Vibrational Modes of Disordered Linear Chains
- 1 January 1962
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 3 (1) , 200-202
- https://doi.org/10.1063/1.1703780
Abstract
The kth normal mode of vibration (i.e., the atomic displacements) of a disordered one‐dimensional lattice (masses and force constants completely arbitrary) with nearest‐neighbor interaction has precisely k − 1 nodes. A fortiori, the same is true for ordered one‐dimensional lattices with any number of atoms per unit cell. This theorem exhibits a close relationship between eigenfunctions in monatomic ordered lattices (to which its application has been known for many years) and disordered lattices; a relationship which appears surprising in view of recent demonstrations of the gross differences exhibited in the distribution of eigenvalues. It is thus suggested that some basic concepts of ordered lattice dynamics—propagation vector, phonon momentum, etc.—may retain some simple validity for disordered solids as well. Some numerical examples are given.This publication has 2 references indexed in Scilit:
- The Design of a Computer Program to Determine the Natural Frequencies and Normal Modes of Vibration of an In-Line Mechanical System of Springs and MassesJournal of the Society for Industrial and Applied Mathematics, 1961
- Vibrational spectra of diatomic chainsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1960