Atomistic Mechanism for Grain Boundary Migration: Molecular Dynamics Studies Hao Zhang a, David J. Srolovitz a, Jack F. Douglas b, and James A. Warren b a Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ b National Institute of Standards and Technology, 100 Bureau Drive, Stop 8554, Gaithersburg, MD Introduction  Grain boundary migration is the central feature of grain growth, recrystallization I. controls final grain size, texture, …  Understanding of boundary structure I. low temperature observations  Understanding of boundary migration I. macroscopic migration rate measurements II. coarse-grained rate theory III. limited atomistic simulations  Mechanisms I. melting/crystallization II. step/kink (SGBD) motion III. cooperative shuffling IV. Coupling motion  Here I.high T MD simulation of GB migration II.analysis of all atomic motion 3-d MD Simulations of Flat Boundary Migration  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: X Y Z Grain Boundary Free Surface Grain 2 Grain   5 (001) tilt boundary Statistical Measures  van Hove correlation function (Self-part), G s  Non-Gaussian Parameter,    Mean First-Passage Time (MFPT),  ( R ) R (R)(R) By looking at G s 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 G s deviates from a Gaussian distribution. This quantity characterizes how rapidly an atom escapes its local environment. Cooperative 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  5 Tilt Boundary Migration Part of the simulation cell  CSL unit cell  Atomic “jump” direction ,  - indicate which lattice Color – indicates plane A/B I IIa III IIb IIc Types of Atomic Motions 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 Conclusions  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 plane III.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 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 Peaks? d IIa = 1.13Ǻ d IIb = 0.71Ǻ d IIc = 1.24Ǻ d III = 1.95 Ǻ  The broad peak at r = 1.3 Ǻ in the G s 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 String Boundary Plane - XY  Colored by Voronoi volume; in crystal, V=11.67Å 3  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 ps1.8 ps3.6 ps4.2 ps3.0 ps Find Strings and Determine their Lengths  The atom is treated as mobile if  Find string pair among mobile atoms using  The Weight-averaged mean string length:  t = 4 ps at 1000K  t = 4 ps at 800K Strings in Stationary & Migrating Boundary  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 Stationary Boundary Migrating Boundary Atomic Configuration During Migration 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-Z Atom 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 Displacements What determines how fast a boundary moves?  The larger the excess volume, the faster the boundary moves  More volume  easier Type II events  faster boundary motion 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 Function Stationary Boundary Migrating Boundary  For  t ~ 0.8ps G s is approximately Gaussian  For  t < t*, G s 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 r 0 begins to disappear