Triclinic System

The triclinic system is the least symmetric of the seven crystal systems, characterized by a complete lack of mirror planes or rotational axes. In this geometry, all three crystallographic axes are of unequal length and intersect at oblique angles, meaning no two axes are perpendicular to one another.

Key Characteristics & Symmetry

From a symmetry standpoint, the triclinic system only possesses translational symmetry and, in some cases, inversion symmetry (a center of symmetry). Because of this high degree of asymmetry, it is the only system that allows just a single Bravais lattice: the primitive ($P$) lattice.

Physical properties in triclinic crystals—such as thermal expansion or electrical conductivity—are highly anisotropic, meaning they vary significantly depending on the direction in which they are measured.

Lattice Parameters

To define a triclinic unit cell, all six parameters must be specified independently:

• Axial lengths: $a \neq b \neq c$
• Interaxial angles: $\alpha \neq \beta \neq \gamma \neq 90^\circ$

Common Examples

• Microcline: A common potassium feldspar.
• Turquoise: A hydrated phosphate of copper and aluminum.
• Kyanite: An aluminosilicate mineral noted for its distinct blue color.
• Copper(II) Sulfate Pentahydrate ($CuSO_4 \cdot 5H_2O$): A well-known laboratory chemical.