  By combining accurate heat capacity and X-ray resonant scattering results we
have resolved the long standing question regarding the nature of the
quadrupolar ordered phases in UPd_3. The order parameter of the highest
temperature quadrupolar phase has been uniquely determined to be antiphase
Q_{zx} in contrast to the previous conjecture of Q_{x^2-y^2} . The azimuthal
dependence of the X-ray scattering intensity from the quadrupolar superlattice
reflections indicates that the lower temperature phases are described by a
superposition of order parameters. The heat capacity features associated with
each of the phase transitions characterize their order, which imposes
restrictions on the matrix elements of the quadrupolar operators.
