Thermodynamic stability and kinematic accessibility of curved grain boundaries in directionally solidified bicrystals

Abstract

Grain boundaries always have a positive excess free energy that drives grain growth and structural evolution during high-temperature heat treatments. Grain boundaries can, however, become trapped in a metastable configuration because of the geometry or composition of the specimens in which they are contained. For example, second phase dispersoids can pin grain boundaries in a polycrystal, and thermal grooves can pin grain boundaries in thin films and wires. In these examples of frustrated grain boundary systems, further reduction in the grain boundary area is energetically preferred, but grain boundary migration is arrested because energy is required to create additional grain boundary surface area and de-pin from the obstacle. In this work, we consider an idealized class of frustrated grain boundaries, namely curved grain boundaries in geometrically complex bicrystals. By calculating the energy landscape of the grain boundary configuration space, we show that the local stability of these curved grain boundaries is a sensitive function of the bicrystal shape. We also assess the trajectory of curved grain boundaries in bicrystals grown via directional solidification to determine which grain boundary configurations are physically realizable. By comparing these two analyses, we find that a curved grain boundary may be thermodynamically metastable but kinematically inaccessible, highlighting the general importance of thermodynamics and kinematics in descriptions of frustrated grain boundary systems encountered in a wide range of different materials.