Lattice dynamics of alkali metals

The experimentally observed dispersion curves of lithium, sodium, and potassium in [ζ00] direction, especially the degeneracy of the zone boundary frequencies and the anomalous crossing in lithium, are reproduced completely by a lattice dynamical which model which takes into account the umklapp processes and the screening associated with the electrons. It is shown that the observed crossing in lithium is associated with the large positive value of the bulk modulus of the electron gas, together with the variation of umklapp contribution to these modes of vibration with the wave vector. The latter leads to the observed degeneracy at the zone boundary point. The role played by umklapp processes in producing effects is discussed.



Die experimentell beobachteten Dispersionskurven von Lithium, Natrium und Kalium in [ζ00]-Richtung, insbesondere die Entartung der Zonengrenzenfrequenzen und die anomale Uberschneidung in Lithium, werden vollstandig durch ein gitterdynamisches Modell wiedergegeben, das Umklapprozesse und Abschirmeffekte durch Elektronen berucksichtigt. Es wird gezeigt, das das beobachtete Uberschneiden in Lithium mit einem grosen positiven Wert des Elastizitatsmoduls des Elektronengases verbunden ist, zusammen mit der Anderung des Umklappbeitrages zu diesen Schwingungsmoden mif dem Wellenvektor. Das letztere fuhrt zu der beobachteten Entartung am Zonengrenzpunkt. Die Rolle der Umklapprosse bei diesen Effekten wird diskutiert.

On the crossing of dispersion curves of alkali metals in [ζ00] direction

It is proposed that the effects of three-body interactions on the phonon dispersion curves of metals be investigated by adding the third-order perturbation term in the electron-ion potential obtained by Lloyd and Sholl (1968) for a local electron-ion potential to the model of Krebs (1965) with two-body forces, or the model of Cheveau (1968) extended to second-nearest neighbours. The constraining equation required by equilibrium is determined for the phenomenological models of Krebs and Cheveau. The constraint equation can be used as an additional equation for determining unknown parameters in these models.

The inclusion of three-body forces and the condition of equilibrium into the models of Krebs and Cheveau

A model for fcc metals is proposed by combining the ion-ion interaction from the axially symmetric model of Lehman et al (1962) with the electron-ion interaction from Krebs' model (1964). The computed frequencies of copper are in excellent agreement with experimental ones.

https://iopscience.iop.org/article/10.1088/0305-4608/3/1/001/pdf

A model for lattice dynamics of fcc metals

Investigations of the dependence of phonon frequencies of alkali metals on their atomic mass reveal that they satisfy an empirical relation Mγv = D(q), a constant which depends on q, with γ = 0.754 ± 0.019 at all wave vectors and hence homologous. It is shown that the observed cross-over of [ζ00] branches of lithium is not an anomalous property, but only manifests itself in alkali metals of smaller atomic mass due to small variations of γ. The role played by atomic mass which is closely related to that of electron gas constant, C′, in producing a cross-over is discussed.



Untersuchungen der Abhangigkeit der Phononenfrequenzen der Alkalimetalle von ihrer Atommasse zeigen, das sie der empirischen Beziehung Mγv = D(q) mit γ = 0,754 ± 0,019 bei allen Wellenvektoren genugen. Es wird gezeigt, das die beobachtete Uberschneidung von [ζ00]-Zweigen von Lithium keine anomale Eigenschaft ist, sondern sich nur in Alkalimetallen mit geringer Atommasse infolge geringer Anderungen von γ ausert. Die Rolle, die die Atommasse beim Auftreten einer Uberschneidung spielt, und die eng verknupft ist mit der der Elektronengaskonstante C′, wird diskutiert.

M.M. Shukla

Papers

Lattice dynamics of alkali metals

A model for lattice dynamics of b.c.c. metals

A model for lattice dynamics of hexagonal close packed metals

The lattice dynamics of Rb1−x Kx alloys

Comment on ``lattice energy in alkali halide crystals''