Crystal powder statistics. IV. Calculation of the line profile using the sampling-line method

The sampling-line method is a convenient procedure for evaluating the line profile of a polycrystalline sample. To deal with size-broadening effects only, the method is applied to Bernoullian and Gaussian samples; the line profile is given by a Lorentzian function in the first case and by a similar function in the second case. For any real polycrystalline sample the intensity decreases as S-2 for large | s | = |S - Shkl|. For a given average thickness the apparent crystallite size is up to 2 times larger than for samples consisting of crystals with the same size and shape.