An ab initio study of structural phase transitions of crystalline aluminium under ultrahigh pressures based on ensemble theory

Hydrostatic Equation of State of bcc Bi by Directly Solving the Partition Function

“…It is known that exactly solving the PF involving a 3N-fold configurational integral far exceeds the capability of the current computer technologies, so the EOS of bcc Bi has never been calculated by directly solving the PF at the level of the first principles calculating the interatomic energies. Recently, a direct integral approach (DIA) to the PF with ultrahigh precision and efficiency was established by Ning et al [27] and has been successfully used to calculate the EOSs of solid copper [27], iridium [28], argon [29], and 2-D materials [30], and to reproduce the phase transitions of crystal vanadium [31], zirconium [32], and aluminum [33]. In particular, a very recent work on the high-temperature and simultaneously high-pressure EOS of tungsten [34] showed that, compared with the available static compression experiments, all the deviations in the calculated results by the DIA were within or comparable to the uncertainty of the experiments.…”

Hydrostatic Equation of State of BCC Bi by Direct Solving the Partition Function

“…It is known that exact solving the PF involving a 3N-fold configurational integral far exceeds the capability of current computer technologies, so the EOS of bcc Bi has never been calculated by direct solving the PF at the level of first principles calculating the interatomic energies. Recently, a direct integral approach (DIA) to the PF with ultrahigh precision and efficiency was established by Ning et al [27], and has been successfully used to calculate the EOS of solid copper [27], iridium [28], argon [29], and 2-D materials [30], and reproduce the phase transition of crystal vanadium [31], zirconium [32], and aluminum [33]. In particular, a very recent work on the high-temperature and simultaneously high-pressure EOS of tungsten [34] showed that compared with available static compression experiments, all the deviations of the calculated results by DIA were within or comparable to the uncertainty of the experiments.…”