Application of the pattern-fitting structure-refinement method of X-ray powder diffractometer patterns

The whole-pattern least-squares fitting method (herein called the pattern-fitting structure-refinement, PFSR, method) developed by Rietveld and used by many with neutron powder data has been extended for use with X-ray powder diffractometer data. Examples of PFSR for specimens in five different space groups are given. Structural parameters generally agree, within 2σ, with those from single-crystal results where available. Atom positions and site occupancies were determined for LaPO₄ Ca₅PO₄)₃F, and quartz. R(pattern) values generally ranged from 9 to 20% while R(Bragg) values were a few percent lower. Reflection profiles were represented by either Gaussian or Cauchy functions: better representations are shown to be needed with an expected result of improved sensitivity accompanying lower R values. Possibilities for improved pattern-stripping for minor phase study via PFSR of the major phase are exhibited. Remarkably precise lattice parameters, e.g. 1 part in 35000 from data all below 2θ < 77° in the fluorapatite case, and parametric characterization of the diffraction broadening of the Bragg profiles are obtained as additional benefits.