Delocalization and phase transitions in Pr: Theory

Abstract

Density-functional electronic structure calculations have been used to investigate the high pressure behavior of Pr at low temperature. Several phase transitions are suggested by these calculations and they agree well with available experimental data. At low pressure, a dhcp $(\mathrm{Pr}\ensuremath{-}\mathrm{I})\ensuremath{\rightarrow}\mathrm{fcc} (\mathrm{Pr}\ensuremath{-}\mathrm{II})$ transition is calculated to occur at 60 kbar. Not considering the Pr-III phase, which is computationally too demanding, Pr-II transforms to the $\ensuremath{\alpha}\ensuremath{-}\mathrm{U}$ (Pr-IV) phase at 165 kbar. This latter transition is accompanied by a volume collapse of about 10% and is driven by delocalization of the $4f$ electrons in Pr. The axial ratios $(b/a$ and $c/a)$ and the internal parameter y of Pr-IV were calculated as a function of compression. y and $c/a$ are rather insensitive to the compression whereas $b/a$ decreases significantly with increasing pressure. At about 1 Mbar a new phase is predicted, namely a body-centered-tetragonal (bct) structure with a $c/a$ axial ratio of 1.78. This new phase is stable up to very high pressures but at a sixfold compression an ultimate hexagonal close-packed (hcp) structure is predicted. The calculated high pressure behavior of Pr is similar to that of the early actinide Pa. Pressure induced increase in $4f\ensuremath{-}\mathrm{orbital}$ overlap, occupation and band width together with an increased electrostatic Coulomb interaction with pressure are the key components in stabilizing the high pressure phases of Pr.