Elastic and Force Constants of a Simple Tetragonal Crystal

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Lattice vibrations of a monatomic simple tetragonal crystal have been discussed and interactions of first, second, third, and fourth nearest neighbors have been taken account of. The equations of motion of an atom along the three crystallographic axes have been set up. Comparing with these the corresponding equations of elastic vibrations, the elastic constants of the simple tetragonal lattice have been expressed in terms of the various force constants and vice versa. Free electrons in the lattice have been supposed to give rise to an additional force constant which has also been evaluated in a similar way.