Triclinic crystal system

Thin-sheet inesite from the Wessels Mine, Hotazel, Kalahari Manganese Field , North Cape, South Africa

The triclinic crystal system is one of the seven crystal systems in crystallography . It includes all point groups that do not have an axis of rotation. The word triklin means triple inclined (from ancient Greek τρία tria "three" and κλίνειν klinein "incline", "bow"). This term refers to the fact that in the triclinic grid system all three axes can be inclined towards each other. The triclinic crystal system is also known as the anorthic crystal system and its lattice system is therefore abbreviated with a (t, however, stands for tetragonal).

Point groups

The triclinic crystal system includes the point groups and . They belong to the triclinic crystal family and can be described with the triclinic grid system . ${\ displaystyle \ 1}$ ${\ displaystyle {\ bar {1}}}$

Grid system

The triclinic grid system has the holoedry . Due to the symmetry elements, there are no conditions for the grid axes, so: ${\ displaystyle {\ bar {1}}}$

${\ displaystyle a \ \ neq \ b \ \ neq \ c \}$
${\ displaystyle \ alpha \ \ neq \ \ beta \ \ neq \ \ gamma \ \ neq \ 90 ^ {\ circ}}$

The grid vectors are chosen so that: c <a <b and the angles α and β are obtuse, while γ is acute.

Bravais grid

Primitive triclines Bravais grid: aP

In triclining there is actually only the primitive Bravais grid . Nevertheless, various centered grids appear in the literature.

Point groups in the triclinic crystal system and their physical properties

In the triclinic crystal system there is exactly one space group in each of the two point groups : P 1 (no. 1) in point group 1 and P 1 (no. 2) in 1 . Template: room group / 1Template: room group / 2

Point group (crystal class)								Physical Properties				Examples
No.	Crystal system	Surname	Schoenflies icon	International symbol ( Hermann-Mauguin )		Tepid class	Associated room groups ( no.)	Enantiomorphism	Optical activity	Pyroelectricity	Piezoelectricity ; SHG effect
No.	Crystal system	Surname	Schoenflies icon	Full	Short	Tepid class	Associated room groups ( no.)	Enantiomorphism	Optical activity	Pyroelectricity	Piezoelectricity ; SHG effect
1	triclinic	triklin-pedial	C ₁	1	1	1	1	+	+	+ [ uvw ]	+	Abelsonite axinite
2	triclinic	triclinic-pinacoidal	C _i ( S ₂ )	1	1	1	2	-	-	-	-	Albite anorthite
↑ In the information on the physical properties, " - " means forbidden due to the symmetry and " + " means allowed. No statement can be made about the magnitude of the optical activity, pyro- and piezoelectricity and the SHG effect purely due to the symmetry. However, one can assume that there is always at least a weak expression of the property. For the pyroelectricity, the direction of the pyroelectric vector is given, if available.

For further triclinic crystallizing chemical substances see category: Triclinic crystal system

Crystal forms of the triclinic crystal system

Crystal forms of the triclinic crystal system using the example of chalcanthite , kyanite , axinite , rhodonite and albite .

literature

Walter Borchardt-Ott: Crystallography . 6th edition. Springer-Verlag, Berlin 2002, ISBN 3-540-43964-1 , pp. 70, 71 .
Hugo Strunz , Ernest H. Nickel: Strunz Mineralogical Tables . 9th edition. E. Schweizerbart'sche Verlagbuchhandlung (Nägele and Obermiller), Stuttgart 2001, ISBN 3-510-65188-X , p. 4 .
Hans-Joachim Bautsch , Will Kleber , Joachim Bohm : Introduction to crystallography . 18th edition. Oldenbourg Wissenschaftsverlag, Berlin 1998, ISBN 3-341-01205-2 , pp. 68, 69 ( limited preview in the Google book search).
Hahn, Theo (Ed.): International Tables for Crystallography Vol. A D. Reidel publishing Company, Dordrecht 1983, ISBN 90-277-1445-2

[Hinweise-1] In the information on the physical properties, " - " means forbidden due to the symmetry and " + " means allowed. No statement can be made about the magnitude of the optical activity, pyro- and piezoelectricity and the SHG effect purely due to the symmetry. However, one can assume that there is always at least a weak expression of the property. For the pyroelectricity, the direction of the pyroelectric vector is given, if available.