Specific heat and thermal-conductivity measurements on cesium and thallous halide crystals at low temperatures

Abstract

Specific-heat and thermal-conductivity measurements in the temperature range of 1.7 to 20 K are reported on single crystals of CsBr, CsI, T1Br, and T1C1 and on a polycrystalline sample of T1I. All crystals display minima in the effective Debye temperatures which are reflected in maxima in $\frac{C}{{T}^{3}}$-versus-$T$ curves, and these extrema are especially pronounced for T1C1. Comparisons are made with the predictions of existing lattice-dynamics calculations, and the specific heat of T1Br is in very good agreement with the shell-model calculations of Cowley and Okazaki. A Schottky specific-heat term is resolved in the cesium halides at the lowest temperatures and attributed to hydroxyl ions; by adopting the zero-field splitting for ${\mathrm{OH}}^{\ensuremath{-}}$ in KC1, hydroxyl concentrations \ensuremath{\sim}${10}^{20}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ are estimated in CsBr and CsI. The $\frac{C}{{T}^{3}}$ maxima are fitted with Einstein terms added to the Debye backgrounds, and these fittings (together with the Schottky fits for CsBr and CsI) yield the following Debye temperatures: CsBr, 145 K; CsI, 124K; T1Br, 116 K; T1C1, 120 K; and T1I, 103 K. Thermal-conductivity data for all crystals display maxima at \ensuremath{\sim}4-5 K and an apparent ${T}^{3}$ boundary-scattering regime at the lowest temperatures. Phonon mean free paths at the higher temperatures are analyzed according to the Peierls relation, and for CsBr and T1C1 it is found that the Debye modes are the dominant heat carriers. For the remaining crystals, the Einstein modes also carry heat. (The Einstein modes at these higher temperatures dominate the specific heats, contributing up to 75% in the case of T1C1.) Thermal-conductivity measurements were also made on thin crystals (\ensuremath{\sim}0.05 cm) of CsBr, T1Br, and T1C1 to examine the boundary-scattering region. It is found that in this region the limiting phonon mean free path for CsBr scales with the crystal dimension, and it is suggested that the suppression of the thermal conductivity may be due to the hydroxyl concentration. For T1Br and T1C1, the limiting phonon mean free path is \ensuremath{\sim}0.01 cm and is independent of the crystal thickness; this behavior is attributed to a mosaic structure within these crystals.