DEPENDENCE OF T-C ON DEBYE TEMPERATURE THETA(D) FOR VARIOUS CUPRATES

I extend the T-c-theta(D) relationship established by Ledbetter and coworkers for La-O and Y-O, and by Dominec for Bi-O, to include Tl-O and Hg-O compounds. In BCS-McMillan materials, theta(D) occurs both in the preexponential factor in the expression T-c - theta(D) exp(-lambda(.1)) and in McMillan's expression for the electron-phonon parameter lambda = C/M <omega(2)>, where <omega> similar to theta(D). In BCS materials, T-c increases with decreasing theta(D), that is with lattice softening. In all five cuprate superconductors listed above, the opposite occurs: T-c increases with lattice stiffening. From these results, I draw two principal conclusions. First, T-c depends on phonons because it depends on theta(D), the quintessential phonon parameter. Second, the T-c-theta(D) relationship for high-T-c oxide superconductors differs dramatically from that for conventional BCS materials.