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Crystal lattices
International Tables for Crystallography (2016). Vol. A, ch. 3.1, pp. 698-719 [ doi:10.1107/97809553602060000929 ]
... one basis to another is described by a transformation matrix P. The transformation of the old basis (a,b,c) to ... group symmetries (a) Two dimensions. Lattice point group22mm4mm6mm Crystal family† m o t h monoclinic (oblique) orthorhombic (rectangular) tetragonal (square) hexagonal (b) Three dimensions. Lattice point group Crystal family† a m o t h c anorthic (triclinic) monoclinic orthorhombic tetragonal ...
Lattice characters
International Tables for Crystallography (2016). Vol. A, Section 3.1.3.5, pp. 712-713 [ doi:10.1107/97809553602060000929 ]
... adopted by the International Union of Crystallography in 1985; cf. de Wolff et al. (1985). The capital letter of the symbols ... character the corresponding interval of values of a suitable parameter p, expressed in the usual parameters of a conventional cell. ...
[more results from section 3.1.3 in volume A]
Detectors for X-rays
International Tables for Crystallography (2006). Vol. C, ch. 7.1, pp. 618-638 [ doi:10.1107/97809553602060000604 ]
... very briefly in the second section of the chapter. Geiger-Müller counters are now obsolete for data collection, but are ... for X-ray detection; an intrinsic layer is sandwiched with p- and n-type thin layers and a high electric field ... individual X-ray photons with a spatial resolution of 6µm. The final section of the chapter discusses storage phosphors, ...
Incommensurate and commensurate modulated structures
International Tables for Crystallography (2006). Vol. C, ch. 9.8, pp. 907-955 [ doi:10.1107/97809553602060000624 ]
... are presented and their use is illustrated with different examples. M* Vector module in m-dimensional reciprocal space (m = 1, 2, 3; normally m = 3), isomorphic to Z ...
The incommensurate versus the commensurate case
International Tables for Crystallography (2006). Vol. C, Section 9.8.5.2, pp. 942-943 [ doi:10.1107/97809553602060000624 ]
... element of the three-dimensional space group are, respectively: for m, n, r, s integers and t real. These conditions are ... become possible. Because the one-to-one correspondence between * and M* is no longer present, there may occur symmetry elements with ...
[more results from section 9.8.5 in volume C]
Structure factor
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.4.3, p. 941 [ doi:10.1107/97809553602060000624 ]
... The diffraction from incommensurate crystal structures has been treated by de Wolff (1974), Yamamoto (1982a,b), Paciorek & Kucharczyk (1985), Petricek, Coppens & Becker ... crystal structure. Acta Cryst. A41, 462-466. Perez-Mato, J. M., Madariaga, G. & Tello, M. J. (1986). Diffraction symmetry ...
[more results from section 9.8.4 in volume C]
Ambiguities in the notation
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.6, pp. 936-937 [ doi:10.1107/97809553602060000624 ]
... h + k + l = even because of the centring and l + m = even and h + m = even for h0lm because of the two glide planes perpendicular ... gamma])c*, the new indices are h, k, l', and m' with l' = l + m and m' = -m. Then the ...
[more results from section 9.8.3 in volume C]
Outline for a superspace-group determination
International Tables for Crystallography (2006). Vol. C, Section 9.8.2, pp. 913-915 [ doi:10.1107/97809553602060000624 ]
... reflections can be written as with H, K, L, and m integer numbers. The basis obtained is the conventional basis for the M* module and corresponds to the choice of a conventional cell ... with , , as Because H = h, K = k, L/2 = l + m/2, and h, k and l are integers with ...
Occupation modulation
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.5, p. 913 [ doi:10.1107/97809553602060000624 ]
... and by one of type B with probability and that p is periodic. The probability of finding an A atom at ... H given by (9.8.1.7). For a simple sinusoidal modulation [m = ±1 in (9.8.1.29)], there are only main reflections and first-order satellites (m = ±1). One may introduce an additional coordinate t ...
[more results from section 9.8.1 in volume C]
Incommensurate and commensurate modulated structures
International Tables for Crystallography (2006). Vol. C, ch. 9.8, pp. 907-955 [ doi:10.1107/97809553602060000624 ]
... found in insulators as well (Tanisaki, 1961, 1963; Brouns, Visser & de Wolff, 1964). The remarkable morphological properties of calaverite could also ... case. In general, they are elements of a vector module M* and can be written as This leads to the ...
International Tables for Crystallography (2016). Vol. A, ch. 3.1, pp. 698-719 [ doi:10.1107/97809553602060000929 ]
... one basis to another is described by a transformation matrix P. The transformation of the old basis (a,b,c) to ... group symmetries (a) Two dimensions. Lattice point group22mm4mm6mm Crystal family† m o t h monoclinic (oblique) orthorhombic (rectangular) tetragonal (square) hexagonal (b) Three dimensions. Lattice point group Crystal family† a m o t h c anorthic (triclinic) monoclinic orthorhombic tetragonal ...
Lattice characters
International Tables for Crystallography (2016). Vol. A, Section 3.1.3.5, pp. 712-713 [ doi:10.1107/97809553602060000929 ]
... adopted by the International Union of Crystallography in 1985; cf. de Wolff et al. (1985). The capital letter of the symbols ... character the corresponding interval of values of a suitable parameter p, expressed in the usual parameters of a conventional cell. ...
[more results from section 3.1.3 in volume A]
Detectors for X-rays
International Tables for Crystallography (2006). Vol. C, ch. 7.1, pp. 618-638 [ doi:10.1107/97809553602060000604 ]
... very briefly in the second section of the chapter. Geiger-Müller counters are now obsolete for data collection, but are ... for X-ray detection; an intrinsic layer is sandwiched with p- and n-type thin layers and a high electric field ... individual X-ray photons with a spatial resolution of 6µm. The final section of the chapter discusses storage phosphors, ...
Incommensurate and commensurate modulated structures
International Tables for Crystallography (2006). Vol. C, ch. 9.8, pp. 907-955 [ doi:10.1107/97809553602060000624 ]
... are presented and their use is illustrated with different examples. M* Vector module in m-dimensional reciprocal space (m = 1, 2, 3; normally m = 3), isomorphic to Z ...
The incommensurate versus the commensurate case
International Tables for Crystallography (2006). Vol. C, Section 9.8.5.2, pp. 942-943 [ doi:10.1107/97809553602060000624 ]
... element of the three-dimensional space group are, respectively: for m, n, r, s integers and t real. These conditions are ... become possible. Because the one-to-one correspondence between * and M* is no longer present, there may occur symmetry elements with ...
[more results from section 9.8.5 in volume C]
Structure factor
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.4.3, p. 941 [ doi:10.1107/97809553602060000624 ]
... The diffraction from incommensurate crystal structures has been treated by de Wolff (1974), Yamamoto (1982a,b), Paciorek & Kucharczyk (1985), Petricek, Coppens & Becker ... crystal structure. Acta Cryst. A41, 462-466. Perez-Mato, J. M., Madariaga, G. & Tello, M. J. (1986). Diffraction symmetry ...
[more results from section 9.8.4 in volume C]
Ambiguities in the notation
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.6, pp. 936-937 [ doi:10.1107/97809553602060000624 ]
... h + k + l = even because of the centring and l + m = even and h + m = even for h0lm because of the two glide planes perpendicular ... gamma])c*, the new indices are h, k, l', and m' with l' = l + m and m' = -m. Then the ...
[more results from section 9.8.3 in volume C]
Outline for a superspace-group determination
International Tables for Crystallography (2006). Vol. C, Section 9.8.2, pp. 913-915 [ doi:10.1107/97809553602060000624 ]
... reflections can be written as with H, K, L, and m integer numbers. The basis obtained is the conventional basis for the M* module and corresponds to the choice of a conventional cell ... with , , as Because H = h, K = k, L/2 = l + m/2, and h, k and l are integers with ...
Occupation modulation
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.5, p. 913 [ doi:10.1107/97809553602060000624 ]
... and by one of type B with probability and that p is periodic. The probability of finding an A atom at ... H given by (9.8.1.7). For a simple sinusoidal modulation [m = ±1 in (9.8.1.29)], there are only main reflections and first-order satellites (m = ±1). One may introduce an additional coordinate t ...
[more results from section 9.8.1 in volume C]
Incommensurate and commensurate modulated structures
International Tables for Crystallography (2006). Vol. C, ch. 9.8, pp. 907-955 [ doi:10.1107/97809553602060000624 ]
... found in insulators as well (Tanisaki, 1961, 1963; Brouns, Visser & de Wolff, 1964). The remarkable morphological properties of calaverite could also ... case. In general, they are elements of a vector module M* and can be written as This leads to the ...
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