Surface Phase Diagrams from Nested Sampling

Atomic-scale modeling of surface phase equilibria often focuses on temperatures near zero Kelvin due to the difficulty in computing the free energy of surfaces at finite temperatures. The Bayesian-inference-based nested sampling (NS) algorithm allows modeling surface phase equilibria at arbitrary temperatures by directly and efficiently calculating the partition function, whose relationship with free energy is well known. In this work, we extend NS to calculate surface phase diagrams, including all relevant translational, rotational, and vibrational contributions to the free energy. We apply NS to the surfaces of the Lennard-Jones solid, recording energies through the iterative compression of surface phase space rather than a specific cooling schedule. We construct the partition function from these recorded energies to calculate ensemble averages of thermodynamic properties, such as the constant-volume heat capacity and temperature-dependent order parameters that characterize the surface structure. Key results include determining the nature of phase transitions on flat and stepped surfaces, which typically feature an enthalpy-driven condensation at higher temperatures and an entropy-driven reordering process at lower temperatures, and the presence of critical points on the phase diagrams of most of the flatter facets. Overall, we demonstrate the ability and potential of NS for surface modeling and, ultimately, materials discovery.