The use of standard deviation of X-ray diffraction lines as a measure of broadening in the Scherrer equation: a curve fitting method

The use of standard deviation as a measure of line broadening in the Scherrer equation is justified on the grounds that, for commonly used approximating curves which can be fitted to X-ray line profiles, the line breadth at half intensity is directly proportional to the standard deviation of the fitted curve. If the crystallite size is known a priori, a standard deviation-width scaling function can be calculated; also some insight can be gained into the nature of the curve describing the diffraction profile. A computer program in Fortran IV has been written which fits Gaussian curve forms to diffraction profiles and computes standard deviations and half widths. The program includes an estimation of background, achieves a fit with an error of 5 %, and runs rapidly.