Error corrections for X-ray powder diffractometry

AbstractThe errors involved in precision lattice parameter determination fall into three broad groups: errors that can be corrected by applying a multiplication factor to the determined parameter(s), errors arising from a constant shift in peak position, and errors arising from a Bragg angle dependent shift in peak position. The latter two sources of error can be corrected by applying analytical techniques to the lattice parameters determined from the measured Bragg peaks. The time and effort involved in this process can be greatly reduced by using computational methods based on extrapolation, least squares analysis with systematic error refinement and pure lattice refinement techniques. Programs for these purposes were evaluated using the Si and LaB6 crystallographic standards certified by NIST. A computer extrapolation method utilizing the function coscotq gave lattice parameters with a precision of 1:100,000 for Bragg peaks at angles greater than 60 °q, but significantly lower levels of precision were ...