An Extended Breathing Shell Model for Alkali Halides and Its Test at Experimental Results

Bluthardt, W.; Schneider, Wolfgang J.; Wanger, Marianne

doi:10.1002/pssb.2220560206

Cited by 8 publications

(2 citation statements)

References 28 publications

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“…We emphasize that a more accurate quantum mechanical treatment no longer reproduces equations of motion in form of the classical shell models. In principle it is no fundamental problem to generalize our results to yield the more complex models of Schroder [2] and Bluthardt et al [3], where additional shell deformations of Al, and E symmetry are introduced. Numerical results for the deformation parameter anif the consequences with respect to the breathing shell model of Schroder will be discussed in a forthcoming paper.…”

Section: Summary and Discussionmentioning

confidence: 92%

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On the quantum mechanical foundation of classical shell models in lattice dynamics

Niedermann

Wagner

1976

Physica Status Solidi (b)

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The approach is based on the adiabatic principle and the harmonic approximation. The aim is to find those quantum mechanical approximations which are necessary to derive expressions of the same structural form as the classical shell model equations of the lattice dynamics of ionic crystals. To this purpose the long range interaction of the ionic dipoles is treated in first order perturbation theory, whereas for the short range part of the adiabatic potential a more restricted approximation is used. By this means equations of motions are obtained of the form of the equations of the classical shell models. But in contrast to the phenomenological models by quantum mechanical arguments two different coordinates are introduced for the description of a TI,-motion of an electronic shell.Es werden diejenigen quantenmechanischen NLiherungen untersucht, die notig sind, um Bewegungsgleichungen von der Form der Gleichungen der klassischen Schalenmodelle abzuleiten. Hierzu xerden das adiabatische Prinzip und die harmonische Niherung benutzt. Die weitreichende Wechselwirkung der Dipole der Ionen wird mit Storungstheorie in erster Niihernng behandelt, wiihrend fiir die kurzreichweitigen Beitriige des adiabatischen Potentials eine spezielle Nitherung Verwendung findet. Damit werden Bewegungsgleichungen von gleicher Form wie die Gleichungen der klassischen Schalenmodelle erhalten. Aber im Gegensatz zu den phinomenologischen Modellen fiihren quantenmechanische vberlegungen zu zwei verschiedenen Koordinaten zur Beschreibung der Tl,-Bewegung einer Elektronenechale.

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Section: Summary and Discussionmentioning

confidence: 92%

“…The quantity Az; mainly describes the translation of $' . In view of equation (3) this means that for the correct basis I$' the dominant term is not centered a t…”

Section: Introduction Of Two Different Shell Translationsmentioning

confidence: 99%

On the quantum mechanical foundation of classical shell models in lattice dynamics

Niedermann

Wagner

1976

Physica Status Solidi (b)

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Hydrides and Deuterides of Lithium and Sodium. I. Model Potentials and Their Use in Perfect Lattice

Haque¹,

Islam²

1990

Physica Status Solidi (b)

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An interionic potential model is developed for lighter and heavier alkali hydrides and deuterides. The method uses a combination of theoretical techniques, empirical fit, and a few plausible assumptions. An assessment of the derived potentials is made by calculating the lattice statics and dynamics of the crystals and by comparing both with experiment (where available) and with other calculations. The potentials are found to describe the elastic and dielectric properties reasonably well. The phonon dispersion curves of hydride and deuteride of sodium are compared with the calculations of Dyck and Jex based on force constant model approach and the results are discussed. The need for further experiments on heavier hydrides and deuterides is stressed.Es wird ein Interionenpotentialmodell fur leichtere und schwerere Alkalihydride und -deuteride entwickelt. Die Methode benutzt eine Kombination von theoretischen Techniken, empirischer Anpassung und einigen wenigen plausiblen Annahmen. Eine Einschatzung der abgeleiteten Potentiale wird durch Berechnung der Gitterstatik und -dynamik der Kristalle und durch Vergleich sowohl mit Experimenten (wenn vorhanden) als auch mit anderen Berechnungen durchgefiihrt. Es wird gefunden, daI3 die Potentiale die elastischen und dielektrischen Eigenschaften verhaltnismaBig gut beschreiben. Die Phononendispersionskurven der Hydride und Deuteride von Natrium werden mit den von Dyck und Jex auf der Grundlage des Kraftkonstantenmodells durchgefiihrten Berechnungen verglichen und die Ergebnisse diskutiert. Die Notwendigkeit weiterer Experimente an schwereren Hydriden und Deuteriden wird hervorgehoben.

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A Direct Approach to Finite Phonon Transport (Realistic Transfer at Boundaries)

Schneider

Wagner

1976

Phonon Scattering in Solids

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An Extended Breathing Shell Model for Alkali Halides and Its Test at Experimental Results

Cited by 8 publications

References 28 publications

On the quantum mechanical foundation of classical shell models in lattice dynamics

On the quantum mechanical foundation of classical shell models in lattice dynamics

Hydrides and Deuterides of Lithium and Sodium. I. Model Potentials and Their Use in Perfect Lattice

A Direct Approach to Finite Phonon Transport (Realistic Transfer at Boundaries)

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