Premium
The use of standard deviation of X‐ray diffraction lines as a measure of broadening in the Scherrer equation: a curve fitting method
Author(s) -
McGehee R.,
Renault J.
Publication year - 1972
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s002188987200977x
Subject(s) - standard deviation , diffraction , line (geometry) , scherrer equation , mathematics , gaussian , measure (data warehouse) , gaussian function , mathematical analysis , optics , statistics , geometry , physics , computer science , quantum mechanics , database
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.