Low temperature specific heat and phonon anomalies in transition metal compounds

Abstract

The specific heat of the following pairs of transition metal compounds (TMC’s) has been measured in the temperature range 1.8<T<100 K : TiN/TiC, NbC/ZrC, and TaC/HfC. Theoretical results for the lattice specific heat, obtained from phonon densities calculated on the basis of appropriate shell models agree well with the experimental data. Values for Debye temperatures and Sommerfeld coefficients are given and compared with previously published data. We show that from the difference in the lattice specific heat between the superconducting and the normal compound of each pair, it is possible to determine the average frequency of the lowest-lying phonon anomalies occurring in the superconducting TMC. For TiN, NbC, and TaC, this frequency was determined to lie at 5.8, 4.8, and 3.1 THz, respectively. These values compare favorably with results from neutron scattering experiments. Thus, specific heat measurements can serve as a valuable tool to determine the mean frequency of the phonon anomalies in the superconducting compounds of this class of materials.