Dependence of Grain Boundary Mobility on Boundary Plane Hao Zhang 1, Mikhail Mendelev 1,2 and David Srolovitz 1 1 PRISM, Princeton University 2 Ames Laboratory

Challenges Neither curvature driven boundary migration experiments nor simulations yield the fundamental kinetic properties for grain boundary migration, M * is the product of the mobility and grain boundary stiffness Reduced mobility is averaged over all possible inclinations The migration of a flat boundary is easier to analyze, but has several limitations Can yield grain boundary mobility dependence on inclination Is the variation of grain boundary mobility correlated with other boundary properties, such as grain boundary energy and self-diffusivity?

Elastically-Driven Migration of a Flat Boundary X Y Z Grain Boundary Free Surface Grain 2 Grain   5 (001) tilt boundary 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 Applied strain constant biaxial strain in x and y free surface normal to z   iz = 0 Driving Force based on linear Elasticity

Measured Driving Force Grain1Grain2 Typical strains 1-2%, out of linear region Measuring driving force Apply strain ε xx =ε yy =ε 0 and σ iz = 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 Fit stress: Driving force Implies driving force of form:

Determination of Mobility p v/p Determine mobility by extrapolation to zero driving force Tension (compression) data approaches from above (below)

Symmetric boundary  Asymmetric boundary  = 14.04º Asymmetric boundary  = 26.57º  Simulation / Bicrystal Geometry [010]  º

Initial Simulation Cell for Different Inclinations

Mobility vs. Inclination No mobility data available at  =0, 45º; zero biaxial strain driving force Mobilities vary by a factor of 4 over the range of inclinations studied at lowest temperature Variation decreases when temperature ↑ (from ~4 to ~2) Minima in mobility occur where one of the boundary planes has low Miller indices

Activation Energy vs. Inclination The variation of activation energy for grain boundary migration over the inclination region we studied is significant The variation of mobility becomes weaker than expected on the basis of activation energy because of the compensation effect Activation energy for the symmetric boundary is unknown

Diffusivity vs. Inclination Diffusivity shows more anisotropic at low temperature than at high temperature Most of local minimum corresponds to one of the grains normal with low Miller indices The  =0º has a change from minimum to maximum

Activation Energy and Compensation Effect The activation energy all lie between 0.5 to 0.6 eV, except for the  º symmetric boundary(1.1 eV) Compensation effect weaken the diffusivity variation based upon the activation energy for self-diffusion

Mobility, Self-diffusion and Energy At low temperature, self-diffusion and grain boundary energy have similar trend, i.e. change from minimum to maximum, but mobility has opposite trend. Mobility, self-diffusion coefficient and grain boundary energy shows local minimum at special inclination (one of the plane normal is low Miller indices) There exists correlation between those three quantities in the inclination range of 18º to 45º.

Conclusion Used stress driven GB motion to determine grain boundary mobility as a function of ,  and T Mobility is a strong function of inclination and temperature Grain boundary self-diffusion is sensitive to inclinations, i.e. grain boundary structure Minima in boundary mobility, self-diffusion coefficient and grain boundary energy occurs where at least one boundary plane is a low index plane In the inclination range from 18º to 45º, there is a strong correlation between grain boundary diffusivity, energy and mobility