The Fourier coefficient of the line profile of a Debye-Scherrer ring broadened by lattice distortion is given as the product of two factors, one of which is due to the fluctuation in the average strain of each particle in the powder and the other is due to the inhomogeneous strain, i.e. the displacements of the unit cells from the average sites. The line profile is of Cauchy type in the case of no fluctuation in the average strain of each particle in the powder, even though the distribution of the displacements is of Gaussian type.
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Hidewo Takahashi (1969) studied this question.
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