Temperature Dependence of Sound Velocity in Disordered Systems with Local Anharmonism

Abstract

Recently we have suggested a model of local anharmonism to describe dynamic and kinetic properties of disordered (amorphous) systems [l, 21. An amorphous system in this model is specified by structural defects being much smaller in size than the wavelength of low-frequency phonons and vibrating in an anharmonic potential along one of the generalized coordinates within the defect space. The effective frequency of oscillations along this coordinate is then dependent on the anharmonic oscillator state. 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]. In our completely isotropic scalar model of the crystal V: = V," = C/e, where C is the shear modulus and e the material density. The effect of point defects on the elastic moduli was intensively studied in the seventies in connection with the problem of radiation-induced defects in solids (see, e.g. [4]). 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]. In an approximation linear in the total defect concentration I ) Kirov street 132, 426001 Izhevsk, Russia. 36*

Temperature and mass dependence of anharmonic defect dynamics

“…At large energies, / 3 tends to the classical value -0.5. The isotope factor p as a function of E for different values of parameter m (or a ) :(1) m = 0.7,(2) 1.05, (3) 1.15The PDVS of the defect for T = 0.1& and different values of parameter m. (1) m = 0.7, (2) 0.9, (3) 1.01, and (4) 1 3.…”