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The Nature of the Phonon Spectrum and the Analysis of Lattice Thermal Conductivity; Nature du Spectre des Phonons et Analyse de la Conductibilite Thermique du Reseau; Kharakter fononnogo spektra i analiz teploprovodnosti reshetki; Naturaleza del Espectro Fononico y Analisis de la Conductividad Termica Reticular

Conference:

Abstract

An analysis of lattice thermal conductivity is presented, wherein a more realistic phonon spectrum is utilized than the usual Debye-like phonon spectrum consisting of one average acoustic branch. We have first used an anisotropic continuum dispersive model in our calculation of the temperature dependence of the lattice thermal conductivity of germanium. The approach that we have utilized in this calculation is a modified version of Callaway's formulation. Houston's six- and three-term integration procedures are used in evaluating rather formidable integrals over lattice frequencies. Suitable prevalent expressions for relaxation times for boundary and impurity scatterings and three-phonon normal and Umklapp processes are used. A good fit to the experimental data of Holland and Slack and Glassbrenner is obtained for germanium from 2 to 1000 Degree-Sign K by adjusting the four constants occurring in the integrals. On the face of reliable neutron spectroscopic evidence, we know that germanium has very disperse transverse branches and for them an anisotropic continuum dispersive model also yields a poor representation. We therefore thought it appropriate to utilize the very elaborate shell model for the lattice dynamics of germanium put forth by Cochran. With a proper adjustment of the parameters entering in our formulation for the calculation  More>>
Authors:
Joshi, S. K.; Sharma, K. C. [1] 
  1. Physics Department, Allahabad University, Allahabad (India)
Publication Date:
Apr 15, 1965
Product Type:
Conference
Report Number:
IAEA-SM-58/20
Resource Relation:
Conference: Symposium on Inelastic Scattering of Neutrons, Bombay (India), 15-19 Dec 1964; Other Information: 29 refs., 2 figs.; Related Information: In: Inelastic Scattering of Neutrons. Vol. I. Proceedings of the Symposium on Inelastic Scattering of Neutrons| 476 p.
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ANISOTROPY; CRYSTAL LATTICES; EXPERIMENTAL DATA; GERMANIUM; NEUTRONS; PHONONS; RELAXATION TIME; SCATTERING; SHELL MODELS; SPECTRA; TEMPERATURE DEPENDENCE; THERMAL CONDUCTIVITY; UMKLAPP PROCESSES
OSTI ID:
22141806
Research Organizations:
International Atomic Energy Agency, Vienna (Austria)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISSN 0074-1884; TRN: XA13M3372096407
Submitting Site:
INIS
Size:
page(s) 285-296
Announcement Date:
Oct 24, 2013

Conference:

Citation Formats

Joshi, S. K., and Sharma, K. C. The Nature of the Phonon Spectrum and the Analysis of Lattice Thermal Conductivity; Nature du Spectre des Phonons et Analyse de la Conductibilite Thermique du Reseau; Kharakter fononnogo spektra i analiz teploprovodnosti reshetki; Naturaleza del Espectro Fononico y Analisis de la Conductividad Termica Reticular. IAEA: N. p., 1965. Web.
Joshi, S. K., & Sharma, K. C. The Nature of the Phonon Spectrum and the Analysis of Lattice Thermal Conductivity; Nature du Spectre des Phonons et Analyse de la Conductibilite Thermique du Reseau; Kharakter fononnogo spektra i analiz teploprovodnosti reshetki; Naturaleza del Espectro Fononico y Analisis de la Conductividad Termica Reticular. IAEA.
Joshi, S. K., and Sharma, K. C. 1965. "The Nature of the Phonon Spectrum and the Analysis of Lattice Thermal Conductivity; Nature du Spectre des Phonons et Analyse de la Conductibilite Thermique du Reseau; Kharakter fononnogo spektra i analiz teploprovodnosti reshetki; Naturaleza del Espectro Fononico y Analisis de la Conductividad Termica Reticular." IAEA.
@misc{etde_22141806,
title = {The Nature of the Phonon Spectrum and the Analysis of Lattice Thermal Conductivity; Nature du Spectre des Phonons et Analyse de la Conductibilite Thermique du Reseau; Kharakter fononnogo spektra i analiz teploprovodnosti reshetki; Naturaleza del Espectro Fononico y Analisis de la Conductividad Termica Reticular}
author = {Joshi, S. K., and Sharma, K. C.}
abstractNote = {An analysis of lattice thermal conductivity is presented, wherein a more realistic phonon spectrum is utilized than the usual Debye-like phonon spectrum consisting of one average acoustic branch. We have first used an anisotropic continuum dispersive model in our calculation of the temperature dependence of the lattice thermal conductivity of germanium. The approach that we have utilized in this calculation is a modified version of Callaway's formulation. Houston's six- and three-term integration procedures are used in evaluating rather formidable integrals over lattice frequencies. Suitable prevalent expressions for relaxation times for boundary and impurity scatterings and three-phonon normal and Umklapp processes are used. A good fit to the experimental data of Holland and Slack and Glassbrenner is obtained for germanium from 2 to 1000 Degree-Sign K by adjusting the four constants occurring in the integrals. On the face of reliable neutron spectroscopic evidence, we know that germanium has very disperse transverse branches and for them an anisotropic continuum dispersive model also yields a poor representation. We therefore thought it appropriate to utilize the very elaborate shell model for the lattice dynamics of germanium put forth by Cochran. With a proper adjustment of the parameters entering in our formulation for the calculation of lattice thermal conductivity, we again find a good fit with the experimental data. We are led to a conclusion that the nature of the phonon spectrum does not greatly influence the analysis of lattice thermal conductivity data according to current approaches and the niceties of the phonon spectrum are lost in the adjustment of the various parameters involved. It is felt that instead of putting too much labour in evaluating the tedious integrals for more realistic lattice dynamical models, it is better to investigate the validity of various relaxation time assumptions that have gone into these integrals. (author) [French] Les auteurs presentent les resultats d'une etude sur la conductibilite thermique des reseaux effectuee au moyen d'un spectre de phonons plus precis que le spectre de phonons analogue au modele de Debye, utilise d'ordinaire, qui est constitue par une seule branche acoustique moyenne. Pour calculer les variations en fonction de la temperature de la conductibilite thermique du reseau du germanium, ils ont utilise tout d'abord un modele anisotrope de dispersion en continu et suivi comme methode une version modifiee de la formulation de Callaway. Pour effectuer la sommation d'integrales complexes sur les frequences du reseau, ils ont applique la methode d'integration a six et trois termes de Houston. On utilise les expressions appropriees des temps de relaxation pour les diffusions a la frontiere et les diffusions dues aux impuretes ainsi que pour le processus normal a trois phonons et le processus Umklapp. Pour le germanium entre 2 et 1000 Degree-Sign K, on obtient une concordance satisfaisante avec les donnees experimentales de Holland et de Slack et Glassbrenner en ajustant les quatre constantes presentes dans les integrales. D'apres des donnees de spectroscopie des neutrons dignes de foi, on sait que le germanium comporte des branches transversales tres dispersees et qu'un modele anisotrope de dispersion en continu en donne aussi une mauvaise representation. Les auteurs ont donc juge bon d'utiliser le modele des couches tres complexes pour la dynamique de reseau du germanium presente pai Cochran. En ajustant les parametres entrant dans la formulation qu'ils ont utilisee pour le calcul de la conductibilite thermique du reseau, ils ont egalement obtenu des resultats concordant avec les donnees experimentales. Ceci leur a donne a penser que la nature du spectre des phonons n'a pas une grande influence sur l'analyse des donnees relatives a la conductibilite thermique du reseau suivant les methodes actuelles, et que le spectre des phonons perd de sa precision en raison de l'ajustement des differents parametres entrant dans les calculs. Les auteurs estiment qu'au lieu de s'attarder a effectuer la sommation d'integrales complexes pour des modeles de la dynamique de reseau plus proches de la realite, il vaudrait mieux etudier la validite des differentes hypotheses relatives au temps de relaxation prises comme base pour l'etablissement de ces integrales. (author) [Spanish] Los autores analizan la conductividad termica reticular utilizando para ello un espectro fononico mas realista que el habitual espectro fononico tipo Debye, consistente en una rama acustica media. Para calcular la influencia de la temperatura sobre la conductividad termica reticular del germanio, emplean en primer termino un modelo dispersivo continuo de caracter anisotropico. Aplican a tal efecto una version modificada de las formulas de Callaway, Utilizan el metodo de integracion de seis y tres terminos de Houston para determinar integrales sumamente complejas que abarquen las frecuencias reticulares, y emplean las expresiones actualmente mas adecuadas para los tiempos de relajacion correspondientes a la dispersion en los bordes y a la dispersion por impurezas, asi como procesos trifononicos normales y procesos de 'Umklapp'. En el caso del germanio se obtiene una concordancia satisfactoria con los datos experimentales de Holland y de Slack y Glassbrenner, entre 2 y 1000 Degree-Sign K, ajustando las cuatro constantes que aparecen en las integrales. Como se sabe por los resultados fidedignos obtenidos por espectroscopia neutronica, el germanio tiene ramas transversales muy dispersas, y un modelo dispersivo continuo de tipo anisotropico tampoco constituye una representacion satisfactoria de las mismas. Por tanto, los autores han estimado oportuno utilizar el complejo modelo de capas propuesto por Cochran para la dinamica reticular del germanio. Ajustando adecuadamente los parametros que figuran en la formula utilizada por los autores para calcular la conductividad termica de la red, se obtiene tambien una concordancia satisfactoria con los datos experimentales. Se llega, pues, a la conclusion de que, segun los criterios actuales, la naturaleza del espectro fononico no ejerce inferencia acusada en el analisis de los datos relativos a la conductividad termica reticular, y de que las sutilezas propias del espectro fononico se pierden con el ajuste de los diversos parametros que intervienen. A juicio de los autores, en lugar de preocuparse demasiado por determinar las laboriosas integrales correspondientes a modelos de dinamica reticular mas realistas, es preferible investigar la validez de las diferentes hipotesis referentes al tiempo de relajacion que intervienen al formular dichas integrales. (author) [Russian] Daetsja analiz teploprovodnosti reshetki, v kotorom ispol'zuetsja bolee realistichnyj fonon- nyj spektr, chem obychnyj debaevskij fononnyj spektr, sostojashhij iz odnoj srednej akusticheskoj vetvi. Vpervye ispol'zovana dispersionnaja model' anizotropnogo sploshnogo spektra v reschete zavisimosti teploprovodnosti reshetki germanija ot temperatury. Primenennyj put' reshenija v jetom raschete predstavljaet soboj izmenennyj variant vyrazhenija Kollujejja. Dlja ocenki dovol'no znachitel'nyh integralov vyshe chastot reshetki ispol'zuetsja procedura integracii shesti i treh chlenov uravnenija Haustona. Primenjajutsja naibolee podhodjashhie rasprostranennye vyrazhenija dlja vremeni relaksacii dlja rassejanija na granice i na primesi, a takzhe dlja treh fononnyh normal'nyh processov i processa Umklappa. Pri pravil'nom podbore chetyreh postojannyh, imejushhihsja v integralah, poluchaetsja horoshee sootvetstvie s jeksperimental'nymi dannymi Hollanda, Slaka i Glassbrennera dlja germanija ot 20 do 1000 Degree-Sign K. Blagodarja nadezhnym dannym nejtronnoj spektroskopii my znaem, chto germanij imeet ochen' razbrosannye poperechnye vetvi, i dispersionnaja model' anizotropnogo sploshnogo spektra takzhe daet o nih plohoe predstavlenie. Pojetomu my schitaem neobhodimym ispol'zovat' ochen' horosho otrabotannuju model' obolochki dlja dinamiki reshetki germanija, predlozhennuju Kohranom. Pri sootvetstvujushhem podbore parametrov, vhodjashhih v nashe vyrazhenie dlja rascheta teploprovodnosti reshetki, my vnov' poluchaem horoshee sootvetstvie s jeksperimental'nymi dannymi. My prishli k vyvodu, chto harakter fononnogo spektra ne vlijaet sil'no na analiz dannyh teploprovodnosti reshetki sushhestvujushhimi metodami, i tochnost' fononnogo spektra terjaetsja v rezul'tate podgonki razlichnyh vhodjashhih sjuda parametrov. Est' mnenie, chto vmesto togo, chtoby tratit' slishkom mnogo vremeni na raschet trudoemkih integralov dlja bolee realistichnyh dinamicheskih modelej reshetki, luchshe izuchit' spravedlivost' razlichnyh predpolozhenij o vremeni relaksacii, vhodjashhih v jeti integraly. (author)}
place = {IAEA}
year = {1965}
month = {Apr}
}