Atomistic Mechanism for Grain Boundary Migration: Molecular Atomistic Mechanism for Grain Boundary Migration: Molecular Dynamics StudiesDynamics StudiesHao ZhangHao Zhangaa, David J. Srolovitz , David J. Srolovitz aa, Jack F. Douglas , Jack F. Douglas bb, and James A. , and James A.

Warren Warren bbaa Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08540NJ 08540bb National Institute of Standards and Technology, 100 Bureau Drive, Stop 8554, National Institute of Standards and Technology, 100 Bureau Drive, Stop 8554, Gaithersburg, MD 20899Gaithersburg, MD 20899

IntroductionIntroduction Grain boundary migration is the

central feature of grain growth, recrystallization

I. controls final grain size, texture, …

Understanding of boundary structureI. low temperature observations

Understanding of boundary migrationI. macroscopic migration rate

measurementsII. coarse-grained rate theoryIII. limited atomistic simulations

MechanismsI. melting/crystallization II. step/kink (SGBD) motionIII. cooperative shufflingIV. Coupling motion

HereI. high T MD simulation of GB migrationII. analysis of all atomic motion

3-d MD Simulations of Flat Boundary 3-d MD Simulations of Flat Boundary MigrationMigration

Molecular dynamics in NVT ensemble

EAM-type (Voter-Chen) potential for Ni

Periodic boundary conditions in x and y

One grain boundary & two free surfaces

Fixed biaxial strain, =xx=yy

Source of driving force is the elastic energy

difference due to crystal anisotropy

Driving force is constant during simulation

Linear elasticity:

At large strains, deviations from linearity occur,

determine driving force from the difference of the

strain energy in the two grains:

21 1

1;

2xx yy A P A

2 (2) (2) (1) (1) 2 31 2 1 2

1 1;

2 3xx yy xx yy xx yyA A P d

X

Y

Z

Grain Boundary

Free Surface

Free Surface

Grain

2G

rain 1

1122

33

1122

33

5 (001) tilt boundary

24 22 3 5 1r t r t

1

1, 0

N

s i ii

G t tN

r r r r

Statistical MeasuresStatistical Measures

van Hove correlation function (Self-part), Gs

Non-Gaussian Parameter,

Mean First-Passage Time (MFPT), (R)

R

(R)

1

1 N

ii

R RN

By looking at Gs for different t, we can trace the path that the atoms takes as they move through the system. Distribution of distances atoms travel on different time scales.

This parameter provides a measure of how much Gs deviates from a Gaussian distribution.

This quantity characterizes how rapidly an atom escapes its local environment.

Cooperative MotionCooperative Motion

Atomic displacements: t=5ps Atomic displacements: t=0.4ps, t=30ps

Boundary Plane - XY

Substantial cooperative motions within boundary plane during migration

All of the atoms that are members of strings of length greater than 4 at t = T*

Atomic Path for Atomic Path for 5 Tilt Boundary 5 Tilt Boundary MigrationMigration

Part of the simulation cellCSL unit cellAtomic “jump” direction

, - indicate which latticeColor – indicates plane A/B

IIIa III II

bIIc

Types of Atomic Motions

Type I: “Immobile” – coincident sites -I, dI= 0 Å

Type II: In-plane jumps (either in A or B plane) – IIa, IIb, IIc, dIIa=dIIb=1.1 Å, dIIc=1.6 Å

Type III: Inter-plane (A/B) jump - III , dIII=2.0 Å

ConclusionsConclusions Molecular dynamics simulations of stress-driven

boundary migration for asymmetric 5 tilt boundaries

Employed statistical measures to quantify grain boundary migration dynamics

Three distinct types of atomic motions observed:I. very small displacement of coincident site atoms II. single atom displacements with significant components

perpendicular to the boundary planeIII. Collective motion of 2-10 atom groups in a string-like motion

parallel to the tilt axis

Type II motions : correlated with excess volume of boundary

I. The atomic motions across the grain boundary plane occurs on a characteristic time scale t* of ~ 130 ps. Applied driving force decreases t*.

II. Type II displacements are rate controlling events

Type III motions: collective motion of group of atoms

I. String-like cooperative motion are intrinsic dynamics within grain boundary, it occurs on the characteristic time scale T* of ~26 ps. Applied driving force tends to decrease T* and biases its motion.

Characterization of Type II MotionCharacterization of Type II Motion

At short time atomic motions are harmonic – transition away from harmonic at long times

Transition behavior occurs on much longer time scales than T* characteristic of string-like motion

The transition occurs at t*~130 ps for the migrating boundary

What Are those What Are those Peaks?Peaks? dIIa = 1.13Ǻ

dIIb = 0.71Ǻ

dIIc = 1.24Ǻ

dIII = 1.95 Ǻ

The broad peak at r = 1.3 Ǻ in the Gs represents Type II displacements (motions IIa and IIc), and the peak of r = 2.0 Ǻ represents Type III displacement (motion III).

Type II displacements are rate controlling events

Formation of a StringFormation of a String

Boundary Plane - XY

Colored by Voronoi volume; in crystal, V=11.67Å3

Excess volume triggers string-like displacement sequence

Net effect – transfer volume from one end of the string to the other

Displacive not diffusive volume transport

0 ps 1.8 ps 3.6 ps 4.2 ps3.0 ps

Find Strings and Determine their Find Strings and Determine their LengthsLengths The atom is treated as mobile if

Find string pair among mobile atoms using

The Weight-averaged mean string length:

0 00.35 0 0.86i ir t rr r

0min 0 , 0 0.43i j i jt t r r r r r

2l

l

l P tl t

lP t

t = 4 ps at 1000K

t = 4 ps at 800K

Strings in Stationary & Migrating Strings in Stationary & Migrating BoundaryBoundary

Even in a stationary boundary, there is substantial string-like cooperative motion

String length shows maximum at T* (~80 ps)

Most of the strings form lines parallel to the tilt-axis

Boundary migration tends to decorrelate the cooperative motion, shorten T* from ~80 ps to ~26 ps

Sta

tionary

B

ou

ndary

Mig

rati

ng

B

ou

ndary

Atomic Configuration During Atomic Configuration During MigrationMigration plane X-Z

Atom positions during a period in

which boundary

moves by 1.5 nm

Color time red=late

time, blue=early

time

Atomic displacements symmetry of the transformation

Trans-boundary plane X-ZAtom positions during boundary moves downward by 1.5 nm

Color – Voronoi volume change – red= ↑over 10%, blue = ↓over 10%

Excess volume triggers Type II displacement events

Type II DisplacementsType II Displacements What determines how fast a boundary What determines how fast a boundary moves?moves?

The larger the excess volume, the faster the boundary moves More volume easier Type II events faster boundary motion

Excess Volume /V N A

Rate Controlling Events

This suggests that both of these quantities provide different views of the same types of events during boundary migration. These events are not the string-like cooperative motions (26 ps = T* << t* = 130 ps).

Displacement Distribution FunctionDisplacement Distribution FunctionStationary Boundary Migrating Boundary

For t ~ 0.8ps Gs is approximately Gaussian For t < t*, Gs for the migrating and stationary boundaries are very

similar. For t > t*, new peaks develop at r = 1.3 and r = 2.0 Ǻ and the

peak at r0 begins to disappear