Pearson symbol

The Pearson symbol, or Pearson notation, is used in crystallography as a means of describing a crystal structure, and was originated by W.B. Pearson. The symbol is made up of two letters followed by a number. For example:

• Diamond structure, cF8
• Rutile structure, tP6

The two (italicised) letters specify the Bravais lattice. The lower case letter specifies the crystal class, and the upper case letter the lattice type. The figure gives the number of the atoms in the unit cell. IUPAC (2005)

Crystal class

a	triclinic
m	monoclinic
o	orthorhombic
t	tetragonal
h	hexagonal and rhombohedral
c	cubic

Lattice type

S,A,B,C	Side face centred
F	All face centred
I	Body centred (from innenzentrierte (German))
R	Rhombohedral
P	Primitive

The letters A, B and C were formerly used instead of S. When the centering had a pair of opposite faces along the X-axis, it was called A-centered. Equivalent centering along the Y- and Z-axes were called B- and C-centered, respectively.

The fourteen possible Bravais lattices are identified by the first two letters:

Crystal class	Lattice symbol	Pearson symbol letters
Triclinic	P	aP
Monoclinic	P	mP
	S	mS
Orthorhombic	P	oP
	S	oS
	F	oF
	I	oI
Tetragonal	P	tP
	I	tI
Hexagonal (and trigonal)	P	hP
Rhombohedral	R	hR
Cubic	P	cP
	F	cF
	I	cI

Pearson symbol and space group

The Pearson symbol does not uniquely identify the space group of a crystal structure, for example both the NaCl structure, (space group Fm3m) and diamond (space group Fd3m) have the same Pearson symbol cF8.

Further reading

• United States Naval Research Laboratory - Pearson symbol (Examples and pictures)