Antiferro--quadrupolar structures in UPd$_3$ inferred from x-ray resonant Bragg diffraction

A systematic analysis of resonant x-ray Bragg diffraction data for UPd$_3$, with signal enhancement at the U M$_{IV}$ edge, including possible structural phase-transitions leads to a new determination of the space groups of the material in the phases between $T_0 = 7.8$ K and $T_{+1}$ = 6.9 K as P222$_1$ and between $T_{-1}$ = 6.7 K and $T_{2}$ = 4.4 K as space group P2$_1$. In addition, the quadrupolar order-parameters, $<Q_{ab}>$, inferred from diffraction data in the phase between $T_{-1}$ and $T_{2}$, are $<Q_{xz}>$ and $<Q_{yz}>$ at the (103) Bragg reflection, and $<Q_{xy}>$ at the (104) reflection.