CALCULATIONS OF THE VIBRATIONAL SPECTRA OF DISORDERED SYSTEMS. 1. VIBRATIONAL SPECTRUM OF A ONE-DIMENSIONAL CHAIN WITH RANDOMLY DISTRIBUTED IMPURITY SPRINGS. 2. THE ELASTIC SPECTRA OF TWO-DIMENSIONAL DISORDERED LATTICES
Abstract
The frequency spectrum of a one-dimensional lattice containing randomly distributed impurity springs was evaluated to first order in the concentration, q, of impurity springs. It is shown that, with some mathematical manipulation, the solution can be placed into correspondence with the solution of Langer for the analogous problem of isotopic impurities. The elastic vibrational spectra of perturbed square lattice systems with nearest-neighbor central and noncentral interactions were derived. The unperturbed system consists of masses, m, on the lattice points and interacting with force constants, alpha, which determines the resistance to compression, and beta, which determines the resistance to shear along the direction (10). In one case, the perturbations are Nq randomly positioned isotopic impurities of mass m', where N is the number of lattice sites. It is shown that the elastic spectrum for this, and all other isotopic impurity systems, is completely determined by the average mass, (1 - q)m + qm'.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1965
- Accession Number
- AD0627638
Entities
People
- Arthur Bienenstock
- Hin-chiu Poon
Organizations
- Harvard University