Evaluation of thermodynamic equations of state across chemistry and structure in the materials project

Abstract

Thermodynamic equations of state (EOS) for crystalline solids describe material behaviors under changes in pressure, volume, entropy and temperature, making them fundamental to scientific research in a wide range of fields including geophysics, energy storage and development of novel materials. Despite over a century of theoretical development and experimental testing of energy-volume (E-V) EOS for solids, there is still a lack of consensus with regard to which equation is indeed optimal, as well as to what metric is most appropriate for making this judgment. In this study, several metrics were used to evaluate quality of fit for 8 different EOS across 87 elements and over 100 compounds which appear in the literature. Our findings do not indicate a clear "best" EOS, but we identify three which consistently perform well relative to the rest of the set. Furthermore, we find that for the aggregate data set, the RMSrD is not strongly correlated with the nature of the compound, e.g., whether it is a metal, insulator, or semiconductor, nor the bulk modulus for any of the EOS, indicating that a single equation can be used across a broad range of classes of materials.

Origin of observed narrow bandgap of mica nanosheets

“…2 . The Vinet equation of states is asserted to be more suited for flexible structures 25 , 26 . Since mica possesses great flexibility with significant anharmonicity, we employed the Vinet equation, which takes the following form 27 , 28 : where E min and V min are the minimum energy and the corresponding volume, respectively; B 0 is the bulk modulus, and is the derivative of the bulk modulus with respect to pressure.…”

Finite Strain Analysis of Shear and Compressional Wave Velocities

“…Significant work has previously been done to compare the results of either experimental measurements or first‐principles (quantum mechanical) calculations against different functional forms for the pressure‐volume equations of state of condensed matter (e.g., Birch, ; Davies, ; Jeanloz, ; Latimer et al, ). The general result is that the Eulerian finite‐strain formulation is consistent with combined infinitesimal‐ and finite‐strain measurements, whereas other popular forms are not (e.g., Murnaghan, Slater, and Lagrangian finite‐strain).…”

Convergence acceleration in machine learning potentials for atomistic simulations

“…We calculated a variety of bulk mechanical and defect properties in each metal and lattice. Specifically, we calculated the Eulerian–Birch 49 equation of state (EOS)-derived quantities such as equilibrium volume-per-atom and cohesive energy; linear-elastic mechanical properties including stiffness matrix elements, the Poisson ratio, as well as bulk, shear, and Young's moduli; and point defect formation energies for vacancies, O h , and T d self-interstitials. The equations and procedures for these property calculations have been fully described elsewhere.…”