An assessment of the long-range electric quadrupole interactions in praseodymium-filled skutterudites

Praseodymium-filled skutterudites RT₄X ₂ are body centered cubic (bcc) structures that belong to the space group Im3 (no.204) where R stands for rare earth elements (Pr, Ce, La, U, etc.), T stands for transition metal ions (Fe, Ru, Os) and X represents pnictogens (P, As, Sb). Three different praseodymium-filled skutterudites are considered in the present study: PrFe₄P₁₂, PrOs₄Sb₁₂ and PrRU₄P₁₂. These materials were explored for their crystal structure and interesting properties. Calculations are made of the following: i) the electric quadrupole moment possessed by the Pr 4f² ground state doublet, ii) the electric quadrupole moment produced by unique displacements of transition metal ions, creating a cubic to tetragonal type of distortion in the crystal, and iii) long-range quadrupole interactions between the Pr 4f² electrons and the transition metal ions. Neglecting the screening effect of the conduction electrons, the quadrupole moment associated with the ground state of the Pr 4f² electrons and with the transition metal ions are found to have similar values when a crude approximation to the radial part of 4f² electrons is used. Long-range quadrupole interactions between the Pr 4f² electrons and the transition metal ions are calculated for their three different alignments. The attractive and repulsive quadrupole interactions exhibited by the two linear quadrupoles based on their different alignments are discussed in the present work. This is a first step for creating a dynamical theory of electric quadrupole interactions in praseodymium-filled skutterudites. A complete dynamical theory should include contributions from long- and short-range quadrupole interactions among the conduction electrons, the Pr 4f² electrons, and the transition metal ions. The present work is limited to the long-range quadrupole interactions between the Pr 4f² electrons and the transition metal ions. Further studies focusing on long and short-range electric quadrupole interactions among the conduction electrons, the Pr 4f² electrons and the transition metal ions would be essential in order to more fully develop the desired theory