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On the Distinction between Debye Bosons and Phonons

Year 2015, Volume: 18 Issue: 4, 277 - 284, 20.07.2015
https://doi.org/10.5541/ijot.5000130678

Abstract

A method is described that allows one to construct the dispersion of the Debye bosons (sound waves) from the known temperature dependence of the sound velocities. The method simply assumes that the sound velocity measured at temperature T gives the slope of the dispersion relation at excitation energy E=kB·T. The associated reduced wave vector is set equal to q/q0=a0kBT/hvL/T. In this way the dispersion of the Debye bosons can be constructed for all thermal energies for which sound velocities vL/T(T) are known. This can be up to melting temperature. Surprisingly, the dispersion of the Debye bosons continues beyond zone boundary. At melting temperature the wavelength of the Debye bosons is of the order of the atomic diameters. The sources of the Debye bosons therefore must have atomic dimensions. Spontaneous generation of Debye bosons by individual atoms is, however, a completely unexplored process. Interactions with the atomistic background of phonons or lattice defects provide damping to the Debye bosons and make vL/T(T) sample and temperature dependent. Quite generally vL/T(T) decreases as a function of increasing temperature. For high energies the dispersion relation of the Debye bosons therefore becomes visibly lower than linear. Interactions between Debye bosons and phonons can modify the dispersion of the acoustic phonons appreciably. Because of their different symmetries the dispersion relations of Debye bosons and acoustic phonons attract each other. It is observed that for low wave vector values the dispersion of the acoustic phonons can assume the linear wave vector dependence of the Debye bosons. At the end of the linear section a functional crossover to a sine-like function of wave vector occurs.

References

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  • U. Köbler, A. Hoser, Renormalization Group Theory- Impact on Experimental Magnetism, Springer, Berlin, 2010.
  • M. Born, K. Huang, Dynamical Theory of Crystal Lattices, Clarendon Press, Oxford, 1956.
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  • U. Köbler, Towards a Field Theory of Magnetism in: K. Pace (Ed.), Recent Developments in Magnetism Research (Nova Science Publishers, Hauppauge, New York, 2013) pp. 1-66.
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  • C.V. Briscoe, C.F. Squire, Elastic constants of LiF from 4.2 K to 300 K by ultrasonic methods, Phys. Rev. 106, 1175-1177, 1957.
  • U. Köbler, Bosons and magnons in ordered magnets, Acta Phys. Pol. A 127, 1694-1701, 2015.
  • H. Witte, E. Wölfel, Electron distributions in NaCl, LiF, CaF2 and Al, Rev. Mod. Phys. 30, 51-55, 1958.
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  • B.M. Powell, P. Martel, A.D.B. Woods, Lattice dynamics of niobium-molybdenum alloys, Phys. Rev. 171, 727, 1968.
  • K.A. Jones, S.C. Moss, R.M. Rose, The Effect of small oxygen additions on the elastic constants and low temperature ultrasonic attenuation of Nb single crystals, Acta Met. 17, 365-372, 1969.
  • R.A. Cowley, W. Cochrane, B.N. Brockhouse, A.D.B. Woods, Lattice dynamics of alkali halide crystals. III. Theoretical, Phys. Rev. 131, 1030-1039, 1963.
  • J.C. Glyden Houmann, R.M. Nicklow, Lattice Dynamics of Terbium, Phys. Rev. B 1, 3943-3952, 1970.
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Year 2015, Volume: 18 Issue: 4, 277 - 284, 20.07.2015
https://doi.org/10.5541/ijot.5000130678

Abstract

References

  • P. Debye, Zur Theorie der spezifischen Wärmen, Ann. Physik 39, 789-839, 1912
  • U. Köbler, A. Hoser, Renormalization Group Theory- Impact on Experimental Magnetism, Springer, Berlin, 2010.
  • M. Born, K. Huang, Dynamical Theory of Crystal Lattices, Clarendon Press, Oxford, 1956.
  • K.G. Wilson, J. Kogut, The renormalization group and the ε expansion, Physics Reports 12C 75-200, 1974.
  • K.G. Wilson, The renormalization group: Critical phenomena and the Kondo problem, Reviews of Modern Phys. 47, 773-840, 1975.
  • U. Köbler, Towards a Field Theory of Magnetism in: K. Pace (Ed.), Recent Developments in Magnetism Research (Nova Science Publishers, Hauppauge, New York, 2013) pp. 1-66.
  • R.F.S. Hearmon in: K.-H. Hellwege and A.M. Hellwege (Eds.), Landolt-Börnstein vol. 18 Springer, Berlin, p. 1, 1984.
  • Y. Endoh, G. Shirane, J. Skalyo, Jr., Lattice dynamics of solid neon at 6.5 and 23.7 K, Phys Rev. B 11, 1681-1688, 1975.
  • Y. Fujii, N.A. Lurie, R. Pynn, G. Shirane, Inelastic neutron scattering from solid 36Ar, Phys. Rev. B 10, 3647- 3659, 1974.
  • J. Skalyo, Jr., Y. Endoh, G. Shirane, Inelastic neutron scattering from solid krypton at 10 K, Phys. Rev. B 9, 1797-1803, 1974.
  • N.A. Lurie, G. Shirane, J. Skalyo, Jr., Phonon dispersion relations in xenon at 10 K, Phys. Rev. B 9 5300-5306, 1974.
  • A.A.Z. Ahmad, H.G. Smith, N. Wakabayashi, M.K. Wilkinson, Lattice dynamics of cesium chloride, Phys. Rev. B 6, 3956-3961, 1972.
  • G. Dolling, H.G. Smith, R.M. Nicklow, P.R. Vijayaraghavan, M.K. Wilkinson, Lattice dynamics of lithium fluoride, Phys. Rev. 168, 970-979, 1968.
  • C.V. Briscoe, C.F. Squire, Elastic constants of LiF from 4.2 K to 300 K by ultrasonic methods, Phys. Rev. 106, 1175-1177, 1957.
  • U. Köbler, Bosons and magnons in ordered magnets, Acta Phys. Pol. A 127, 1694-1701, 2015.
  • H. Witte, E. Wölfel, Electron distributions in NaCl, LiF, CaF2 and Al, Rev. Mod. Phys. 30, 51-55, 1958.
  • G. Schoknecht, Röntgen-kristallstrukturanalyse mit faltungsintegralen, ii. meßverfahren und bestimmung der elektronendichte in NaCl, Z. Naturforschung 12a, 983- 996, 1957.
  • B.M. Powell, P. Martel, A.D.B. Woods, Lattice dynamics of niobium-molybdenum alloys, Phys. Rev. 171, 727, 1968.
  • K.A. Jones, S.C. Moss, R.M. Rose, The Effect of small oxygen additions on the elastic constants and low temperature ultrasonic attenuation of Nb single crystals, Acta Met. 17, 365-372, 1969.
  • R.A. Cowley, W. Cochrane, B.N. Brockhouse, A.D.B. Woods, Lattice dynamics of alkali halide crystals. III. Theoretical, Phys. Rev. 131, 1030-1039, 1963.
  • J.C. Glyden Houmann, R.M. Nicklow, Lattice Dynamics of Terbium, Phys. Rev. B 1, 3943-3952, 1970.
  • T. Takagahara, ”Electron-Phonon interactions in semiconductor quantum dots” in Semiconductor Quantum Dots, Y. Masumoto, T. Takagahara (Eds.) Berlin: Springer, pp. 115-147.
  • A. Tanaka, S. Onari, T. Arai, Phys. Rev. B 47, 1237- 1243, 1933.
There are 23 citations in total.

Details

Primary Language English
Journal Section Regular Original Research Article
Authors

Ulrich Köbler

Publication Date July 20, 2015
Published in Issue Year 2015 Volume: 18 Issue: 4

Cite

APA Köbler, U. (2015). On the Distinction between Debye Bosons and Phonons. International Journal of Thermodynamics, 18(4), 277-284. https://doi.org/10.5541/ijot.5000130678
AMA Köbler U. On the Distinction between Debye Bosons and Phonons. International Journal of Thermodynamics. December 2015;18(4):277-284. doi:10.5541/ijot.5000130678
Chicago Köbler, Ulrich. “On the Distinction Between Debye Bosons and Phonons”. International Journal of Thermodynamics 18, no. 4 (December 2015): 277-84. https://doi.org/10.5541/ijot.5000130678.
EndNote Köbler U (December 1, 2015) On the Distinction between Debye Bosons and Phonons. International Journal of Thermodynamics 18 4 277–284.
IEEE U. Köbler, “On the Distinction between Debye Bosons and Phonons”, International Journal of Thermodynamics, vol. 18, no. 4, pp. 277–284, 2015, doi: 10.5541/ijot.5000130678.
ISNAD Köbler, Ulrich. “On the Distinction Between Debye Bosons and Phonons”. International Journal of Thermodynamics 18/4 (December 2015), 277-284. https://doi.org/10.5541/ijot.5000130678.
JAMA Köbler U. On the Distinction between Debye Bosons and Phonons. International Journal of Thermodynamics. 2015;18:277–284.
MLA Köbler, Ulrich. “On the Distinction Between Debye Bosons and Phonons”. International Journal of Thermodynamics, vol. 18, no. 4, 2015, pp. 277-84, doi:10.5541/ijot.5000130678.
Vancouver Köbler U. On the Distinction between Debye Bosons and Phonons. International Journal of Thermodynamics. 2015;18(4):277-84.

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