Crystal equilibrium and phonon dispersion in rare‐earth H.C.P. metals

Abstract

The phonon dispersionin two h.c.p. rare-earth metals Tb and Ho are investigated on the basis of a model which uses a 5-neighbour-central pair potential for close-range forces and a screened Coulomb interaction for long-range forces. The model considers completely the equilibrium of the ionic lattice in a medium of an uniform electron gas. Consequently two equilibrium conditions, necessary for the h.c.p. structure, are deduced and used in the study.Es wird die Phononendispersion in den beiden hexagonal dicht gepackten Metallrn der Seltenen Erden T b und Ho auf der Grundlage eines Modells untersucht, das ein 5-Nachbarn-Zentral-Paarpotential fur kurzreichweitige Krafte und abgeschirmte Coulomb-Wechselwirkung fur langreichweitige Krafte benutzt. Das Model1 berucksichtigt vollstandig das Gleichgewicht des Ionengitters im Medium eines gleichformigen Elektronengases. Konsequenterweise werden zwei Gleichgewichtsbedingungen, die fur die hexagonal dicht gepackte Struktur notwendig sind, abgeleitet und fur die Untersuchung benutzt.

A Model for Lattice Dynamics of Lanthanides

“…metals. The elastic constants of holmium have been measured by Palmer [14] have also calculated phonon dispersion relations of holmium. I n this case these authors have also neglected electron-ion interaction for atoms belonging to the non-basal plane.…”

“…The elastic constants of terbium have been measured bySalama et al [ 111 in the temperature range 78 to 300 "C.Houmann and Nicklow [la] have measured phonon dispersion curves for terbium a t room temperature using inelastic scattering of thermal neutrons. Upadhyay and Verma [ I 3 1 and Sinha and Upadhyay[14] have studied pho-Phonon dispersion curves for a) Tb and b) Ho along symmetry directions. 0 , A experimental points non dispersion of terbium using different expression8 for electron-ion interactions.…”