Neutron small-angle scattering: experimental techniques and applications

Schmatz, W.; Springer, T.; Schelten, J.; Ibel, K.

doi:10.1107/s0021889874008880

Cited by 241 publications

(109 citation statements)

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“…The conditions for the vector Q optimization in Cartesian geometry has been given by Schmatz et al (1974), and for the scalar Q optimization in cylindrical geometry by Kozlova et al (1980); the full results are given in Appendices B and C. For the scalar Q measurement, the radial bin width should be 2 -~'2 of the linear dimension of the detector element of the optimized vector Q instrument. This optimization determines the value of the radial bin width A R that should be used for circularly averaging data taken on an x-y detector.…”

Section: Discussionmentioning

confidence: 99%

“…The results give the condition L 1 = L 2. The optimization conditions for the transverse dimensions are xl =Yl =2xl =2yl =x3 =y3 =R(A2/2) (B6) in Cartesian geometry (this is the case treated elsewhere (Schmatz et al, 1974) with equal primary and secondary flight paths) and…”

Section: B Resolution Of Vector Qmentioning

confidence: 99%

“…It has long been believed (Schmatz, Springer, Schelten & Ibel, 1974) that the optimization conditions of the geometry for small-angle scattering experiments require that the incident and scattered flight paths be equal. This also implies that the linear dimensions of the effective radiation source and the detector elements be equal and be twice those of the sample.…”

Section: Introductionmentioning

confidence: 99%

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Optimization of the experimental resolution for small-angle scattering

Mildner¹,

Carpenter²

1984

J Appl Cryst

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The instrumental optimization conditions for most small-angle scattering experiments in which the data are azimuthally symmetric require that the scattered flight path be equal to the incident flight path. This is in contrast to a recent analysis which shows that under some conditions the incident and scattered flight paths are in a ratio of two to one. The equal flight-path condition is also valid for experiments measuring sharp (Bragg-like) peaks, or where the intensity is required at specific scattering vectors, as in low-angle diffraction of ordered or semiordered systems. The implications of the optimization conditions on the resolution and count rates at the detector are discussed for both types of experiment, and the dependence of the resolution on the spectrometer geometry is considered.

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Section: Discussionmentioning

confidence: 99%

Section: B Resolution Of Vector Qmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimization of the experimental resolution for small-angle scattering

Mildner¹,

Carpenter²

1984

J Appl Cryst

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“…1). The special features of the scattering technique are amply described in recent papers [10,11,12]. All measurements are performed on a small-angle scattering spectrometer of the Laboratoire Léon-Brillouin set on a cold neutron guide of the EL3 reactor at Saclay [10].…”

mentioning

confidence: 99%

“…2) Recent progress in neutron scattering techniques [10,11,12] has allowed a precise observation of the coil pair correlation function, in dilute as well as in semi-dilute solutions, over the entire intermediate The first is currently being studied and will be published elsewhere [13]. We will be concerned here with two 1) In a good solvent, in the limit of zero concentration, it is well-known [4] that the excluded volume interaction v swells the coil only if This condition expresses in fact the Ginzbourg criterion of the critical phenomena [14].…”

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confidence: 99%

Cross-over in polymer solutions

et al. 1978

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Résumé. 2014 La fonction de corrélation de paire P(r) pour les polymères en solution a été mesurée par diffusion de neutrons aux petits angles dans l'intervalle 3 RG ~ r ~ I où RG est le rayon de giration et l la longueur du monomère. A la température thêta cette fonction est décrite par la loi de Debye 1/r. En bon solvant (limite haute température) et à la limite de la concentration nulle, S. F. Edwards prédit que cette fonction est uniformément proportionnelle à r-4/3.Cependant le résultat expérimental montre que pour des concentrations assez élevées ou pour des températures intermédiaires la fonction P(r) présente les deux comportements. On trouve qu'ils sont séparés par des longueurs de cross-over r* qui dépendent de la température et de la concentration. Le scaling de r* est relié au scaling de la longueur de corrélation 03BE et du rayon RG dans le diagramme température-concen tration.Abstract. 2014 Using a small-angle neutron scattering experiment, we measured the pair correlation function P(r) in polymer solutions in the interval 3 RG ~ r ~ l, where RG is the radius of gyration and I the step length. At the theta temperature, this function is known to follow the characteristic Debye law P(r) ~ r-1. In good solvents (high temperature limit) and in the limit of zero polymer concentration this function is uniformly proportional to r-4/3, as predicted by S. F. Edwards.We observe however, that at higher concentrations or intermediate temperatures, P(r) exhibits both characteristic behaviours, depending on the range of r. The cross-over distances r* which separate the patterns are found to depend upon concentration and temperature. The scaling of r* is related to the scaling of the screening length 03BE and the radius RG in the temperature-concentration diagram.

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