Cubic crystal system

In crystallography, the cubic (or isometric) crystal system is a special way that crystals can form. In this system, the basic shape, called the unit cell, looks like a cube. This is one of the most common shapes for real crystals and minerals.

A rock containing three crystals of pyrite (FeS2). The crystal structure of pyrite is primitive cubic, and this is reflected in the cubic symmetry of its natural crystal facets.

There are three main types of cubic crystals. The first is called primitive cubic, also known as simple cubic. The second type is body-centered cubic, which has atoms in the middle of the cube and at the corners. The third type is face-centered cubic, where atoms are at the corners and the centers of each face of the cube.

Even though these crystals are described using cubes, the small parts that repeat to make the crystal, called primitive unit cells, might not always look like perfect cubes. This system helps scientists learn how atoms are arranged in many everyday materials.

Bravais lattices

Further information: Bravais lattice

The cubic crystal system has three main types of patterns called Bravais lattices.

primitive cell of BCC lattice

The primitive cubic lattice (cP) has points only at the corners of the cube. Each point is shared among eight cubes.

The body-centered cubic lattice (cI) adds a point in the middle of the cube.

primitive translations of FCC lattice

The face-centered cubic lattice (cF) adds points to the centers of each face of the cube.

These lattices have different ways of arranging atoms.

Bravais lattice	Primitive cubic	Body-centered cubic	Face-centered cubic
Pearson symbol	cP	cI	cF
Unit cell

Crystal classes

Further information: Crystallographic point group

The isometric crystal system has special names for how crystals can be arranged. These names are written in different ways, such as Schönflies notation, Hermann–Mauguin notation, orbifold, and Coxeter notation. There are 36 different ways these cubic shapes can be organized, and they are shown in a table.

Other names for this system include normal class, holohedral, and galena type.

No.	Point group					Type	Example	Space groups
No.	Name	Schön.	Intl	Orb.	Cox.	Type	Example	Primitive	Face-centered	Body-centered
195–197	Tetartoidal	T	23	332	[3,3]⁺	enantiomorphic	Ullmannite, Sodium chlorate	P23	F23	I23
198–199	Tetartoidal	T	23	332	[3,3]⁺	enantiomorphic	Ullmannite, Sodium chlorate	P2₁3		I2₁3
200–204	Diploidal	T_h	m3 (2/m 3)	3*2	[3⁺,4]	centrosymmetric	Pyrite	Pm3, Pn3	Fm3, Fd3	I3
205–206	Diploidal	T_h	m3 (2/m 3)	3*2	[3⁺,4]	centrosymmetric	Pyrite	Pa3		Ia3
207–211	Gyroidal	O	432	432	[3,4]⁺	enantiomorphic	Petzite	P432, P4₂32	F432, F4₁32	I432
212–214	Gyroidal	O	432	432	[3,4]⁺	enantiomorphic	Petzite	P4₃32, P4₁32		I4₁32
215–217	Hextetrahedral	T_d	43m	*332	[3,3]		Sphalerite	P43m	F43m	I43m
218–220	Hextetrahedral	T_d	43m	*332	[3,3]		Sphalerite	P43n	F43c	I43d
221–230	Hexoctahedral	O_h	m3m (4/m 3 2/m)	*432	[3,4]	centrosymmetric	Galena, Halite	Pm3m, Pn3n, Pm3n, Pn3m	Fm3m, Fm3c, Fd3m, Fd3c	Im3m, Ia3d

Single element structures

Atoms in solids usually stick together tightly. The simplest cubic shape, called primitive cubic, has very few atoms and is rare in nature. It is found in a material called polonium.

Two other cubic shapes, called body-centered cubic (bcc) and face-centered cubic (fcc), have more atoms and are found often in nature. Examples of bcc include iron, chromium, tungsten, and niobium. Examples of fcc include aluminium, copper, gold, and silver.

Another important cubic shape is the diamond cubic structure. It is seen in materials like carbon, silicon, germanium, and tin.

Multi-element structures

Compounds that have more than one kind of building block, like binary compounds, often form shapes based on the cubic crystal system. These shapes can be seen as two or more sets of points that fit together, with each set in the spaces of the others.

Caesium chloride structure

One common structure is called the "caesium chloride" or B2 structure. It looks like a body-centered cubic shape but is made of two different kinds of atoms. In this structure, moving in one direction changes the type of atom you see. You can think of it as two simple cubic shapes stacked on top of each other, one for each kind of atom. In caesium chloride, each atom is surrounded by eight atoms of the other kind, forming a cube around it.

This structure is found in some compounds made from alkali metals under special conditions. It is common when the two kinds of atoms are about the same size.

Rock-salt structure

Another common structure is the rock-salt structure, named after table salt. Here, each kind of atom forms its own shape, and the two shapes fit together like a 3D checkerboard. Each atom is surrounded by six atoms of the other kind, arranged like the points of a star.

This graphic shows the interlocking simple cubic lattices of cesium and chlorine. You can see them separately and as they are interlocked in what looks like a body-centered cubic arrangement

Fluorite structure

Main article: Fluorite structure

The fluorite structure is similar to the rock-salt structure but has twice as many of one kind of atom compared to the other.

Zincblende structure

The zincblende structure is named after a mineral form of zinc sulfide. In this structure, each atom is surrounded by four atoms of the other kind, arranged like the points of a pyramid. This structure is also found in many important materials used in electronics.

This group is also known as the II-VI family of compounds.

A zincblende unit cell

This group is also known as the III-V family of compounds.

Heusler structure

Main article: Heusler compound

The Heusler structure is a common way for three different elements to arrange themselves, especially when one of them is a transition metal.

Iron monosilicide structure

The iron monosilicide structure has a special twisty shape and is found in some compounds made from transition metals and silicon or germanium.

Copper halides with the zincblende structure
	Fluorides	Chlorides	Bromides	Iodides
Copper	Copper(I) fluoride	Copper(I) chloride	Copper(I) bromide	Copper(I) iodide

Beryllium and Group 12 chalcogenides with the zincblende structure
	Sulfides	Selenides	Tellurides	Polonides
Beryllium	Beryllium sulfide	Beryllium selenide	Beryllium telluride	Beryllium polonide
Zinc	Zinc sulfide	Zinc selenide	Zinc telluride	Zinc polonide
Cadmium	Cadmium sulfide	Cadmium selenide	Cadmium telluride	Cadmium polonide
Mercury	Mercury sulfide	Mercury selenide	Mercury telluride	–

Group 13 pnictogenides with the zincblende structure
	Nitrides	Phosphides	Arsenides	Antimonides
Boron	Boron nitride*	Boron phosphide	Boron arsenide	Boron antimonide
Aluminium	Aluminium nitride*	Aluminium phosphide	Aluminium arsenide	Aluminium antimonide
Gallium	Gallium nitride*	Gallium phosphide	Gallium arsenide	Gallium antimonide
Indium	Indium nitride*	Indium phosphide	Indium arsenide	Indium antimonide

Transition metal silicides and germanides with the FeSi structure
	Silicides	Germanides
Chromium	Chromium(IV) silicide	Chromium(IV) germanide
Manganese	Manganese monosilicide	Manganese germanide
Iron	Iron monosilicide	Iron germanide
Cobalt	Cobalt monosilicide	Cobalt germanide

Weaire–Phelan structure

A Weaire–Phelan structure has a special balance and shape. It is made from three different ways of stacking tetradecahedrons with pyritohedral shapes in between. You can find this pattern in chemistry, where it is called a "type I clathrate structure". Some gases like methane, propane, and carbon dioxide form structures where water molecules are connected by hydrogen bonded links, and the gas molecules fit into the special shapes of this structure.