High-temperature fcc phase of Pr: Negative thermal expansion and intermediate valence state

A high-temperature angle-dispersive synchrotron radiation diffraction study has revealed the double hexagonal-close-packed-to-face-centered-cubic (dhcp-to-fcc) transformation in the Pr metal occurring martensitically between 575 and 1035 K. The high-temperature fcc phase shows a negative thermal expansion in the range 600--800 K, attributed to the $4f$-electron delocalization. A phenomenological theory is developed, which explains consistently the observed effect in terms of the mean valence variation of the metal as a function of temperature; it also predicts the existence of an isostructural phase transition and of a critical end point of a gas-liquid type in compressed Pr. The analysis of published data on P-T variation of conductivity of Pr supports this prediction.