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# Crystallography

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Crystallography most often refers to the experimental methods used to determine the arrangement of atoms in solids. More traditionally, it is the scientific study of crystals.

Crystallographic methods all rely on the analysis of the diffraction patterns that emerge from a sample that is targetted by a beam of some type. The beam is not always electromagnetic radiation, even though X-rays are the most common choice.

For some purposes electrons or neutrons are used, which is possible due to the wave properties of particles that are described by quantum mechanics. Crystallographers often explicitly state the type of illumination used when refering to a method, as with the terms X-ray diffraction, neutron diffraction and electron diffraction. Crystallography by itself typically implies X-rays.

Crystallography is used to generate a kind of image of how the atoms in a material are arranged. The most familiar way to generate an image is with a lens, such as the lenses that a microscope uses to image the fine features of a sample. But the wavelengths of radiation employed by microscopes are long compared both to atomic bond[?] lengths and to the sizes of atoms, so these features are not resolvable in the images of either light or traditional electron microscopes.

Employing shorter wavelengths implies abandoning microscopy and true imaging, however, because there exists no material with which to focus such illumination in the form of a lens. (That said, scientists have had some success focusing X-rays with microscopic Fresnel zone plates[?] made from gold recently). Generally, in diffraction-based imaging, the only wavelengths used are those that are too short to be focused.

Producing an image from a diffraction pattern requires sophisticated mathematics and often an iterative process of modelling and refinement. In this process, the mathematically predicted diffraction patterns of an hypothesized or "model" structure are compared to the actual pattern generated by the crystalline sample. Models are refined until their predicted patterns match to as great a degree as can be achieved without radical revision of the model.

Ideally, researchers make several initial guesses, which through refinement all converge on the same answer. The mathematical methods for the analysis of diffraction patterns only apply to patterns, which in turn result only when waves diffract from orderly arrays. Hence crystallography applies for the most part only to crystals, or to molecules which can be coaxed to crystalize for the sake of measurement.

In fact, a certain amount of molecular information can be deduced from the patterns that are generated by fibers and powders, which while not as perfect as a solid crystal, may exhibit a degree of order. This level of order can be sufficient to deduce the structure of simple molecules, or to determine the coarse features of more complicated molecules (the double-helical structure of DNA, for example, was deduced from an X-ray diffraction pattern that had been generated by a fibrous sample).

Crystallography is a tool that is often employed by materials scientists. In single crystals, the effects of the crystalline arrangement of atoms is often easy to see macroscopically, because the natural shapes of crystals reflect the atomic structure. In addition, physical properties are often controlled by crystalline defects. The understanding of crystal structures is an important prerequisite for understanding crystallographic defects.

A number of other physical properties are linked to crystallography. For example, the minerals in clay form small, flat, platelike structures. Clay can be easily deformed because the platelike particles can slip along each other in the plane of the plates, yet remain strongly connected in the direction perpendicular to the plates.

In another example, when iron, which at room temperature has a body-centered cubic (bcc) structure, is heated up, it will transform to a face centered cubic (fcc) structure, called austenite. The fcc structure is a close-packed structure, and the bcc structure is not, which explains why the volume of the iron decreases when this transformation occurs.

Crystallography is useful in phase identification: That is, when performing some kind of processing on a material, it is often desired to find out what compounds and what phases are present in the material. Each phase has a characteristic arrangement of atoms. Techniques like X-ray diffraction can be used to identify which patterns are present in the material, and thus which compounds are present (note: the determination of the "phases" within a material should not be confused with the more general problem of "phase determination," which refers to the phase of waves as they diffract from planes within a crystal, and which is a necessary step in the interpretation of complicated diffraction patterns).

Crystallography covers the enumeration of the symmetry patterns which can be formed by atoms in a crystal and for this reason has a relation to group theory and geometry. See Symmetry group.

X-ray crystallography is the primary method for determining the molecular conformations of proteins and other biological macromolecules (the double-helical structure of DNA, for example, was deduced from X-ray diffraction patterns). The diffraction patterns from protein crystals can be very complex, and their analysis requires computers and sophisticated techniques. Synchrotrons[?] are often used as X-ray sources, because of the purer and more complete patterns such sources can generate.

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