The Vibrational Spectrum of a Monatomic Face-Centered Cubic Crystal Lattice

Citation

Leighton, Robert Benjamin (1947) The Vibrational Spectrum of a Monatomic Face-Centered Cubic Crystal Lattice. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/XK5M-Y579. https://resolver.caltech.edu/CaltechETD:etd-01092004-101503

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by[...]. Abstract is included in .pdf document. The equations of motion of the atoms of a face-centered, cubic crystal lattice are written, assuming central, Hooke's Law forces between each atom and its eighteen nearest neighbors, and the secular determinant defining the normal frequencies is obtained. This determinant is written as a product of third order determinant. The properties of the roots of the secular determinant are discussed, and it is shown that the surfaces of constant frequency have the symmetry properties (in reciprocal-vector space) of a body-centered cubic lattice. This fact is used to simplify the computation of the distribution of the normal frequencies. The frequency spectrum is found by actually modeling the constant frequency surfaces in plaster of Paris and measuring the volumes enclosed between successive surfaces. The frequency spectrum so obtained is used in the evaluation of the specific heat of a general crystal of the type treated, and numerical values are presented for the element silver. The present theory (that of Born and von Karman), is in much better agreement with the experimental values for temperatures below 100[degrees]k than is the Debye theory. Certain anomalies in the specific heat curves of silver and potassium chloride at temperatures below 10[degrees]K are not explicable in terms of the atomic model that is used.

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