Low-temperature specific heats of lanthanum and yttrium phosphate glasses

Summary

The specific heats of (R₂O₃) _x (P₂O₅)_1−x glasses containing high concentrations of La³⁺ and Y³⁺ ions have been measured between 1.5K and 30K. It is shown that, in addition to the usual Debye contribution, there is an excess specific heat arising from localized vibrational states which has been discussed in terms of two distinct models. The first predicts a maximum in the temperature dependence of the excess specific heat associated with the crossover frequency from phonon to fracton behaviour. The phonon-fracton density of states used to fit the excess specific heat gives rise to model parameters having the same magnitudes as those found previously for other glasses including samarium phosphates. The second model, formulated on the basis of soft vibrations in glasses, predicts a minimum in the excess specific heat, which is also observed.