International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. C, ch. 2.1, pp. 2425
https://doi.org/10.1107/97809553602060000576 Chapter 2.1. Classification of experimental techniques
J. R. Helliwell^{a}
^{a}Department of Chemistry, University of Manchester, Manchester M13 9PL, England In crystallography research directed at crystal structure analysis, the probes and methods span the use of Xrays, neutrons and electrons and sample states that are in various degrees of order (i.e. single crystal, powder, fibre, surface, amorphous or liquid). Thus a summary of diffractionbased methods used in the study of the structure of matter are tabulated in this chapter. 
The diffraction of a wave of characteristic length, λ, by a crystal sample requires that λ is of the same order in size as the interatomic separation. Beams of Xrays, neutrons, and electrons can easily satisfy this requirement; for the latter two, the wavelength is determined by the de Broglie relationship λ = h/p, where h is Planck's constant and p is the momentum.
We can define `diffraction geometry' as the description of the relationship between the beam and the sample orientation and the subsequent interception of the diffracted rays by a detector of given geometry and imaging properties. Each diffracted ray represents successful, constructive interference. The full stimulation of a reflection is achieved either by using a continuum of values of λ incident on the crystal, as used originally by Friedrich, Knipping & von Laue (1912) (the Laue method) or alternatively by using a monochromatic beam and rotation or precession of a crystal (movingcrystal methods) or a set of randomly oriented crystallites (the powder method).
The analysis of singlecrystal reflection intensities allows the threedimensional architecture of molecules to be determined. However, a single crystal cannot always be obtained. Diffraction from noncrystalline samples, i.e. fibres, amorphous materials or solutions, yields less detailed, but often very valuable, molecular information. Another method, surface diffraction, involves the determination of the organization of atoms deposited on the surface of a crystal substrate; a surface of perfectly repeating identical units, in identical environments, on such a substrate is sometimes referred to as a twodimensional crystal. Ordered twodimensional arrangements of proteins in membranes are studied by electron diffraction and, more recently, by undulator Xradiation. Another experimental probe of the structure of matter is EXAFS (extended Xray absorption fine structure). This technique yields details of the local environment of a specific atom whose Xray absorption edge is stimulated; the atom absorbs an Xray photon and yields up a photoelectron, which can be scattered by neighbouring atoms. Interpretation of EXAFS therefore closely follows lowenergy electrondiffraction (LEED) theory. All these methods (Table 2.1.1) can be called methods of structure analysis. Techniques for examining the perfection of crystals are also very important. Defects in crystals represent irregularities in the growth of a perfect crystalline array. There are many types of defect. The experimental technique of Xray topography (Chapter 2.7 ) is used to image irregularities in a crystal lattice.
Notes

Xray techniques have expanded in the 1970's and 1980's with the utilization of synchrotron radiation. The methods based on the use of neutrons and electrons have developed. Broadly speaking, the diffraction geometry is independent of the nature of the wave and depends only on its state, namely, the wavelength, λ, the spectral bandpass, δλ/λ, the convergence/divergence angles, and the beam direction. In what follows, the term monochromatic refers to the case where there is, practically speaking, a very small but finite wavelength spread. Similarly, the term polychromatic refers to the situation where the wavelength spread is of the same order as the mean wavelength. The technical means by which a given beam (of Xrays, neutrons or electrons) is conditioned vary, as do the means of detection. These methods are dealt with in the following pages as far as they relate to the geometry of diffraction.
In the previous version of International Tables (IT II, 1959, Part 4), various diffraction geometries were detailed and a variety of numerical tables were given. The numerical tables have mainly been dispensed with since the use of handheld calculators and computers has rendered them obsolete.