Journal of Applied Crystallography · 1977 · 182 citations · 0 references
Natural SciencesMaterials EngineeringMaterials ScienceCeramic MaterialsCrystal StructureMaterials CharacterizationCrystal LatticeCrystalline MaterialsCrystallographyStructure DeterminationX-ray CrystallographyX-ray DiffractionBragg CurveCrystal Structure DeterminationCrystal Structure RefinementLattice ParametersPattern RefinementPowder DiffractionPowder X-ray DiffractionSingle-crystal Crystallography
The study demonstrates that PFSR can be used to refine the major phase and thereby improve pattern stripping for minor phase analysis. PFSR, a whole‑pattern least‑squares refinement originally developed for neutron data, was extended to X‑ray powder diffraction, applied to specimens in five space groups, and used Gaussian or Cauchy reflection profiles to determine atom positions, occupancies, and improve sensitivity. The refined structural parameters agreed within 2σ with single‑crystal results, R(pattern) values ranged from 9–20 %, and lattice parameters were determined with a precision of one part in 35 000, along with parametric characterization of Bragg‑profile broadening.
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.