Intensity profile of Debye-Scherrer line from small crystallites

The exact intensity formula of the h-line profile from small crystallites has been obtained as the orientational average of the diffraction intensity of the h plane given by Ino & Minami [Acta Cryst. (1979), A35, 163-170]. While the formula is expressed as a triple integral including a sine Fourier integral, it can be expressed asymptotically with respect to the crystal size according to the theorem of asymptotic expansion of a Fourier integral. Hence the profile can be estimated by the sum of terms of single-integral type. The first term is of the same type as Wilson's formula but it has been shown that second and third terms improve considerably the accuracy of the asymptotic estimation especially for a very small crystal. The h-line profile can be successfully calculated for quite a small crystal of any shape and any crystal system by the asymptotic formula, which can be computed as easily as Wilson's formula.