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Point groups and crystal classes
International Tables for Crystallography (2016). Vol. A, ch. 3.2, pp. 720-776 [ doi:10.1107/97809553602060000930 ]
... 3.2.1. Crystallographic and noncrystallographic point groups Th. Hahn a andH. Klapper a 3.2.1.1. Introduction and definitions | | A point group1 is a ... brief introduction to point-group symbols is provided in Hahn & Klapper (2005). General symbolCrystal system TriclinicMonoclinic (top) Orthorhombic (bottom)TetragonalTrigonalHexagonalCubic ... variation of the values and signs of the Miller indices h, k, l or the point coordinates x, y, z. ...
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]
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 ]
... was subsequently extensively applied and further extended by J. D. H. Donnay (1940), and in many later papers by Donnay & Donnay ... be switched by an external magnetic field. Much later, von Hámos & Thiessen (1931) succeeded in visualizing magnetic domains by means ... is not a proper subgroup of some other proper subgroup H, i.e. if there exists no group H such that ...
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 ...
Programs for structure determinations with twinned crystals
International Tables for Crystallography (2013). Vol. D, Section 3.3.11.6, p. 477 [ doi:10.1107/97809553602060000917 ]
... Sigma]7 merohedral twins are contained in two publications by Klapper & Hahn (2010, 2012). References Betteridge, P. W., Carruthers, J. ... especially ch. 3. New York: Wiley. Eitel, M. & Bärnighausen, H. (1968). Programm zur Verfeinerung von Strukturen verzwillingter Kristalle. Universit ... for testing twinning by merohedry. J. Appl. Cryst. 34, 405. Klapper, H. & Hahn, Th. (2010). The application of eigensymmetries ...
[more results from section 3.3.11 in volume D]
Coherent and incoherent twin interfaces
International Tables for Crystallography (2013). Vol. D, Section 3.3.10.9, pp. 468-469 [ doi:10.1107/97809553602060000917 ]
... Alloys, especially chs. 8 and 20. Oxford: Pergamon. Cottrell, A. H. (1955). Theoretical Structural Metallurgy, 2nd ed., especially ch. 14.5. ... Section 1.5, pp. 25-41. Oxford: Clarendon Press. Van Bueren, H. G. (1961). Imperfections in Crystals, especially chs. 13.4 and ...
[more results from section 3.3.10 in volume D]
Pseudo-merohedry and ferroelasticity
International Tables for Crystallography (2013). Vol. D, Section 3.3.9.3, p. 450 [ doi:10.1107/97809553602060000917 ]
Pseudo-merohedry and ferroelasticity 3.3.9.3. Pseudo-merohedry and ferroelasticity The large group of pseudo-merohedral twins (irrespective of their lattice index) contains a very important subset which is characterized by the physical property ferroelasticity. Ferroelastic twins result from a real or virtual phase transition involving a change of the crystal family ...
[more results from section 3.3.9 in volume D]
Conclusions
International Tables for Crystallography (2013). Vol. D, Section 3.3.8.7, p. 446 [ doi:10.1107/97809553602060000917 ]
Conclusions 3.3.8.7. Conclusions In conclusion, the lattice theory of twinning, presented in this section, can be summarized as follows: (i) The lattice theory represents one of the first systematic theories of twinning; it is based on a clear and well defined concept and thus has found widespread acceptance, especially for the ...
[more results from section 3.3.8 in volume D]
International Tables for Crystallography (2016). Vol. A, ch. 3.2, pp. 720-776 [ doi:10.1107/97809553602060000930 ]
... 3.2.1. Crystallographic and noncrystallographic point groups Th. Hahn a andH. Klapper a 3.2.1.1. Introduction and definitions | | A point group1 is a ... brief introduction to point-group symbols is provided in Hahn & Klapper (2005). General symbolCrystal system TriclinicMonoclinic (top) Orthorhombic (bottom)TetragonalTrigonalHexagonalCubic ... variation of the values and signs of the Miller indices h, k, l or the point coordinates x, y, z. ...
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]
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 ]
... was subsequently extensively applied and further extended by J. D. H. Donnay (1940), and in many later papers by Donnay & Donnay ... be switched by an external magnetic field. Much later, von Hámos & Thiessen (1931) succeeded in visualizing magnetic domains by means ... is not a proper subgroup of some other proper subgroup H, i.e. if there exists no group H such that ...
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 ...
Programs for structure determinations with twinned crystals
International Tables for Crystallography (2013). Vol. D, Section 3.3.11.6, p. 477 [ doi:10.1107/97809553602060000917 ]
... Sigma]7 merohedral twins are contained in two publications by Klapper & Hahn (2010, 2012). References Betteridge, P. W., Carruthers, J. ... especially ch. 3. New York: Wiley. Eitel, M. & Bärnighausen, H. (1968). Programm zur Verfeinerung von Strukturen verzwillingter Kristalle. Universit ... for testing twinning by merohedry. J. Appl. Cryst. 34, 405. Klapper, H. & Hahn, Th. (2010). The application of eigensymmetries ...
[more results from section 3.3.11 in volume D]
Coherent and incoherent twin interfaces
International Tables for Crystallography (2013). Vol. D, Section 3.3.10.9, pp. 468-469 [ doi:10.1107/97809553602060000917 ]
... Alloys, especially chs. 8 and 20. Oxford: Pergamon. Cottrell, A. H. (1955). Theoretical Structural Metallurgy, 2nd ed., especially ch. 14.5. ... Section 1.5, pp. 25-41. Oxford: Clarendon Press. Van Bueren, H. G. (1961). Imperfections in Crystals, especially chs. 13.4 and ...
[more results from section 3.3.10 in volume D]
Pseudo-merohedry and ferroelasticity
International Tables for Crystallography (2013). Vol. D, Section 3.3.9.3, p. 450 [ doi:10.1107/97809553602060000917 ]
Pseudo-merohedry and ferroelasticity 3.3.9.3. Pseudo-merohedry and ferroelasticity The large group of pseudo-merohedral twins (irrespective of their lattice index) contains a very important subset which is characterized by the physical property ferroelasticity. Ferroelastic twins result from a real or virtual phase transition involving a change of the crystal family ...
[more results from section 3.3.9 in volume D]
Conclusions
International Tables for Crystallography (2013). Vol. D, Section 3.3.8.7, p. 446 [ doi:10.1107/97809553602060000917 ]
Conclusions 3.3.8.7. Conclusions In conclusion, the lattice theory of twinning, presented in this section, can be summarized as follows: (i) The lattice theory represents one of the first systematic theories of twinning; it is based on a clear and well defined concept and thus has found widespread acceptance, especially for the ...
[more results from section 3.3.8 in volume D]
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