Vibration Frequency Spectra of Disordered Lattices. II. Spectra of Disordered OneDimensional Lattices
Abstract
By using a combination of the momenttrace method and a new method, the "deltafunction" method, the vibrational frequency spectrum of a randomly disordered, twocomponent, isotopic, linear chain has been computed for a wide range of the concentrations of the two kinds of particles and of their mass ratios. In addition the particular case of a chain in which the mass of one of the isotopic constituents becomes infinite can be treated exactly, and the results of this analysis shed light on the form of the spectra for lattices with large but finite mass ratios for the two constituents. The spectra are characterized by the disappearance of the squareroot singularity at the maximum frequency which is found in ordered onedimensional lattices, and by the appearance of impurity bands, the nature of which is discussed. Finally, the zeropoint energy of a randomly disordered lattice is calculated and compared with the zeropoint energy of an ordered lattice and of the separated phases.
 Publication:

Physical Review
 Pub Date:
 July 1959
 DOI:
 10.1103/PhysRev.115.24
 Bibcode:
 1959PhRv..115...24D