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
  1. ^ W. B. Pearson, "A Handbook of Lattice Spacings and Structures of Metals and Alloys", Vol. 2, Pergamon Press, Oxford, 1967.
  2. ^ Nomenclature of Inorganic Chemistry IUPAC Recommendations 2005; IR-3.4.4, pp. 49–51; IR-11.5, pp. 241–242. IUPAC.
  3. ^ 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.