  Studies in atomic-scale modeling of surface phase equilibria often focus on
temperatures near zero Kelvin due to the challenges in calculating the free
energy of surfaces at finite temperatures. The Bayesian-inference-based nested
sampling (NS) algorithm allows for modeling phase equilibria at arbitrary
temperatures by directly and efficiently calculating the partition function,
whose relationship with free energy is well known. This work extends NS to
calculate adsorbate phase diagrams, incorporating all relevant configurational
contributions to the free energy. We apply NS to the adsorption of
Lennard-Jones (LJ) gas particles on low-index and vicinal LJ solid surfaces and
construct the canonical partition function from these recorded energies to
calculate ensemble averages of thermodynamic properties, such as the
constant-volume heat capacity and order parameters that characterize the
structure of adsorbate phases. Key results include determining the nature of
phase transitions of adsorbed LJ particles on flat and stepped LJ surfaces,
which typically feature an enthalpy-driven condensation at higher temperatures
and an entropy-driven reordering process at lower temperatures, and the effect
of surface geometry on the presence of triple points in the phase diagrams.
Overall, we demonstrate the ability and potential of NS for surface modeling.
