ThePearson symbol, orPearson notation, is used incrystallography as a means of describing acrystal structure.^[1] It was originated byWilliam Burton Pearson and is used extensively in Pearson's handbook of crystallographic data for intermetallic phases.^[2] The symbol is made up of two letters followed by a number. For example:

• Diamond structure, cF8
• Rutile structure, tP6

The two letters in the Pearson symbol specify theBravais lattice, and more specifically, the lower-case letter specifies thecrystal family, while the upper-case letter thelattice type.^[3] The number at the end of the Pearson symbol gives the number of the atoms in the conventionalunit cell (atoms which satisfy${\displaystyle 1>x,y,z\ge 0}$ for the atom's position${\displaystyle (x,y,z)}$ in the unit cell).^[4] The following two tables give the six letters possible for the crystal family and the five letters possible 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.^[5]

The fourteen possibleBravais lattices are identified by the first two letters:

The Pearson symbol does not uniquely identify thespace 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. 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.^[4] Examples of how to write this would be hP12-MgZn${\displaystyle {}_2}$ or cF8-C. Prototypical compounds for particular structures can be found on theInorganic Crystal Structure Database (ICSD) or on the AFLOW Library of Crystallographic Prototypes.^[6][7][8]

• Crystal structure
• Bravais lattice
• Strukturbericht designation

• "Inorganic crystal structure database (ICSD)". Retrieved13 December 2022.
• "AFLOW Library of Crystallographic Prototypes". Retrieved13 December 2022.

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

• Crystallography

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