Comments welcome via email:
natalie@wfu.edu.

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First-principles estimation of partition functions representing disordered
lattices such as the cubic phases of Li_{2}OHCl and Li_{2}OHBr

Jason David Howard and N. A. W. Holzwarth

*Physical Review B * **99** 014109 (2019)
(local copy)

In order to develop computational methods that can simulate
thermodynamic properties of disordered materials at a first principles
level, we investigate the use of a random set of
configurations to evaluate the
canonical partition function of lattice-based disordered systems.
Testing the sampling method on the one and two dimensional Ising models
indicates that for the ordered system at low temperature,
convergence is achieved when
The number of samples 𝒮 is
comparable or larger than the number of configurations Ω,
while for the partially disordered system at high temperature,
convergence is achieved
for smaller sample
sizes as low as 𝒮 ≈ Ω/100 or 𝒮
≈ Ω/1000.
The sampling method is combined with first principles calculations
to examine the ordered ↔ disordered phase transition
for the Li ion electrolyte materials Li_{2}OHCl and Li_{2}OHBr.
Static lattice internal energies and
harmonic phonon free energies
were incorporated into the evaluation of the partition function.
The evaluation of the partition
function depends on the value of Ω corresponding to the number
of metastable states of the system. Accordingly,
we developed a method of
approximating Ω using the properties of the sampled
configurations. The results of the calculations are consistent with
the experimental observation that the transition temperature for
the orthorhombic ↔ cubic phase transition is
higher for Li_{2}OHCl than for Li_{2}OHBr. We expect the
sampling method to be generally useful for investigating the
thermodynamic properties of other disordered lattice
systems.
We also investigate a ``disordered subspace function'' which is
shown to satisfy inequality relationships with respect to the
Helmholtz free energy.