By Professor Dr. Werner Massa (auth.)

To clear up a crystal constitution skill to figure out the ideal spatial preparations of the entire atoms in a chemical compound within the crystalline country. this data provides a chemist entry to a wide range of knowledge, together with connectivity, conformation, and actual bond lengths and angles. furthermore, it implies the stoichiometry, the density, the symmetry and the 3 dimensional packing of the atoms within the strong. due to the fact interatomic distances are within the area of100-300 pm or 1-3 A, 1 microscopy utilizing noticeable mild (wavelength Ä ca. 300-700 nm) isn't really acceptable (Fig. l. l). In 1912, Max von Laue confirmed that crystals are in response to a 3 dimensionallattice which scatters radiation with a wavelength within the area of interatomic distances, i. e. X -rays with Ä = 50-300 pm. the method bywhich this radiation, with out altering its wave size, is switched over via interference via the lattice to an enormous variety of observable "reflections" with attribute instructions in house is termed X-ray diffraction. the strategy through which the instructions and the intensities of those reflections are measured, and the ordering of the atoms within the crystal deduced from them, is named X-ray struc ture research. the next bankruptcy offers with the lattice homes of crystals, the place to begin for the reason of those interference phenomena. Interatomic distances Crystals . . . . . . . . . .

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H. and W. 1. Bragg (father and son) showed that this angle could be calculated very easily in terms of the path difference between a ray reßected by one plane and that reßected by the next plane after it in the lattice. Only those angles iJ are allowed, where the path difference 2d sin iJ is an integral multiple of the wavelength: 2d sin iJ = nA (n = 1,2,3 ... ) with its characteristic spacing d, the possible angles iJ are exactly defined for each order of diffraction n. It should be noted that this condition for the measurement of a specific reßection from the plane hkl does stillleave the crystallographer some freedom: when the crystal is orientated to the X-ray beam with the correct value of iJ, it is possible to rotate the crystal to any Fig.

For an orthogonal, two-dimensional system (Fig. 8 gives: a 2 b2 h2 . k2 = (ah2 + k2b 2 2 ) . 10) b2 In a three dimensional orthogonal (e. g. 11) b Fig. 11. Calculation of the interplanar spacing d for a set of planes hkl in a two-dimensional orthogonal system. 7The Quadratic Form of the Bragg Equation 2S In the general, non-orthogonal eases, use must be made of the eosine law and the unit eell angles. 5) to ealeulate the seattering angle tJ. 3. g. from powder diffraetion. 3. The quadratic form of the Bragg equation in the seven crystal systems.

The knowledge that a special position is occupied can give important information ab out a structure. If, for example, the central atom of a complex lies on position 4c in space group Pnma, that implies that the complex must have the corresponding point symmetry, here m (Cs ). g. for C-centering 0)+. This means that for the general position as well as every special position, another atom with the coordinates (x + y + z) is generated as weIl. Further information in Fig. 9, will be referred to later.