Strukturbericht designation

In crystallography, a Strukturbericht designation or Strukturbericht type is a system of detailed crystal structure classification by analogy to another known structure. The designations were intended to be comprehensive but are mainly used as supplement to space group crystal structures designations, especially historically.[1][2] Each Strukturbericht designation is described by a single space group, but the designation includes additional information about the positions of the individual atoms, rather than just the symmetry of the crystal structure. While Strukturbericht symbols exist for many of the earliest observed and most common crystal structures, the system is not comprehensive, and is no longer being updated. Modern databases such as Inorganic Crystal Structure Database index thousands of structure types directly by the prototype compound (i.e. "the NaCl structure" instead of "the B1 structure").[3] These are essentially equivalent to the old Stukturbericht designations.

History

The designations were established by the journal Zeitschrift für Kristallographie – Crystalline Materials, which published its first round of supplemental reviews under the name Strukturbericht from 1913-1928.[4] These reports were collected into a book published in 1931 by Paul Peter Ewald and Carl Hermann which became Volume 1 of Strukturbericht.[5] While the series was continued after the war under the name Structure reports, which was published through 1990,[6] the series stopped generating new symbols. Instead, some new additional designations were given in books by Smithels,[7] and Pearson.[8]

For the first volume, the designation consisted of a capital letter (A,B,C,D,E,F,G,H,L,M,O) specifying a broad category of compounds, and then a number to specify a particular crystal structure. In the second volume, subscript numbers were added, some early symbols were modified (e.g. what was initially D1 became D0₁, D2 became D0₂, etc.), and the categories were modified (types I,K,S were added). In the third volume, the class I was renamed J. Later designations began to use a lower case letter in subscripts as well.[9]

A-compounds

The 'A' compounds are reserved for structures made up of atoms of all the same chemical element.

A compounds
Strukturbericht designation	Prototype	Space group	Description
A1	Cu	Fm3m	Cubic close-packed structure (also: Face-centered cubic structure)
A2	W	Im3m	Body-centered cubic structure
A3	Mg	P6₃/mmc	Hexagonal close-packed structure
A3'	α-La	P6₃/mmc	α-La structure (ABAC Barlow packing)
A4	C (diamond)	Fd3m	Diamond cubic structure
A5	β-Sn	I4₁/amd
A6	Indium	I4/mmm	Indium structure
A7	α-As	R3m
A8	gray Se	P3₁21	Also called γ-Se, but that term is also used for a monoclinic form.
A9	C (graphite)	P6₃/mmc	Hexagonal graphite structure
A10	α-Hg	R3m
A11	α-Ga	Cmca	α-Gallium structure
A12	α-Mn	I43m	α-Manganese structure
A13	β-Mn	P4₁32	β-Manganese structure
A14	I₂	Cmca	Molecular iodine structure
A15	β-W	Pm3n	Weaire–Phelan structure
A16	α-S	Fddd
A17	P	Cmca	Black phosphorus structure
A18	Cl	P4₂/ncm	Incorrect structure[10]
A19 -> A_i, A_h	Po (incorrectly)	C2
A20	α-U	Cmcm
A_a	α-Pa	I4/mmm
A_b	β-U	P4₂/mnm	σ phase
A_c	α-Np	Pnma
A_d	β-Np	P4/nmm
A_f	γ-HgSn_6-10	P6/mmm
A_g	B	P4₂/nnm
A_h	α-Po	Pm3m	Simple cubic structure
A_i	β-Po	R3m
A_k	γ-monoclinic Se	P2₁/c
A_l	β-monoclinic Se	P2₁/c

B-compounds

'B' designates compounds of two elements with equal numbers of atoms.

B compounds
Strukturbericht designation	Prototype	Space group	Description
B1	NaCl	Fm3m	Rock salt structure
B2	CsCl	Pm3m	caesium chloride structure
B3	ZnS	F43m	Zincblende structure
B4	ZnS	P6₃mc	Wurtzite crystal structure
B5	4H SiC	P6₃mc	Moissanite (4H polytype) structure
B6	6H SiC	P6₃mc	Moissanite(6H polytype) structure
B7	Si-C 15R	R3m	15R-SiC structure
B8 -> B8₁
B8₁	NiAs	P6₃/mmc	Nickeline structure
B8₂	Ni₂In	P6₃/mmc
B9	α-HgS	P3₂21	Cinnabar structure
B10	PbO	P4/nmm	Lead(II) oxide/Litharge structure
B11	γ-CuTi	P4/nmm
B12 -> B_k	BN (incorrectly)[11]	P6₃mc	Originally reported boron nitride structure
B13	β-NiS	R3m	β-Nickel sulfide/Millerite structure
B14	FeAs	Pnma	Westerveldite structure
B15 -> B27
B16	GeS	Pnma	Germanium(II) sulfide/Herzenbergite structure
B17	PtS	P4₂/mmc	Platinum(II) sulfide/Cooperite structure
B18	CuS	P6₃/mmc	Copper monosulfide/Covellite structure
B19	β′-AuCd	Pmma	The martensitic β′-AuCd structure
B20	FeSi	P2₁3	FeSi/Fersilicite structure
B21	α-CO	P2₁3	α-Carbon monoxide structure
B24	TlF-II (incorrectly)[12]	Fmmm	Originally reported Thallium(I) fluoride structure
B26	CuO	C2/c	Copper(II) oxide/Tenorite structure
B27	FeB	Pnma	Iron boride structure
B28 -> B20
B29 -> B16	SnS (incorrectly)	Pnma	Tin(II) sulfide structure
B30	MgZn	Imm2
B31 -> B14	MnP	Pnma
B32	NaTl	Fd3m
B33	CrB	Cmcm	Chromium(III) boride structure
B34	PdS	P4₂/m	Palladium(II) sulfide structure
B35	CoSn	P6/mmm
B37	SeTl	I4/mcm
B_a	CoU	I2₁3
B_b	ζ-AgZn	P3
B_c -> B33	CaSi	Cmcm
B_d	η-NiSi
B_e	CdSb	Pbca
B_f -> B33	CrB		(duplicate of B33)
B_g	MoB	I4₁/amd	Molybdenum boride structure
B_h	WC	P6m2	Tungsten carbide structure
B_i	AsTi	P6₃/mmc
B_k	BN	P6₃/mmc	Boron nitride structure
B_l	AsS
B_m	TiB

C-compounds

'C' designates compounds of the stoichiometry AB₂.

C compounds
Strukturbericht designation	Prototype	Space group	Description
C1	CaF₂	Fm3m	Fluorite structure
C1_b	AgAsMg	F43m	Half Heusler structure
C2	FeS₂	Pa3	Pyrite structure
C3	Cu₂O	Pn3m	Cuprite structure
C4	TiO₂	P4₂mnm	Rutile structure
C5	TiO₂	I4₁/amd	Anatase structure
C6	CdI₂	P3m1	Cadmium iodide structure
C7	MoS₂	P6₃/mmc	Molybdenum disulfide structure
C8	β-SiO₂	P6₂22	β-Quartz structure
C9	β-Cristobalite	Fd3m	Idealized β-Cristobalite structure
C10	β-Tridymite	P6₃/mmc	β-Tridymite structure
C11 -> C11_a,C11_b
C11_a	CaC₂	I4/mmm
C11_b	MoSi₂	I4/mmm	Molybdenum disilicide structure
C12	CaSi₂
C13	HgI₂	P4₂/nmc	Coccinite structure
C14	MgZn₂	P6₃/mmc	MgZn₂ Laves phase
C15	MgCu₂	Fd3m	MgCu₂ Laves phase
C15_b	AuBe₅	F43m
C16	CuAl₂	I4/mcm	Khatyrkite structure
C18	FeS₂	Pnnm	Marcasite structure
C19	α-Sm	R3	α-Samarium structure (ABCBCACAB Barlow packing)
C21	TiO₂	Pbca	Brookite structure
C22	Fe₂P (incorrectly)	P321
C23	PbCl₂	Pnma	Cotunnite structure
C24	HgBr₂	Cmc2₁	Mercury(II) bromide structure
C25 -> C28	HgCl₂	Pnma	Mercury(II) chloride structure
C27	CdI₂	P6₃mc
C28	HgCl₂
C29 -> C23	SrH₂	Pnma	Strontium hydride structure
C30	SiO₂	P4₁2₁2	α–Cristobalite structure
C32	AlB₂	P6/mmm	Aluminium diboride structure
C33	Bi₂Te₃	R3m	Bismuth telluride structure
C34	AuTe₂	C2/m
C35	CaCl₂	Pnnm	Calcium chloride structure
C36	MgNi₂	P6₃/mmc	MgNi₂ Laves phase
C37	Co₂Si	Pnma
C38	Cu₂Sb	P4/nmm
C39 -> C15
C40	CrSi₂	P6₂22
C41 -> C14
C42	SiS₂	Ibam	Silicon disulfide structure
C43	ZrO₂	P2₁/c	Baddeleyite structure
C44	GeS₂	Fdd2	Germanium disulfide structure
C46	AuTe₂	Pma2	Krennerite structure
C47	SeO₂	P4₂/mbc	Selenium dioxide structure
C48 -> C11_b
C49	ZrSi₂	Cmcm
C50	PdCl₂	Pnnm	α-Palladium(II) chloride structure
C51 -> C16
C53	Sr Br₂	P4/n
C54	TiSi₂	Fddd	Titanium disilicide structure
C_a	Mg₂Ni	P6₂22
C_b	CuMg₂	Fddd
C_c	ThSi₂	I4₁/amd
C_e	PdSn₂	Aba2
C_g	ThC₂	C2/c
C_h	Cu₂Te	P6/mmm
C_k	LiZn₂

D-compounds

'D' designates compounds of arbitrary stoichiometry. Originally, D1-D10 were set aside for stoichiometry AB₃, D11-D20 for stoichiometry AB_n for n > 3, D31-D50 for (AB_n)₂, and D51 up for the A_mB_n for arbitrary m and n.[9]

D compounds
Strukturbericht designation	Prototype	Space group	Description
D0₂	CoAs₃	Im3	Skutterudite structure
D0₃	BiF₃	Fm3m	Bismuth trifluoride structure
D0₄	CrCl₃	P3₁12	Chromium(III) chloride structure
D0₅	BiI₃	R3	Bismuth(III) iodide structure
D0₆	LaF₃	P3c1	Lanthanum trifluoride/Fluocerite structure
D0₉	α-ReO₃	Pm3	α-Rhenium trioxide structure
D0₁₁	Fe₃C	Pnma	Cementite structure
D0₁₂	FeF₃	R3c
D0₁₄ -> D0₁₂	AlF₃	R32	Aluminium fluoride structure
D0₁₅	AlCl₃	C2/m	Aluminium chloride structure
D0₁₇	BaS₃	P42₁m
D0₁₈	Na₃As	P6₃/mmc	Sodium arsenide structure
D0₁₉	Ni₃Sn	P6₃/mmc
D0₂₀	Al₃Ni	Pnma
D0₂₁	Cu₃P	P6₃cm	Copper(I) phosphide structure
D0₂₂	Al₃Ti	I4/mmm
D0₂₃	Al₃Zr	I4/mmm
D0₂₄	Ni₃Ti	P6₃/mmc
D0_a	β-TiCu₃	Pmmn
D0_c -> D0'_c	SiU₃	I4/mcm
D0'_c	Ir₃Si	I4/mcm
D0_d	AsMn₃	Cmcm
D0_e	Ni₃P	I4
D1	NH₃	P2₁3
D1₂	SiF₄	I43m	Silicon tetrafluoride structure
D1₃	Al₄Ba	I4/mmm
D1_a	Ni₄Mo	I4/m
D1_b	Al₄U	Imma
D1_c	PtSn₄	Aba2
D1_d	Pb₄Pt	P4/nbm
D1_e	B₄Th	P4/mbm	B₄Th structure
D1_f -> C_b	Mn₄B
D1_g	B₄C
D2 -> D0₂
D2₁	CaB₆	Pm3m	Calcium hexaboride structure
D2₃	NaZn₁₃	Fm3c
D2_b	Mn₁₂Th	I4/mmm
D2_c	MnU₆	I4/mcm
D2_d	CaCu₅	P6/mmm
D2_e	BaHg₁₁	Pm3
D2_f	UB₁₂	Fm3m
D2_g	Fe₈N	I4/mmmm
D2_h	Al₆Mn	Cmcm
D3₁	Hg₂Cl₂	I4/mmm	Calomel structure
D5₁	Al₂O₃	R3c	Corrundum structure
D5₂	La₂O₃	P3m1
D5₃	Mn₂O₃	Ia3	Manganese(III) oxide/Bixbyite structure
D5₄	Sb₂O₃	Fd3m
D5₅	Ag₂O₃	Pn3m
D5₈	Sb₂S₃	Pnma	Antimony trisulfide/Stibnite structure
D5₉	Zn₃Pt₂	P4₂/nmc
D5₁₀	Cr₃C₂	Pnma
D5₁₁	Sb₂O₃	Pccn	Antimony trioxide/Valentinite structure
D5₁₂	β–Bi₂O₃
D5₁₃	Al₃Ni₂	P3m1
D5_a	Si₂U₃	P4/mbm
D5_b	Pt₂Sn₃	P6₃/mmc
D5_c	Pu₂C₃	I43d
D5_e	Ni₃S₂	R32	Nickel subsulfide/Heazlewoodite structure
D5_f	As₂S₃	P2₁/n	Arsenic trisulfide structure
D7₁	Al₄C₃	R3m	Aluminium carbide structure
D7₂	Co₃S₄	Fd3m
D7₃	Th₃P₄	I43d	Th₃P₄ structure
D7_a	𝛿-Ni₃Sn₄
D7_b	Ta₃B₄	Immm
D8₁	Fe₃Zn₁₀	I43m
D8₂	Cu₅Zn₈	I43m	Gamma brass structure
D8₃	Cu₉Al₄	P43m
D8₄	Cr₂₃C₆	Fm3m	Cr₂₃C₆ crystal structure/Chromium(II) carbide structure
D8₅	Fe₇W₆	R3m
D8₆	Cu₁₅Si₄	I43d
D8₈	Mn₅Si₃	P6₃/mcm
D8₉	Co₉S₈	Fm3m
D8₁₀	Cr₅Al₈	R3m
D8₁₁	Co₂Al₅	P6₃/mmc
D8_a	Mn₂₃Th₆,Cu₁₆Mg₆Si₇ (G-phase)	Fm3m
D8_b	σ-CrFe	P4₂/mnm
D8_c	Mg₂Zn₁₁	Pm3
D8_d	Co₂Al₉	P2₁/c
D8_e	Mg₃₂(Al,Zn)₄₉	Im3
D8_f	Ge₇Ir₃	Im3m
D8_g	Ga₂Mg₅	Ibam
D8_h	W₂B₅	P6₃/mmc
D8_i	Mo₂B₅	R3m
D8_k	Th₇S₁₂	P6₃/m
D8_l	Cr₅B₄	I4/mcm
D8_m	W₅Si₃	I4/mcm
D10₁	C₃Cr₇	Pnma
D10₂	Fe₃Th₇	P6₃mc
D31 -> D3₁
D51 -> D5₁
D52 -> D5₂
D61 -> D6₁
D81 -> D8₁
D82 -> D8₂
D83 -> D8₃

E to K compounds

Letters between 'E' and 'K' designate more complex compounds.

E through K compounds
Strukturbericht designation	Prototype	Space group	Description
E0₁	PbFCl	P4/nmm	Matlockite structure
E0₃	CdOHCl	P6₃mc
E0₅	FeOCl		Iron oxychloride structure
E0₇	FeAsS	P2₁/c	Arsenopyrite structure
E1₁	CuFeS₂	I42d	Chalcopyrite structure
E1_a	MgCuAl₂	Cmcm
E1_b	AgAuTe₄	P2/c	Sylvanite structure
E2₁	CaTiO₃	Pm3m	Perovskite structure
E2₂	FeTiO₃	R3	Ilmenite structure
E2₄	NH₄CdC₁₃	Pnma
E3	CdAl₂S₄	I4
E3₃	FeSb₂S₄	Pnam	Berthierite structure
E8₁	Eu₂Ir₂O₇	Fd3m	Pyrochlore structure
E9₁	Ca₃Al₂O₆	Pm3m
E9₃	Fe₃W₃C	Fd3m
E9₄	Al₅C₃N	P6₃mc
E9_a	Al₇Cu₂Fe	P4/mnc
E9_b	Al₈FeMg₃Si₆	P62m
E9_c	Mn₃Al₉Si	P6₃/mmc
E9_d	AlLi₃N₂	Ia3
E9_e	CuFe₂S₃	Pnma	Cubanite structure
F0₁	NiSSb	P2₁3	Ullmannite structure
F0₂	COS	R3m	Carbonyl sulfide structure
F5₁	CrNaS₂	R3m
F5₂	KN₃	I4/mcm
F5₄	NH₄O₂Cl	P42₁m
F5₆	CuSbS₂	Pnma	Chalcostibite structure
F5₉	KCNS	Pbcm
F5₁₀	KAg(CN)₂	P31c
F5₁₃	KBO₂	R3c
F5_a	FeKS₂	C2/c
F51 -> F5₁
F52 -> F5₂
F61 -> E1₁
G0₁	CaCO₃	R3c	Calcite structure
G0₂	CaCO₃	Pmcn	Aragonite structure
G0₆	KClO₃	P2₁/m
G3	NaClO₃	P2₁3	Sodium chlorate structure
G3₂	Na₂SO₃	P3	Sodium sulfite structure
G4 -> E2₂
G5 -> E2₁
G7₁	CeCO₃F	P62c	Bastnäsite structure
H0₁	CaSO₄	Cmcm	Anhydrite structure
H0₂	BaSO₄	Pnma	Baryte structure
H0₃ -> S1₁
H0₅	KClO₄	Pnma	Potassium perchlorate structure
H0₇	BPO₄	I4
H1 -> H0₁
H1₁	Al₂MgO₄	Fd3m	Spinel structure
H1₂ -> S1₂
H1₃ -> S1₃
H1₅	K₂PtC₁₄	P4/mmmm
H1₆	β-K₂SO₄	Pnma
H2 -> H0₂
H2₁	Ag₃PO₄	P43n	Silver phosphate structure
H2₄	Cu₃S₄V	P43m
H2₅	AsCu₃S₄	Pmn2₁	Enargite structure
H2₆	Cu₂FeS₄Sn	I42m	Stannite structure
H3 -> S1₁
H3₁ -> S1₄
H4	CaWO₄	I4₁/a	Scheelite structure
H5₇	Ca₅(PO₄)₃F,Cl,OH	P6₃/m	Apatite structure
H11 -> H1₁
H12 -> S1₂
H13 -> S1₃
H15 -> H1₅
H31 -> S1₄
H61 -> J1₁
I1₁ -> J1₁
I1₁₃ -> J1₁₃
J1₁	K₂PtCl₆	Fm3m
J1₁₃	K₂GeF₆	P3m1
K0₁	K₂S₂O₅	P2₁/m
K1₁	KSO₃	P321
K1₂	CsSO₃	P6₃mc
K3₁	Cs₃CoC₁₅	I4/mcm
K4₁	NH₄SO₄	P2₁/c

L-compounds

'L' designates intermetallic compounds.

L compounds
Strukturbericht designation	Prototype	Space group	Description
L1₀	CuAu	P4/mmm
L1₁	CuPt	R3m
L1₂	Cu₃Au	Pm3m	Cu₃Au structure
L1₃	CdPt₃	Cmmm
L1_a	CuPt₃
L2₁	AlCu₂Mn	Fm3m	Heusler compounds
L2₂	Sb₂Tl₇	Im3m
L2_a	𝛿-CuTi	P4/mmm
L6₀	CuTi₃	P4/mmm
L'1	Fe₄N	Pm3m
L'1₂	AlF₃C		Perovskite structure
L'2	ThH₂	I4/mmm
L'2_b	ThH₂	I4/mmm
L'3 -> B8₁	Fe₂N
L'3₂	β-V₂N	P31m
L6₀	Ti₃Cu	P4/mmm
L10 -> L1₀
L'10 -> L'1
L11 -> L1₁
L12 -> L1₂
L13 -> L1₃
L20 -> B2
L'20 -> L'2
L21 -> L2₁
L22 -> L2₂

S-compounds

S compounds
Strukturbericht designation	Prototype	Space group	Description
S1₁	ZrSiO₄	I4₁/amd	Zircon structure
S1₂	Mg₂SiO₄	Pnma	Forsterite structure
S1₃	Be₂SiO₄	R3	Phenakite structure
S1₄	Al₂Ca₃Si₃O₁₂	Ia3d	Garnet structure
S2₁	Sc₂Si₂O₇	C2/m	Thortveitite structure
S3₁	Be₃Al₂Si₆O₁₈	P6/mcc	Beryl structure
S3₂	BaSi₄O₉	P6c2
S5₃	Ca₂MgSi₂O₇	P42₁m	Åkermanite structure
S6	NaAlSi₂O₆H₂O	I43d
S6₂	Na₈Al₆Si₆O₂₄C_l2	P43n

References

"Index by Strukturbericht Designation". US Naval Laboratory Center for Materials Physics and Technology. 1 Sep 1995. Retrieved 6 Apr 2019.
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. arXiv:1806.07864. doi:10.1016/j.commatsci.2017.01.017. ISSN 0927-0256. S2CID 119490841.
Allmann, Rudolf; Hinek, Roland (2007-08-17). "The introduction of structure types into the Inorganic Crystal Structure Database ICSD". Acta Crystallographica Section A. International Union of Crystallography (IUCr). 63 (5): 412–417. Bibcode:2007AcCrA..63..412A. doi:10.1107/s0108767307038081. ISSN 0108-7673. PMC 2525864. PMID 17703075.
Bragg, W. L. (1931). "Strukturbericht, 1913–1928". Nature. 128 (3230): 511–512. Bibcode:1931Natur.128..511B. doi:10.1038/128511a0. ISSN 0028-0836. S2CID 4079798.
Ewald, Paul Peter; Hermann, C. (1931). Zeitschrift für Kristallographie, Kristallgeometrie, Kristallphysik, Kristallchemie. Leipzig: Akademische Verlagsgesellschaft m.b.H.
"International Union of Crystallography: Structure reports". Retrieved 6 Apr 2019.
Smithells, Colin J (1949). Metals reference book (2nd ed.). New York: Interscience Publishers. OCLC 568858.
Pearson, W. B. (1964). A handbook of lattice spacings and structures of metals and alloys. Oxford: Pergamon Press. doi:10.1016/C2013-0-08243-6. ISBN 978-1-4832-1318-7. OCLC 883896503. S2CID 239866683.
Mehl, Michael J. (2019). "A Brief History of Strukturbericht Symbols and Other Crystallographic Classification Schemes". Journal of Physics: Conference Series. IOP Publishing. 1290 (1): 012016. Bibcode:2019JPhCS1290a2016M. doi:10.1088/1742-6596/1290/1/012016. ISSN 1742-6588.
Keesom, W.H.; Taconis, K.W. (1936). "On the crystal structure of chlorine". Physica. Elsevier BV. 3 (1–4): 237–242. Bibcode:1936Phy.....3..237K. doi:10.1016/s0031-8914(36)80226-2. ISSN 0031-8914.
PEASE, R. S. (1950). "Crystal Structure of Boron Nitride". Nature. Springer Science and Business Media LLC. 165 (4201): 722–723. Bibcode:1950Natur.165..722P. doi:10.1038/165722b0. ISSN 0028-0836. PMID 15416803. S2CID 2503156.
Berastegui, P.; Hull, S. (2000). "The Crystal Structures of Thallium(I) Fluoride". Journal of Solid State Chemistry. Elsevier BV. 150 (2): 266–275. Bibcode:2000JSSCh.150..266B. doi:10.1006/jssc.1999.8587. ISSN 0022-4596.

External links

"Crystal Lattice Structures: Index by Strukturbericht Designation". Retrieved 2020-05-01.
"Library of Crystallographic Prototypes - Strukturbericht Designations". Retrieved 2020-05-01.

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