Summary
Metallic lattice is visualized as a series of point ions immersed in an electron gas. The total interaction with the metal is supposed to consist of ion-ion central interaction and ion-electron interaction. The former has been incorporated along the lines of Born-Karman and the latter has been accounted for by considering the ionic charge as smeared over the metal. The force corresponding to the strain developed within the Wigner-Seitz sphere is averaged over the whole sphere. The phonon dispersion relations along the symmetry direction and the (θ-T)-curve have been plotted for zirconium (Zr) and thallium (Tl) with force constants effective up to fourth neighbour only. The theoretical values are found to be closer to the experimental data.
Riassunto
Un reticolo metallico si visualizza come una serie di ioni puntiformi immersi in un gas di elettroni. Si suppone che l’interazione totale consista di un’interazione centrale ione-ione e di un'interazione ione-elettrone. Si è incorporata la prima secondo la linea di Born-Karman e si è tenuto conto della seconda considerando la carica ionica sparsa sul metallo. Si fa la media sulla sfera della forza corrispondente allo sforzo sviluppato entro la sfera di Wigner-Seitz. Si sono poste in diagramma le relazioni di dispersione fononiche lungo la direzione di simmetria e la curva θ-T per lo zirconio (Zr) ed il tallio (Tl) con costanti di forza efficaci solo sino al quarto vicino. Si trova che i valori teorici sono prossimi ai dati sperimentali.
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Singh, S.P., Maurya, J.R. & Kushwaha, S.S. An electron gas model for the lattice dynamics of thallium and zirconium. Nuovo Cim B 29, 159–168 (1975). https://doi.org/10.1007/BF02732236
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DOI: https://doi.org/10.1007/BF02732236