Error corrections for x-ray powder diffractometry

The 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 coscotθ gave lattice parameters with a precision of 1:100,000 for Bragg peaks at angles greater than 60°θ, but significantly loer levels of precision were obtained when lower angle Bragg peaks were included in the extrapolation. Low levels of precision were obtained when either corrected or uncorrected peak positions were analyzed by least squares in combination with a refinement of selected systematic errors. By contrast, a lattice refinement method with no facility for dealing with systematic errors yielded lattice parameters with a precision better than 1:100,000 regardless of whether any prior corrections had been applied to eliminate errors in peak position. An even greater precision of 1:500,000 was obtained when this lattice refinement method was applied to peak positions corrected by a second order polynomial fit to data from an internal standard.