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Understanding anisotropic microstrain broadening in Rietveld refinement Andreas Leineweber* Max Planck Institute for Intelligent Systems (formerly Max Planck Institute for Metals Research), Heisenbergstraße 3, 70569 Stuttgart, Germany Received April 11, 2011; accepted September 23, 2011 Line-broadening analysis / Rietveld refinement / Microstrain / Strain / Microstructure Abstract. Anisotropic, i.e. hkl-dependent microstrain broadening of Bragg peaks as observed in powder-diffrac- tion measurements often obstructs finding a good descrip- tion of the peak profiles

Description of anisotropically microstrain-broadened line profiles by Edgeworth series Andreas Leineweber* Max Planck Institute for Metals Research, Heisenbergstraße 3, 70569 Stuttgart, Germany Received January 20, 2009; accepted May 13, 2009 Microstructure / Microstrain / Line-broadening analysis / Composition variations / Distributions Abstract. The diffraction effects within the Stokes-Wil- son approximation of a non-Gaussian microstrain distribu- tion in a macroscopically isotropic specimen are described by anisotropic Edgeworth series. This Edgeworth series

substitution of Mg and Ca. In this paper, we present molar volumes of pyrope, grossular, and four garnet solid solutions synthesized dry at 6 GPa with a multi-anvil (MA) device and the XRD profile analysis results. There is a complex correlation between microstrain inside the garnet structure and the non-ideal mixing properties along the pyrope-grossular binary. A compositionally dependent degree of short-range Ca-Mg ordering that develops during annealing after MA crystallization may also be partly responsible for the asymmetrical shape of the excess volume in the pyrope

Z. Kristallogr. Proc. 1 (2011) 37-42 / DOI 10.1524/zkpr.2011.0005 37 © by Oldenbourg Wissenschaftsverlag, München Microstrain in nanocrystalline samples from atomistic simulation A. Leonardi1,*, K. R. Beyerlein1,2, T. Xu2, M. Li2, M. Leoni1, P. Scardi1 1 University of Trento, Department of Material Engineering, Trento, Italy 2 Georgia Institute of Technology, Atlanta, USA * Contact author; e-mail: Alberto.Leonardi@ing.unitn.it Keywords: microstrain, line profile analysis, atomistic modelling Abstract. Atomistic modelling was employed to

Z. Kristallogr. Suppl. 30 (2009) 97-102 / DOI 10.1524/zksu.2009.0014 97 © by Oldenbourg Wissenschaftsverlag, München Thermally induced microstrain broadening in polycrystalline hexagonal zinc A. Leineweber1,*, E. J. Mittemeijer1, A. C. Lawson2, J. A. Roberts2, J. A. Valdez2, W. S. Kreher3 1 Max Planck Institute for Metals Research, Stuttgart, Germany 2 Los Alamos National Laboratory, Los Alamos, New Mexico, USA 3 Institute for Materials Science, Dresden University of Technology, Dresden, Germany * a.leineweber@mf.mpg.de Keywords: thermal

Z. Kristallogr. Suppl. 23 (2006) 117-122 117 © by Oldenbourg Wissenschaftsverlag, München Anisotropic microstrain broadening due to compositional inhomogeneities and its parametrisation A. Leineweber*, E. J. Mittemeijer Max Planck Institute for Metals Research, Heisenbergstraße 3, D-70569 Stuttgart, Germany *Contact author; e-mail: a.leineweber@mf.mpg.de Keywords: line broadening, microstrain, iron nitrides, composition variations Abstract. The anisotropic and asymmetric microstrain-like line broadening of hexagonal ε-FeNy (y = 0.407) was analysed

Linienprofilanalyse von Röntgen-Weitwinkelreflexen mittels Fourier-Transformation zur Bestimmung von Mikrospannungen und parakristallinen Störungen W. Vogel, J. Haase und R. Hosemann Fritz-Haber-Institut der Max-Planck-Gesellschaft. Berlin-Dahlem (Z. Naturforsch. 29a. 1 1 5 2 - 1 1 5 8 [1974] ; eingegangen am 24. Mai 1974) Analysis of X-Ray Line Profiles for Microstrains and Paracrystalline Distortions by Fourier Transformation Many synthetic and biopolymers are paracrystalline. The same holds for some catalysts, graph- ites and semiconductors. This can

Z. Kristallogr. Suppl. 30 (2009) 103-108 / DOI 10.1524/zksu.2009.0015 103 © by Oldenbourg Wissenschaftsverlag, München The hkl dependences of microstrain and of macrostress-induced macrostrain; a comparison for intrinsically extremely anisotropic cementite, Fe3C A. Leineweber*, T. Gressmann, M. Nikolussi, E. J. Mittemeijer Max Planck Institute for Metals Research, Heisenbergstr. 3, 70569 Stuttgart, Germany *a.leineweber@mf.mpg.de Keywords: residual stress analysis, macrostrain, microstrain, elastic anisotropy, line-profile analysis Abstract

mixing, whereas volume derivatives, thermal expansion, and bulk modulus show negative deviation from ideal mixing ( Du et al. 2015 ). Lattice strain arising from local structural heterogeneities in substitutional pyrope-grossular solid solutions has been thought to produce elastic energies that strongly affect the macroscopic enthalpy and volume of mixing (e.g., Geiger 2001 , 2008 ; Dapiaggi et al. 2005 ). However, a more recent study by Du et al. (2016) shows that microstrain does not correlate well with either the positive excess mixing volume or enthalpy

29, 2011, accepted January 1, 2012 Iron carbide / Microstrain / Line-broadening analysis / Rietveld refinement / Powder diffraction structure analysis / X-ray diffraction / First-principles calculations Abstract. X-ray powder-diffraction data recorded using different wave lengths as well as neutron powder diffrac- tion data on Hägg carbide, c-Fe5C2, were evaluated by Rietveld or Pawley refinements, respectively. Likewise, employing different starting models, first-principles calcu- lations using density functional theory (DFT) involving structure optimisation with