atomistic mechanism for grain boundary migration: molecular dynamics studies
DESCRIPTION
11. 22. 33. Free Surface. 22. 11. q. I. 33. Grain 2. III. IIa. IIb. IIc. Z. Grain Boundary. X. Grain 1. Y. R. Introduction. 3-d MD Simulations of Flat Boundary Migration. Cooperative Motion. Statistical Measures. Free Surface. Boundary Plane - XY. - PowerPoint PPT PresentationTRANSCRIPT
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