The precision of diffraction peak location

Much of crystallography is concerned with the accurate location of the cent re of diffraction peak profiles. Simple analytical expressions are derived for estimating the precision of diffraction peak location that can be achie ved for Gaussian diffraction peaks with a flat background, in terms of the standard deviation, integrated intensity and peak height (H) to background (B) ratio. Two formulations are derived using standard methods: one for the case of very low background, the other for significant backgrounds. It is found that in cases of significant background, peak position is less well d etermined by a factor of [1+2(2(1/2))B/H](1/2) compared with the case of no background. The applicability of the expression has been demonstrated by M onte Carlo simulation of Gaussian profiles and by the analysis of real data collected at a large number of neutron and synchrotron sources, largely as part of the VAMAS TWA20 project. While the solution is presented for Gauss ian peak shapes, it is believed to be approximately correct for a wide rang e of other common diffraction peak shapes (Lorentzian, Voigtian etc.). The method is applied to the assessment of the variation in optimal measuring t ime as a function of the depth of the gauge volume for residual strain scan ning measurements.