t Solid State CommunicatiOOS, Vol.32, pp.ll9 3—1I95. Pergamon Press Ltd. 1979. Printed in Great Britain. ON THE THERMAL CONDUCTIVITY OF GLASSES M.A. Continentino Instituto de Fisica, Universidade Federal Fluminense, Niter~i,Brasil (Rec~eAived10 Ju.~yby R.C.C.LeLte; ~Lfrt uA.i~ed~onin 25.07.19) We estimate the numerical contribution of the interaction between like defects in glasses for the linewidth (tf Ti’) obtained in acoustical experiments. This interaction gives origin to a diffusion process with a very large diffusion constant (D = lO—~cm2 sec’). The thermal conductivity due to this diffusion process is calculated. Its temperature dependence is also obtained. 1. Introduction The random local field —-tcyh = E where Scientific interest on glasses has Ei is the energy difference betwe~nth~two incresead considerably in the last years due to states of the ith defect. In the case of the discovery by Zeller and Pohi (1) of a large isotropic coupling between pseudospins and linear term in the specific heat versus phonons the interaction J~°~ is given by (6) temperature curve, at low temperatures in a x x G.G. q variety of these substances. From the XX 1 L theoretical point of view progress has been 2 r cos (q~r..) (2) made assuming the existence of tunneling states ~ 3 in these materials (2) (3). The microscopic X origin of these excitations is not yet known where Gi is a coupling constant between defects and may be specific to different kinds of and phonons, typically of the order of one glasses. The fact that they provide a basis for electronvolt, rj is the distance between the understanding of various thermal and pseudospins i an~j and q is the modulus of the wavevector of longitu~inalphonons with acoustic experiments suggests that tunneling modes are inherent excitations of amorphous energy ~w E and velocity v~. The quantity p substances (4). The basic assumption of th is the density of the glass. For an isotropic is . zz model is that in a glassy material an atom or a coupling Jjj = 0. However in more general cases group of atoms has two alternative ~ one has (6) inside the amorphous Structure. These two level systems (TLS) are quantum mechanical entities C~G~ and so tunneling is possible between adjacent — 1 3 = — G~G~~) _____ 13 positions without thermal activation. A ~ A(r )3 IJ A(r. •)3 constant density of states for such excitations 13 iJ at low energies leads to a linear dependence of where A = 64ir p V2. with v the velocity of the specific heat on temperature (2) (3). xx Besides, these localized modes can also act as sound. This expression for is an as’mptotic form valid for r• . scattering centers for phonons. This mechanism 1 qL, while at long is generally accepted as responsible for the distances it exhi~its the long range behaviour T2 dependence of the thermal conductivity of given by (2). glasses at low temperatures (5). The interaction between defects manifests This picture of a glass as an assembly of itself in the existence of a transverse isolated defects with randomly distributed relaxation time T2 which is measured in characteristics is however incomplete. It has acoustic experiments (4). In general there been shown by Joffrin and Levelut (6) that the are two contributions to T 2 arising from the phonon field provides an efficient coupling longitudinal J~ and transverse J~ between defects, as for example conduction interactions respectively. The tr~tsverse electrons couple spins in a spin glass. contribution is due solely to the interaction between “like” ‘spins” while all defects 2. Interaction between defects contribute to the linewidth arising from the The formal analogy between a two level longitudinal interaction. The term “like” system and a spin 1/2 allows one to write the spins” requires a definition. We shall following hamiltonian for a glass at low consider as “like” “spins” those defects whose temperatures (7) mutual interaction J~ is larger than the modulus of their dif~rence i.e. i and j z 1 XX +— + are “like” if ). E. — E. (8). Although H = — y 1’iE h.S. + — Z J.. (S.S + sTs. ) + ii 4 .. 13 1 3 i 3 it is generally assumed (6) 3that the i 13 interaction between like defects is very small, it is not yet known to what extent it + E Js~s~ contributes to the linewidth in an acoustic 1] 1 j (1) experiment (4). In this paper we estimate the ii 1193