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:

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) [2]

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
FAll face centred
IBody centred (from innenzentrierte (German))[3]
RRhombohedral
PPrimitive

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.[3]

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

Crystal classLattice symbolPearson symbol letters
TriclinicPaP
Monoclinic P mP
S mS
Orthorhombic PoP
SoS
FoF
IoI
Tetragonal PtP
ItI
Hexagonal (and trigonal) PhP
Rhombohedral RhR
CubicPcP
FcF
IcI

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.

References

  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
  3. ↑ 3.0 3.1 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

Further reading