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.^[1] 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 family, and the upper-case letter the centering type. The number at the end of the Pearson symbol gives the number of the atoms in the conventional unit cell.^[2]

Crystal family
a	triclinic = anorthic
m	monoclinic
o	orthorhombic
t	tetragonal
h	hexagonal
c	cubic

Centring type + number of translation equivalent points
P	Primitive	1
S, A, B, C	One side/face centred	2
I	Body-centred (from German: innenzentriert)^[3]	2
R	Rhombohedral centring (see below)	3
F	All faces centred	4

The letters A, B and C were formerly used instead of S. When the centred face cuts the X axis, the Bravais lattice is called A-centred. In analogy, when the centred face cuts the Y or Z axis, we have B- or C-centring respectively.^[3]

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

Crystal family	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	P	hP
	R	hR
Cubic	P	cP
	F	cF
	I	cI

^ W. B. Pearson, "A Handbook of Lattice Spacings and Structures of Metals and Alloys", Vol. 2, Pergamon Press, Oxford, 1967.
^ Nomenclature of Inorganic Chemistry IUPAC Recommendations 2005; IR-3.4.4, pp. 49–51; IR-11.5, pp. 241–242. IUPAC.
^ ^a ^b Page 124 in chapter 3. "Crystallography: Internal order and symmetry" in Cornelius Klein & Cornelius S. Hurlbut, Jr.: "Manual of Mineralogy", 21st edition, 1993, John Wiley & Sons, Inc., ISBN 0-471-59955-7.

[1] W. B. Pearson, "A Handbook of Lattice Spacings and Structures of Metals and Alloys", Vol. 2, Pergamon Press, Oxford, 1967.

[IUPAC-2] Nomenclature of Inorganic Chemistry IUPAC Recommendations 2005; IR-3.4.4, pp. 49–51; IR-11.5, pp. 241–242. IUPAC.

[Klein_&_Hurlbut-3] Page 124 in chapter 3. "Crystallography: Internal order and symmetry" in Cornelius Klein & Cornelius S. Hurlbut, Jr.: "Manual of Mineralogy", 21st edition, 1993, John Wiley & Sons, Inc., ISBN 0-471-59955-7.

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