Abstract
The relationships among the pressure P, volume V, and temperature T of solid-state materials are described by their equations of state (EOSs), which are often derived from the consideration of the finite-strain energy or the interatomic potential. These EOSs consist of typically three parameters to determine from experimental P-V-T data by fitting analyses. In the empirical approach to EOSs, one either refines such fitting parameters or improves the mathematical functions to better simulate the experimental data. Despite over seven decades of studies on EOSs, none has been found to be accurate for all types of solids over the whole temperature and pressure ranges studied experimentally. Here we show that the simple empirical EOS, P = α1(PV) + α2(PV)2 + α3(PV)3, in which the pressure P is indirectly related to the volume V through a cubic polynomial of the energy term PV with three fitting parameters α1–α3, provides accurate descriptions for the P-vs-V data of condensed matter in a wide region of pressure studied experimentally even in the presence of phase transitions.
Highlights
We show that the simple empirical equations of state (EOSs), P = α1(PV) + α2(PV)2 + α3(PV)[3], in which the pressure P is indirectly related to the volume V through a cubic polynomial of the energy term PV with three fitting parameters α1 − α3, provides accurate descriptions for the P-vs-V data of condensed matter in a wide region of pressure studied experimentally even in the presence of phase transitions
In testing whether an isothermal equations of state (EOSs) is accurate over the entire range of pressure studied experimentally, the ideal systems to analyze would be elemental chalcogens Te, Se and S because they have been studied at room temperature over wide pressure ranges (i.e., 0–330 GPa for Te, 0–150 GPa for Se, and 0–213 GPa for S), because each chalcogen undergoes a number of phase transitions with increasing P, and because their room-temperature atomic structures are known under widely different pressures
We begin our analysis by first determining the relative energies of its known atomic structures at various P on the basis of density functional theory (DFT) calculations, the details of which are described in Methods
Summary
We show that the simple empirical EOS, P = α1(PV) + α2(PV)2 + α3(PV)[3], in which the pressure P is indirectly related to the volume V through a cubic polynomial of the energy term PV with three fitting parameters α1 − α3, provides accurate descriptions for the P-vs-V data of condensed matter in a wide region of pressure studied experimentally even in the presence of phase transitions. We establish that the cubic approximation with three fitting parameters α1–α3 is accurate enough in describing the P-vs-V data for condensed matter in a wide region of pressure experimentally probed even in the presence of several structural phase transitions.
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