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Noncentral forces and lattice vibration in transition metals

Нецентральные силы и колебания решетки в переходных металлах

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

The frequency wave vector dispersion relations for phonons in vanadium and molybdenum have been computed along the principal symmetry directions [ξ00], [ξξ0] and [ξξξ] on the basis of a latticedynamical model which takes into account the Clark, Gazis and Wallis' type angular forces and also the effect of electron-ion interaction as outlined by Krebs. The present scheme is found to give a plausible explanation of phonon dispersion curves and a reasonably good agreement with experimental values obtained from the recent neutron scattering measurements.

Резюме

Вычисляются дисперсионные соотношения, устанавливающие связь между частотой и волновым вектором, для фононов в ванадии и молибдене вдоль главных направлений симметрии [ξ00], [ξξ0] и [ξξξ] на основе динамической модели решетки, которая учитывает силы, создающие вращающий момент, типа Кларка, Газиса и Уоллеса, а также эффект электрон-ионного взаимодействия, рассмотренный Кребсом. Предложенная схема дает правдоподобное объяснение кривых дисперсии фононов и удовлетворительно согласуется с экспериментальными данными, полученными из недавних измерений рассеяния нейтронов.

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References

  1. K. Fuch:Proc. Roy. Soc., A157, 444 (1936).

    Article  ADS  Google Scholar 

  2. J. deLaunay:Solid State Physics, edited byF. Seitz andD. Turnbull, Vol.2 (New York, N. Y., 1956), p. 276.

  3. B. Dayal andB. B. Tripathi:Proc. Roy. Soc., A266, 122 (1962).

    Article  ADS  Google Scholar 

  4. W. C. Overton jr.:Phys. Rev.,127, 1107 (1962).

    Article  ADS  Google Scholar 

  5. B. C. Clark, D. C. Gazis andR. F. Wallis:Phys. Rev.,134, A 1486 (1964).

    Article  ADS  Google Scholar 

  6. P. S. Yuen andY. P. Varshni:Phys. Rev.,164, 895 (1967).

    Article  ADS  Google Scholar 

  7. P. S. Yuen andY. P. Varshni:Phys. Rev.,174, 766 (1968).

    Article  ADS  Google Scholar 

  8. J. Behari andB. B. Tripathi:Phys. Lett.,29 A, 313 (1969).

    Article  Google Scholar 

  9. J. Behari andB. B. Tripathi:Journ. Phys. Soc. Japan,28, 346 (1970).

    Article  ADS  Google Scholar 

  10. P. K. Sharma andS. K. Joshi:Journ. Chem. Phys.,39, 2633 (1963).

    Article  ADS  Google Scholar 

  11. P. K. Sharma andS. K. Joshi:Journ. Chem. Phys.,40, 662 (1964).

    Article  ADS  Google Scholar 

  12. G. Bose, H. C. Gupta andB. B. Tripathi:Journ. Phys. F,2, 426 (1972).

    Article  ADS  Google Scholar 

  13. K. Krebs:Phys. Rev.,138, 143 (1965).

    Article  ADS  Google Scholar 

  14. J. Launay de:Journ. Chem. Phys.,21, 1975 (1953).

    Article  ADS  Google Scholar 

  15. A. B. Bhatia:Phys. Rev.,97, 363 (1955).

    Article  ADS  MATH  Google Scholar 

  16. A. B. Bhatia andG. K. Horton:Phys. Rev.,98, 1715 (1955).

    Article  ADS  Google Scholar 

  17. M. M. Shukla andB. Dayal:Journ. Phys. Chem. Sol.,26, 1343 (1965).

    Article  ADS  Google Scholar 

  18. P. S. Mahesh andB. Dayal:Phys. Rev.,143, 443 (1966).

    Article  ADS  Google Scholar 

  19. A. K. Singh andP. K. Sharma:Journ. Phys. Soc. Japan,26, 425 (1969).

    Article  ADS  Google Scholar 

  20. S. Pal andR. B. Singh:Journ. Phys. Soc. Japan,35, 1487 (1973).

    Article  ADS  Google Scholar 

  21. D. Pines:Solid State Physics, Vol.1 (New York, N. Y., 1955), p. 394;Elementary Excitations in Solids (New York, N. Y., 1967).

    Google Scholar 

  22. D. I. Bolef:Journ. Appl. Phys.,32, 100 (1961).

    Article  ADS  Google Scholar 

  23. R. Colella andB. W. Batterman:Phys. Rev. B,1, 3913 (1970).

    Article  ADS  Google Scholar 

  24. A. D. B. Woods andS. H. Chen:Solid State Comm.,2, 233 (1964).

    Article  ADS  Google Scholar 

  25. A. D. B. Woods, B. N. Brockhouse, R. H. March, A. T. Stewart andR. Bowers:Phys. Rev.,128, 1112 (1962).

    Article  ADS  Google Scholar 

  26. B. N. Brockhouse, T. Arase, G. Caglioti, K. R. Rao andA. D. B. Woods:Phys. Rev.,128, 1099 (1962).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of Allahabad, Allahabad

    V. P. Singh, J. Prakash & M. P. Hemkar

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  1. V. P. Singh
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  2. J. Prakash
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  3. M. P. Hemkar
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Riassunto

Si sono calcolate le relazioni di dispersione del vettore d'onda della frequenza per i fononi nel vanadio e nel molibdeno lungo le principali direzioni di simmetria [ξ00], [ξξ0] e [ξξξ] sulla base di un modello di dinamica reticolare che tien conto delle forze angolari del tipo di Clark, Gazis e Wallis ed anche dell'effetto dell'interazione elettroneione come è stata delineata da Krebs. Si trova che questo schema dà una spiegazione plausibile delle curve di dispersione dei fononi e un accordo ragionevolmente buono con i valori sperimentali ottenuti dalle recenti misure dello scattering di neutroni.

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Singh, V.P., Prakash, J. & Hemkar, M.P. Noncentral forces and lattice vibration in transition metals. Nuovo Cim B 28, 476–482 (1975). https://doi.org/10.1007/BF02726672

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  • DOI: https://doi.org/10.1007/BF02726672

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