La structure des systèmes désordonnés et sa mesure par diffraction

Barnes, Adrian C; Fischer, H.; Salmon, Philip S.

doi:10.1051/jp4:2002818

Cited by 7 publications

(11 citation statements)

References 18 publications

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“…Since scattering is an interference phenomena it averages all information over the part of the sample that is illuminated by the beam. 4 This beam spot is large compared to the wave length, unlike the structural information in question, which is of the order of the wave length or even smaller in size. The situation is reversed in case of microscopy that works well above the diffraction limit imposed by the wave length.…”

Section: Scattering As An Analytical Tool For Condensed Mattermentioning

confidence: 99%

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An introduction to the theory of nuclear neutron scattering in condensed matter

Schober

2014

Journal of Neutron Research

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We give an introduction into the theory of neutron scattering in condensed matter with a strong focus on inelastic scattering. Magnetic scattering and polarisation will be excluded from the discussion. The scattering of non-relativistic particles in a potential leads to the concepts of scattering amplitude, partial waves, scattering length, and the Born series. In order to illustrate the formalism with simple examples we allow ourselves a short detour to diffraction. The Born approximation is then augmented to include inelastic scattering from compounds with internal degrees of freedom. This leads to the master equation of neutron scattering that establishes a link between the experimental cross sections and quantum mechanical transition amplitudes. The master equation is reformulated in terms of coherent and incoherent scattering functions, which in turn are expressed in terms of density correlation functions. The abstract formalism is illustrated by explicitly calculating the cross sections for some simple model systems. Considerable attention is given to the scattering involving vibrations in harmonic systems. Explicit expressions are derived that couple inelastic scattering cross sections to the phonon density of states and dispersion relations. We will finish the inelastic part by discussing the effect of multi-phonons and conclude with some remarks concerning the identification of anharmonic effects. The last section is devoted to putting the formalism of scattering theory into the context of a statistical description of the particle beam.

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Section: Scattering As An Analytical Tool For Condensed Mattermentioning

confidence: 99%

“…This allows for a variety of methods of X-ray spectroscopy. 4 We will be more precise in Section 11 where we introduce the notion of coherence volume.…”

Section: Scattering As An Analytical Tool For Condensed Mattermentioning

confidence: 99%

An introduction to the theory of nuclear neutron scattering in condensed matter

Schober

2014

Journal of Neutron Research

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“…Traditionally it was used for liquids [7,8] and amorphous materials [9], more recently for the study of disorder in crystalline materials, and now with increasing popularity it is used to study nanostructured materials. Traditionally it was used for liquids [7,8] and amorphous materials [9], more recently for the study of disorder in crystalline materials, and now with increasing popularity it is used to study nanostructured materials.…”

Section: The Atomic Pdfmentioning

confidence: 99%

“…PDF methods grew out of a rich history of RDF studies of the structure of liquids [7,47,48], glasses, and amorphous materials [9]. PDF methods grew out of a rich history of RDF studies of the structure of liquids [7,47,48], glasses, and amorphous materials [9].…”

Section: Example: Disorder Due To Alloying In Bulk Semiconductor Alloysmentioning

confidence: 99%

Local Structure of Bulk and Nanocrystalline Semiconductors Using Total Scattering Methods

Božin¹,

Juhás²,

Billinge³

2013

Characterization of Semiconductor Heterostructures and Nanostructures

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“…Mais même dans ce cas, des corrections doivent être mises en place afin de corriger des contributions inélastiques. Ces corrections sont connues sous le nom de corrections de Placzek [25].…”

Section: Moments Et Règles De Somme Pour La Fonction De Diffusionunclassified

Diffusion des neutrons par la matière cristalline ou amorphe non-magnétique

Schober

2010

JDN 16 – Diffusion Inélastique Des Neutrons Pour l'Etude Des Excitations Dans La Matiére Condensée

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Résumé. Nous présentons une introduction de la diffusion des neutrons par la matière cristalline ou amorphe non-magnétique, en mettant l'accent sur la diffusion inélastique. Le point de départ de notre discussion sera la diffusion d'une particule non-relativiste par un potentiel. Ce cas simple nous permettra d'introduire les notions d'amplitude et de longueur de diffusion, les ondes partielles ainsi que la série de Born. Nous passerons ensuite aux systèmes composés comportant des degrés de liberté internes. L'équation maîtresse établira le lien entre la section efficace de diffusion et les transitions entre les niveaux d'excitation, dans le cadre de l'approximation de Born. Cette équation peut être formulée en terme de fonctions de diffusion cohérentes et incohérentes. Pour illustrer les effets d'interférences, qui constituent la base de la diffusion des neutrons, nous effectuerons un petit détour par la diffraction optique. C'est le potentiel de Fermi qui décrit l'interaction des neutrons thermiques et froids avec les noyaux des atomes. Ce potentiel étant basé sur l'opérateur de densité du système il est possible d'exprimer les résultats de la mesure à l'aide des fonctions de corrélation de la densité. Le formalisme théorique sera ensuite confronté à l'expérience. Nous finirons ce chapitre en montrant comment les fonctions de corrélation de la densité peuvent être calculées pour des systèmes harmoniques en s'appuyant sur le concept des phonons. Nous présenterons les expressions qui relient les mesures de diffusion inélastique des neutrons à la densité d'états de phonons et aux courbes de dispersion. Nous discuterons les effets des multiphonons sur les spectres et nous concluerons par quelques remarques concernant la caractérisation d'effets anharmoniques.

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La structure des systèmes désordonnés et sa mesure par diffraction

Cited by 7 publications

References 18 publications

An introduction to the theory of nuclear neutron scattering in condensed matter

An introduction to the theory of nuclear neutron scattering in condensed matter

Local Structure of Bulk and Nanocrystalline Semiconductors Using Total Scattering Methods

Diffusion des neutrons par la matière cristalline ou amorphe non-magnétique

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