The structural phase transitions with electric-quadrupole long-range order in ${\mathrm{NpO}}_2\left(Fm3\mathrm{}¯\overrightarrow{m}\mathrm{Pn}3\mathrm{}¯m\right)$ and ${\mathrm{UO}}_2\left(Fm3\mathrm{}¯\overrightarrow{m}\mathrm{Pa}3\mathrm{}¯\right)$ are analyzed from a group theoretical point of view. In both cases, the symmetry lowering involves three quadrupolar components belonging to the irreducible representation $T_{2g}\left({\Gamma }_5\right)$ of $O_h$ and condensing in a triple-$\overrightarrow{q}$ structure at the X point of the Brillouin zone. The $\mathrm{Pa}3\mathrm{}¯$ structure is close to $\mathrm{Pn}3\mathrm{}¯m,$ but allows for oxygen displacements. The $\mathrm{Pa}3\mathrm{}¯$ ordering leads to an effective electrostatic attraction between electronic quadrupoles while the $\mathrm{Pn}3\mathrm{}¯m$ ordering results in a repulsion between them. It is concluded that the $\mathrm{Pn}3\mathrm{}¯m$ 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 $\mathrm{Pn}3\mathrm{}¯m$ and $\mathrm{Pa}3\mathrm{}¯,$ and the effect of domains on resonant x-ray scattering experiments.

• Received 20 December 2002

DOI:https://doi.org/10.1103/PhysRevB.68.054112