Lattice specific heat of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$

We present a calculation of the lattice specific heat of the high-temperature superconductor ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, based on a full lattice-dynamical description. The availability of a realistic lattice specific-heat function is of importance for separating the nonlattice (and possibly anomalous) contributions from the measured total specific heat. It provides a test for the appropriateness of the fitting functions and fitting ranges used in the literature, to separate the lattice contribution from the total. It is found that the Debye region [FTHETA(0)=465.5 K] extends only up to 3 K [≊0.006FTHETA(0)]. Strong deviations from Debye behavior in the range 3 to 20 K lead to a 30% drop in FTHETA(T); this roughly covers the range of Debye temperatures obtained from the experiments by various fitting procedures. One of the reasons for this spread in experimental Debye temperatures is that, if the lattice specific heat is assumed to be of the form β${\mathit{T}}^3$ outside the Debye region, an improper fitting of the measured data can lead to the wrong Debye temperature and also to the appearance of spurious nonlattice contributions to ${\mathit{c}}_{\mathit{v}}$. Sound velocities are a natural by-product of this calculation; direct comparison with experimental values for ceramic samples is not possible.