Effects of Surface and Grain Boundary on Temperature-Pressure Nano-Phase Diagrams

Temperature-pressure phase diagrams can provide guidance for materials preparation and application, but nano-phase diagrams are scarce. Coordination environment of atoms located at surface and grain boundary is different to that of interior ones, indicating the non-negligible surface and grain boundary effects on nano-phase transitions. The surface effect has been universally considered in previous theoretical models, but its size-dependence has been ignored, while the grain boundary effect has rarely been explored. Here, the surface and grain boundary effects are modeled using a thermodynamic approach to construct the nano-phase diagrams of carbon and boron nitride. As the size is reduced, the additional pressure induced by these two effects raises, contributing to the transition from thermodynamically stable phases to metastable ones, and the phase boundary shifts to low temperature and low pressure. Our prediction agrees well with available literature results.