The specific heats of samples of BaCuO2 and BaCuO2.14, on which magnetizati
on and/or neutron-diffraction measurements had been made earlier, were meas
ured for the temperature range 0.35 less than or equal to T less than or eq
ual to 30 K in magnetic fields to 7 T. BaCuO2+x has a complex structure wit
h 90 formula units in a bcc unit cell; 6 Cu are "lone spins,'' 48 are in 8
Cu6O12 "ring clusters," and 36 are in 2 Cu18O24 "sphere clusters." The ring
and sphere clusters have ferromagnetically ordered ground states with spin
s S=3 and 9, respectively. Antiferromagnetic ordering of the ring clusters
occurs with a Neel temperature T-N(0)similar to 15 K. The specific heat of
BaCuO2 shows a cooperative ordering anomaly associated with the antiferroma
gnetic ordering of the ring clusters. Schottky-like anomalies, having maxim
a at similar to 5 and similar to 0.7 K, are identified with the ordering of
the sphere clusters and the lone spins, respectively. Only Schottky-like a
nomalies are observed for the specific heat of BaCuO2.14. It is suggested t
hat the increase in the Cu oxidation state, due to the addition of 0.14 mol
of O, increases Cu-O covalent bonding (spin compensation) and/or produces
nonmagnetic Cu3+, which in addition to the known increase in the Cu-O bond
lengths, disrupts the superexchange paths that lead to the antiferromagneti
c ordering of the ring clusters in BaCuO2. For BaCuO2 the magnetic entropy
was 90% of that predicted for the ordering of the three Cu structures. On t
he other hand, the magnetic entropy for BaCuO2.14 was only 65% of that pred
icted, which suggests a relative large suppression of some magnetic entitie
s due to the addition of 0.14 mol of O. Although BaCuO2+x is an insulator,
the specific heat has a T-proportional component that is magnetic field dep
endent and is presumably associated with the magnetic degrees of freedom.