  We report the phase diagram of the doping series U_2Pt_xRh_(1-x)C_2, studied
through measurements of resistivity, specific heat and magnetic susceptibility.
The Neel temperature of U_2RhC_2 of ~ 22 K is suppressed with increasing Pt
content, reaching zero temperature close to x=0.7, where we observed signatures
of increased quantum fluctuations. In addition, evidence is presented that the
antiferromagnetic state undergoes a spin-reorientation transition upon
application of an applied magnetic field. This transition shows non-monotonic
behaviour as a function of x, peaking at around x=0.3. Superconductivity is
observed for x>=0.9, with T_c increasing with increasing x. The reduction in
T_c and increase in residual resistivity with decreasing Pt content is
inconsistent with the extension of the Abrikosov-Gor'kov theory to
unconventional superconductivity.
