Unit Cell Dimensions

"The unit cell of a mineral is the smallest divisible unit of a mineral that possesses the symmetry and properties of the mineral. It is a small group of atoms, from four to as many as 1000, that have a fixed geometry relative to one another. The atoms are arranged in a "box" with parallel sides called the unit cell which is repeated by simple translations to make up the crystal. The atoms may be at the corners, on the edges, on the faces, or wholly enclosed in the box, and each cell in the crystal is identical. This is what was meant by an "ordered internal arrangement" in our definition of a mineral. It is the reason why crystals have such nice faces, cleavages, and regular properties." (Joe Smyth, University of Colorado)

Crystal System	Unit Cell Volume
Isometric	V = a³
Tetragonal	V = a²c
Hexagonal	V = a²c sin(60°)
Trigonal	V = a²c sin(60°)
Orthorhombic	V = abc
Monoclinic	V = abc sin(β)
Triclinic	V = abc (1- cos² α - cos² β - cos² γ) + 2(cos(α) cos(β) cos(γ))^½

Where a, b, and c are the unit cell axes dimensions and α, β, and γ are the inclination angles of the axes in the unit cell.

Isometric	Tetragonal	Hexagonal Trigonal	Orthorhombic	Monoclinic	Triclinic

Where:
Cell Volume is in Angstroms³
Z is in Formula Units per Cell
Molecular Weight is in grams/mole
Den(Calc) is in grams/cubic centimeter
and 0.60225 is the Avogadro constant / 1.0 x 10²⁴ - note: (10^-8 angstroms/centimeter)³

Unit Cell Dimensions

Unit Cell Dimensions

Definition

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