Characterization of Atomic Motions Governing Grain Boundary Dynamics

1. Characterization of Atomic Motions Governing Grain Boundary Dynamics Hao Zhang, David J. Srolovitz Princeton University Jack F. Douglas, James A. Warren National Institute of Standards and Technology

2. I III IIa IIb IIc Reminder • Types of Atomic Motions • Type I • “Immobile” – coincident sites - I dI = 0 Å • Type II • In-plane jumps – IIa, IIb, IIc • dIIa=dIIb=1.1 Å, dIIc=1.6 Å • Type III • Inter-plane jump - III • dIII=2.0 Å, atoms are likely to form string-like cooperative motion S5 [010] Tilt Asymmetric Boundary ▲,○- indicate which lattice Color – indicates plane A/B H. Zhang, D. J. Srolovitz, Acta Materialia, 54: 623; 2006

3. Outstanding Questions • What is the relationship between Type II and Type III displacements? • Type II ~100 ps, Type III ~10 ps • Does string-like cooperative motion contribute to grain boundary migration? • String || Tilt axis, Migration ┴ Grain boundary • Accurate, quantitative measurementsrequired to develop boundary migration theory • Previous studies are based upon image analysis • Can this analysis be done on-the-fly? • Previous studies require to quench atomic configurations frequently

4. String-Like Motions in Supercooled Liquids Several measures have been developed to describe this type of cooperative motion in liquids • Van Hove Correlation Function Gs • Non-Gaussian Parameter a2 • Dynamic Entropy / Mean First-passage Time, S(R)/t(R) 1. C. Donati, J. F. Douglas, W. Kob, et al., Phys Rev Lett 80, 2338 (1998). 2. Y. Gebremichael, T. B. Schroder, F. W. Starr, et al., Phys Rev E 6405 (2001). 3. Y. Gebremichael, M. Vogel, and S. C. Glotzer, J Chem Phys 120, 4415 (2004).

5. R t(R) Statistical Measurements van Hove correlation function (Self-part), Gs • Note: 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, a2 Note: thisparameter provides a measure of how much Gs deviates from a Gaussian distribution. Mean First-Passage Time (MFPT), t(R) Note: This quantity characterizes how rapidly an atom escapes its local environment.

6. Find Strings and Determine their Lengths l(Dt) • The atom is treated as mobile if • Find string pair among mobile atoms using • The Weight-averaged mean string length: Dt = 4 ps at 1000K Dt = 4 ps at 800K

7. Simulation Detail • S5 [010] tilt grain boundary with inclination a = 21.8º • Voter-Chen potential for nickel • Temperature = 800K • In the case of migrating grain boundary, apply biaxial strain exx=eyy=2% and free surfaces in Z; grain boundary migrates 2.5 nm • Save atomic configurations every 0.4 ps

8. Cooperative Motion in a Stationary Boundary All of the atoms that are members of strings of length greater than 4 at Dt = T* in a boundary plane (X-Y) view • 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

9. Displacement Distribution Function • Gs and a2 indicate Gaussian behavior when Dt<0.8 ps • The first peak in Gs represents the thermal vibration amplitude • Second and third peak corresponds the distance to the first and second nearest neighbors in the perfect crystal • No peaks in Gs are associated with the distance of Type II events – motion from one lattice to another (migration)

10. Cooperative Motion in a Migrating Boundary All of the atoms that are members of strings of length greater than 4 at Dt = T* in a boundary plane (X-Z) view • Boundary migration tends to decorrelate the cooperative motion, shorten T* from ~80 ps to ~26 ps • String along tilt axis belongs to Type III displacements

11. Rate Controlling Events • 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,

12. Rate Controlling Events (Cont’d) 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).

13. Gs for Migrating Grain Boundary • For Dt ~ 0.8ps 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 r0 begins to disappear

14. What Are those 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

15. Conclusion • We employed statistical measures to quantify grain boundary migration dynamics • 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. • The atomic motions (Type II displacements) 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