Grain-boundary metastability and its statistical properties

Grain-boundary (GB) structure and properties are usually analyzed in terms of ground-state (minimum-energy) GB states. However, global equilibrium is rarely achieved in materials. In this paper, we investigate the nature of GB metastability and its impact on material properties. Higher-energy GB states can be the result of nonequilibrium processes or simply thermal excitations. While the existence of limited GB metastability is widely known for a few simple GBs, we demonstrate that the multiplicity of metastable GB states is, in general, very large. This conclusion is based upon extensive atomistic bicrystal simulations for both symmetric tilt GBs and twist GBs in three very different materials. The energies of these GB states are densely distributed so that the dependence of the GB energy on misorientation is better described as an energy band rather than as a single curve as in the traditional picture. Based upon the distribution of metastable GB states, we introduce a GB statistical-mechanics picture and apply it to predict finite-temperature equilibrium and nonequilibrium properties. When GB multiplicity exists, GB structures can be thought of as domains of different GB states separated by various classes of line defects. The existence of a large set of metastable GB states, very close in energy, suggests an analogy between the behaviors of GBs and glasses and implies the potential for GB engineering.