#GRAIN BOUNDARY FREE#

Accordingly, there are three generalized forces (per unit area) associated with these motions (variations of the free energy with respect to three displacements). Hence, GB motion is associated with three orthogonal diplacements (and velocities): GB migration (perpendicular to the GB plane) and translations of one grain with respect to the other (in two directions tangent to the GB plane). The shear-coupling factor (ratio of GB sliding and migration rates) also depends on the nature of the driving force ( 44). However, if the GB mobility does depend on the nature of the driving force, the notion of a GB mobility should be expanded. This dependence contradicts the widely accepted notion that GB mobility is an intrinsic GB property (independent of the source of the driving force). Recent studies ( 42– 45) suggest that, because of shear coupling, GB mobility depends on the origin of the driving force for GB migration (stress versus jumps in chemical potential across a GB). The importance of shear coupling in microstructure evolution is illustrated in experimental observations of stress-assisted grain growth in nanocrystalline metals ( 27, 30). Shear coupling has been reported in experiments for both metals and ceramics and in a wide range of MD simulations ( 34– 44). GB migration may also be driven by the application of a shear across the GB plane. Olmsted and coworkers ( 17, 20) systematically studied the mobility of 388 GBs (different macroscopic, bicrystallographic degrees of freedom) in Ni as a function of temperature. More recently, molecular dynamics (MD) simulations have been employed to study GB mobilities in bicrystals as a function of many of the same variables ( 13– 22) and driving forces ( 13, 15). GB mobility has been measured in many different metals and ceramics and as a function of several variables (e.g., temperature, bicrystallography, and solute concentration) in bicrystal experiments with different types of driving forces, as summarized in ref. Normally, the GB mobility is defined ( 1) as the ratio of the GB velocity v to the thermodynamic driving force (per area) F in the limit of infinitesimal driving force, M = lim F → 0 v / F. The most important dynamical property for the evolution of polycrystalline microstructures (e.g., grain growth, recrystallization) is the grain-boundary (GB) mobility. We demonstrate that stress generation during GB migration (shear coupling) necessarily slows grain growth and reduces GB mobility in polycrystals.

Finally, we examine the impact of the generalization of the mobility for applications in classical capillarity-driven grain growth. For any GB, which disconnection modes dominate depends on the nature of the driving force and the mobility component of interest. T c is related to the operative disconnection mode(s) and its (their) energetics. We develop a disconnection dynamics-based statistical model that suggests that GB mobilities follow an Arrhenius relation with respect to temperature T below a critical temperature T c and decrease as 1 / T above it. We demonstrate that some of these mobility components increase with temperature, while, surprisingly, others decrease. Performing molecular dynamics (MD) simulations on a symmetric-tilt GB in copper, we demonstrate that all six components of the GB mobility tensor are nonzero (the mobility tensor is symmetric, as required by Onsager). Hence, the GB mobility must be a tensor (the off-diagonal components indicate shear coupling). GB motion can be driven by a jump in chemical potential across a GB or by shear applied parallel to the GB plane the driving force has three components. While the GB velocity is normally associated with motion of the GB normal to the GB plane, there is often a tangential motion of one grain with respect to the other across a GB i.e., the GB velocity is a vector. The grain-boundary (GB) mobility relates the GB velocity to the driving force.

Grain boundary