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Pearson symbol

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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 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
F All face centred
I Body centred (from innenzentrierte (German))[3]
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.[3]

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.

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. ^ 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

Further reading

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