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Guide to the use of the space-group tables
International Tables for Crystallography (2016). Vol. A, ch. 2.1, pp. 142-174 [ doi:10.1107/97809553602060000926 ]
... in Chapters 2.2 and 2.3 (with exercises) is provided by Hahn & Wondratschek (1994); see also Müller (2013). Section 2.1.1 ... the volume. 2.1.1. Conventional descriptions of plane and space groups Th. Hahn a andA. Looijenga-Vos b 2.1.1.1. Classification of space ...
Piezoelectricity
International Tables for Crystallography (2016). Vol. A, Section 3.2.2.6, p. 741 [ doi:10.1107/97809553602060000930 ]
Piezoelectricity 3.2.2.6. Piezoelectricity In piezoelectric crystals, an electric dipole moment can be induced by compressional and torsional stress. For a uniaxial compression, the induced moment may be parallel, normal or inclined to the compression axis. These cases are called longitudinal, transverse or mixed compressional piezoeffect, respectively. Correspondingly, for torsional stress, the ...
[more results from section 3.2.2 in volume A]
Sub- and supergroups of the general point groups
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.4.3, pp. 735-737 [ doi:10.1107/97809553602060000930 ]
Sub- and supergroups of the general point groups 3.2.1.4.3. Sub- and supergroups of the general point groups In Figs. 3.2.1.4 to 3.2.1.6, the subgroup and supergroup relations between the two-dimensional and three-dimensional general point groups are illustrated. It should be remembered that the index of a group-subgroup relation ...
[more results from section 3.2.1 in volume A]
Point groups and crystal classes
International Tables for Crystallography (2016). Vol. A, ch. 3.2, pp. 720-776 [ doi:10.1107/97809553602060000930 ]
... and noncrystallographic rod groups. 3.2.1. Crystallographic and noncrystallographic point groups Th. Hahn a andH. Klapper a 3.2.1.1. Introduction and definitions | | A point ... A brief introduction to point-group symbols is provided in Hahn & Klapper (2005). General symbolCrystal system TriclinicMonoclinic (top) Orthorhombic ( ...
Crystallographic groups in one dimension
International Tables for Crystallography (2016). Vol. A, Section 2.1.3.16, p. 172 [ doi:10.1107/97809553602060000926 ]
... for Crystallography (2002). Vol. A, 5th ed., edited by Th. Hahn. Dordrecht: Kluwer Academic Publishers. [Abbreviated as IT A (2002). ... F., Buerger, M. J., Donnay, J. D. H., Fischer, W., Hahn, Th., Koptsik, V. A., Mackay, A. L., Wondratschek, H., ...
[more results from section 2.1.3 in volume A]
Symbols of symmetry elements
International Tables for Crystallography (2016). Vol. A, Section 2.1.2, pp. 144-148 [ doi:10.1107/97809553602060000926 ]
... for Crystallography (2002). Vol. A, 5th ed., edited by Th. Hahn. Dordrecht: Kluwer Academic Publishers. [Abbreviated as IT A (2002). ... Abbreviated as IT (1935).] Flack, H. D., Wondratschek, H., Hahn, Th. & Abrahams, S. C. (2000). Symmetry elements in ...
Conventional coordinate systems and cells
International Tables for Crystallography (2016). Vol. A, Section 2.1.1.2, pp. 142-144 [ doi:10.1107/97809553602060000926 ]
Conventional coordinate systems and cells 2.1.1.2. Conventional coordinate systems and cells A plane group or space group usually is described by means of a crystallographic coordinate system, consisting of a crystallographic basis (basis vectors are lattice vectors) and a crystallographic origin (origin at a centre of symmetry or at a point ...
[more results from section 2.1.1 in volume A]
Tables of the crystallographic point-group types
International Tables for Crystallography (2016). Vol. A, Section 3.2.3, pp. 742-771 [ doi:10.1107/97809553602060000930 ]
Tables of the crystallographic point-group types 3.2.3. Tables of the crystallographic point-group types The crystallographic point-group types are listed in Tables 3.2.3.1 and 3.2.3.2 for two-dimensional and for three-dimensional space, respectively. No listings are presented for the noncrystallographic point-group types (i.e. having axes of orders ...
Twinning and domain structures
International Tables for Crystallography (2013). Vol. D, ch. 3.2, pp. 397-412 [ doi:10.1107/97809553602060000916 ]
... terminologies of bicrystals, twins and domain structures is presented by Hahn et al. (1999). An extensive treatment of bicrystallography is ... action and orbits, can be found in the book by Hahn & Wondratschek (1994). A concise presentation of group actions and ... groups [for their definition and properties see Bradley & Cracknell (1972), Hahn & Wondratschek (1994), IT A (2005), IT A1 (2004), Janssen ( ...
Domain structures (by V. Janovec)
International Tables for Crystallography (2013). Vol. D, Section 3.3.12, p. 477 [ doi:10.1107/97809553602060000917 ]
Domain structures (by V. Janovec) 3.3.12. Domain structures (by V. Janovec) Domain structure is a special kind of twinning which results from lowering of crystal symmetry at a phase transition. A homogeneous phase with higher symmetry (called the parent phase) breaks into a non-homogeneous twinned phase (ferroic phase) with lower ...
International Tables for Crystallography (2016). Vol. A, ch. 2.1, pp. 142-174 [ doi:10.1107/97809553602060000926 ]
... in Chapters 2.2 and 2.3 (with exercises) is provided by Hahn & Wondratschek (1994); see also Müller (2013). Section 2.1.1 ... the volume. 2.1.1. Conventional descriptions of plane and space groups Th. Hahn a andA. Looijenga-Vos b 2.1.1.1. Classification of space ...
Piezoelectricity
International Tables for Crystallography (2016). Vol. A, Section 3.2.2.6, p. 741 [ doi:10.1107/97809553602060000930 ]
Piezoelectricity 3.2.2.6. Piezoelectricity In piezoelectric crystals, an electric dipole moment can be induced by compressional and torsional stress. For a uniaxial compression, the induced moment may be parallel, normal or inclined to the compression axis. These cases are called longitudinal, transverse or mixed compressional piezoeffect, respectively. Correspondingly, for torsional stress, the ...
[more results from section 3.2.2 in volume A]
Sub- and supergroups of the general point groups
International Tables for Crystallography (2016). Vol. A, Section 3.2.1.4.3, pp. 735-737 [ doi:10.1107/97809553602060000930 ]
Sub- and supergroups of the general point groups 3.2.1.4.3. Sub- and supergroups of the general point groups In Figs. 3.2.1.4 to 3.2.1.6, the subgroup and supergroup relations between the two-dimensional and three-dimensional general point groups are illustrated. It should be remembered that the index of a group-subgroup relation ...
[more results from section 3.2.1 in volume A]
Point groups and crystal classes
International Tables for Crystallography (2016). Vol. A, ch. 3.2, pp. 720-776 [ doi:10.1107/97809553602060000930 ]
... and noncrystallographic rod groups. 3.2.1. Crystallographic and noncrystallographic point groups Th. Hahn a andH. Klapper a 3.2.1.1. Introduction and definitions | | A point ... A brief introduction to point-group symbols is provided in Hahn & Klapper (2005). General symbolCrystal system TriclinicMonoclinic (top) Orthorhombic ( ...
Crystallographic groups in one dimension
International Tables for Crystallography (2016). Vol. A, Section 2.1.3.16, p. 172 [ doi:10.1107/97809553602060000926 ]
... for Crystallography (2002). Vol. A, 5th ed., edited by Th. Hahn. Dordrecht: Kluwer Academic Publishers. [Abbreviated as IT A (2002). ... F., Buerger, M. J., Donnay, J. D. H., Fischer, W., Hahn, Th., Koptsik, V. A., Mackay, A. L., Wondratschek, H., ...
[more results from section 2.1.3 in volume A]
Symbols of symmetry elements
International Tables for Crystallography (2016). Vol. A, Section 2.1.2, pp. 144-148 [ doi:10.1107/97809553602060000926 ]
... for Crystallography (2002). Vol. A, 5th ed., edited by Th. Hahn. Dordrecht: Kluwer Academic Publishers. [Abbreviated as IT A (2002). ... Abbreviated as IT (1935).] Flack, H. D., Wondratschek, H., Hahn, Th. & Abrahams, S. C. (2000). Symmetry elements in ...
Conventional coordinate systems and cells
International Tables for Crystallography (2016). Vol. A, Section 2.1.1.2, pp. 142-144 [ doi:10.1107/97809553602060000926 ]
Conventional coordinate systems and cells 2.1.1.2. Conventional coordinate systems and cells A plane group or space group usually is described by means of a crystallographic coordinate system, consisting of a crystallographic basis (basis vectors are lattice vectors) and a crystallographic origin (origin at a centre of symmetry or at a point ...
[more results from section 2.1.1 in volume A]
Tables of the crystallographic point-group types
International Tables for Crystallography (2016). Vol. A, Section 3.2.3, pp. 742-771 [ doi:10.1107/97809553602060000930 ]
Tables of the crystallographic point-group types 3.2.3. Tables of the crystallographic point-group types The crystallographic point-group types are listed in Tables 3.2.3.1 and 3.2.3.2 for two-dimensional and for three-dimensional space, respectively. No listings are presented for the noncrystallographic point-group types (i.e. having axes of orders ...
Twinning and domain structures
International Tables for Crystallography (2013). Vol. D, ch. 3.2, pp. 397-412 [ doi:10.1107/97809553602060000916 ]
... terminologies of bicrystals, twins and domain structures is presented by Hahn et al. (1999). An extensive treatment of bicrystallography is ... action and orbits, can be found in the book by Hahn & Wondratschek (1994). A concise presentation of group actions and ... groups [for their definition and properties see Bradley & Cracknell (1972), Hahn & Wondratschek (1994), IT A (2005), IT A1 (2004), Janssen ( ...
Domain structures (by V. Janovec)
International Tables for Crystallography (2013). Vol. D, Section 3.3.12, p. 477 [ doi:10.1107/97809553602060000917 ]
Domain structures (by V. Janovec) 3.3.12. Domain structures (by V. Janovec) Domain structure is a special kind of twinning which results from lowering of crystal symmetry at a phase transition. A homogeneous phase with higher symmetry (called the parent phase) breaks into a non-homogeneous twinned phase (ferroic phase) with lower ...
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