The phase diagram (T versus x) of the superconducting heavy-fermion system
U1-xThxBe13 has two irregular points which mark the endpoints of the concen
tration range where in the specific heat a double maximum structure (indica
ting two successive phase transitions) is observed. Thus at each irregular
point at least three phase boundary lines meet and, if all phase transition
s are of second order, a fourth second-order phase boundary line is expecte
d. We present specific heat measurements carefully performed on samples clo
se to the critical concentrations. As no indication of a fourth-phase bound
ary line at the irregular points was found, we discuss the thermodynamic al
ternatives to this scenario. (C) 1999 Elsevier Science B.V. All rights rese
rved.