Lattice Dynamics and Infrared Absorption of Cesium Halides

Mahler, G.; Engelhardt, Peter

doi:10.1002/pssb.2220450217

Cited by 31 publications

(9 citation statements)

References 21 publications

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“…If we restrict the general shell model equations to forces acting via the shells only (R = S = T), we obtain the following set of equahions for the ionic displacements u and the relative coordinates w [5] :…”

Section: Theorymentioning

confidence: 99%

Mean‐Square Ionic Displacements and Force Constants of Crystals with the CsCl Type Structure

Jex

Müllner

Dyck

1974

Physica Status Solidi (b)

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Mean-square vibrational amplitudes of ions in the diatomic lattices of crystals with the CsCl type structure have recently been determined in the high temperature region by elastic scattering of neutrons. An evaluation of mean-square displacements in terms of frequency moments is derived and connections with the force constants of the crystals are worked out. The difference of the vibrational amplitudes of the two ions is calculated from the experimental data and by means of force constants derived from phonon measurements.Vor kurzem wurden die mittleren Schwingungsamplitudenquadrate zweiatomarer Gitter mit CsC1-Struktur im Bereich hoher Temperaturen aus Experimenten mit elastisch gestreuten Neutronen bestimmt. Zur Interpretation der Daten wird eine Entwicklung nach Frequenzmomenten angegeben und der Zusammenhang mit den Kraftekonstanten des Schalenmodells aufgezeigt. Am Beispiel einer linearen Kette werden die allgemeinen Resultate erlautert und die Differenz der mittleren Schwingungsamplituden berechnet.

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Section: Theorymentioning

confidence: 99%

Mean‐Square Ionic Displacements and Force Constants of Crystals with the CsCl Type Structure

Jex

Müllner

Dyck

1974

Physica Status Solidi (b)

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“…It was shown by MAHLER and ENGELHARDT (1971) that the lattice dynamics of the alkali halides with cesium chloride structur, CsCI, CsBr, and CsI can be calculated in a very similar way to that of the other alkali halides by using the breathing-shell model (SCHRO- DER, 1966). Consequently, they tried to calculate the infrared absorption of these crystals along the lines which have been followed in the foregoing sections.…”

Section: Ff)mentioning

confidence: 97%

“…at a frequency where the determinant of 1 + go v, (23.15) below, is about to have a zero). Martin has used a breathing-shell model for the host lattice (MAHLER and ENGELHARDT, 1971) and has tried to fit the peak at 40 wavenumbers in CsI : K + (Fig. 21.5) by varying nearest-neighbor central and noncentral force constants at the defect, as well as the central force constants between the nearest neighbors of the defect.…”

Section: Information Contained In Defect-induced Spectramentioning

confidence: 99%

Vibrational Infrared and Raman Spectra of Non-Metals

Bilz¹,

Strauch²,

Wehner³

1984

Light and Matter Id / Licht Und Materie Id

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The vibrational properties of crystals determine the photon infrared absorption, inelastic neutron scattering and, to a large extent, inelastic photon scattering by phonons, i.e., Raman scattering. The interpretation of infrared and Raman spectra requires, therefore, an understanding of the basic features of lattice dynamics. The quantum theory of solids describes the crystal properties in terms of elementary excitations and their mutual interactions. Dynamic properties are represented by phonons (lattice vibrations) and their interactions mainly with other phonons (anharmonicity), electrons (electron-phonon coupling), and photons (interaction with radiation). This characterizes the scope of the article. Its emphasis is on the interrelation between theory and experiment, i.e., on the microscopic or model interpretation of experimental spectra.Work on infrared absorption and Raman scattering of non-metallic solids was summarized twenty years ago in two review articles in this Encyclopedia by LECOMTE (1958) and by MIZUSHIMA (1958). Since then, many important new experimental data have become available, thanks to very refined techniques for measuring spectra of pure and imperfect single crystals. Furthermore, the theory of the interactions of phonons and photons has been much improved, stimulated by the remarkable development of the theory of lattice vibrations and the mathematical techniques of many-body physics.In this article we describe the dispersion and absorption of infrared radiation and Raman scattering in non-metallic crystals, both perfect and containing point defects. At present, quantitative calculations are usually restricted to diatomic crystals, especially those with simple structures such as the alkali halides or germanium and its homologues, since our knowledge of lattice vibrations is still rather poor for polyatomic and low-symmetry crystals. The theory of lattice vibrations, as reviewed by COCHRAN and COWLEY (1967) in Vol. XXV /2a of this Encyclopedia, constitutes the background and the natural starting point for our investigations. There are other recent reviews by LUDWIG (1967), COCHRAN (1971), MARADUDIN et al. (1971), SINHA (1973), and several articles in: HORTON and MARADUDIN (eds., 1974). A summary of the developments during the last few years is given in Chap. B.An important part of the theory of lattice vibrations is the construction of models. A good example is the so-called shell model for phonons (see Sect. 4) which describes the adiabatic linear electron-ion interaction in terms of localized charges and coupling constants. This provides a natural explanation of some long-range ion-ion forces in insulators in terms of induced dipole forces. Anharmonic extensions of this shell model and its modifications seem very desirable, and first attempts in this direction are discussed.Models can often give a qualitatively and sometimes quantitatively correct description of certain processes in terms of a few parameters. They provide, therefore, an orientation for microscopic approaches. Furthermo...

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“…An interpretation of the data in these representations is useful for an understanding of the critical points in the density of states and also of some optical properties. It is known that infrared absorption does not arise from the high symmetry critical points X, M, R, r, so that the interior of the Brillouin zone plays an important role [6].…”

Section: One-phonon Density Of Statesmentioning

confidence: 99%

“…in q-space to be checked. Our final calculations were made with Mahler's breathing shell model [6] which gave the overall best fit for all branches [I].…”

Section: Introductionmentioning

confidence: 99%

Properties of CsBr Derived from the Phonon Density of States

Daubeet

Jex

Müllner

1973

Physica Status Solidi (b)

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Detailed calculations are presented for the one-and two-phonon density of states in CsBr. These densities are based on models fitted to phonons determined by inelastic neutron scattering. Most of the 800 phonons are in off-symmetry directions. The densities and physical properties of CsBr derived from integrals over the frequency distribution are compared with optical measurements (infrared absorption, Raman scattering, infrared absorption from U-centers) with caloric data (specific heat, frequency moments), and with elastic scattering experiments (Debye-Waller factors, Debye temperatures).Die Ein-und Zweiphononenfrequenzverteilung von CsBr wurde mit einem Gittermodell berechnet, das an Phononen aus dem irreduziblen Volumen der Brillouinzone angepal3t wurde. Etwa 800 Phononenenergien wurden mit inelastischer Neutronenstreuung bestimmt ; die Mehrzahl der Daten stammt von AuBersymmetrierichtungen. Die Frequenzverteilungen nnd ebenso daraus abgeleitete integrale Kristalleigenschaften des CsBr werden mit pptischen Messungen (Ultrarotabsorption, Raman-Streuung, Ultrarotabsorption an U-Zentren), mit kalorischen MeBdaten (spezifische Warme, Frequenzmomente) und elastischen Rtreuexperimenten (Debye-Waller-Faktoren, Debye-Temperaturen) verglichen.

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Lattice Dynamics and Infrared Absorption of Cesium Halides

Cited by 31 publications

References 21 publications

Mean‐Square Ionic Displacements and Force Constants of Crystals with the CsCl Type Structure

Mean‐Square Ionic Displacements and Force Constants of Crystals with the CsCl Type Structure

Vibrational Infrared and Raman Spectra of Non-Metals

Properties of CsBr Derived from the Phonon Density of States

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