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Elastic macro strain and stress determination by powder diffraction: spherical harmonics analysis starting from the Voigt model
Author(s) -
Popa Nicolae C.,
Balzar Davor,
Vogel Sven C.
Publication year - 2014
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576713029208
Subject(s) - isotropy , spherical harmonics , harmonics , stress (linguistics) , anisotropy , diffraction , cauchy stress tensor , tensor (intrinsic definition) , stress–strain curve , materials science , geometry , physics , mathematical analysis , mathematics , optics , deformation (meteorology) , composite material , linguistics , philosophy , quantum mechanics , voltage
A new approach for the determination of the elastic macro strain and stress in textured polycrystals by diffraction is presented. It consists of expanding the strain tensor weighted by texture in a series of generalized spherical harmonics where the ground state is defined by the strain/stress state in an isotropic sample in the Voigt model. In contrast to similar expansions already reported by other authors, this new approach provides expressions valid for any sample and crystal symmetries and can easily be implemented in whole powder pattern fitting, including Rietveld refinement. An earlier article [Popa & Balzar (2001). J. Appl. Cryst. 34 , 187–195] reported a similar model, but with a spherical harmonics expansion around the hydrostatic strain/stress state of the isotropic polycrystal. The availability of several different models is beneficial in order to allow one to select the representation in which the ground state is the closest to the actual stress state in the sample.