Study of an Impurity Mode Using Specific-Heat Measurements

Abstract

The low-frequency impurity mode in KCl: Li first observed through thermal-conductivity measurements by Baumann has been studied by measuring the specific heat between 0.06 and 2.0\ifmmode^\circ\else\textdegree\fi{}K for lithium concentrations from 2\ifmmode\times\else\texttimes\fi{}${10}^{17}$ to 8\ifmmode\times\else\texttimes\fi{}${10}^{18}$${\mathrm{cm}}^{\ensuremath{-}3}$. The specific-heat anomaly is of the Schottky type. In crystals doped with ${\mathrm{Li}}^{6}$Cl, the anomaly peaks at a temperature 40% higher than in crystals doped with ${\mathrm{Li}}^{7}$Cl. This large isotope effect proves the correctness of the model proposed by Lombardo and Pohl according to which this mode is caused by the tunneling of the substitutional ${\mathrm{Li}}^{+}$ ion between several equivalent off-center equilibrium sites. The influence of a static electric field on the specific-heat anomaly has also been studied. It can be explained through a polarization of the tunneling states. The analysis of our data is based on the calculations by Gomez, Bowen, and Krumhansl, and by Devonshire. We conclude that the zero-field tunnel splitting is ${10}^{\ensuremath{-}4}$ eV (0.82 ${\mathrm{cm}}^{\ensuremath{-}1}$), that the potential minima between which the ion can tunnel are displaced by 1.2 \AA{} in the $〈111〉$ directions from the center of the potassium vacancy, and that the effective positive charge ${e}^{*}$ of the lithium ion is 0.5 of the electronic charge, with an error of \ifmmode\pm\else\textpm\fi{}10%. At high concentrations the anomaly broadens. This is interpreted through a concentration-dependent stress broadening of the tunneling states. The data provide no evidence for a dipole-dipole interaction of a ferroelectric type. Contrary to the prediction by Quigley and Das, no tunneling states have been observed through specific-heat measurements in KBr: Li. Hence, it is concluded that the reason for the occurrence of a central instability of impurity ions is still not fully understood.