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Prog. Theor. Phys. Vol. 29 No. 2 (1963) pp. 191-205

[ Full Text PDF : FREE ACCESS (933K) ]

Resonance Scattering of Lattice Waves by Isotopes

Shozo Takeno

Department of Physics, Faculty of Science, Hokkaido University, Sapporo

(Received August 30, 1962)

Abstract:

An investigation is made of the scattering of lattice waves by isotopes in a Bravais lattice by studying classical time-independent equations of motion for the displacement of atoms from their equilibrium positions. Expressions for the cross section or the intensity, of a scattered wave by an isolated isotope and by a pair of isotopes are obtained from the solutions of the equations of motion. It is shown that a resonance scattering occurs when the difference between the mass of an atom of the host crystal and that of an isotope exceeds a certain critical value. The Rayleigh scattering formula obtained by Pomeranchuk and Klemens is shown to be valid only when the mass difference is small. As a model, a simple cubic lattice with the nearest neighbour interaction is studied in detail, and the scattering cross section as well as the intensity of the scattered wave is evaluated explicitly as a function of the frequency and the mass difference. It is suggested that (1) a very heavy isotope causes a sharp resonance scattering in the low frequency region, and (2) in the high frequency region a resonance scattering occurs only when the mass of the isotope is so small that it causes a localized mode.


URL : http://ptp.ipap.jp/link?PTP/29/191/
DOI : 10.1143/PTP.29.191

[ Full Text PDF : FREE ACCESS (933K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 29 No. 2 (1963) pp. 328-330 :
    Frequency Spectrum of a Lattice with Heavy Isotopes
    Shozo Takeno
  2. Progress of Theoretical Physics Vol. 29 No. 6 (1963) pp. 937-938 :
    Scattering of Spin Waves by Point Imperfections
    Shozo Takeno
  3. Progress of Theoretical Physics Vol. 30 No. 1 (1963) pp. 144-145 :
    Mass-Difference Scattering and Lattice Thermal Conductivity
    Shozo Takeno
  4. Progress of Theoretical Physics Vol. 33 No. 3 (1965) pp. 363-379 :
    A High-Frequency Resonant Mode in Lattice Vibrations
    Shozo Takeno
  5. Progress of Theoretical Physics Vol. 33 No. 4 (1965) pp. 614-623 :
    Localized Modes of the Extended Defect
    Itaru Kobori
  6. Progress of Theoretical Physics Vol. 34 No. 2 (1965) pp. 313-314 :
    Time Dependent Problems of Scattering in Linear Lattice System
    Hideki Sabata, Hiroshi Nakazawa and Ei Teramoto
  7. Progress of Theoretical Physics Vol. 38 No. 5 (1967) pp. 995-1022 :
    Theory of Impurity-Induced Infrared Absorption in Alkali Halide Crystals
    Shozo Takeno
  8. Progress of Theoretical Physics Vol. 39 No. 3 (1968) pp. 593-600 :
    Lattice Vibration of a Linear Chain with Long-Range Interaction
    Kazushige Ishii
  9. Progress of Theoretical Physics Vol. 42 No. 5 (1969) pp. 1003-1019 :
    The Inelastic Scattering of an Electron by a Nonmagnetic Impurity in a Crystal
    Shozo Takeno
  10. Progress of Theoretical Physics Vol. 48 No. 5 (1972) pp. 1468-1473 :
    Frequency Spectrum and Low-Temperature Specific Heat of Noncrystalline Solids
    Shozo Takeno and Masaki Goda

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