International Tables for

The electron distribution, p(r), has been computed by quantum mechanics for all neutral atoms and many ions and the values off(Q), as well as coefficients for a useful empirical approximation, are tabulated in the International Tables for Crystallography vol C [2]. In general,is a maximum equal to the nuclear charge, Z, lor Q = 0 and decreases monotonically with increasing Q. 

These include rotation axes of orders two, tliree, four and six and mirror planes. They also include screM/ axes, in which a rotation operation is combined witii a translation parallel to the rotation axis in such a way that repeated application becomes a translation of the lattice, and glide planes, where a mirror reflection is combined with a translation parallel to the plane of half of a lattice translation. Each space group has a general position in which the tln-ee position coordinates, x, y and z, are independent, and most also have special positions, in which one or more coordinates are either fixed or constrained to be linear fimctions of other coordinates. The properties of the space groups are tabulated in the International Tables for Crystallography vol A [21]. 

All tenus in the sum vanish if / is odd, so (00/) reflections will be observed only if / is even. Similar restrictions apply to classes of reflections with two indices equal to zero for other types of screw axis and to classes with one index equal to zero for glide planes. These systematic absences, which are tabulated m the International Tables for Crystallography vol A, may be used to identify the space group, or at least limit die... 

Brown P J 1999 Magnetic form factors International Tables for Crystallography 2n6 edn, vol C, ed A J C Wilson and E Prince (Dordrecht Kluwer) section 4.4.5... 

Flahn Th (ed) 1992 International Tables for Crystallography vo A (Dordrecht Kluwer)... 

Wiison A J C and Prinoe E (eds) 1999 Mathematical, Physical and Chemical Tables (International Tables for Crystallography C) 2nd edn (Dordreoht Kiuwer)... 

International Tables for Crystallography, Vol. A, Space-Group Symmetry, edited by Theo Hahn, 2nd ed. (Kluwer Academic, Dordrecht, 1989). 

The 230 space-group types are listed in full in International Tables for Crystallography, Volume A [48], Whenever crystal symmetry is to be considered, this fundamental tabular work should be consulted. It includes figures that show the relative positions of the symmetry elements as well as details concerning all possible sites in the unit cell (cf. next section). 

The different sets of positions in crystals are called Wyckoff positions. They are listed for every space-group type in International Tables for Crystallography, Volume A, in the following way (example space-group type Nr. 87, 74/m) ... 

A two-dimensional disorder results when rod-like polymeric molecules are mutually shifted with statistical frequency. Translational symmetry then only exists in the direction of the molecules, and not in the transverse directions. The rod is a three-dimensional object with one-dimensional translational symmetry. Its symmetry is that of a rod group. Layer groups and rod groups are subperiodic groups. They are listed in detail in International Tables for Crystallography, Volume E. 

Set up the Barnighausen tree for the relation between disordered and ordered AuCu3, including the relations between the Wyckoff positions (Fig. 15.1, p. 158). You will need International Tables for Crystallography [48], Volume A, and advantageously also Volume A1 [181]. Will ordered AuCu3 form twins ... 

International Tables for Crystallography, Vol. D Physical Properties of Crystals (A. Authier, ed.), Chapter 3.1 (J.-C. Toledano, V. Janovec, V. Kospky, J. F. Scott, P. Boek) Structural phase transitions. Kluwer, 2003. 

International Tables for Crystallography, Vol. A1 Symmetry Relations between Space Groups. (H. Wondratschek, U. Muller, eds.). Kluwer, 2004. 

Bricogne, G. (1993) Fourier transforms in crystallography theory, algorithms, and applications, In International Tables for Crystallography, Vol. B, Reciprocal Space, Shmueli, U. (Ed.), Dordrecht, Kluwer Academic Publishers, Holland, pp. 23-106. 

International Tables for X-Ray Crystallography, Vol. C, Kluwer Academic Publishers, Dordrecht, 1995. 

Macgillavry CH, Rieck GD (eds.) (1968) International Tables for X-ray Crystallography, vol. 2. Physical and Chemical Tables. The Kynoch Press, Birmingham... 

Rossmann, M. G., and Arnold, E. (Eds.) (2001). International Tables for Crystallography Kluwer Academic Publishers, Dorderecht, The Netherlands. 

A number of points are relevant for a full crystallochemical characterization for each of them a few noteworthy remarks will be presented in the following. To this end, crystallographic conventions, nomenclature and symbols will be used. For a summary of these and of the corresponding definitions the most important reference book is International Tables for Crystallography (Hahn 2002). 

Hahn, T. (ed.) (2002) International Tables for Crystallography (Springer, Dordrecht, The Netherlands). 

For symmetry determinations, the choice of the pertinent technique among the available techniques greatly depends on the inferred crystallographic feature. A diffraction pattern is a 2D finite figure. Therefore, the symmetry elements displayed on such a pattern are the mirrors m, the 2, 3, 4 and 6 fold rotation axes and the combinations of these symmetry elements. The notations given here are those of the International Tables for Crystallography [1]. 

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