Substitutional disorder diffraction and domain size

The relation between the diffraction and the distribution of the linear dimensions of the ordered domains in substitutionally disordered polycrystalline material is elaborated. It is shown that, contrary to some theoretical expectances and experimental efforts, the fundamental reflections do not broaden (negligible change of cell dimensions with ordering being assumed). The forbidden reflections, on the contrary, are shown to be suitable, through their broadening, for the investigation of this disorder. The integral breadth is calculated for three important types of size distribution. The possibility of obtaining the average domain size from the integral breadth is analyzed in relation to these distributions. The variance may provide a second parameter for the size distribution, thus allowing selection among different plausible types. Therefore its relation to the size distribution is also elaborated.