Phonon Scattering in Condensed Matter pp 325-327 | Cite as

# Revision of the Statistical Mechanics of Phonons to Include Phonon Linewidths

Conference paper

## Abstract

Zubarev[1] in 1960 obtained the “smeared” Bose-Einstein (B-E) function in order to take into account the fact that the eigenenergy associated with a fixed phonon wave vector q and fixed polarization index j is not precisely defined but, instead, is smeared by phonon-phonon and phonon-electron interactions. The ratio Γ(qj)/ω(qj) is often quite small, i.e., of the order of 0.01 or less, where Γ is the phonon linewidth and ħ ω is the eigenenergy. However, in strongly anharmonic crystals Γ /ω may be as large as 0.3 at certain points of the Brillouin zone. In such dramatic cases, one would suspect that such phonon linewidths would have some observable effect on the thermodynamic properties. Zubarev represented the effect of “smearing” on the statistical properties by the infinite integral[1], in which we have deleted the indices (q,j) for convenience. The term in square brackets in (1) is the usual B-E function, while in L, the usual Lorentzian function, \( \overline \omega \) is the average or center frequency of the distribution.

$$ \overline n = \int_{ - \infty }^\infty d \omega \;{\left[ {\exp (\frac{{h\omega }}{{kT}}) - 1} \right]^{ - 1}}\;L(\omega ;\overline \omega ,\Gamma )\;, $$

(1)

$$ L(\omega ;\overline \omega ,\Gamma )\; = \;(\Gamma /\pi ){\left[ {{{(\omega - \overline \omega )}^2} + {\Gamma ^2}} \right]^{ - 1}}, $$

(2)

### Keywords

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### References

- 1.D. N. Zubarev: [translation; Soviet Phys.-Usp. 3, 320 (1960)].Google Scholar
- 2.P. M. Morse and H. Feshbach: Theoretical Physics, McGraw Hill, New York, (1953).MATHGoogle Scholar
- 3.A. A. Maradudin and E. A. Fein: Phys. Rev. 128, 2562 (1962).CrossRefGoogle Scholar
- 4.B. N. Brockhouse, T. Arase, G. Caglioti, M. Sikamoto, R. N. Sinclair, and A. D. Woods: Inelastic Scattering of Neutrons, IAEA, Vienna (1961).Google Scholar
- 5.W. C. Overton, Jr.: J. Phys. Chem. Solids 29, 711 (1968).CrossRefADSGoogle Scholar

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