Hence, William Hallowes Miller in 1839 was able to give each face a unique label of three small integers, the Miller indices which remain in use for identifying crystal faces. René Just Haüy (1784) discovered that every face of a crystal can be described by simple stacking patterns of blocks of the same shape and size. Steno showed that the angles between the faces are the same in every exemplar of a particular type of crystal. The Danish scientist Nicolas Steno (1669) pioneered experimental investigations of crystal symmetry. Johannes Kepler hypothesized in his work Strena seu de Nive Sexangula (A New Year's Gift of Hexagonal Snow) (1611) that the hexagonal symmetry of snowflake crystals was due to a regular packing of spherical water particles. The hexagonal symmetry of snowflakes results from the tetrahedral arrangement of hydrogen bonds about each water molecule.Ĭrystals, though long admired for their regularity and symmetry, were not investigated scientifically until the 17th century. History Early scientific history of crystals and X-rays By contrast, inelastic X-ray scattering methods are useful in studying excitations of the sample such as plasmons, crystal-field and orbital excitations, magnons, and phonons, rather than the distribution of its atoms. If the material under investigation is only available in the form of nanocrystalline powders or suffers from poor crystallinity, the methods of electron crystallography can be applied for determining the atomic structure.įor all above mentioned X-ray diffraction methods, the scattering is elastic the scattered X-rays have the same wavelength as the incoming X-ray. If single crystals of sufficient size cannot be obtained, various other X-ray methods can be applied to obtain less detailed information such methods include fiber diffraction, powder diffraction and (if the sample is not crystallized) small-angle X-ray scattering (SAXS). Similar diffraction patterns can be produced by scattering electrons or neutrons, which are likewise interpreted by Fourier transformation. X-ray crystallography is related to several other methods for determining atomic structures. Poor resolution (fuzziness) or even errors may result if the crystals are too small, or not uniform enough in their internal makeup. The two-dimensional images taken at different orientations are converted into a three-dimensional model of the density of electrons within the crystal using the mathematical method of Fourier transforms, combined with chemical data known for the sample. The crystal is illuminated with a finely focused monochromatic beam of X-rays, producing a diffraction pattern of regularly spaced spots known as reflections. The goniometer is used to position the crystal at selected orientations. In a single-crystal X-ray diffraction measurement, a crystal is mounted on a goniometer. X-ray crystal structures can also account for unusual electronic or elastic properties of a material, shed light on chemical interactions and processes, or serve as the basis for designing pharmaceuticals against diseases. X-ray crystallography is still the primary method for characterizing the atomic structure of new materials and in discerning materials that appear similar by other experiments. The method also revealed the structure and function of many biological molecules, including vitamins, drugs, proteins and nucleic acids such as DNA. In its first decades of use, this method determined the size of atoms, the lengths and types of chemical bonds, and the atomic-scale differences among various materials, especially minerals and alloys. Since many materials can form crystals-such as salts, metals, minerals, semiconductors, as well as various inorganic, organic, and biological molecules-X-ray crystallography has been fundamental in the development of many scientific fields. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their crystallographic disorder, and various other information. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions.
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