Structure type
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) | cP1 | 43 | |
A1 |
Copper , Cu cubic face-centered lattice (fcc) cubic closest packing of spheres (ccp) |
Fm 3 m (No. 225) | cF4 | γ- iron , gold | 1728 |
A2 |
Tungsten , W body-centered cubic lattice (bcc) |
In 3 m (No. 229) | cI2 |
Vanadium , V
α- iron |
1146 |
A3 |
Magnesium , Mg hexagonal close packing of spheres (hcp) |
P 6 3 / mmc (No. 194) | hP2 | Cobalt , Co | 1049 |
A3 ' | α- lanthanum , La dhcp structure |
P 6 3 / mmc (No. 194) | hP4 | Nd, Cf | 81 |
A4 | Diamond , c | Fd 3 m (No. 227) | cF8 | Silicon , Si | 156 |
A5 | β- tin, Sn | I 4 1 / amd (No. 141) | tI4 | NbRu | 105 |
A6 | Indium , In | I 4 / mmm (No. 139) | tI2 | MnNi | 81 |
A7 | Arsenic , as | R 3 m (No. 166) | hR2 | Bi, AsSb | 105 |
A8 | γ- selenium , Se | P 3 1 21 (No. 152) | hP3 | Te | 45 |
A9 | Graphite , c | P 6 3 / mmc (No. 194) | hP4 | BN | 14th |
A12 | α- manganese , Mn | I 4 3 m (No. 217) | cI58 | Er 5 Mg 24 , Al 12 Mg 17 | 126 |
A13 | β- manganese , Mn | P 4 1 32 (No. 213) | cP20 | Fe 2 Re 3 , Mg 3 Ru 2 | 53 |
A14 | Iodine , I 2 | Cmce (No. 64) | oS8 | Br 2 | 26th |
A15 | Cr 3 Si | Pm 3 n (No. 223) | cP8 | V 3 Si, Nb 3 Sn , Nb 3 Ge | 655 |
B. | |||||
B1 | Sodium chloride (NaCl) | Fm 3 m (No. 225) | cF8 | FeO, PbS | 4798 |
B2 | Cesium chloride (CsCl) | Pm 3 m (No. 221) | cP2 | FeAl, NiAl | 1734 |
B3 | Sphalerite type (ZnS) | F 4 3 m (No. 216) | cF8 | BP, InAs, CuI | 1595 |
B4 | Wurtzite type (ZnS) | P 6 3 mc (No. 186) | hP4 | GaN | 713 |
B8 | Nickel Arsenide (NiAs) ( Nickelin ) | P 6 3 / mmc (No. 194) | hP4 | PdTe, FeSe | 680 |
C. | |||||
C1 | Fluorite (CaF 2 ) | Fm 3 m (No. 225) | cF12 | SrCl 2 , Li 2 O | 1301 |
C2 | Pyrite (FeS 2 ) | Pa 3 (No. 205) | cP12 | PtP 2 , SiP 2 | 337 |
C3 | Cuprite (Cu 2 O) | Pn 3 m (No. 224) | cP6 | Pb 2 O, Ag 2 O | 42 |
C4 | Rutile (TiO 2 ) | P 4 2 / mnm (No. 136) | tP6 | MgF 2 | 752 |
C5 | Anatase (TiO 2 ) | I 4 1 / amd (No. 141) | tI12 | TiNF | 63 |
C6 | Cadmium iodide (CdI 2 ) | P 3 m 1 (No. 164) | hP3 | VCl 2 , Ti 2 O, SnS 2 | 261 |
C7 | Molybdenite (MoS 2 (4H)) | P 6 3 / mmc (No. 194) | hP6 | Pt 2 B, TaReSe 4 | 81 |
C8 | β- quartz (SiO 2 ) (high quartz,> 846 K) | P 6 2 22 (No. 180) | hP9 | BeF 2 | 24 |
C8a | α- quartz (SiO 2 ) (deep quartz, <846 K) | P 3 1 21 (No. 152) | hP9 | GrO 2 | 176 |
C9 | Cristobalite (SiO 2 ) HT | Fd 3 m (No. 227) | cF24 | 75 | |
C10 | Tridymite (SiO 2 ) HT | P 6 3 / mmc (No. 194) | hP12 | 9 | |
C14 | MgZn 2 hexagonal Laves phase |
P 6 3 / mmc (No. 194) | hP12 | Np 5 Si 3 U 4 , HoMg 2 | 1251 |
C15 | Cu 2 Mg cubic Laves phase |
Fd 3 m (No. 227) | cF24 | Al 2 Ca, CsBi 2 | 2704 |
C18 | Marcasite (FeS 2 ) | Pnnm (No. 58) | oP6 | RuP 2 , RuAs 2 | 199 |
C19 | Cadmium Chloride (CdCl 2 ) | R 3 m (No. 166) | hR3 | Ho 2 C anti type | 45 |
C21 | Brookite (TiO 2 ) | Pbca (No. 61) | oP24 | HfO 2 | 24 |
D. | |||||
D0 2 | Skutterudit (CoAs 3 ) | Im 3 (No. 204) | cI32 | NiP 3 , ReO 3 | 126 |
D5 1 | Corundum (Al 2 O 3 ) | R 3 c (No. 167) | hR10 | Ti 2 O 3 | 398 |
D5 8 | Stibnite (antimonite, Sb 2 S 3 ) | Pnma (No. 62) | oP20 | Sc 2 As 3 , Sc 3 P 2 | 167 |
E. | |||||
E1 1 | Chalcopyrite (CuFeS 2 ) | I 4 2 d (No. 122) | tI16 | ZnGeP 2 , ZnSiP 2 | 612 |
E2 1 | Perovskite (ideal) (CaTiO 3 ) | Pm 3 m (No. 221) | cP5 | CsHgF 3 , KCoF 3 | 2685 |
E2 2 | Ilmenite (FeTiO 3 ) | R 3 (No. 148) | hR10 | LiNbO 3 , NaMnCl 3 | 268 |
F. | |||||
F5 1 | Delafossite (CuFeO 2 ) | R 3 m (No. 166) | hR4 | RbHoO 2 , NaCrS 2 | 1147 |
G | |||||
G0 1 | Calcite (CaCO 3 ) | R 3 c (No. 167) | hR10 | LuBO 3 , NaNO 3 | 312 |
G0 2 | Aragonite (CaCO 3 ) | Pnma (No. 62) | oP20 | KNO 3 | 125 |
H | |||||
H1 1 | Spinel (MgAl 2 O 4 ) | Fd 3 m (No. 227) | cF56 | Fe 3 O 4 , MgCr 2 S 4 | 4148 |
H2 | Barite (BaSO 4 ) | Pnma (No. 62) | oP24 | CsGaBr 4 , KBF 4 | 172 |
L. | |||||
L1 1 | AuCu | P 4 / mmm (No. 123) | tP2 | LiBi, HgPd | 133 |
L1 2 | Auricupride (Cu 3 Au) | Pm 3 m (No. 221) | cP4 | NpSi 3 , In 3 Lu | 1522 |
L2 1 | Heusler phase (AlCu 2 Mn) | Fm 3 m (No. 225) | cF16 | Li 3 Sb | 1203 |
S. | |||||
S1 1 | Zircon (ZrSiO 4 ) | I 4 1 / amd (No. 141) | tI24 | LuVO 4 , LuPO 4 | 386 |
S1 2 | Forsterite (Mg 2 SiO 4 , see also Oliving group ) | Pnma (No. 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) | cI160 | Fe 5 Tb 3 O 13 | 737 |
S2 1 | Thortveitite (Sc 2 Si 2 O 7 ) | C 2 / m (No. 12) | mS22 | Mg 2 As 2 O 7 | 67 |
S6 | Analcime (NaAlSi 2 O6H 2 O) | I 4 3 d (No. 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) | 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
- Will Kleber , Hans-Joachim Bautsch , Joachim Bohm , Detlef Klimm: Introduction to crystallography . 19th edition. Oldenbourg Wissenschaftsverlag, Munich 2010, ISBN 978-3-486-59075-3 .
- J. Lima-de-Faria, E. Hellner, F. Liebau, E. Makovicky, E. Parthé (1990). Nomenclature of inorganic structure types. Acta Cryst. A46 , 1-11. doi : 10.1107 / S0108767389008834 .
Web links
Individual evidence
- ^ Hartmut Bärnighausen: Group-Subgroup Relations between Space Groups: A Useful Tool in Crystal Chemistry, "MATCH", Communication in Mathematical Chemistry 1980, 9 , 139–175.
- ↑ 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 .
- ↑ The former name of this group of rooms was Ccma .
- ↑ Michael Szönyi (Ed.): Study dictionary geosciences . vdf Hochschulverlag , Zurich 2006, ISBN 978-3-8252-2812-5 , p. 82 ( limited preview in Google Book search).
- ↑ keyword isotypy , spectrum Lexikon Chemie
- ↑ 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 .