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.
KeywordsDiffusion Constant Debye Temperature Critical Amplitude Large Wave Number Anharmonic Lattice
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