Determination of the elastic constants of argon

Gsänger, Marcel; Egger, H.; Lüscher, E.

doi:10.1016/0375-9601(68)91011-6

Cited by 34 publications

(37 citation statements)

References 4 publications

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“…The theory of these critical points (VAN HOVE, 1953;PHILLIPS, 1956;ROSENSTOCK, 1955ROSENSTOCK, , 1957 leads to the following general results: 1) For analytical critical points P; with index i in an s-dimensional q-space a Taylor expansion exists in a region around qc' with By = ± 1, where i is the number of negative Br In this expansion and qrocl(q-qJI is defined in a locally transformed system. 2) In an s-dimensional Brillouin zone there exist, for each branch j, at least G) analytical critical points, p;.…”

Section: Vqw2(qj)q=qc =0mentioning

confidence: 99%

“…Classical electrodynamics cannot explain the fact that ions in a solid keep large mean distances of the order of Angstroms, while the attractive Coulomb forces between electrons and nuclei suggest a collapse of the whole system into a very dense cluster with particle distances of nuclear dimensions. Quantum mechanics tells us that this phenomenon is not caused by a breakdown of Coulomb's law at very small distances but follows from two non-classical principles: 1) The uncertainty principle which implies that the kinetic energy of electrons is enhanced if their charge distribution is compressed;…”

Section: B Phonons In Insulatorsmentioning

confidence: 99%

“…The basic physical information is contained in I s( ifJ) which is independent of the sample's geometrical properties. Therefore, one usually converts the directly measured experimental data, Is (1)) into the corresponding quantities inside the sample. This conversion, in general, requires the knowledge of 1) the sample shape, 2) the refractice-index tensor, 3) the geometry of the light beam, and 4) the orientations of the crystal symmetry axes relative to the light beams.…”

Section: A) Non-relativistic Theory Of Inelastic Scatteringmentioning

confidence: 99%

“…q~O) in terms of the transition matrix elements of the dipole operator (7.48) m=Imz=eIy,==eR, (7.50) , , Here we need no specification of the dipole matrix elements (7.54) We only assume that boundary conditions of the system are chosen to ensure that the Rnm are well-defined quantities. 1 If we are dealing with an isotropic (e.g. cubic) system, I: reduces to a scalar so that the real and imaginary parts of S may be conveniently expressed by the refractive index n and the absorption constant k:…”

Section: -I E= ---A=-[h A]mentioning

confidence: 99%

“…After LOMMEL's (1871) and SMEKAL's (1923) early discussion of inelastic scattering of light, the Raman effect in crystals was detected by LANDSBERG and MANDELSTAM (1928) at about the same time as RAMAN and KRISHNAN (1928) found the effect in liquids and gases. A few years later FERMI and RASETTI (1931) discovered the second-order Raman effect 1 For further details of the situation around 1912 see the historical remarks by BORN and DEBYE at the Copenhagen Conference 1963 (BORN, 1963; DEBYE, 1963 's (1948) subsequent attempt to analyze the diamond spectra. In the following years, parallel with the improved understanding of lattice dynamics, the theory has been refined using Green function methods and satisfactory models for the lattice vibrations (COWLEY, 1963;LOUDON, 1964).…”

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confidence: 96%

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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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Section: Vqw2(qj)q=qc =0mentioning

confidence: 99%

Section: B Phonons In Insulatorsmentioning

confidence: 99%

Section: A) Non-relativistic Theory Of Inelastic Scatteringmentioning

confidence: 99%

Section: -I E= ---A=-[h A]mentioning

confidence: 99%

mentioning

confidence: 96%

See 3 more Smart Citations

Vibrational Infrared and Raman Spectra of Non-Metals

Bilz¹,

Strauch²,

Wehner³

1984

Light and Matter Id / Licht Und Materie Id

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Elastic Constants of Argon at 4.2 °K from Phonon Measurements

Dörner

Egger

1971

Physica Status Solidi (b)

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Phonon measurements with inelastic neutron scattering have been analyaed carefully, by use of the resolution ellipsoids of the three-axis spectrometer. The slopes of the dispersion curvm at the low frequency phonons are taken to be the sound Velocities. From these sound velocities the elastic constants are calculated: C,, = (3.67 f 0.14). 10'O dyn C,, = (1.74 f 0.17). 1Olo dyn crn-l, C,, = (2.34 f 0.11) -lolo dyn cm-a. Theoretical calculations with an accurate pair potential in the self-consistent phonon approximation give the best agreement for a model without anharmonicity and without three-body forces. Neutronen-Messungen iiber Phononen in festem Argon bei 4,2 OK werden mit Hilfe von Auflosungsellipaoiden fur das Drei-Achsen-Spektrorneter anelysiert. Aus den Steigungen der Dispersionskurven bei niederfrequenten Phononen werden die Schallgeschwindigkeiten bestimrnt. Danach ergeben sich f i r die elastischen Konstanten die Werb: C,, = (3,67 f *0,14).011°dyn C~-~; C ,~ = (1,74f0,17). 1Olo dyncm-*;C,,= (2,34 f 0,11)-1010dyncm-2.Theoretische Rechnungen nach der selbst-konsistenten Phonon-Naherung geben die beste ubereinstimmung fiir ein Modell ohne Anharmonizitat und ohne Drei-Korper-Kriifte.

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Analysis of lattice thermal conductivity of solid argon at low temperatures

Gupta

Trikha

1977

Physica Status Solidi (b)

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An attempt is made to analyse the lattice thermal conductivity of solid argon at low temperatures, using Holland's model. The dispersion relation q = C sin-' (w/wmax), for transverse phonom, is used to determine vg/vi in the conductivity integrals. A fairly good agreement is obtained between the calculated and the experimental results of Clayton and Batchelder, in the temperature range 1.5 to 20 K. The dislocation density and the average grain size of the polycrystalline specimen are determined to be 2.5 x 10" m-2 and 0.05 mm, respectively.

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Determination of the elastic constants of argon

Cited by 34 publications

References 4 publications

Vibrational Infrared and Raman Spectra of Non-Metals

Vibrational Infrared and Raman Spectra of Non-Metals

Elastic Constants of Argon at 4.2 °K from Phonon Measurements

Analysis of lattice thermal conductivity of solid argon at low temperatures

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