Thermodynamics of the superconducting phase transformation in highT_cceramics with magnetoelectric effects

A second order phase transformation in a dielectric ceramic superconductor is shown to relate jumps in physical properties to the ratio of state variables, i.e., to the phase boundary, near the critical point. The major jumps in specific heat, compressibility, permittivity, permeability, and spinodal composition curvature, between the normal and superconducting phases, are found from the continuity of the entropy, volume, electromagnetic fields (with zero fields), and chemical equilibrium. The thermal expansion, pyroelectric effects, and the piezoelectromagnetic effects are important differences between ceramic and metallic superconductors. The most important conclusions from experimental measurements are that the lattice plays a minor role in the superconductor transformation while the magnetoelectric jump may be related to the jump in permeability, i.e., the Meissner effect, and the jump in permittivity. The oxygen miscibility gap which controls order/disorder transformations thermodynamically mandate that only metastable compositions are obtained in the metal oxide, so absolute stability of the system may never be achieved. An explicit criterion to suggest other superconductor systems is given from magnetoelectric materials, i.e., some of the pervoskites.