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CRYSTALSThe relaxation time governing the dielectric loss of smoky quartz crystals appears to level off as a function of temperature below 12OK, approaching a value of about 1 msec. The relaxational behaviour of the colour centres is discussed in terms of tunnelling processes.Under favorite conditions, lattice imperfections at which electrons are trapped (e.g. colour centres) may exhibit a Debye type dielectric response [1,2]. A very clear case is found with smoky quartz crystals [3], which has recently been reinvestigated [4] by the present authors, especially between 20 ° and 160OK. In this letter we wish to report our measurements on the temperature dependence of the dielectric relaxation time extended downwards to 4°K, using the same specimen, with E //c-axis.According to the well-known Debye relaxation theory the dielectric loss factor tg 8 as a function of frequency and temperature should follow the expression 4~ {E + 2~ 2 Np 2 wTin which e is the dielectric constant of the matrix, N and p the concentration and dipole strength of the centres, and T the absolute temperature.

SynopsisDielectric loss measurements on smoky quartz crystals over a wide frequency and temperature range showed, besides the well-known relaxation process at low temperatures, also a new relaxation mechanism, which becomes dominant above 100°K. There are strong arguments that both processes are due to the same type of colour centres. The rate theory in its simplest form cannot be held. The experiments are discussed with the help of Sussmann's theory of intermediate states including tunnelling processes.The deviations of the tan 6 curves from the theoretical Debye curve, due to a spread in relaxation times, were studied. At low temperature there appeared to be a uniform relation between the measured mean value (T) and the experimentally determi~led spread "rn/'rr., defined by the Fr6hlich distribution function g(T) oc r-1 for TL < z < ZH.The upper limit rH has, at constant temperature, a nearly constant value for various samples. The lower limit rL, however, varies by more than a factor 10. At high temperature only a very small spread in, values was found.I. Introduction. Several experimental and theoretical studies have been made in the iield of dielectrics in order to get more insight into the processes which lead to the relaxation of permanent electric dipoles in solids and the interactions which determine the temperature and frequency dependence of the dielectric function.In this paper we will report on the behaviour of the electric dipoles, associated with the colour centres in smoky quartz. The optical and magnetic properties of these colour centres have been studied by many authors in detaill-S). S t e v e 1 s and V o 1 g e r 7) reported the first dielectric measurements. They measured dielectric losses of the Debye type in the temperature range from 16-70°K at low frequencies on both natural smoky quartz and Xirradiated synthetic quartz crystals. They assumed that the electrons trapped at the interstitial ions, thus forming colour centres, also give rise to the high dielectric losses, found in this temperature range. These electrons in association with their trapping centres, which are effectively positively charged, obviously form electric dipoles which at each instant may point