Structure type

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A structure type includes crystal structures that have the same symmetry , i. i.e., have the same space group and in which the same point positions are occupied (given in the Wyckoff sequence). In addition, the atomic environments ( coordination polyhedra ) must match, which requires an approximate equality of the axial relationships (cell shape). Crystalline substances that belong to the same structure type are called isotypes . The stoichiometry of isotypic substances must match; the type of atoms, the bond character and the distance between atoms, on the other hand, play no role in the classification. The structure type is in principle a purely geometric specification. However, this is sufficient to bring order to an unmanageable number of connections. In addition, relationships can be shown using structure types and their associated symmetry. The structure type is documented as an aid to such an order finding in the inorganic crystal structure database ICSD. As of November 2019, this database contains 216032 entries. Almost 76% of the entries are summarized in around 9,400 structure types.

Structure types can be used to classify crystal structures made up of ions, atoms and groups of atoms, such as B. the sulfate group SO 4 2− are built up. Structure types are less suitable for molecular structures, as they occur with most organic compounds.

The most important structure types include element structures such as the cubic closest packing of spheres , the hexagonal closest packing of spheres and the body-centered cubic lattice. The sodium chloride type is even more common . In addition to sodium chloride , magnesium oxide and lead sulfide , this includes around 800 mostly ionic compounds, but also compounds and mixed crystals with a strong covalent bond.

Further types are often derived from highly symmetrical structure types by reducing symmetry. For some types there are whole family trees (e.g. perovskite). The most symmetrical type is then the aristotype.

The 20 most common structure types are: NaCl (table salt), spinel (MgAl 2 O 4 ), GdFeO 3 (symmetry- reduced perovskite), Cu 2 Mg (cubic Laves phase), CaTiO 3 (cubic perovskite), CeAl 2 Ga 2 (also BaGa 4 ), CsCl, Cu (cubic close packing of spheres), ZnS (sphalerite), AuCu 3 (auricupride, ordered Cu type), LaAlO 3 (another perovskite), CaF 2 (fluorite), MgZn 2 (hexagonal Laves phase ), Heusler-AlCu 2 Mn, CuFeO 2 (Delafossit), bcc-W (cubic body-centered), CaCu 5 , TiNiSi / MgSrSi, hcp-Mg (hexagonal close packing of spheres) and ZnNiAl / Fe 2 P. These 20 types have in ICSD all over 1000 representatives and thus represent about 18% of all entries.

nomenclature

The structure types are usually named after a substance (element, compound or mineral). A different nomenclature has been used in the structural reports since 1923 (until 1939). This nomenclature is in international use under the German name (French notation structure report , English structure report designation ) and is still widely used, especially in metallurgy.

The nomenclature of the structure reports divides the structure types according to their composition into groups, which are indicated by capital letters. Within the groups, the structure types were numbered according to the order in which they were discovered. The structure reports end in 1939. After 1945 they are continued as Structure Reports, but without giving any further names to structure types.

  • A: elements
  • B: AB connections
  • C: AB 2 compounds
  • D: A m B n compounds
  • E:> 2 elements without pronounced complex formation
  • F: with two- or three-atom complexes
  • G: with tetratomic complexes
  • H: with five-atom complexes
  • L: alloys
  • M: mixed crystals
  • O: organic compound
  • S: silicates

Another method of describing structure types are the Pearson symbols . They indicate the Bravais lattice and the number of atoms per (standardized) unit cell. However, since the atoms can sit in different positions, the Pearson symbols alone are not sufficient to separate structure types from one another. The Wyckoff sequence, which describes the occupied point positions, is used for a further distinction. Structures that have the same Wyckoff sequence and the same Pearson symbol are called isopointal . Isopointal structures can be easily searched for in the ICSD database. For a further delimitation, further criteria must then be used, such as axial ratios, beta angles, ANX formulas, necessary and excluded chemical elements.

Selected structure types

Designation in the
structure reports		 Structure type,
main representative (prototype)		 Space group Pearson
symbol		 further examples Number in ICSD

(March 2020)

A.
A h α- polonium , Po
cubic primitive lattice (sc)		 Pm 3 m (No. 221)Template: room group / 221 cP1 43
A1 Copper , Cu
cubic face-centered lattice (fcc)
cubic closest packing of spheres (ccp)		 Fm 3 m (No. 225)Template: room group / 225 cF4 γ- iron , gold 1728
A2 Tungsten , W
body-centered cubic lattice (bcc)		 In 3 m (No. 229)Template: room group / 229 cI2 Vanadium , V

α- iron

1146
A3 Magnesium , Mg
hexagonal close packing of spheres (hcp)		 P 6 3 / mmc (No. 194)Template: room group / 194 hP2 Cobalt , Co 1049
A3 ' α- lanthanum , La
dhcp structure		 P 6 3 / mmc (No. 194)Template: room group / 194 hP4 Nd, Cf 81
A4 Diamond , c Fd 3 m (No. 227)Template: room group / 227 cF8 Silicon , Si 156
A5 β- tin, Sn I 4 1 / amd (No. 141)Template: room group / 141 tI4 NbRu 105
A6 Indium , In I 4 / mmm (No. 139)Template: room group / 139 tI2 MnNi 81
A7 Arsenic , as R 3 m (No. 166)Template: room group / 166 hR2 Bi, AsSb 105
A8 γ- selenium , Se P 3 1 21 (No. 152)Template: room group / 152 hP3 Te 45
A9 Graphite , c P 6 3 / mmc (No. 194)Template: room group / 194 hP4 BN 14th
A12 α- manganese , Mn I 4 3 m (No. 217)Template: room group / 217 cI58 Er 5 Mg 24 , Al 12 Mg 17 126
A13 β- manganese , Mn P 4 1 32 (No. 213)Template: room group / 213 cP20 Fe 2 Re 3 , Mg 3 Ru 2 53
A14 Iodine , I 2 Cmce (No. 64)Template: room group / 64 oS8 Br 2 26th
A15 Cr 3 Si Pm 3 n (No. 223)Template: room group / 223 cP8 V 3 Si, Nb 3 Sn , Nb 3 Ge 655
B.
B1 Sodium chloride (NaCl) Fm 3 m (No. 225)Template: room group / 225 cF8 FeO, PbS 4798
B2 Cesium chloride (CsCl) Pm 3 m (No. 221)Template: room group / 221 cP2 FeAl, NiAl 1734
B3 Sphalerite type (ZnS) F 4 3 m (No. 216)Template: room group / 216 cF8 BP, InAs, CuI 1595
B4 Wurtzite type (ZnS) P 6 3 mc (No. 186)Template: room group / 186 hP4 GaN 713
B8 Nickel Arsenide (NiAs) ( Nickelin ) P 6 3 / mmc (No. 194)Template: room group / 194 hP4 PdTe, FeSe 680
C.
C1 Fluorite (CaF 2 ) Fm 3 m (No. 225)Template: room group / 225 cF12 SrCl 2 , Li 2 O 1301
C2 Pyrite (FeS 2 ) Pa 3 (No. 205)Template: room group / 205 cP12 PtP 2 , SiP 2 337
C3 Cuprite (Cu 2 O) Pn 3 m (No. 224)Template: room group / 224 cP6 Pb 2 O, Ag 2 O 42
C4 Rutile (TiO 2 ) P 4 2 / mnm (No. 136)Template: room group / 136 tP6 MgF 2 752
C5 Anatase (TiO 2 ) I 4 1 / amd (No. 141)Template: room group / 141 tI12 TiNF 63
C6 Cadmium iodide (CdI 2 ) P 3 m 1 (No. 164)Template: room group / 164 hP3 VCl 2 , Ti 2 O, SnS 2 261
C7 Molybdenite (MoS 2 (4H)) P 6 3 / mmc (No. 194)Template: room group / 194 hP6 Pt 2 B, TaReSe 4 81
C8 β- quartz (SiO 2 ) (high quartz,> 846 K) P 6 2 22 (No. 180)Template: room group / 180 hP9 BeF 2 24
C8a α- quartz (SiO 2 ) (deep quartz, <846 K) P 3 1 21 (No. 152)Template: room group / 152 hP9 GrO 2 176
C9 Cristobalite (SiO 2 ) HT Fd 3 m (No. 227)Template: room group / 227 cF24 75
C10 Tridymite (SiO 2 ) HT P 6 3 / mmc (No. 194)Template: room group / 194 hP12 9
C14 MgZn 2
hexagonal Laves phase 		P 6 3 / mmc (No. 194)Template: room group / 194 hP12 Np 5 Si 3 U 4 , HoMg 2 1251
C15 Cu 2 Mg
cubic Laves phase		 Fd 3 m (No. 227)Template: room group / 227 cF24 Al 2 Ca, CsBi 2 2704
C18 Marcasite (FeS 2 ) Pnnm (No. 58)Template: room group / 58 oP6 RuP 2 , RuAs 2 199
C19 Cadmium Chloride (CdCl 2 ) R 3 m (No. 166)Template: room group / 166 hR3 Ho 2 C anti type 45
C21 Brookite (TiO 2 ) Pbca (No. 61)Template: room group / 61 oP24 HfO 2 24
D.
D0 2 Skutterudit (CoAs 3 ) Im 3 (No. 204)Template: room group / 204 cI32 NiP 3 , ReO 3 126
D5 1 Corundum (Al 2 O 3 ) R 3 c (No. 167)Template: room group / 167 hR10 Ti 2 O 3 398
D5 8 Stibnite (antimonite, Sb 2 S 3 ) Pnma (No. 62)Template: room group / 62 oP20 Sc 2 As 3 , Sc 3 P 2 167
E.
E1 1 Chalcopyrite (CuFeS 2 ) I 4 2 d (No. 122)Template: room group / 122 tI16 ZnGeP 2 , ZnSiP 2 612
E2 1 Perovskite (ideal) (CaTiO 3 ) Pm 3 m (No. 221)Template: room group / 221 cP5 CsHgF 3 , KCoF 3 2685
E2 2 Ilmenite (FeTiO 3 ) R 3 (No. 148)Template: room group / 148 hR10 LiNbO 3 , NaMnCl 3 268
F.
F5 1 Delafossite (CuFeO 2 ) R 3 m (No. 166)Template: room group / 166 hR4 RbHoO 2 , NaCrS 2 1147
G
G0 1 Calcite (CaCO 3 ) R 3 c (No. 167)Template: room group / 167 hR10 LuBO 3 , NaNO 3 312
G0 2 Aragonite (CaCO 3 ) Pnma (No. 62)Template: room group / 62 oP20 KNO 3 125
H
H1 1 Spinel (MgAl 2 O 4 ) Fd 3 m (No. 227)Template: room group / 227 cF56 Fe 3 O 4 , MgCr 2 S 4 4148
H2 Barite (BaSO 4 ) Pnma (No. 62)Template: room group / 62 oP24 CsGaBr 4 , KBF 4 172
L.
L1 1 AuCu P 4 / mmm (No. 123)Template: room group / 123 tP2 LiBi, HgPd 133
L1 2 Auricupride (Cu 3 Au) Pm 3 m (No. 221)Template: room group / 221 cP4 NpSi 3 , In 3 Lu 1522
L2 1 Heusler phase (AlCu 2 Mn) Fm 3 m (No. 225)Template: room group / 225 cF16 Li 3 Sb 1203
S.
S1 1 Zircon (ZrSiO 4 ) I 4 1 / amd (No. 141)Template: room group / 141 tI24 LuVO 4 , LuPO 4 386
S1 2 Forsterite (Mg 2 SiO 4 , see also Oliving group ) Pnma (No. 62)Template: room group / 62 oP28 NaCdPO 4 , Na 2 BaF 4 867
S1 4 Garnet , Grossular (Al 2 Ca 3 Si 3 O 12 ) Ia 3 d (No. 230)Template: room group / 230 cI160 Fe 5 Tb 3 O 13 737
S2 1 Thortveitite (Sc 2 Si 2 O 7 ) C 2 / m (No. 12)Template: room group / 12 mS22 Mg 2 As 2 O 7 67
S6 Analcime (NaAlSi 2 O6H 2 O) I 4 3 d (No. 220)Template: room group / 220 cI208 NaGaSi 2 O 6 H 2 O 22nd
S6 2 Sodalite (Na 8 Al 6 Si 6 O 24 Cl 2 ) P 4 3 n (No. 218)Template: room group / 218 cP46 Mg 3 (BeSiO 4 ) 2 S 365
*) The number also contains multiple determinations

Associated terms

Anisotype
In addition to the isotype, there is also an anisotype. The places of cations and anions are interchanged, calcium fluoride (CaF 2 ) and lithium oxide (Li 2 O) are mentioned as examples . Li 2 O crystallizes in the anti-CaF 2 type
Aristotype
Is the idealized trunk structure from which the given structure is derived through a reduction in symmetry. Thus the aristotype of the AuCu 3 type is the Cu type or the aristotype of the GdFeO 3 type is the CaTiO 3 type.
Homeotype
In the strict sense, two crystal structures are isotypic only if they have an analogous chemical molecular formula, the same symmetry ( space group ) and extensive similarity in the atomic arrangement . The term homeotype was coined for crystals that do not fully correspond to this, but are nevertheless very similar in their structures. Thus, for example, carbon modification diamond and sphalerite (ZnS), calcite (CaCO 3 ) and dolomite (CaMg (CO 3 ) 2 ) and quartz (SiO 2 ) and berlinite (AlPO 4 homöotyp).
Isopointal
Two structures are referred to as isopointal, which correspond in the Pearson symbol and Wyckoff sequence. Nevertheless, they can belong to different structure types.
Isotype
Substances that belong to the same structural type are referred to as isotype or isostructural (from ancient Greek ἴσος isos "equal", and ancient Greek τύπος typos "essence, character"). The opposite is heterotype .
Polytype
On the one hand, denotes the phenomenon that a substance can appear in different stacking sequences of layered structural units, such as B. in the ZnS. On the other hand, the same substance can occur in different structure types, caused by pressure or temperature changes. The high pressure form of carbon is diamond, while graphite is stable at normal pressure.
Wyckoff sequence
The International Tables for Crystallography include: a. the 230 room groups are listed with their various point locations . The point positions are numbered alphabetically. The letter a is given the position with the highest symmetry, usually located in the zero point 0 0 0 of the cell. The general position xyz without intrinsic symmetry gets the highest letter. The Wyckoff sequence indicates which positions are occupied and how often. So the NaCl type has the Wyckoff sequence "b a". The Wyckoff sequence is not entirely unambiguous, but for some space groups it depends on the choice of zero. The Wyckoff sequence of the spinel type "ed a" changes to "ec b" when shifted by 0.5 0.5 0.5. In order to avoid such ambiguities, the structures should be standardized before a comparison (e.g. with the Structure Tidy program).

See also

literature

Web links

Commons : Structure report  - album with pictures, videos and audio files

Individual evidence

  1. ^ Hartmut Bärnighausen: Group-Subgroup Relations between Space Groups: A Useful Tool in Crystal Chemistry, "MATCH", Communication in Mathematical Chemistry 1980, 9 , 139–175.
  2. ↑ Rudolf Allmann , Roland Hinek: The introduction of structure types into the Inorganic Crystal structure database ICSD, Acta Cryst. A63 , 2007, 412-417. doi : 10.1107 / S0108767307038081 .
  3. ↑ The former name of this group of rooms was Ccma .
  4. ↑ Michael Szönyi (Ed.): Study dictionary geosciences . vdf Hochschulverlag , Zurich 2006, ISBN 978-3-8252-2812-5 , p. 82 ( limited preview in Google Book search).
  5. ↑ keyword isotypy , spectrum Lexikon Chemie
  6. ↑ LM Gelato, E. Parthé (1987). STRUCTURE TIDY - a computer program to standardize crystal structure data. J. Appl. Cryst. 20 , 139-143. doi : 10.1107 / S0021889887086965 .