The triclinic crystal system is one of the seven fundamental lattice systems used to classify crystalline solids. It is the most general and least symmetric of the seven: the three unit-cell edges have different lengths and the three interaxial angles are all unequal and not constrained to 90 degrees. Because of this lack of orthogonality and equality, triclinic crystals often appear skewed or 'leaning' rather than boxlike.
Unit cell and defining characteristics
In the triclinic system the unit cell is described by three unequal vectors a, b and c and three independent angles α, β and γ. None of the angles is required to be a right angle, and the only requirement is that they are not all equal in the special ways that define higher-symmetry systems. The triclinic lattice therefore allows the most general parallelepiped as its repeating unit.
- Axes: a ≠ b ≠ c
- Angles: α ≠ β ≠ γ (none necessarily 90°)
- Bravais lattice: only the primitive (P) lattice occurs in this system
Symmetry and space groups
The triclinic system has very limited symmetry. There are two triclinic crystal classes: one with only the identity operation (often written P1) and one that includes an inversion center (written P-1). These correspond to two space groups in three-dimensional crystallography. Because symmetry operations are minimal, triclinic crystals do not exhibit rotational axes of order greater than one or mirror planes that relate the three axes.
Occurrence, examples and uses
Triclinic symmetry appears in a variety of minerals and laboratory-grown salts. A commonly cited example is copper sulfate pentahydrate, which forms characteristic triclinic crystals under many conditions. Some feldspars and other rock-forming minerals also adopt triclinic structures. The generality of the triclinic lattice makes it important for crystallographers: many low-symmetry distortions of higher-symmetry phases are described by triclinic unit cells.
For a visual overview of crystal systems, including triclinic geometry, see crystal system diagrams. For specific examples and crystal data, consult resources on mineral structures such as the copper sulfate example illustrated here.
Notable distinctions: because triclinic cells lack perpendicular axes and repeated equalities, their diffraction patterns and symmetry analyses are more complex than those of cubic or orthorhombic systems. The name "triclinic" reflects the three unequal, oblique directions that define the cell, and it serves as the baseline, lowest-symmetry category in crystallographic classification.