Thermodynamic stability limit of the crystalline state from the Gibbs perspective

Understanding the superheating of crystals may serve as essential information for unraveling the mechanisms of homogeneous melting. Superheated crystals have been observed in experiments for decades and have broad implications in nanoscale embedded devices; however, the full extent of the metastable superheated crystalline state within equilibrium thermodynamic changes remains uncertain. Here, we investigate this problem from a geometrical perspective of the Gibbs's volume-entropy-internal energy thermodynamic surface. We find that in a homogeneous melting process, the limit of the superheated crystal can be defined as the state at which the crystal's internal energy or enthalpy, depending on whether the constraint condition is constant volume or pressure, equals the value of this property at the state where heterogeneous freezing begins. We demonstrate that the thermodynamic foundations of several different melting simulation methods, which previously were understood as mostly independent from each other, can be unified and elucidated from the same rigorous and quantitative perspective of the Gibbs surface. By tracking the trajectories of atoms relative to their equilibrium positions, we have identified the mechanisms of cooperative diffusion in the superheated face-centered-cubic Lennard-Jones crystal. Such diffusive motion is undergone in a manner that hops toward the first-nearest neighbor while keeping the crystalline structure unchanged.