Extinction corrections from equivalent reflections

Corrections for secondary extinction evaluated from the diffraction intensities for equivalent reflections with different path lengths provide an independent check on values that minimize differences between observed and calculated structure factors. Comparison of equivalent intensities also avoids any extinction-parameter bias, which originates in correlation of the extinction corrections with bonding-electron contributions to X-ray structure factors. Corrections from the comparison of equivalent reflections for several X-ray diffraction studies on small crystals of ionic compounds are markedly less than those that minimize differences between observed and calculated structure factors. The discrepancies that originate in extinction-parameter bias are exacerbated by the unfavourable form of the statistical distribution function for the residuals when differences between observed and calculated structure factors are minimized. Analysis of intensities for equivalent reflections, although more demanding experimentally, provides least-squares residuals closer to the normal distribution required for reliability in nonlinear least-squares processes.