194:
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.
523:
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.
58:. 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.
149:
583:
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.,
462:) 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 (
477:
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
505:
568:
780:
697:
Hicks, David; Mehl, Michael J.; Esters, Marco; Oses, Corey; Levy, Ohad; Hart, Gus L. W.; Toher, Cormac; Curtarolo, Stefano (2021).
649:
Hicks, David; Mehl, Michael J.; Gossett, Eric; Toher, Cormac; Levy, Ohad; Hanson, Robert M.; Hart, Gus; Curtarolo, Stefano (2019).
466:), but the following figure gives the number of translationally equivalent points in the primitive rhombohedral setting. Examples:
552:
W. B. Pearson, "A Handbook of
Lattice Spacings and Structures of Metals and Alloys", Vol. 2, Pergamon Press, Oxford, 1967.
512:
588:
601:
Mehl, Michael J.; Hicks, David; Toher, Cormac; Levy, Ohad; Hanson, Robert M.; Hart, Gus; Curtarolo, Stefano (2017).
35:, and was originated by W. B. Pearson. The symbol is made up of two letters followed by a number. For example:
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Confusion also arises in the rhombohedral lattice, which is alternatively described in a centred hexagonal (
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United States Naval
Research Laboratory - Pearson symbol (Examples and pictures)
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The fourteen possible
Bravais lattices are identified by the first two letters:
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of a crystal structure. For example, both the NaCl structure (space group Fm
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8-C. Prototypical compounds for particular structures can be found on the
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515:(ICSD) or on the AFLOW Library of Crystallographic Prototypes.
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2 are used to designate the Hg and Bi structures respectively.
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Nomenclature of
Inorganic Chemistry IUPAC Recommendations 2005
699:"The AFLOW Library of Crystallographic Prototypes: Part 3"
651:"The AFLOW Library of Crystallographic Prototypes: Part 2"
603:"The AFLOW Library of Crystallographic Prototypes: Part 1"
117:
Centring type + number of translation equivalent points
567:; IR-3.4.4, pp. 49–51; IR-11.5, pp. 241–242.
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760:"AFLOW Library of Crystallographic Prototypes"
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54:The two (italicised) letters specify the
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16:Means of describing a crystal structure
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513:Inorganic Crystal Structure Database
438:= 120°) or primitive rhombohedral (
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174:Rhombohedral centring (see below)
407:m) have the same Pearson symbol
726:10.1016/j.commatsci.2021.110450
703:Computational Materials Science
677:10.1016/j.commatsci.2018.10.043
655:Computational Materials Science
629:10.1016/j.commatsci.2017.01.017
607:Computational Materials Science
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403:m) and diamond (space group Fd
391:Pearson symbol and space group
1:
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534:Strukturbericht designation
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31:as a means of describing a
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210:Pearson-symbol letters
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136:One side/face centred
70:triclinic = anorthic
500:{\displaystyle _{2}}
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147:Body-centred (from
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39:Diamond structure,
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46:Rutile structure,
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185:All faces centred
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661:: S1-S1011.
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18:
765:13 December
750:13 December
682:13 December
634:13 December
613:: S1-S828.
397:space group
94:tetragonal
78:monoclinic
716:2012.05961
709:: 110450.
668:1806.07864
620:1806.07864
540:References
302:Tetragonal
228:Monoclinic
133:S, A, B, C
102:hexagonal
327:Hexagonal
215:Triclinic
150:‹See Tfd›
125:Primitive
790:Category
528:See also
519:Caution
481:12-MgZn
434:= 90°,
587:
470:1 and
154:German
110:cubic
711:arXiv
663:arXiv
615:arXiv
569:IUPAC
352:Cubic
23:, or
767:2022
752:2022
684:2022
636:2022
585:ISBN
19:The
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625:doi
611:136
507:or
411:8.
792::
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623:.
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605:.
576:^
557:^
509:cF
479:hP
472:hR
468:hR
464:hR
458:=
454:=
450:,
446:=
442:=
430:=
426:,
422:,
418:=
409:cF
383:cI
371:cF
359:cP
346:hR
334:hP
321:tI
309:tP
296:oI
284:oF
272:oS
260:oP
247:mS
235:mP
222:aP
188:4
177:3
166:2
156::
139:2
128:1
48:tP
41:cF
769:.
754:.
729:.
723::
713::
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665::
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627::
617::
591:.
571:.
493:2
460:γ
456:β
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448:c
444:b
440:a
436:γ
432:β
428:α
424:c
420:b
416:a
405:3
401:3
379:I
367:F
355:P
342:R
330:P
317:I
305:P
292:I
280:F
268:S
256:P
243:S
231:P
218:P
182:F
171:R
163:)
159:i
144:I
122:P
107:c
99:h
91:t
83:o
75:m
67:a
50:6
43:8
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