The Influence of Local Anharmonism on the Low‐Temperature Heat Conductivity in Disordered Systems

Abstract

A model of a disordered system containing anharmonic quasi-local modes is considered. The influence of such local anharmonism on the low-temperature heat coefficient is analyzed. It is shown that taking into account the local anharmonism results in qualitatively different T-dependences of the heat conductivity coefficient for different anharmonic parameters. The results obtained can be used in interpreting some experimental data.

Temperature Dependence of Sound Velocity in Disordered Systems with Local Anharmonism

“…2. The appearance of a maximum in this temperature range is rather unexpected, as it is attributed to the presence of TLS in amorphous materials [6], but in our model, like the TLS one, this maximum is of quantum nature: without regard of zero-point vibrations in solving equation (10) of [2] this maximum would not arise. This follows immediately from Fig.…”

“…The distribution function is defined in the interval (al, aZ) with the vertex at the point a,. Interpretation of the results obtained follows immediately from the discussion in [2]. In the case of weak anharmonism (curve 1) the defects are in ground states within the whole temperature range considered and a spectrum softening occurs with rising temperature, which results in a decrease in sound velocity.…”

“…The temperature dependence of the quantity z ( T ) for various values of the parameter a was thoroughly discussed in [2]. In an approximation linear in the total defect concentration I ) Kirov street 132, 426001 Izhevsk, Russia.…”

“…If the phonon scattering at these defects is of resonance character, the variation of oscillator states with temperature results in a strong temperature dependence of the generalized density of vibrational states of a system [l], which gives rise to anomalous T-dependences of physical quantities. In [2] it is shown, in particular, that the behaviour of the low-temperature lattice heat conductivity coefficient in disordered systems can qualitatively change depending upon the local anharmonism parameters. In this note we present the results of an investigation of the adiabatic sound velocity in amorphous materials carried out in the local anharmonism model.The methods of sound velocity calculation in defect crystals are presented in detail in [3].…”

“…According to the results of these works the contribution to the elastic modulus variation (AC) can be written as [3] AC,lim t,(k, o = 0) , k-0 where t, is the one-site scattering matrix at site s, k is a wave vector. It follows from (1) that the nonzero contribution comes only from the defect vibrations with even symmetry.In the model [5] this is the F,, representation for which, with regard of the results of [2], one can obtain where CI = coo/& is a continuously distributed (with distribution function @(a)) random variable describing the defect type; z = w(T)/wo; Ro is a dimensionless parameter (see [2]). The temperature dependence of the quantity z ( T ) for various values of the parameter a was thoroughly discussed in [2].…”