La théorie dynamique classique de la diffraction des rayons X est étendue au cas des cristaux ayant subi une déformation quelconque et des ondes non planes. La méthode consiste à résoudre les équations de Maxwell en considérant les déformations et la courbure des ondes comme des perturbations du premier ordre.
On obtient ainsi un système différentiel simple dont la résolution n'est en général possible que numériquement.
Une application particulière est faite au cas des cristaux courbés. On en déduit une méthode numérique simple de calcul du pouvoir réflecteur des cristaux courbés. Le résultat de mesures absolues est en bon accord avec la théorie.
On expose ensuite une méthode approximative de calcul de l'augmentation du pouvoir réflecteur due à la présence de dislocations. La comparaison avec les mesures est satisfaisante.
Enfin on donne quelques résultats de la résolution numérique directe du système fondamental dans le cas de dislocations isolées. Ceci permet de prévoir la structure des images de dislocations obtenues par transmission. Ici encore on note un accord satisfaisant avec les expériences faites par plusieurs autres auteurs.
The program presented here performs an automatic indexing of powder patterns by means of a trial‐and‐error method. It has been optimized and presents a good flexibility. It can account for various additional information, known a priori. In addition, extensive error computations are included in it, leading to a good reliability, even with some incidental errors. Moreover its input and printout have been implemented so that the program can be easily used even by non‐specialists.
As a consequence of several technological developments, the speed and sensitivity of solution X‐ray (and neutron) scattering studies have recently risen by factors which may be as large as 105; formal problems – like assessing the information content of the data and retrieving that information in structural terms – have thus become of immediate practical interest. The general problem of the information content of scattering experiments is discussed; its mathematical expression is derived, which depends on both the experimental data (observed values and estimated accuracy) and the a priori stochastic assumptions on the structure of the sample. The practical application of these notions to solution scattering studies involves several steps, three of which – choice of the degrees of freedom, data reduction and error analysis – are dealt with in this work. The first step is to specify the minimal number of independent parameters necessary and sufficient to describe the whole of the scattering properties of the system. Whenever the solute particles are of finite dimensions the entire scattering curve is defined by its values at a one‐dimensional lattice; if, moreover, the asymptotic trend of the scattering curves is known, then the degrees of freedom are the ideal intensities at a finite number of points plus a small number of parameters describing the asymptotic trend. It is also possible to include among the degrees of freedom a few subsidiary parameters like the normalization factors. The next step is, starting from a composite set of data, to determine the most probable numerical value of each degree of freedom and to evaluate its range of uncertainty. This is discussed within the framework of variable‐contrast studies, assuming that the invariant‐volume hypothesis is fulfilled. An algorithm is formulated which treats all the experimental observations and determines simultaneously all the degrees of freedom and the error matrix. The algorithm also allows one to introduce additional linear constraints on the degrees of freedom. As an example, the algorithm is applied to solution X‐ray scattering data recorded with a low‐density serum lipoprotein. The determination of the maximal chord of the particle – an important parameter in the informational analysis – turns out to be rather tricky.
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