Methods for First-Principles Alloy Thermodynamics

Traditional first-principles calculations excel at providing formation energies at absolute zero, but obtaining thermodynamic information at nonzero temperatures requires suitable sampling of all the excited states visited in thermodynamic equilibrium, which would be computationally prohibitive via brute-force quantum mechanical calculations alone. In the context of solid-state alloys, this issue can be addressed via the coarse-graining concept and the cluster expansion formalism. This process generates simple, effective Hamiltonians that accurately reproduce quantum mechanical calculation results and that can be used to efficiently sample configurational, vibrational, and electronic excitations and enable the prediction of thermodynamic properties at nonzero temperatures. Vibrational and electronic degrees of freedom are formally eliminated from the problem by writing the system’s partition function in a nested form in which the inner sums can be readily evaluated to yield an effective Hamiltonian. The remaining outermost sum corresponds to atomic configurations and can be handled via Monte Carlo sampling driven by the resulting effective Hamiltonian, thereby delivering thermodynamic properties at nonzero temperatures. This article describes these techniques and their implementation in the alloy theoretic automated toolkit, an open-source software package. The methods are illustrated by applications to various alloy systems.