create the artificial monolayer

0.03eV/atom– The A row lies between the valley of NbAnd the C rows lies between the Nb

• Two-body Morse

• EAM ,CuNb in CsCl, first-principle

using VASP.

Potential for the bi-layer atoms ( )( ) (1 )M Mr RCuNb M Mr D e D

' ( ) ( ) ( )

1cut

CuNb CuNb CuNb cut

m

cut CuNb

r rcut

r r r

r drm r dr

M.J.Demkowicz, Jour.Necluar.Mater.372(2008)

Cu-Nb J.wang, et,al, Acta 56(2008)3111

Cu-Nb J.wang, et.al, Acta 56(2008)5685

Cu-Nb Hoagland et.al, Philos.Mag, 2006

Cu-Ni / Cu-Ag Hoagland et.al, Philos.Mag, 2002

Cu-Nb S. Shao, et.al, Model.Sim.MSE 2010

Details about the structure construction in papers

J.wang, et.al,Acta,2008

region 1 ——region 2

PBC:

in the x and z directions.

Cu:42 185.9530 A ;19 48.5677A;

Nb: 23 185.9614 A ; 17 48.5958A;[112]Nba

[110]2Cua

[111]2Cua

[112]2Cua

KS1

KS2

u / x 0.04785 u / 0.09209z / x 0.02763w / 0.05317w z displacemnt gradient

Cu inserting strained monolayer

additional PBC displacemnt gradient

u / x 0.4144 4e u / 0.4867 3z e

/ x 0.1441 4w e / 0.8811 4w z e

Cu-Nb J.wang, et,al, Acta 56(2008)3111

X,z=18.6 nm y=4.86

Cu-Nb J.wang, et,al, Acta 56(2008) 5685

Cu-Nb Hoagland et.al, Philos.Mag, 2006

Ksmin

Relaxation:Translate in 3 directions, but rotation is not allowed Excess energy：(relative to their respective cohesive energy. )

Another way to construct the interfaceFixing bottom

wide enough

Cu-Nb S. Shao, et.al, Model.Sim.MSE 2010

Two sets of Slip plane.10.5

dislocations through interface

Dislocation transmission

Interface-dislocation interaction

Modulus interactionModulus interaction

Size interactionSize interaction

Chemical interactionChemical interaction

“ ”ineraction“ ”ineraction

Modulus interaction

modulus mismatch (Koehler barrier) introduce an image force

Koehler stress to move a screw dislocation from a softer layer to a harder layer against its elastic image

(a/2) screw dislocations are considered to be split into Shockley partials

1 2( ) /kf E E h

* 1 1 2

2 1

( )4 ( )k

bh

Size interactionvan der Merwe misfit dislocations /coherency stresscoherency stress in multilayers:

lattice parameter misfit between the lamellae, elastic constants of the individual lamellae, volume fraction of the lamellae and wavelength of the multilayer system

Misfit dislocations ——forest-type obstacles

* ,

0,

d c

c

a ba

Chemical interactiongamma surface mismatch introduce a localized force on the gliding dislocations

the negative elastic interaction energy between the Shockley partials

the total energy of the stacking fault bounding the partials.

The stress on the leading dislocation of the a pile-up

the stacking fault energy

el chE E E

elE

chE

* 2 , , , ( )ich i i Cu Ni Cuwhereb b

i

Calculation details

relaxation

defect visualizatin

thermodynamic stress

elastic constant

strain related

interface constructioninterface construction

Relaxation[quenching MD]

Relaxation[quenching MD]

calculation certain properties

calculation certain properties

{Wang, et.al, Acta (2008)5685}

Interface dislocation displacement field: Barnett-Lothe solution.

field is applied to both the movable and fixed region

Dislocation line is parallel to Z axis

Relaxation Quenching MD until the force on any atom

Lattice glide dislocation enters the interface

disregistry analysis

Pairs of atoms straddle the desired shear plane

relaxed system

atoms in the sheared systems

The disregistry

r r

ij i jr r r

d d d

ij i jr r r

d

ij ijr r

{Shao, Modelling Simul. Mater.Sci.Eng.18(2010)} conjugate gradient procedure

energy minimization

parallel atomistic simulation code LAMMPS

visualization of the defects: atomic excess energy, coordinate number;

centro-symmetry parameter

• centro-symmetry parameter:

• Atomeye function to compute P

• pairs of the opposite nearest neighbors

2

1,

| |i ii

P R R

2

1,

2

1,2

| |

2 | |

i ii

jj

R Rc

R

i iR andR

Indentation lattice glide dislocation

Indentation on Cu-Nb bi-layer

[adsorption]

Indentation on Nb-Cu bi-layer

[transmission]

• rigid spherical indenter with radius R = 40Å• quadratic repulsive force• center of the top surface

DB 1.45nm from the interface in Cu Array relaxed by energy minimization Shockley partials B D

•The lead Shockley partials enter the interface leaving trailing Shockley in the Cu near original site of DB•If the Burgers changed into BD, the enters the interface instead•The observation that one of the partials enters the interface, irrespective of sign, denies the possibility that this response is caused by small residual stresses or coherency stresses local to the interface.

B D

Results and Discussion

Slip systems in Cu/Nb

Core spreading of lattice glide dislocation within the interfaces

Sheared interface attracts lattice glide dislocation Interface

Interface shear strength

Elastic interaction between a dislocation and interface