Crystal structures and cation distributions in simple spinels from powder XRD structural refinements: MgCr₂O₄, ZnCr₂O₄, Fe₃O₄ and the temperature dependence of the cation distribution in ZnAl₂O₄

Abstract

The crystal structure and cation distributions in the spinels MgCr₂O₄, ZnCr₂O₄, Fe₃O₄ and a suite of ZnAl₂O₄ samples annealed at 900 to 1400° C and then rapidly quenched, have been determined by powder X-ray diffraction, using several different X-ray procedures and both conventional structure-factor refinement and whole-pattern (or Rietveld) refinement methods. The chromite spinels are expected from crystal chemical considerations to have an almost completely normal cation distribution (inversion parameter, x, equal to zero). In agreement with this expectation, three samples of MgCr₂O₄ annealed at 900, 1100 and 1300° C, and ZnCr₂O₄ were all found to have x=0 within two estimated standard deviations (esd), suggesting that the accuracy with which cation distributions in spinels may be determined by powder XRD is close to the estimated precision. Slightly better results are obtained assuming neutral-atom scattering curves rather than half-ionized or fully ionized, but the differences are small (within the esd). The results from the Rietveld refinements are similarly in good agreement with those using the conventional structure factor refinement approach (agreement within the combined esd's), although in detail the Rietveld procedure sometimes produces small systematic differences in refined parameters.

The suite of ZnAl₂O₄ spinels show a smooth increase in x from 0.01 at 900° C to 0.05 at 1300° C, and this behaviour is well described by the simple thermodynamic model for disordering in spinels with α_Zn-Al=89 kJ/mol, assuming β=−20 kJ/mol. The oxygen positional parameters for Fe₃O₄ are similar to those from published single crystal studies, indicating that the powder method also yields accurate interatomic distances in spinels.