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Theory of the Influence of Phonon-Phonon and Electron-Phonon Interactions on the Scattering of Neutrons by Crystals; Theorie de l'influence des interactions phonon-phonon et electron-phonon sur la diffusion des neutrons par des cristaux; Teoriya vliyaniya vzaimodejstvij fonon-fonon iehlvktron-fonon na rasseyanie nejtronov kristalla-; Teoria de la influencia de las interacciones fonon-fonon y electron-fonon en la dispersion de neutrones por cristales

Conference:

Abstract

As predicted by harmonic theory the coherent inelastic spectrums of neutrons, scattered by a single, non-conducting crystal, for a particular angle of scattering consists of a number of delta-function peaks superposed on a continuous background. The peaks correspond to one-phonon processes in which one phonon is absorbed or emitted by the neutron; the background arises from multi-phonon processes. When anharmonic forces (phonon-phonon interactions) are present, the delta-function peaks are broadened into finite peaks, while their central frequencies are shifted with respect to the harmonic values. In the case of a metal there is in addition to phonon-phonon interactions an interaction between phonons and conduction electrons, which also gives a contribution to the displacement and broadening oftheone-phononpeaks. Continuing earlier work of Van Hove (sho considered the relatively simple case of a non-conductin crystal in its ground state (T = 0{sup o}K) ), we have studied the shifts and widths of the scattering peaks as a 'result of the above-mentioned interactions by means of many particle perturbation theory, making extensive use of diagram techniques. Prerequisite to the entire discussion is the assumption that, independent of the strength of the interactions, the width of each peak is small compared to the value of  More>>
Authors:
Kokkedee, J J.J. [1] 
  1. Institute for Theoretical Physics of the University of Utrecht (Netherlands)
Publication Date:
Jan 15, 1963
Product Type:
Conference
Resource Relation:
Conference: Symposium on Inelastic Scattering of Neutrons in Solids and Liquids, Chalk River (Canada), 10-14 Sep 1962; Other Information: Abstract also available in Russian; 5 figs., 16 refs.; Related Information: In: Inelastic Scattering of Neutrons in Solids and Liquids. V. I. Proceedings of the Symposium on Inelastic Scattering of Neurons in Solids and Liquids| 486 p.
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; CRYSTALS; DELTA FUNCTION; ELECTRON-PHONON COUPLING; ELECTRONS; GROUND STATES; INTERACTIONS; NEUTRON DIFFRACTION; NEUTRONS; PEAKS; PERTURBATION THEORY; PHONONS; SCATTERING
OSTI ID:
22086584
Research Organizations:
International Atomic Energy Agency, Vienna (Austria); United Nations Educational, Scientific and Cultural Organization (France)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISSN 0074-1884; TRN: XA13R0070045022
Submitting Site:
INIS
Size:
page(s) 15-36
Announcement Date:
Apr 18, 2013

Conference:

Citation Formats

Kokkedee, J J.J. Theory of the Influence of Phonon-Phonon and Electron-Phonon Interactions on the Scattering of Neutrons by Crystals; Theorie de l'influence des interactions phonon-phonon et electron-phonon sur la diffusion des neutrons par des cristaux; Teoriya vliyaniya vzaimodejstvij fonon-fonon iehlvktron-fonon na rasseyanie nejtronov kristalla-; Teoria de la influencia de las interacciones fonon-fonon y electron-fonon en la dispersion de neutrones por cristales. IAEA: N. p., 1963. Web.
Kokkedee, J J.J. Theory of the Influence of Phonon-Phonon and Electron-Phonon Interactions on the Scattering of Neutrons by Crystals; Theorie de l'influence des interactions phonon-phonon et electron-phonon sur la diffusion des neutrons par des cristaux; Teoriya vliyaniya vzaimodejstvij fonon-fonon iehlvktron-fonon na rasseyanie nejtronov kristalla-; Teoria de la influencia de las interacciones fonon-fonon y electron-fonon en la dispersion de neutrones por cristales. IAEA.
Kokkedee, J J.J. 1963. "Theory of the Influence of Phonon-Phonon and Electron-Phonon Interactions on the Scattering of Neutrons by Crystals; Theorie de l'influence des interactions phonon-phonon et electron-phonon sur la diffusion des neutrons par des cristaux; Teoriya vliyaniya vzaimodejstvij fonon-fonon iehlvktron-fonon na rasseyanie nejtronov kristalla-; Teoria de la influencia de las interacciones fonon-fonon y electron-fonon en la dispersion de neutrones por cristales." IAEA.
@misc{etde_22086584,
title = {Theory of the Influence of Phonon-Phonon and Electron-Phonon Interactions on the Scattering of Neutrons by Crystals; Theorie de l'influence des interactions phonon-phonon et electron-phonon sur la diffusion des neutrons par des cristaux; Teoriya vliyaniya vzaimodejstvij fonon-fonon iehlvktron-fonon na rasseyanie nejtronov kristalla-; Teoria de la influencia de las interacciones fonon-fonon y electron-fonon en la dispersion de neutrones por cristales}
author = {Kokkedee, J J.J.}
abstractNote = {As predicted by harmonic theory the coherent inelastic spectrums of neutrons, scattered by a single, non-conducting crystal, for a particular angle of scattering consists of a number of delta-function peaks superposed on a continuous background. The peaks correspond to one-phonon processes in which one phonon is absorbed or emitted by the neutron; the background arises from multi-phonon processes. When anharmonic forces (phonon-phonon interactions) are present, the delta-function peaks are broadened into finite peaks, while their central frequencies are shifted with respect to the harmonic values. In the case of a metal there is in addition to phonon-phonon interactions an interaction between phonons and conduction electrons, which also gives a contribution to the displacement and broadening oftheone-phononpeaks. Continuing earlier work of Van Hove (sho considered the relatively simple case of a non-conductin crystal in its ground state (T = 0{sup o}K) ), we have studied the shifts and widths of the scattering peaks as a 'result of the above-mentioned interactions by means of many particle perturbation theory, making extensive use of diagram techniques. Prerequisite to the entire discussion is the assumption that, independent of the strength of the interactions, the width of each peak is small compared to the value of the frequency at its centre; only then the peaks can be considered as being well defined with respect to the background to higher order in the interactions. This condition is expected to be fulfilled for temperatures which are not too high and values of the phonon wave vector which are not too large. Our procedure yields closed formulae for the partial scattering function describing the peaks, which can be evaluated to arbitrarily high accuracy. In particular an expansion for calculating the line shift and line width in powers of u/d and in terms of simple connected diagrams is obtained (u is an average atomic or ionic displacement, d is the smallest interatomic or interionic distance in the crystal). Approximate calculations are performed to give some insight into the orders of magnitude of the effects under study. (author) [French] Comme le predit la theorie harmonique, le spectre de la diffusion inelastique coherente de neutrons par un monocristal non conducteur, pour un angle de diffusion donne, se compose d'une serie de pics de fonction delta, qui se superposent a un bruit de fond continu. Les pics correspondent a des phenomenes a un phonon, dans lesquels un phonon est absorbe ou emis par le neutron; le bruit de fond provient de phenomenes a plusieurs phonons. Lorsqu'il existe des forces anharmoniques (interaction phonon-phonon) les pics de fonction delta s'elargissent pour former des pics finis et leur frequence centrale est dephasee par rapport aux valeurs harmoniques. Dans le cas d'un metal il y a, en plus des interactions phonon-phonon, une interaction entre les phonons et les electrons de conduction, laquelle contribue a dephaser et elargir encore davantage les pics a un phonon. Continuant les travaux de Van Hove (qui avait considere le cas relativement simple d'un cristal non conducteur a l'etat fondamental, soit T = 0{sup o}K) l'auteut a etudie les deplacements et les largeurs des pics de diffusion resultant des interactions indiquees plus haut, a l'aide de la theorie de la perturbation a plusieurs particules, en ayant largement recours a la methode des diagrammes. Il admet, avant tout examen du probleme, que quelle que soit la force des interactions, la largeur de chaque pic est petite par rapport a la valeur de la frequence en son centres dans ces conditions seulement, on peut considerer que les pics sont bien definis par rapport au bruit de fond, si les calculs d'interaction sont pousses jusqu'aux ordres superieurs. On estime que cette hipothbse est realisee tant que les temperatures ne sont pas trop elevees et que les valeurs du vecteur d'onde des phonons ne sont pas trop considerables. La methode appliquee par l'auteur lui permet d'obtenir des formules fermees pour la fonction de diffusion partielle decrivant les pics, qui peuvent etre calculees avec une approximation aussi pousee qu'on le desire. L'auteur a obtenu notamment une expression qui permet de calculer le dephasage et la largeur des raies en puissances de u/d et en fonction de diagrammes connectes simples (u etant le deplacement atomique ou ionique moyen et d la plus petite distance interatomique ou interionique dans le cristal). Des calculs approches donnent une idee de l'ordre de grandeur des effets etudies. (author) [Spanish] Como permite predecir la teoria armonica, el espectro de neutrones dispersados coherente e inelasticamente por un monocristal no conductor consiste, para un angulo de dispersion determinado, en una serie de picos de function delta supetpuestos a un fondo continuo. Los picos corresponden a procesos en que el neutron absorbe o emite un solo fonon; el fondo se debe a procesos de varios fonones. Cuando intervienen fuerzas anarmonicas (interacciones fonon-fonon), los picos de funcion delta se ensanchan, convirtiendose en picos finitos y sus frecuencias centrales se desplazan respecto de los valores armonicos. En el caso de los metales, ademas de las interacciones fonon-fonon existe interaccion entre los fonones y los electrones de conduccion, lo que tambien contribuye al desplazamiento y ensanchamiento de los picos correspondientes a los procesos de un solo fonon. Prosiguiendo trabajos anteriores de Van Hove (quien investigo el caso relativamente sencillo de un cristal no conductor en el estado fundamental (T = 0{sup o}K) ), el autor ha estudiado el desplazamiento y la amplitud de los picos de dispersion resultantes de las mencionadas interacciones aplicando la teoria de las perturbaciones originadas por partfbulas multiples y utilizando ampliamente tecnicas de diagramas. Un requisito indispensable para dicho estudio es la hipotesis de que, sea cual fuere la intensidad de las interacciones, la amplitud de cada pico es pequena en comparacion con el valor de la frecuencia en el centro: solo en tal caso puede considerarse que los picos estan bien definidos respecto del fondo correspondiente a las interacciones de oiden mas elevado. Cabe esperar que esta condicion se cumpla para temperaturas no demasiado elevadas y valores de vector de onda fononico no excesivamente grandes. El procedimiento del autor permite obtener formulas cerradas de la funcion de dispersion parcial que describe los picos; estos pueden evaluarse con el grado de precision que se desee. En particular, se obtiene un desarrollo para calcular en potencias de u/d y en funcion de diagramas simples conectados el desplazamiento y la anchura de las rayas (u es el desplazamiento atomico o ionico medio y d es la distancia minima interatomica en el cristal). El autor efectua calculos aproximados para dar una idea del orden de magnitud de los efectos estudiados. (author)}
place = {IAEA}
year = {1963}
month = {Jan}
}