X-ray particle-size broadening

X-ray diffraction profiles and Fourier coefficients are given for particles distributed according to experimentally verified size distributions. Calculations are based upon the log normal distribution of sphere diameters and intercept lengths in addition to a normal distribution of column heights. It is found that the diffraction profile is not sensitive to the fine details of the distribution but rather the mean column height and the column-height variation coefficient. Errors in particle-size determinations will result from an improper choice of the variation coefficient. Two simplified models are given that describe the diffraction profiles for a large range of variation coefficients.