A NEW LOOK AT THE FUNDAMENTALS OF LATTICE VIBRATIONS
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Date
1956
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Publisher
Ohio State University
Abstract
Lattice vibrations are considered on basis of characteristic modes of a large molecule rather than as standing wave patterns in a quasi-continuous medium with arbitrary boundary conditions. Symmetry properties are used in solution of problem for uniform linear chain without recourse to the controversial Born-Von Karman cyclic end conditions. An iterative process, based on Lagrange’s equation with ""extra"" forces, is developed for treating such modifications of the uniform linear chain as: alternating masses, both nearest and next-nearest neighbor coupling, change in masses and/or force constants near ends of the chain, ""impure"" mass in midst of the chain, coupling of linear chains to form planar and three-dimensional arrays, etc. The method permits proper approximations as the number of particles becomes very large. Interesting results are obtained for two- and three-dimensional arrays on the basis of valence-type vibrational forces similar to those employed in small molecules.
Description
Author Institution: Department of Physics and Astronomy, The Ohio State University