**Step free energies at faceted solid surfaces: Theory and atomistic
calculations for steps on the Cu(111) surface**

R Freitas and T Frolov and M Asta, PHYSICAL REVIEW B, 95, 155444 (2017).

DOI: 10.1103/PhysRevB.95.155444

A theory for the thermodynamic properties of steps on faceted
crystalline surfaces is presented. The formalism leads to the definition
of step excess quantities, including an excess step stress that is the
step analogy of surface stress. The approach is used to develop a
relationship between the temperature dependence of the step free energy
(gamma(st)) and step excess quantities for energy and stress that can be
readily calculated by atomistic simulations. We demonstrate the
application of this formalism in thermodynamic-integration (TI)
calculations of the step free energy, based on molecular-dynamics
simulations, considering < 110 > steps on the *111* surface of a
classical potential model for elemental Cu. In this application we
employ the Frenkel-Ladd approach to compute the reference value of
gamma(st) for the TI calculations. Calculated results for excess energy
and stress show relatively weak temperature dependencies up to a
homologous temperature of approximately 0.6, above which these
quantities increase strongly and the step stress becomes more isotropic.
From the calculated excess quantities we compute gamma(st) st over the
temperature range from zero up to the melting point (Tm). We find that.
st remains finite up to T-m, indicating the absence of a roughening
temperature for this *111* surface facet, but decreases by roughly fifty
percent from the zero-temperature value. The strongest temperature
dependence occurs above homologous temperatures of approximately 0.6,
where the step becomes configurationally disordered due to the formation
of point defects and appreciable capillary fluctuations.

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