Atomistic Mechanism for Grain Boundary Migration Molecular Dynamics
Atomistic Mechanism for Grain Boundary Migration: Molecular Dynamics Studies Hao a Zhang , a, David J. Srolovitz Jack F. Douglas b, and James A. Warren b Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08540 b National Institute of Standards and Technology, 100 Bureau Drive, Stop 8554, Gaithersburg, MD 20899 a Introduction § Grain boundary migration is the central feature of grain growth, recrystallization controls final grain size, texture, … low temperature observations Understanding of boundary migration § EAM-type (Voter-Chen) potential for Ni § van Hove correlation function (Self-part), Gs X Y Periodic boundary conditions in x and y q One grain boundary & two free surfaces 11 22 33 Fixed biaxial strain, = xx= yy 22 § Driving force is constant during simulation § Linear elasticity: § At large strains, deviations from linearity occur, melting/crystallization step/kink (SGBD) motion cooperative shuffling Coupling motion determine driving force from the difference of the strain Atomic displacements: Dt=0. 4 ps, t=30 ps By looking at Gs for different Dt, we can trace the path that the atoms takes as they move through the system. Distribution of distances atoms travel on different time scales. § Non-Gaussian Parameter, a 2 Grain Boundary Source of driving force is the elastic energy Atomic displacements: Dt=5 ps Free Surface difference due to crystal anisotropy Mechanisms I. III. IV. Molecular dynamics in NVT ensemble 11 Grain 1 I. macroscopic migration rate measurements II. coarse-grained rate theory III. limited atomistic simulations § Boundary Plane - XY Grain 2 § § § Understanding of boundary structure I. § Cooperative Motion Statistical Measures Z I. § 3 -d MD Simulations of Flat Boundary Migration 33 Free Surface This parameter provides a measure of how much Gs deviates from a Gaussian distribution. § Mean First-Passage Time (MFPT), t(R) R S 5 (001) tilt boundary energy in the two grains: Here This quantity characterizes how rapidly an atom escapes its local environment. I. high T MD simulation of GB migration II. analysis of all atomic motion Formation of a String 0 ps 1. 8 ps 3. 0 ps Find Strings and Determine their Lengths 3. 6 ps § The atom is treated as mobile if 4. 2 ps § Substantial cooperative motions within boundary plane during migration t(R) Strings in Stationary & Migrating Boundary Atomic Configuration During Migration All of the atoms that are members of strings of length greater than 4 at Dt = T* Dt = 4 ps at 800 K plane X-Z Atom positions during a period in which boundary moves by 1. 5 nm Stationary Boundary § Find string pair among mobile atoms using Dt = 4 ps at 1000 K Boundary Plane - XY § § § Even in a stationary boundary, there is substantial stringlike cooperative motion Colored by Voronoi volume; in crystal, V=11. 67Å3 § 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 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 Atomic Path for S 5 Tilt Boundary Migration Color time red=late time, blue=early time Migrating Boundary § The Weight-averaged mean string length: § Atomic displacements symmetry of the transformation motion, shorten T* from ~80 ps to ~26 ps Type II Displacements What determines how fast a boundary moves? Characterization of Type II Motion Trans-boundary plane X-Z Atom positions during boundary moves downward by 1. 5 nm Color – Voronoi volume change – red= ↑over 10%, blue = ↓over 10% I IIa III IIb IIc Part of the simulation cell §CSL unit cell §Atomic “jump” direction , - indicate which lattice Color – indicates plane A/B Types of Atomic Motions § At short time atomic motions are harmonic – transition away from harmonic at Type I: “Immobile” – coincident sites -I, d. I= 0 Å Type II: In-plane jumps (either in A or B plane) – IIa, IIb, IIc, d. IIa=d. IIb=1. 1 Å, d. IIc=1. 6 Å Type III: Inter-plane (A/B) jump - III , d. III=2. 0 Å long times § The larger the excess volume, the faster the boundary moves § More volume easier Type II events faster boundary motion § Excess volume triggers Type II displacement events Rate Controlling Events Displacement Distribution Function Stationary Boundary What Are those Peaks? string-like motion § The transition occurs at t*~130 ps for the migrating boundary Conclusions d. IIa = 1. 13Ǻ Migrating Boundary § Transition behavior occurs on much longer time scales than T* characteristic of d. IIb = 0. 71Ǻ d. IIc = 1. 24Ǻ d. III = 1. 95 Ǻ § Molecular dynamics simulations of stress-driven boundary migration for asymmetric S 5 tilt boundaries § Employed statistical measures to quantify grain boundary migration dynamics § Three distinct types of atomic motions observed: I. II. III. § Type II motions : correlated with excess volume of boundary I. 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). § For Dt ~ 0. 8 ps Gs is approximately Gaussian § For Dt < t*, Gs for the migrating and stationary boundaries are very similar. § For Dt > t*, new peaks develop at r = 1. 3 and r = 2. 0 Ǻ and the peak at r 0 begins to disappear II. § 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 § very small displacement of coincident site atoms single atom displacements with significant components perpendicular to the boundary plane Collective motion of 2 -10 atom groups in a string-like motion parallel to the tilt axis The atomic motions across the grain boundary plane occurs on a characteristic time scale t* of ~ 130 ps. Applied driving force decreases t*. 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.
- Slides: 1