Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2005-10-20
Physics
Condensed Matter
Other Condensed Matter
25 pages, 3 figures, revtex4. Updated version contains much more general bounds than original version
Scientific paper
10.1103/PhysRevB.73.174105
Using general properties of the crystal site representation normal mode matrix, we provide some very simple bounds on localized modes in simple, body-centered and face-centered cubic crystals with substitutional point defects. We derive a trace condition constraint on the net change in crystal eigenfrequencies caused by the introduction of a defect, with the condition being a completely general one which holds for any combination of central and non-central crystal force-constants and for all-neighbor interactions. Using this condition we show that the sufficient condition for producing localized modes in an arbitrary cubic crystal by a mass change at the defect site is that the defect mass be less than one half of that of the host atom mass which it replaces, and that the sufficient condition for producing localized modes in an arbitrary cubic crystal by force-constant changes alone is that the defect site self force-constant be greater than twice that of the pure crystal self force-constant of the host atom which it replaces.
Lipkin Harry J.
Mannheim Philip D.
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