Energy Spectrum and Phonon Excitation Damping in Many‐Component Amorphous Solids

Abstract

Phonon excitations in many-component amorphous solids are treated using the Green's function method. The equation for the energy spectrum of phonon excitations is obtained. This equation takes into account the hard core in the interatomic interaction potential, the temperature dependence of phonon frequencies, and their damping, caused by phonon scattering on structure fluctuations. Zeroth approximation is considered in a space with arbitrary dimensionality. In this case it coincides with the quasi-crystalline one. The explicit expressions for the optic and acoustic modes as well as for the longitudinal and transverse velocity of sound are obtained as example in the two-component case. In the space of arbitrary dimension the asymptotic of damping is studied for the one-component system in the long-wave region. Numerical calculations of the "frequency-wave vector" dependence are performed for some amorphous metals in the quasi-crystalline approximation. A OIITAWCKUX MOA, npOAOJIbHOfi A IIOnepe9-HOG CKOPOCTA 3ByKa. npOBeAeH0 UCCJIeAOBaHAe aCAMnTOTRKH 3aTyXaHAX B AIIHHHOBOJIHOBOfi 06-JIaCTU AJIX OAHOKOMIIOHeHTHOfi CACTeMbI B IIpOCTpaHCTBe npOU3BOJIbHOfi pa3MePHOCTA. BbIIIOnHeHbI YHCJIeHHbIe PaCWTbI 3aBHCAMOCTH ,,9aCTOTa-BOJIHOBOfi BeKTOp" AJIX PRAa aMOPI$HbIX MeTanJIOB B KBa3AKpACTaJIJIAYeCKOM n p u 6 n~~e~~~.Tenax. IIonyseHo ypameme nnr! s~e p r e~u r e c~o r o cnempa (PoHoHHbIx B036YXAeHUfi, yvaTbrsaIoruee

On Collective Variables Method in the Microscopic Theory of Alloys

“…determines the B * kλ B kλ quantities. Actually, B * kλ B kλ are dimensionless weight factors of the Fourier components of the Green function "displacement-displacement" averaged over configurational states [61]. Equations (5.47) are solved numerically.…”

Electron–Phonon Interaction Influence on Electron and Phonon Excitations in Amorphous Metals

“…configurationally averaged Green functions that are constructed on the operators As in [39,40] the spectrum of phonon excitations will be found from the poles of Using (4.1) one comes to the equation in matrix form…”

“…The mass operator (4.12) is a complex value. The expression for real and imaginary parts fph(q, o) are given in [39]. For fe-ph(q, 0) one has…”

“…In the matrices (&(q))"O the evidence of a "hard core" in the interatomic interaction potential is taken into account [39,40,431. These matrices coincide with those defined in [39,401 with the only difference that here the following changes are performed @(R) + @'(R), @'(R) --f @"(R), i.e., the renormalization of the interatomic interaction potential due to anharmonic effects is not taken into account. Let us perform the configuration averaging in (3.1).…”

“…In Section2 the model Hamiltonian for the electron-phonon interaction is considered. Sections 3 and 4 are devoted to the study of interacting electron and phonon excitations in one-component amorphous metals [36,371. In Section 5 the summary of the results obtained is presented.…”