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 multiplicati on factor to the determined parameter(s), errors arising from a constant sh ift 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 appl ying analytical techniques to the lattice parameters determined from the me asured Bragg peaks. The time and effort involved in this process can be gre atly reduced by using computational methods based on extrapolation, least s quares analysis with systematic error refinement and pure lattice refinemen t techniques. Programs for these purposes were evaluated using the Si and L aB6 crystallographic standards certified by NIST. A computer extrapolation method utilizing the function coscot theta gave lattice parameters with a p recision of 1: 100,000 for Bragg peaks at angles greater than 60 degrees th eta, but significantly lower levels of precision were obtained when lower a ngle Bragg peaks were included in the extrapolation. Low levels of precisio n were obtained when either corrected or uncorrected peak positions were an alyzed by least squares in combination with a refinement of selected system atic 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 i nternal standard.