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Polycrystal elastic constants for triclinic crystal and physical symmetry
Author(s) -
Morris Peter R.
Publication year - 2006
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/s0021889806016645
Subject(s) - triclinic crystal system , symmetry (geometry) , spherical harmonics , homogeneous space , orientation (vector space) , crystallography , crystal (programming language) , physics , elastic modulus , function (biology) , mathematical analysis , classical mechanics , mathematics , geometry , crystal structure , chemistry , thermodynamics , computer science , programming language , evolutionary biology , biology
The problem of obtaining the Voigt average for the elastic stiffnesses with texture‐describing weight functions has been solved for triclinic crystal and physical symmetries. The average is obtained by expanding the T ijklmnpq , which relate the elastic stiffnesses in the rotated reference frame, , to those of the principal elastic stiffnesses, c mnpq , in generalized spherical harmonics, multiplying by the orientation distribution function and integrating over all orientations. The condition imposed to assure a unique expansion results in the absence of terms with odd L , so that the results are completely determinable from conventional X‐ray pole figures. This is the most general case, from which all higher‐symmetry solutions may be obtained by application of symmetry operations. The Reuss average for elastic compliances may be obtained in a similar fashion.