  Surface energies and surface elasticity largely affect the mechanical
response of nanostructures as well as the physical phenomenon associated with
surfaces such as evaporation and adsorption. Studying surface energies at
finite temperatures is therefore of immense interest for nanoscale
applications. However, calculating surface energies and derived quantities from
atomistic ensembles is usually limited to zero temperature or involve
cumbersome thermodynamic integration techniques at finite temperature. Here, we
illustrate a technique to identify the energy and elastic properties of
surfaces of solids at non-zero temperature based on a Gaussian phase packets
(GPP) approach (which in the isothermal limit coincides with a maximum-entropy
formulation). Using this setup, we investigate the effect of temperature on the
surface properties of different crystal faces for six pure metals -- copper,
nickel, alumimum, iron, tungsten and vanadium -- thus covering both FCC and BCC
lattice structures. While the obtained surface energies and stresses usually
show a decreasing trend with increasing temperature, the elastic constants do
not show such a consistent trend across the different materials and are quite
sensitive to temperature changes. Validation is performed by comparing the
obtained surface energy densities of selected BCC and FCC materials to those
calculated via molecular dynamics.
