Symmetry lowering at the structural phase transitions inNpO2andUO2

Abstract

The structural phase transitions with electric-quadrupole long-range order in ${\mathrm{NpO}}_{2}(Fm3\ifmmode\bar\else\textasciimacron\fi{}\stackrel{\ensuremath{\rightarrow}}{m}\mathrm{Pn}3\ifmmode\bar\else\textasciimacron\fi{}m)$ and ${\mathrm{UO}}_{2}(Fm3\ifmmode\bar\else\textasciimacron\fi{}\stackrel{\ensuremath{\rightarrow}}{m}\mathrm{Pa}3\ifmmode\bar\else\textasciimacron\fi{})$ are analyzed from a group theoretical point of view. In both cases, the symmetry lowering involves three quadrupolar components belonging to the irreducible representation ${T}_{2g}({\ensuremath{\Gamma}}_{5})$ of ${O}_{h}$ and condensing in a triple-$\stackrel{\ensuremath{\rightarrow}}{q}$ structure at the X point of the Brillouin zone. The $\mathrm{Pa}3\ifmmode\bar\else\textasciimacron\fi{}$ structure is close to $\mathrm{Pn}3\ifmmode\bar\else\textasciimacron\fi{}m,$ but allows for oxygen displacements. The $\mathrm{Pa}3\ifmmode\bar\else\textasciimacron\fi{}$ ordering leads to an effective electrostatic attraction between electronic quadrupoles while the $\mathrm{Pn}3\ifmmode\bar\else\textasciimacron\fi{}m$ ordering results in a repulsion between them. It is concluded that the $\mathrm{Pn}3\ifmmode\bar\else\textasciimacron\fi{}m$ structure can be stabilized only through some additional process such as strengthening of the chemical bonding between Np and O. We also derive the relevant structure-factor amplitudes for $\mathrm{Pn}3\ifmmode\bar\else\textasciimacron\fi{}m$ and $\mathrm{Pa}3\ifmmode\bar\else\textasciimacron\fi{},$ and the effect of domains on resonant x-ray scattering experiments.