Elastic Stiffnesses, Debye Temperatures, and Tc in Cuprates
H M. Ledbetter, K Sudook
For cuprate superconductors and related oxides, we review some aspects of their elastic constants. We consider the systematics of the bulk-modulus/atomic-volume (B/Va) relationship. For nonsuperconducting oxides, the B-Va diagram shows that most oxides fall in three sets: (1) rocksalt crystal structure, AO; (2) perovskite crystal structure, ACO3; and (3) transition-metal oxides ranging through stoichiometries of AO, A3O4, A2O. Seventeen oxide superconductors show a surprisingly narrow Va range and a relatively narrow range of B=116 19 GPa. B- Va slopes depart from expectations from a simple ionic-crystal model. Within a superconductor subgroup for example, La-O or Tl-O, higher B corresponds to higher Tc. Because the in-plane (CuO2-plane) compressibility probably varies little among these cuprates, the out-of-plane compressibility should correlate inversely with Tc. We consider also the relationship between Tc and the Debye characteristic temperature θ, which enters the BCS Tc expression in two ways. (Theta values come simply and accurately from the elastic constants.) Contrary to BCS (electron-phonon) superconductors where lattice softening (lower θ) increases Tc, in the cuprates Tc increases with increasing θ. This implies strongly that phonons participate in the basic high-Tc mechanism in cuprates, even though most theories ignore phonons.
Elastic Stiffnesses, Debye Temperatures, and T<sub>c</sub> in Cuprates