The design and operation of a new small-angle X-ray scattering instrument, optimized for high throughput at a synchrotron source, high angular and wavelength resolution, large sample cross-sectional area, accurate energy tuning, excellent signal-to-noise ratio and harmonic rejection are presented. The principles of design and implementation are given, as are the details of primary calibration of absolute intensity and experimental desmearing. The instrument has been tested for application to anomalous-scattering measurements near the chromium K edge. Preliminary results on samples of a heat-treated steel are presented as a demonstration of the capability of this experiment to separate the microstructure evolution as a function of temperature of a chromium-rich precipitate from the thermal behavior of other precipitates in the steel.

The performance of an X-ray optical system often depends critically on the local angular divergence of the X-ray beam. For example, in systems for radiography, tomography and diffraction topography, the angular divergence of the incident beam at a point in the sample determines the limiting spatial resolution. In this paper, formulas are derived for the local divergence in the diffracted beam of the non-dispersive asymmetric reflection double-flat-crystal monochromator, illuminated by synchrotron or characteristic radiation. The formulas are analyzed to determine the general behavior of the local divergence as a function of the asymmetry factors of the crystal reflections. For synchrotron radiation, one surprising conclusion is that the local divergence of the magnifying monochromator is always greater than that of the symmetric monochromator, significantly so for even moderate magnification factors. This result, which contradicts a claim in the literature, is attributed to a prismatic property of asymmetric reflection that has not previously been identified.

An energy-conservation relation is derived between the power absorption, energy flux and absorption coefficient of an arbitrary fundamental mode in the n-beam dynamical theory of X-ray diffraction. From this relation, it is proven that the 4n fundamental modes selected by arbitrary incidence conditions are evenly divided into two types. The types are distinguished by the sign of their absorption coefficient and by the sign of their energy flux through a plane of constant absorption. In a bounded crystal, they represent reflected and refracted beams. It is noteworthy that these results apply for arbitrary n, even though the solution of the n-beam equations only satisfies Maxwell's equations in the limit of infinite n. In this limit, the energy-conservation relation is equivalent to Poynting's theorem.