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Lecture

Small-Angle X-ray Scattering II

Description

This lecture covers the different Q-regimes in small-angle x-ray scattering, including the low, intermediate, and high Q regimes, as well as the idealized shapes used in the analysis such as spheres, ellipsoids, rods, and platelets. It also discusses the general comments on scattering curves, the contrast of particles, and the coherence factor. The lecture further explores the scattering curves for single particles versus random ensembles, focusing on ellipsoids in fixed and randomly oriented ensembles, solid and hollow spheres, rods, platelets, and Gaussian chains.

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Related concepts (16)

Earth ellipsoid

An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations. It is a spheroid (an ellipsoid of revolution) whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation.

Geodesics on an ellipsoid

The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an oblate ellipsoid, a slightly flattened sphere. A geodesic is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface. The solution of a triangulation network on an ellipsoid is therefore a set of exercises in spheroidal trigonometry .

Ellipsoid

An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is characterized by either of the two following properties. Every planar cross section is either an ellipse, or is empty, or is reduced to a single point (this explains the name, meaning "ellipse-like").

Bessel ellipsoid

The Bessel ellipsoid (or Bessel 1841) is an important reference ellipsoid of geodesy. It is currently used by several countries for their national geodetic surveys, but will be replaced in the next decades by modern ellipsoids of satellite geodesy. The Bessel ellipsoid was derived in 1841 by Friedrich Wilhelm Bessel, based on several arc measurements and other data of continental geodetic networks of Europe, Russia and the British Survey of India.

Hayford ellipsoid

The Hayford ellipsoid is a geodetic reference ellipsoid, named after the US geodesist John Fillmore Hayford (1868–1925), which was introduced in 1910. The Hayford ellipsoid was also referred to as the International ellipsoid 1924 after it had been adopted by the International Union of Geodesy and Geophysics IUGG in 1924, and was recommended for use all over the world. Many countries retained their previous ellipsoids. The Hayford ellipsoid is defined by its semi-major axis a = 6378388.000m and its flattening f = 1:297.

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