Thermodynamic Origin of the Elusive Orthorhombic Phase of PrP5O14: A First-Principles Study

The stability of the competing orthorhombic Pnma and monoclinic P21/c phases of Praseodymium pentaphosphate (PrP5O14) have been studied using density functional theory (DFT). At 0 K, the Pnma structure is found to be preferred over the P21/c one with the enthalpy change with pressure of both phases highlighting a shift in phase preference from Pnma to P21/c at ∼2.5 GPa. Independently of the predicted high-pressure structural phase transition at 0 K, our computed elastic properties and phonon dispersion bands as a function of pressure indicate a phonon instability at ∼4.5 GPa due to the appearance of imaginary frequencies, followed by a dynamical instability at 8.5 GPa due to the violation of the Born criteria on the Pnma structure of PrP5O14. These results eliminate the orthorhombic structure as a possible high-pressure candidate for the monoclinic P21/c polymorph. Furthermore, the relative stability of the orthorhombic and monoclinic polymorphs has been evaluated at ambient pressure and as a function of temperature by means of vibrational free-energy calculations. The results indicate a free-energy crossing at 42 K, with the Pnma phase being energetically favored from 0 K to 42 K, after which the P21/c phase becomes preferred. These results demonstrate why PrP5O14 can only be obtained at ambient pressure in the monoclicnic P21/c polymorph, different to other rare earth pentaphosphates.