Chemical reasonableness in Rietveld analysis: Inorganics

Abstract

Besides statistical and graphical measures, many structural features can be used to assess the quality of a Rietveld refinement. These include the metric symmetry of the lattice (which can assist in determining the true symmetry and in identifying isostructural compounds), bond distances and angles (which should fall within normal ranges), displacement coefficients, refined stoichiometry, the absolute values of the standard uncertainties of the fractional coordinates, the hydrogen bonding pattern, the presence of approximate symmetry, the presence of unindexed peaks in the pattern, and whether the refinement converges at all. Chemical knowledge can be built into a Rietveld refinement though the use of restraints and rigid bodies. A knowledge of chemical reasonableness proved important in refining the correct structures of [Fe(H2O)6](BF4)2, (Ba1.5Sr0.5)TiO4, and (Ba1.25Sr0.75)TiO4.

A Rietveld tutorial—Mullite

“…From the refined structural parameters (Table IV) we can calculate the composition of the mullite as Al 4.85 Si 1.18 O 9.77 , and thus carry out quantitative phase analysis on the atomic scale as well. It is important to check the chemical reasonableness of the refined results (Kaduk, 2007). The (unconstrained) sum of the positive charges in the unit cell is +19.28 and the sum of the negative charges is −19.54.…”

The crystal structure of Na(NH4)Mo3O10·H2O

“…Isotropic displacement parameters were refined for the Na, N, and Mo atoms, with the H atoms for the ammonium ion constrained to 1.3 times the value of the N atom. The isotropic displacement parameter for the O atoms refined to a fairly low value, a common issue in the presence of heavy atoms (Kaduk, 2007), but stayed positive with the use of the anomalous scattering factors. The position of the H atom for the water molecule was added late in the refinement based on the results of the density functional theory (DFT) calculation.…”