Triclinic crystal system: Difference between revisions

Latest revision as of 11:49, 15 February 2025

An article about the triclinic crystal system in crystallography

Overview[edit]

The triclinic crystal system is one of the seven crystal systems in crystallography. It is the least symmetric of all the crystal systems, characterized by three axes of unequal length that intersect at oblique angles. This system is defined by the absence of any symmetry other than the identity operation.

Characteristics[edit]

In the triclinic system, the unit cell is defined by three vectors of unequal length, denoted as \(a\), \(b\), and \(c\). The angles between these vectors, \(\alpha\), \(\beta\), and \(\gamma\), are all different and none of them are 90 degrees. This lack of symmetry results in a very flexible and adaptable structure, allowing for a wide variety of crystal shapes.

Crystallographic Axes[edit]

Microcline, a mineral that crystallizes in the triclinic system

The axes in the triclinic system are labeled as \(a\), \(b\), and \(c\), with the angles \(\alpha\), \(\beta\), and \(\gamma\) representing the angles between \(b\) and \(c\), \(a\) and \(c\), and \(a\) and \(b\) respectively. The general conditions for the triclinic system are:

\(a \neq b \neq c\)
\(\alpha \neq \beta \neq \gamma \neq 90^\circ\)

Examples[edit]

One of the most well-known minerals that crystallizes in the triclinic system is microcline, a type of feldspar. Microcline is often found in granite and is known for its distinctive grid-like twinning pattern, known as "tartan twinning".

Symmetry[edit]

The triclinic system has the lowest symmetry of all the crystal systems. It possesses only a single symmetry operation, which is the identity operation. This means that there are no rotational or reflectional symmetries present in the triclinic system.

Related pages[edit]

@@ Line 1: / Line 1: @@
-The '''triclinic''' (or '''anorthic''') '''crystal system''' is one of the 7 crystal systems in crystallography. A crystal system is a geometric classification system used to describe the arrangement of atoms in a crystalline solid. In the triclinic system, the crystal is described by three basis vectors of unequal length, similar to the orthorhombic system. However, the angles between these vectors are all different and none of them are equal to 90 degrees.
+{{Short description|An article about the triclinic crystal system in crystallography}}
+== Overview ==
+The '''triclinic crystal system''' is one of the seven [[crystal system|crystal systems]] in [[crystallography]]. It is the least symmetric of all the crystal systems, characterized by three axes of unequal length that intersect at oblique angles. This system is defined by the absence of any symmetry other than the identity operation.
 == Characteristics ==
+In the triclinic system, the unit cell is defined by three vectors of unequal length, denoted as \(a\), \(b\), and \(c\). The angles between these vectors, \(\alpha\), \(\beta\), and \(\gamma\), are all different and none of them are 90 degrees. This lack of symmetry results in a very flexible and adaptable structure, allowing for a wide variety of crystal shapes.
-Triclinic crystal systems are characterized by the following properties:
+== Crystallographic Axes ==
+[[File:Microcline.jpeg|thumb|right|Microcline, a mineral that crystallizes in the triclinic system]]
-* Three unequal lattice vectors (a, b, and c)
+The axes in the triclinic system are labeled as \(a\), \(b\), and \(c\), with the angles \(\alpha\), \(\beta\), and \(\gamma\) representing the angles between \(b\) and \(c\), \(a\) and \(c\), and \(a\) and \(b\) respectively. The general conditions for the triclinic system are:
-* Angles between the vectors are all different (α, β, and γ) and none are equal to 90 degrees
+* \(a \neq b \neq c\)
-* The simplest triclinic lattice is the primitive triclinic lattice (P), which has lattice points at the corners of the unit cell
+* \(\alpha \neq \beta \neq \gamma \neq 90^\circ\)
-* Triclinic systems have the lowest symmetry among the seven crystal systems, with only two point groups (1 and -1)
-== Bravais Lattices ==
-There is only one Bravais lattice in the triclinic crystal system, the primitive triclinic lattice (P). In this lattice, there is only one lattice point per unit cell, located at the corners.
-== Point Groups ==
-Triclinic crystal systems have two point groups:
-Triclinic Pinacoidal (point group 1): This group has no symmetry operations other than the identity operation.
-Triclinic Pedial (point group -1): This group has inversion symmetry (center of symmetry) as the only operation.
 == Examples ==
+One of the most well-known minerals that crystallizes in the triclinic system is [[microcline]], a type of [[feldspar]]. Microcline is often found in [[granite]] and is known for its distinctive grid-like twinning pattern, known as "[[tartan twinning]]".
-Some minerals that crystallize in the triclinic crystal system include:
+== Symmetry ==
+The triclinic system has the lowest symmetry of all the crystal systems. It possesses only a single symmetry operation, which is the identity operation. This means that there are no rotational or reflectional symmetries present in the triclinic system.
-* Microcline (a type of potassium feldspar)
+== Related pages ==
-* Axinite (a group of calcium aluminum borosilicate minerals)
+* [[Crystal system]]
-* Rhodonite (a manganese inosilicate)
+* [[Crystallography]]
-* Turquoise (a hydrous phosphate of copper and aluminum)
+* [[Microcline]]
-== Comparison with other crystal systems ==
+* [[Feldspar]]
-The triclinic system is unique among the seven crystal systems in that it has the least symmetry and the most general set of lattice parameters. In comparison, the other six crystal systems have more constraints on the lengths and angles of their lattice vectors, resulting in higher symmetry.
-== See also ==
-* [[Crystallography]]
-* [[Crystal system]]
-* [[Orthorhombic crystal system]]
-* [[Monoclinic crystal system]]
-{{stub}}
 [[Category:Crystallography]]
-[[Category:Crystal systems]]
+[[Category:Mineralogy]]
-[[Category:Triclinic crystal system]]