The Pearson symbol, or Pearson notation, is used in
crystallography as a means of describing a
crystal structure
In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystal, crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric pat ...
, and was originated by W. B. Pearson. The symbol is made up of two letters followed by a number. For example:
* Diamond structure, ''cF''8
* Rutile structure, ''tP''6
The two (italicised) letters specify the
Bravais lattice
In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by
: \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n ...
. 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.
[Nomenclature of Inorganic Chemistry IUPAC Recommendations 2005](_blank)
IR-3.4.4, pp. 49–51; IR-11.5, pp. 241–242. IUPAC
The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
.
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[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., .], , 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.
The fourteen possible Bravais lattices are identified by the first two letters:
Pearson symbol and space group
The Pearson symbol does not uniquely identify the
space group
In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it uncha ...
of a crystal structure. For example, both the NaCl structure (space group Fmm) and diamond (space group Fdm) have the same Pearson symbol ''cF''8.
Confusion also arises in the rhombohedral lattice, which is alternatively described in a centred hexagonal (''a'' = ''b'', ''c'', ''α'' = ''β'' = 90°, ''γ'' = 120°) or primitive rhombohedral (''a'' = ''b'' = ''c'', ''α'' = ''β'' = ''γ'') setting. The more commonly used hexagonal setting has 3 translationally equivalent points per unit cell. The Pearson symbol refers to the hexagonal setting in its letter code (''hR''), but the following figure gives the number of translationally equivalent points in the primitive rhombohedral setting. Examples: ''hR''1 and ''hR''2 are used to designate the Hg and Bi structures respectively.
Because there are many possible structures that can correspond to one Pearson symbol, a prototypical compound may be useful to specify.
Examples of how to write this would be ''hP''12-MgZn
or ''cF''8-C. Prototypical compounds for particular structures can be found on the
Inorganic Crystal Structure Database
Inorganic Crystal Structure Database (ICSD) is a chemical database founded in 1978 by Günter Bergerhoff (University of Bonn) and I. D. Brown (University of McMaster, Canada). It is now produced by FIZ Karlsruhe in Europe and the U.S. National I ...
(ICSD) or on the AFLOW Library of Crystallographic Prototypes.
Caution
The Pearson symbol should only be used to designate simple structures (elements, some binary compound) where the number of atoms per unit cell equals, ideally, the number of translationally equivalent points.
References
External Links
*
*{{cite web, url=http://www.aflow.org/prototype-encyclopedia/, title=AFLOW Library of Crystallographic Prototypes, accessdate=13 December 2022
Further reading
United States Naval Research Laboratory - Pearson symbol (Examples and pictures)
Crystallography