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The Sextic Polynomial of Crystal Elasticity
Author(s) -
Head A. K.
Publication year - 1985
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221320111
Subject(s) - mathematics , elasticity (physics) , polynomial , symmetry (geometry) , constant (computer programming) , hexagonal crystal system , pure mathematics , mathematical analysis , geometry , physics , crystallography , chemistry , computer science , thermodynamics , programming language
It has previously been proved that the sextic polynomial of crystal elasticity is not explicitly solvable for arbitrary elastic constants and directions except for hexagonal symmetry. In the case of cubic symmetry there are special elastic constants known for which the polynomial is solvable for all directions. A search is made over the range of physically significant elastic constants for any further special cases. It is conducted with an extension to Galois theory that gives a measure of how far any particular polynomial is from being solvable rather than just a yes‐no result. No further special elastic constants are found and it appears very probable than none can exist although there is not a strict proof of this.