The bcc phase of barium is a superconductor. Tc increases steeply with pressure from 0.06 K at 37 kbar to 0.5 K at 48 kbar. A fit of McMillan's expression for Tc suggests a Tc already in the millikelvin range at 30 kbar. Phonon softening as inferred from the decreasing melting curve is insufficient to account for the rise of Tc with pressure.
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Probst et al. (1977) studied this question.
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