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Reliable non‐linear elastic constants
Author(s) -
Dunstan D. J.,
Bosher S. H. B.
Publication year - 2003
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.200301591
Subject(s) - taylor series , observable , third order , lagrangian , stress (linguistics) , series (stratigraphy) , simple (philosophy) , strain (injury) , constant (computer programming) , mathematical analysis , mathematics , materials science , physics , quantum mechanics , computer science , medicine , paleontology , philosophy , linguistics , theology , epistemology , programming language , biology
The values given in the literature for the third‐order elastic constants c IJK of the standard semiconductors have long been suspect. We have applied modern statistical analysis to the raw data from which the databook c IJK were obtained, and we give revised values with reliable error estimates for Si, Ge and GaAs. The databook c IJK are appropriate for an expansion of the elastic energy of a body as a Taylor series in Lagrangian strain η IJ , but there are formidable mathematical difficulties in using Lagrangian strain in the analysis of physical problems. To facilitate such analysis, we introduce effective second‐order elastic constants for materials under finite strain. From these, strain, stress and pressure derivatives are readily calculated. The pressure derivatives are given for Si, Ge and GaAs. Using the stress derivatives, the relationships between physical observables such as acoustic velocities and the databook c IJK can be obtained by simple algebra.