MOLECULAR DYNAMICS SIMULATION OF STRESS INDUCED GRAIN BOUNDARY MIGRATION IN NICKEL

1. σ Free Surface 11 22 v/p 33 q Grain 2 22 11 33 ε* Grain Boundary Z ε • Application of Driving Force • Ideally, we want • constant driving force during simulation • avoid NEMD • no boundary sliding • Use elastic driving force • even cubic crystals are elastically anisotropic – equal strain  different strain energy • driving force for boundary migration: difference in strain energy density between two grains • Apply strain • apply constant biaxial strain in x and y • free surface normal to z provides zero stress in z Grain1 Grain2 Grain 1 X • Linear Elastic Estimate of Driving Force • Non-symmetric tilt boundary • [010] tilt axis • boundary plane (lower grain) is (001) • Present case: S5 (36.8º) • Strain energy density • determine using linear elasticity Y Free Surface p GB Motion at Zero Strain Non-Linear Driving Force Driving Force • Non-linear dependence of driving force on strain2 • Driving forces are larger in tension than compression for same strain (up to 13% at e0=0.02) • Compression and tension give same driving force at small strain (linearity) Expand stress in powers of strain: Implies driving force of form: • Fluctuations get larger as T↑ Steady State Migration (Typical) Velocity vs. Driving Force Mobility Determination of Mobility 1000K 800K 1200K 1400K • At high T, fluctuations can be large • Velocity from mean slope • Average over long time (large boundary displacement) • Velocity under tension is larger than under compression (even after we account for elastic non-linearity) • Difference decreases as T ↑ • Activation energy for GB migration • is ~ 0.26 ±0.08eV • Determine mobility by extrapolation to zero driving force • Tension (compression) data approaches from above (below) MOLECULAR DYNAMICS SIMULATION OF STRESS INDUCED GRAIN BOUNDARY MIGRATION IN NICKEL Hao Zhang, Mikhail I. Mendelev, David J. Srolovitz Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08540 • Background • Goal: Determine grain boundary mobility from atomistic simulations • Methods based upon capillarity driving force are useful, but not sufficient • gives reduced mobility, M*=M(g+g”), rather thanM • boundary stiffness g+g”not readily available from atomistic simulations • average over all inclinations • Flat boundary geometry can be used to directly determine mobility, but subtle (Schönfelder, et al.) • Molecular Dynamics • Velocity Verlet • Voter-Chen EAM potential for Ni • Periodic BC in X, Y, free BC in Z • Hoover-Holian thermostatand velocity rescaling • 12,000 - 48,000 atoms, 0.5-10 ns Non-Linear Stress-Strain Response • Typical strains • as large as 4% (Schönfelder et al.) • 1-2% here • Strain energy density • Apply strain εxx=εyy=ε0and σzz=0 to perfect crystals, measure stress vs. strain and integrate to get the strain contribution to free energy • Includes non-linear contributions to elastic energy • Conclusion • Developed new method that allows for the accurate determination of grain boundary mobility as a function of misorientation, inclination and temperature • Activation energy for grain boundary migration is finite; grain boundary motion is a thermally activated process • Activation energy is much smaller than found in experiment (present results 0.26 eV in Ni, experiment 2-3 eV in Al) • The relation between driving force and applied strain2 and the relation between velocity and driving force are all non-linear • Why is the velocity larger in tension than in compression?