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Scattering Density (scattering + density)

Distribution by Scientific Domains

Chemistry	100%

Selected Abstracts

Multiphase approximation for small-angle scattering

JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 1 2010
Dragomir Tatchev
The two-phase approximation in small-angle scattering is well known and is still the dominant approach to data analysis. The intensity scattered at small angles is proportional to the second power of the difference between the scattering densities of the two phases. Nevertheless, scattering contrast variation techniques are widely used, and they are obviously suitable for multiphase systems or systems with gradually varying scattering density, since if no parasitic scattering contributions are present the scattering contrast variation would only change a proportionality coefficient. It is shown here that the scattered intensity at small angles of a multiphase system can be represented as a sum of the scattering of two-phase systems and terms describing interference between all pairs of phases. Extracting two-phase scattering patterns from multiphase samples by contrast variation is possible. These two-phase patterns can be treated with the usual small-angle scattering formalism. The case of gradually varying scattering density is also discussed. [source]

Contrast analysis of the composition of ribosomes extracted with different purification procedures

JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 4 2000
Giuseppe Briganti
The composition and hydration of E. coli ribosomes isolated with different purification protocols has been analysed by combining two experimental techniques: measurements of small-angle neutron scattering (SANS), for two different isotopic solvent compositions, and refractive index (RI) increments. From the contrast between the solvent and solute scattering densities and the molar polarizability, determined experimentally with SANS and RI measurements, three independent equations are obtained and three unknown quantities are determined: (i) the volume of the solute hydrated skeleton Vs, (ii) the material contained in it, namely the biological components, intrinsic (rRNA and proteins) and extrinsic, such as aminoacylsynthetase and elongation factors, (iii) the number of water molecules structurally bound to the ribosome and non-exchangeable with the solvent. From the form factor at infinite contrast, a second definition of the solute volume is obtained, , which represents the volume within the contour surface of the ribosome. This value is generally larger than Vs and can include a certain amount of water molecules, i.e. those inside the volume (,Vs). Considering the molar volume of this water to be equal to that of the bulk water, it is possible to evaluate its amount. The particle density calculated from the ribosome components in , including proteins, RNA, bound and unbound water molecules, corresponds to the buoyant density measured for E. coli 70S particles. The two ribosomal preparations display different performances in protein synthesis; hence the results indicate that the optimal condition corresponds to a wider skeleton and contour volume but containing a smaller amount of segregated water molecules. It is believed that the method provides a reliable technique to determine the composition of ribosomes under various experimental conditions. [source]

Multiphase approximation for small-angle scattering

The algebraic approach to the phase problem

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2005
A. Cervellino
A rather detailed report is presented on the present status of the algebraic approach to the phase problem in the case of an ideal crystal in order to make clear that some points must still be proven for it to apply to neutron scattering. To make this extension, the most important results that were previously obtained in the case of X-ray scattering are derived again by a different procedure. By so doing, the three-dimensional case is treated explicitly, the polynomial equations in a single variable whose roots determine the positions of the scattering centres are explicitly reported and the procedure is shown to generalize to neutron scattering, overcoming the difficulty related to the non-positivity of the scattering density. In this way, it is fully proven that the atomicity assumption removes the phase ambiguity in the sense that the full diffraction pattern of an ideal crystal can uniquely be reconstructed from a suitable finite portion of it in both X-ray and neutron scattering. The procedures able to isolate these portions that contain the pattern's full information are also given. [source]

Solution of the crystallographic phase problem by iterated projections

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2003
Veit Elser
An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual reciprocal-space formulations of atomicity. The new algorithm implements atomicity constraints in real space, as well as intensity constraints in reciprocal space, by projections that restore each constraint with the minimal modification of the scattering density. To recover the true density, the two projections are combined into a single operation, the difference map, which is iterated until the magnitude of the density modification becomes acceptably small. The resulting density, when acted upon by a single additional operation, is by construction a density that satisfies both intensity and atomicity constraints. Numerical experiments have yielded solutions for atomic resolution X-ray data sets with over 400 non-hydrogen atoms, as well as for neutron data, where positivity of the density cannot be invoked. [source]