Short- and Long-Range Order Parameters in Disordered Solid Solutions

Abstract

For a crystalline solid made up of a partially ordered array of structural units of more than one type it is shown that the state of order may be described and defined in terms of the self-convolution, or Patterson, function of the structure. The peak heights of the Patterson function are proportional to the short-range order parameters, ${\alpha }_i$. The periodic component is described by the long-range order parameters, defined as the limiting values of the ${\alpha }_i$ at large distances from the origin. The limitations of previous definitions of long-range order parameters are discussed.