Relation between Elastic Constants and Second- and Third-Order Force Constants for Face-Centered and Body-Centered Cubic Lattices

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Abstract
The symmetry properties of a lattice are used to relate the second and third order force constants to the elastic constants of the lattice and to ascertain the number of independent force constants. Explicit relations are obtained for a face-centered cubic lattice with nearest neighbor interaction between atoms, and for a body-centered cubic lattice with nearest and next-nearest neighbor interactions. Corresponding relations are obtained for central forces in these two lattices.

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