Free energy of grain boundary phases: Atomistic calculations for Σ5(310)[001] grain boundary in Cu

Atomistic simulations are employed to demonstrate the existence of a well-defined thermodynamic phase transformation between grain boundary (GB) phases with different atomic structures. The free energy of different interface structures for an embedded-atom-method model of the Sigma 5(310)[001] symmetric tilt boundary in elemental Cu is computed using the nonequilibrium Frenkel-Ladd thermodynamic integration method through molecular dynamics simulations. It is shown that the free-energy curves predict a temperature-induced first-order interfacial phase transition in the GB structure in agreement with computational studies of the same model system. Moreover, the role of vibrational entropy in the stabilization of the high-temperature GB phase is clarified. The calculated results are able to determine the GB phase stability at homologous temperatures less than 0.5, a temperature range particularly important given the limitation of the methods available hitherto in modeling GB phase transitions at low temperatures. The calculation of GB free energies complements currently available 0 K GB structure search methods, making feasible the characterization of GB phase diagrams.