First-principles calculation of the configurational energy density of states for a solid-state ion conductor with a variant of the Wang and Landau algorithm

Jason D. Howard
Phys. Rev. E 102, 063304 – Published 14 December 2020
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Abstract

In this work, a variant of the Wang and Landau algorithm for calculation of the configurational energy density of states is proposed. The algorithm was developed for the purpose of using first-principles simulations, such as density functional theory, to calculate the partition function of disordered sublattices in crystal materials. The expensive calculations of first-principles methods make a parallel algorithm necessary for a practical computation of the configurational energy density of states within a supercell approximation of a solid-state material. The algorithm developed in this work is tested with the two-dimensional (2d) Ising model to bench mark the algorithm and to help provide insight for implementation to a materials science application. Tests with the 2d Ising model revealed that the algorithm has good performance compared to the original Wang and Landau algorithm and the 1/t algorithm, in particular the short iteration performance. A proof of convergence is presented within an adiabatic assumption, and the analysis is able to correctly predict the time dependence of the modification factor to the density of states. The algorithm was then applied to the lithium and lanthanum sublattice of the solid-state lithium ion conductor Li0.5La0.5TiO3. This was done to help understand the disordered nature of the lithium and lanthanum. The results find, overall, that the algorithm performs very well for the 2d Ising model and that the results for Li0.5La0.5TiO3 are consistent with experiment while providing additional insight into the lithium and lanthanum ordering in the material. The primary result is that the lithium and lanthanum become more mixed between layers along the c axis for increasing temperature. In part, the simulation of the disordered Li0.5La0.5TiO3 system serves as a benchmark for what size systems are currently and in the near future practical to calculate with density functional theory methods.

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  • Received 30 January 2020
  • Revised 20 October 2020
  • Accepted 4 November 2020

DOI:https://doi.org/10.1103/PhysRevE.102.063304

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Jason D. Howard*

  • Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA

  • *jdhoward@anl.gov

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Vol. 102, Iss. 6 — December 2020

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