Vegard’s law in random two-dimensional alloys

Abstract

Abstract In all the work on the vibrational spectra of disordered alloys, much less attention has been given to changes in bond lengths, than has been given to changes in masses and force constants. However, length changes are often important in determining both local and global properties. In this paper, we focus on length changes in the simplest non-trivial systems. We have found it convenient to set up an effective medium theory, of the kind that Roger Elliott has exploited so effectively in many problems. In the end we find simple qualitative explanations for our results that have direct and obvious experimental consequences.