Nature of soft vibrational modes in metallic glasses

A general theory of vibrational excitations in metallic glasses is presented, based on the disclination model of the structure of solids with local icosahedral symmetry. The representation of nonorthogonal plane waves is used, which allows one to separate the diagonal terms in the Hamiltonian, and also the terms describing scattering of these waves by fluctuations of the density and the force constants, and by topological structure fluctuations. We have derived and solved the Dyson equation for the Green’s function. We have obtained an analytical expression for the density of vibrational states of the glass. The nature of the soft vibrational modes is discussed. It is shown that these modes are resonant modes, whose presence is due to the fluctuations of the density and the force constants. Special attention is given to the role of forward scattering and the nature of the spatial variation in the amplitude of the given modes. Fiz. Tverd. Tela (St. Petersburg) 41, 372–379 (March 1999)