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 bravais lattice. the lower case letter specifies the crystal family, and the upper case letter the centring type. the number at the end of the pearson symbol gives the number of the atoms in the conventional unit cell. iupac (2005) [2]

    crystal family
    a triclinic = anorthic
    m monoclinic
    o orthorhombic
    t tetragonal
    h hexagonal
    c cubic
    centring type + number of translation equivalent points
    p primitive 1
    s,a,b,c one side/face centred 2
    i body centred (from innenzentriert (in german))[3] 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.[3]

    the fourteen possible bravais lattices are identified by the first two letters:

    crystal family 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 p hp
    r hr
    cubic p cp
    f cf
    i ci
  • pearson symbol and space group
  • caution
  • references
  • further reading

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 Bravais lattice. The lower case letter specifies the crystal family, and the upper case letter the centring type. The number at the end of the Pearson symbol gives the number of the atoms in the conventional unit cell. IUPAC (2005) [2]

Crystal family
a triclinic = anorthic
m monoclinic
o orthorhombic
t tetragonal
h hexagonal
c cubic
Centring type + number of translation equivalent points
P Primitive 1
S,A,B,C One side/face centred 2
I Body centred (from innenzentriert (in German))[3] 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.[3]

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

Crystal family 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 P hP
R hR
Cubic P cP
F cF
I cI