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 centering type. The number at the end of the Pearson symbol gives the number of the atoms in the conventional unit cell.[2]
Crystal family
a
triclinic = anorthic
m
monoclinic
o
orthorhombic
t
tetragonal
h
hexagonal
c
cubic
Centring type + number of translation equivalent points
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:
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.
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.[2] Examples of how to write this would be hP12-MgZn or cF8-C. Prototypical compounds for particular structures can be found on the Inorganic Crystal Structure Database (ICSD) or on the AFLOW Library of Crystallographic Prototypes.[4][5][6]
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
^W. B. Pearson, "A Handbook of Lattice Spacings and Structures of Metals and Alloys", Vol. 2, Pergamon Press, Oxford, 1967.
^ abNomenclature of Inorganic Chemistry IUPAC Recommendations 2005; IR-3.4.4, pp. 49–51; IR-11.5, pp. 241–242. IUPAC.
^ abPage 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., ISBN0-471-59955-7.
^Mehl, Michael J.; Hicks, David; Toher, Cormac; Levy, Ohad; Hanson, Robert M.; Hart, Gus; Curtarolo, Stefano (2017). "The AFLOW Library of Crystallographic Prototypes: Part 1". Computational Materials Science. 136: S1-S828. doi:10.1016/j.commatsci.2017.01.017. Retrieved 13 December 2022.
^Hicks, David; Mehl, Michael J.; Gossett, Eric; Toher, Cormac; Levy, Ohad; Hanson, Robert M.; Hart, Gus; Curtarolo, Stefano (2019). "The AFLOW Library of Crystallographic Prototypes: Part 2". Computational Materials Science. 161: S1-S1011. doi:10.1016/j.commatsci.2018.10.043. Retrieved 13 December 2022.
^Hicks, David; Mehl, Michael J.; Esters, Marco; Oses, Corey; Levy, Ohad; Hart, Gus L. W.; Toher, Cormac; Curtarolo, Stefano (2021). "The AFLOW Library of Crystallographic Prototypes: Part 3". Computational Materials Science. 199: 110450. doi:10.1016/j.commatsci.2021.110450. Retrieved 13 December 2022.
External Links
"Inorganic crystal structure database (ICSD)". Retrieved 13 December 2022.
"AFLOW Library of Crystallographic Prototypes". Retrieved 13 December 2022.
Further reading
January 20, 2023
pearson, symbol, pearson, notation, used, crystallography, means, describing, crystal, structure, originated, pearson, symbol, made, letters, followed, number, example, diamond, structure, rutile, structure, tp6the, italicised, letters, specify, bravais, latti. 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 tP6The two italicised letters specify the Bravais lattice 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 2 Crystal family a triclinic anorthicm monoclinico orthorhombict tetragonalh hexagonalc cubicCentring type number of translation equivalent points P Primitive 1S A B C One side face centred 2I Body centred from German innenzentriert 3 2R Rhombohedral centring see below 3F All faces centred 4The 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 lettersTriclinic P aPMonoclinic P mPS mSOrthorhombic P oPS oSF oFI oITetragonal P tPI tIHexagonal P hPR hRCubic P cPF cFI cIContents 1 Pearson symbol and space group 2 Caution 3 References 4 External Links 5 Further readingPearson symbol and space group EditThe Pearson symbol does not uniquely identify the space group of a crystal structure For example both the NaCl structure space group Fm3 m and diamond space group Fd3 m have the same Pearson symbol cF8 Confusion also arises in the rhombohedral lattice which is alternatively described in a centred hexagonal a b c a b 90 g 120 or primitive rhombohedral a b c a b g 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 2 Examples of how to write this would be hP12 MgZn2 displaystyle 2 or cF8 C Prototypical compounds for particular structures can be found on the Inorganic Crystal Structure Database ICSD or on the AFLOW Library of Crystallographic Prototypes 4 5 6 Caution EditThe 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 Edit W B Pearson A Handbook of Lattice Spacings and Structures of Metals and Alloys Vol 2 Pergamon Press Oxford 1967 a b Nomenclature of Inorganic Chemistry IUPAC Recommendations 2005 IR 3 4 4 pp 49 51 IR 11 5 pp 241 242 IUPAC a b Page 124 in chapter 3 Crystallography Internal order and symmetry in Cornelius Klein amp Cornelius S Hurlbut Jr Manual of Mineralogy 21st edition 1993 John Wiley amp Sons Inc ISBN 0 471 59955 7 Mehl Michael J Hicks David Toher Cormac Levy Ohad Hanson Robert M Hart Gus Curtarolo Stefano 2017 The AFLOW Library of Crystallographic Prototypes Part 1 Computational Materials Science 136 S1 S828 doi 10 1016 j commatsci 2017 01 017 Retrieved 13 December 2022 Hicks David Mehl Michael J Gossett Eric Toher Cormac Levy Ohad Hanson Robert M Hart Gus Curtarolo Stefano 2019 The AFLOW Library of Crystallographic Prototypes Part 2 Computational Materials Science 161 S1 S1011 doi 10 1016 j commatsci 2018 10 043 Retrieved 13 December 2022 Hicks David Mehl Michael J Esters Marco Oses Corey Levy Ohad Hart Gus L W Toher Cormac Curtarolo Stefano 2021 The AFLOW Library of Crystallographic Prototypes Part 3 Computational Materials Science 199 110450 doi 10 1016 j commatsci 2021 110450 Retrieved 13 December 2022 External Links Edit Inorganic crystal structure database ICSD Retrieved 13 December 2022 AFLOW Library of Crystallographic Prototypes Retrieved 13 December 2022 Further reading EditUnited States Naval Research Laboratory Pearson symbol Examples and pictures Retrieved from https en wikipedia org w index php title Pearson symbol amp oldid 1127223674, wikipedia, wiki, book, books, library,
