Composition-Induced Microstrain Broadening: From Pattern Decomposition to whole Powder Pattern Modelling Procedures

Leineweber, Andreas

doi:10.4028/www.scientific.net/msf.651.131

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…Otherwise, a suitable probability density function must be derived or guessed. For example, earlier work by Leineweber , employed an Edgeworth series to approximate the non-Gaussian N distribution in ε–FeN y .…”

Section: Resultsmentioning

confidence: 99%

Phase Selectivity and Stability in Compositionally Complex Nano (nA_1/n)Co₂O₄

Wang,

Metz,

Calì

et al. 2023

Chem. Mater.

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A family of compositionally complex spinels with the formula(nA 1/n )Co 2 O 4 (A = combinations of Mg, Cr, Mn, Fe, Co, Ni, Cu, and Zn) was synthesized using a low-temperature softtemplating method. The phase selectivity and the temperature stability window for the series were found to depend strongly upon the A-site composition and only modestly on the number of elements (n) present on the A-site. Select control reactions and in situ high-temperature X-ray diffraction (XRD) uncovered a propensity for temperature-activated de-mixing for compositions containing Mg, Ni, Mn, and Fe. The A-site cations exhibit spatially heterogeneous distributions in the as-formed spinels, which diminish with intermediate thermal annealing, as shown by scanning transmission electron microscopy (STEM)/energy dispersive spectroscopy (EDS) and X-ray line profile analysis. The single spinel phases obtained are metastable, separating into a mix of impurity phases and multiple spinel phases with higher temperature annealing. Furthermore, we demonstrate that a "continuous lattice" parameterization of the compositionally complex oxide structure provides a rapid means by which to examine the heterogeneity of the cation distribution through full profile refinement. The demonstrated tunability of the cation distribution or clustering in these compositionally complex spinels via thermodynamic levers affords interesting opportunities for rational design of functional materials.

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Section: Resultsmentioning

confidence: 99%

Phase Selectivity and Stability in Compositionally Complex Nano (nA_1/n)Co₂O₄

Wang,

Metz,

Calì

et al. 2023

Chem. Mater.

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Understanding anisotropic microstrain broadening in Rietveld refinement

Leineweber¹

2011

Zeitschrift Für Kristallographie

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Anisotropic, i.e. hkl-dependent microstrain broadening of Bragg peaks as observed in powder-diffraction measurements often obstructs finding a good description of the peak profiles during Rietveld refinement. This review describes strategies to model this type of structural line broadening. Emphasis is put, further, on the possible physical background of the refined width parameters in terms of compositional, thermal and elastic microstrain. Methods are described to extract thus quantitative microstructural information. Moreover, it is shown how the anisotropy of the microstrain broadening can reveal the anisotropy of intrinsic properties of the solid, which may otherwise be difficult to determine, e.g. compositional lattice-parameter changes or elastic compliance.

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Crystal structure determination of Hägg carbide, χ-Fe₅C₂ by first-principles calculations and Rietveld refinement

Leineweber¹,

Shang

Liu

et al. 2012

Zeitschrift Für Kristallographie

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X-ray powder-diffraction data recorded using different wave lengths as well as neutron powder diffraction data on Hägg carbide, χ-Fe5C2, were evaluated by Rietveld or Pawley refinements, respectively. Likewise, employing different starting models, first-principles calculations using density functional theory (DFT) involving structure optimisation with respect to energy were performed for χ-Fe5C2. The results from diffraction and DFT imply a crystal structure having a monoclinic C2/c symmetry with a quite regular (monocapped) trigonal-prismatic coordination of C by Fe atoms. The anisotropy of the microstrain broadening observed in the powder-diffraction patterns agrees with the anisotropy of the reciprocal Young’s module obtained from elastic constants calculated by DFT. The anisotropic microstrain broadening can to some degree, be modelled allowing for a triclinic distortion of the metric of χ-Fe5C2 (deviation of the lattice angle γ from 90°) involving reflection spitting, which mimics the hkl-dependently broadened reflections. This distortion corresponds to the most compliant shear direction of the monoclinic χ-Fe5C2. The anisotropic microstrain broadening results from microstress induced e.g. by anisotropic thermal expansion inducing misfit between the grains, in association with the intrinsic anisotropic elastic compliance of χ-Fe5C2. This anisotropic microstrain broadening was likely the origin of previous proposals of triclinic P-1 space-group symmetry for the crystal structure of χ-Fe5C2, which is rejected in the present work.

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Composition-Induced Microstrain Broadening: From Pattern Decomposition to whole Powder Pattern Modelling Procedures

Cited by 3 publications

References 23 publications

Phase Selectivity and Stability in Compositionally Complex Nano (nA_1/n)Co₂O₄

Phase Selectivity and Stability in Compositionally Complex Nano (nA_1/n)Co₂O₄

Understanding anisotropic microstrain broadening in Rietveld refinement

Crystal structure determination of Hägg carbide, χ-Fe₅C₂ by first-principles calculations and Rietveld refinement

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Composition-Induced Microstrain Broadening: From Pattern Decomposition to whole Powder Pattern Modelling Procedures

Cited by 3 publications

References 23 publications

Phase Selectivity and Stability in Compositionally Complex Nano (nA1/n)Co2O4

Phase Selectivity and Stability in Compositionally Complex Nano (nA1/n)Co2O4

Understanding anisotropic microstrain broadening in Rietveld refinement

Crystal structure determination of Hägg carbide, χ-Fe5C2 by first-principles calculations and Rietveld refinement

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Product

Resources

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Phase Selectivity and Stability in Compositionally Complex Nano (nA_1/n)Co₂O₄

Phase Selectivity and Stability in Compositionally Complex Nano (nA_1/n)Co₂O₄

Crystal structure determination of Hägg carbide, χ-Fe₅C₂ by first-principles calculations and Rietveld refinement