Understanding the quadrupolar structures of UPd3

UPd3 exhibits four phase transitions below , attributed to a succession of antiferroquadrupolar (AFQ) orderings of the 5f2 uranium ions localised on the quasi-cubic sites of the dhcp crystal structure. From earlier polarised neutron diffraction measurements in a magnetic field, we proposed that the order parameter of the phase below T0 is Qx2-y2 and a model for the order parameters of the four phases was subsequently developed. This model has now been tested experimentally with measurements of the azimuthal dependence of the intensities of the quadrupolar reflections in the different phases, by means of X-ray resonant scattering (XRS) studies at ESRF. The results indicate that the order parameter, in zero field, of the phase below T0 is Qzx. Our model provides an explanation for these apparently contradictory results. New measurements of the heat capacity of UPd3 at low temperatures have revealed the entropy changes at each of the four transitions. We find that the entropy changes (DeltaS) at T0 and are minimal, whereas DeltaS is large at . From this information together with the new XRS results, we have extended our model to provide an explanation of the AFQ structures of UPd3.