The Pearson symbol, or Pearson notation, is used in

crystallography Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the Ancient Greek word (; "clear ice, rock-crystal"), and (; "to write"). In J ...

as a means of describing a

crystal structure In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that repeat ...

. It was originated by

William Burton Pearson William is a masculine given name of Germanic origin. It became popular in England after the Norman conquest in 1066,All Things William"Meaning & Origin of the Name"/ref> and remained so throughout the Middle Ages and into the modern era. It is ...

and is used extensively in Pearson's handbook of crystallographic data for intermetallic phases. The symbol is made up of two letters followed by a number. For example: *

Diamond Diamond is a Allotropes of carbon, solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Diamond is tasteless, odourless, strong, brittle solid, colourless in pure form, a poor conductor of e ...

structure, cF8 *

Rutile Rutile is an oxide mineral composed of titanium dioxide (TiO2), the most common natural form of TiO2. Rarer polymorphs of TiO2 are known, including anatase, akaogiite, and brookite. Rutile has one of the highest refractive indices at vis ...

structure, tP6

Construction

The two letters in the Pearson symbol 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 ...

, and more specifically, the lower-case letter specifies the

crystal family In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices (an infinite array of discrete points). Space groups (symmetry groups ...

, while the upper-case letter the lattice type. The number at the end of the Pearson symbol gives the number of the atoms in the conventional

unit cell In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector In mathematics, a unit vector i ...

(atoms which satisfy

1 > x,y,z \geq 0

for the atom's position

(x,y,z)

in the unit cell).Nomenclature of Inorganic Chemistry IUPAC Recommendations 2005
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 ...

. The following two tables give the six letters possible for the crystal family and the five letters posible for the lattice type:

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 a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that ...

of a crystal structure. For example, both the NaCl structure (space group Fmm) and diamond (space group Fdm) have the same Pearson symbol cF8. Due to this constraint, 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. 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: hR1 and hR2 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 hP12-MgZn

_2

or cF8-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 at the University of Bonn in Germany and I. D. Brown at McMaster University in Canada. It is now produced by FIZ Karlsruhe in Europe and t ...

(ICSD) or on the AFLOW Library of Crystallographic Prototypes.

References

External links

* *{{cite web, url=http://www.aflow.org/prototype-encyclopedia/, title=AFLOW Library of Crystallographic Prototypes, accessdate=13 December 2022

Construction

Pearson symbol and space group

See also

References

External links

Further reading