Universal relationships for the phonon spectra in BCC,FCC, and HCP crystals with a short-range interatomic interaction |
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Authors: | V G Vaks I A Zhuravlev A D Zabolotskii |
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Institution: | 1.Russian Research Center Kurchatov Institute,Moscow,Russia;2.Moscow Institute of Physics and Technology,Dolgoprudnyi, Moscow oblast,Russia |
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Abstract: | The frequencies of the phonon branches that correspond to the vibrations of the close-packed atomic planes in bcc, fcc, and
hcp crystals with short-range interatomic interaction are shown to be described by a universal relationship, which only contains
two parameters for each branch, for any polarization λ. These phonon branches correspond to the (ξ, ξ, 0) direction in bcc
crystals, the (ξ, ξ, ξ) direction in fcc crystals, and the (0, 0, ξ) direction in hcp crystals. This universal relationship
can only be violated by long-range interactions, namely, the interactions outside the sixth coordination shell in a bcc crystal,
the fifth coordination shell in an fcc crystal, and the eleventh or tenth coordination shell in an hcp crystal. The effect
of these long-range interactions for each phonon branch can be quantitatively characterized by certain parameters Δ
nλ, which are simply expressed in terms of the frequencies of three phonons of the branch. The values of these parameters are
presented for all bcc, fcc, and hcp metals whose phonon spectra are measured. In most cases, the proposed relationships for
the frequencies are found to be fulfilled accurate to several percent. In the cases where the Δ
nλ parameters are not small, they can give substantial information on the type and scale of long-range interaction effects in
various metals. |
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