Three-Phonon Zone-Boundary Processes and Melting of Solids
Vibrational theories of melting [1,2], which presuppose a critical amplitude of vibration, have enjoyed considerable empirical success. But the critical amplitude determined empirically for a vibrational catastrophe is surprisingly small and a fundamental definition of such a catastrophe is lacking. An hypothesis is advanced herein addressing these issues. Lindemann’s law is obtained from the 3-phonon transition rate without reference to a critical amplitude upon the assumption that zone-boundary (ZB) phonons cease to be valid excitations at the melting point. Corollary to this assumption is the onset of single-particle random movement on the time scale (2ωD)-1 where ωD is the Debye angular frequency. Results obtained for the Lindemann constant and for diffusion constants compare favorably with experiment for alkali metals and halides.
KeywordsHalide RbCl CsCl RbBr
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