Cascading crystallographic transitions α → ω → β → β’→ β" and melting curve of elemental zirconium

Pressure-induced structural phase transitions of zirconium: an ab initio study based on statistical ensemble theory

“…Despite of the following experiment [21] failing to find the phenomenon, the experiment by Stavrou et al [22] successfully reproduced the transition of β → β ′ at the transition pressure of 58 GPa accompanied with a prominent 4% volume collapse and attributed the driving force to the anharmonicity of lattice dynamics in β-phase [29], which was manifested by their quantum molecular dynamics (QMD) simulations of a quenching process from 1000 K to 300 K at a cooling rate of 100 K per picosecond. Gal [30] further indicated a second isostructural transition of β ′ → β ′ ′ above 110 GPa by more cautiously fitting the data from [22] to two commonly-used empirical Birch-Murnaghan [31] and Vinet [32] equations of states (EOSs). Nevertheless, three latest hydrostatic and nonhydrostatic experiments up to 150 GPa separately conducted by Pigott et al [23], Anzellini et al [24] and O'Bannon et al [25] did not exhibit the evidence of the phenomenon and the impacts from sample impurity, non-hydrostaticity or the inaccurately calibrated EOS of the pressure markers were respectively considered to be the cause accounting for the observed abnormal volume collapse in [20,22].…”

“…According to the determined transition pressure, the P-V EOSs of α and ω-phases in a pressure range of 0-25 GPa at 300 K by equation ( 2) are plotted in figure 3 (the higher end of the pressure range of the ω-phase is discussed in the next subsection). The atomic volume at ambient conditions, V 0 , by the EOS is determined to be 23.58 Å 3 /atom, and the relative deviations, |V 0(DIA) − V 0(EXP) |/V 0(EXP) , are about 1.11% compared with 23.32 Å 3 /atom from R [27] using third-order Birch-Murnaghan EOS, 1.25% compared with 23.20 Å 3 /atom from [24] using Rydberg-Vinet EOS [74] and 1.64% compared with 23.2 Å 3 /atom from [30] using Vinet EOS to fit the data measured in [22]. The relative deviations of P-V EOS, |P DIA − P EXP |/P EXP , of the α-phase are 0.34%, 0.69% and 1.01% compared with the experimental data from [20,22] and [24] respectively, and are 0.68%, 1.14% and 1.46% respectively in terms of the ω-phase.…”

Una extensión teórica aplicada a los ácidos puros de cadena larga en la fase líquida para analizar su comportamiento en la fase sólida

“…to mention that Gal 2021[23], has analysed the phases α, ß, ß› and ß" which showed different bulk moduli K T and K To ' and different zero pressure volumes (Vo) than those reported in the literature.…”