  Specific heat measurements in zero magnetic field are presented on a
homologous series of geometrically frustrated, antiferromagnetic, Heisenberg
garnet systems. Measurements of Gd3Ga5O12, grown with isotopically pure Gd,
agree well with previous results on samples with naturally abundant Gd, showing
no ordering features. In contrast, samples of Gd3Te2Li3O12 and Gd3Al5O12 are
found to exhibit clear ordering transitions at 243 mK and 175 mK respectively.
The effects of low level disorder are studied through dilution of Gd3+ with
non-magnetic Y3+ in Gd3Te2Li3O12. A thorough structural characterization, using
X-ray diffraction, is performed on all of the samples studied. We discuss
possible explanations for such diverse behavior in very similar systems.
