P.A. Cox - Inorganic chemistry (793955), страница 25
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In regular binarysolids the ratio of CN values must reflect the stoichiometry. Bothregular and irregular coordination geometries can be found.Many binary structures can be derived from a close-packed array ofone element by filling either tetrahedral or octahedral holes betweenthe close-packed layers with atoms of the other kind.An alternative view of binary structures is to consider coordinationpolyhedra of one element (normally tetrahedra or octahedra), linkedtogether by sharing corners, edges or faces.Element structures (D2)Binary compounds: factorsinfluencing structure (D4)Close packingLinked polyhedraRelated topicsCoordination number and geometryBinary compounds are ones with two elements present. ‘Simple’ crystal structures may be classed as ones in whicheach atom (or ion) is surrounded in a regular way by atoms (or ions) of the other kind.
Even with this limited scopemany structures are possible. Figure 1 shows a selection of simple ones that exemplify some important principles.Although many are found with ionic compounds, some of these structures are shown by compounds with covalentbonding, and a discussion of the bonding factors involved in favoring one structure rather than another is deferred toTopic D4. Figure 1 shows the structure name and the stoichiometry (AB, AB2, etc.).
When the two elements A and Bare not equivalent A is drawn smaller and with shading. In ionic compounds this is more often the metallic (cationic)element. If the role of anions and cations is reversed we speak of the anti-structure: thus Li2O has the anti-fluorite(CaF2) structure, and Cs2O the anti-CdI2 structure.From the local point of view of each atom the most important characteristics of a structure are the coordinationnumber (CN) and coordination geometry. In the examples shown these are the same for all atoms of the sametype. Coordination numbers must be compatible with the stoichiometry.
In AB both A and B have the same CN, theexamples shown beingZinc blende (4:4); Rocksalt (6:6); NiAs (6:6); CsCl (8:8).When the stoichiometry is AB2 the CN of A must be twice that of B:Rutile (6:3); CdI2 (6:3); Fluorite (8:4).D3—BINARY COMPOUNDS: SIMPLE STRUCTURES107Fig. 1. A selection of binary structures.In the structures shown many of the atoms have a regular coordination geometry:CN=2: linear (B in ReO3);CN=3: planar (B in rutile);CN=4: tetrahedral (A and B in zinc blende, B in fluorite);CN=6: octahedral (A and B in rocksalt, A in NiAs, rutile and CdI2);CN=8: cubic (A and B in CsCl, A in fluorite).These geometries are expected in ionic compounds, as they lead to the greatest spacing between ions with the samecharge.
Other geometries are sometimes found, however, especially for the nonmetal B atom:108SECTION D—STRUCTURE AND BONDING IN SOLIDSCN=2: bent (SiO2 structures, not shown);CN=3: pyramidal (in CdI2);CN=6: trigonal prismatic (in NiAs).The explanation of these must involve nonionic factors (see Topic D4).Close packingMany binary structures can be derived from close-packed arrays of atoms of one kind (see Topic D2). Figure 2 showsthat between adjacent close-packed layers are octahedral and tetrahedral holes (labeled O and T) such that atoms ofanother kind occupying these sites would be octahedrally or tetrahedrally coordinated.
For ionic compounds we canimagine the larger ions (usually the anions) forming the close-packed array, and cations occupying some of the holes. Ineither hexagonal (hcp) or cubic close-packed (ccp or fcc) arrays of B there is one octahedral and two tetrahedralholes per B atom. Table 1 shows some binary structures classified in this way. Thus filling all the octahedral holes in afcc array generates the rocksalt structure (in which the original B atoms are also octahedrally coordinated); doing thesame in an hcp array gives the NiAs structure.
Filling all the tetrahedral holes in an fcc anion array gives theantifluorite structure, more commonly found with anions and cations reversed as in fluorite (CaF2) itself. A similararrangement is never found in an hcp array, as the tetrahedral holes occur in pairs that are very close together.Fig. 2. Octahedral (O) and tetrahedral (T) holes between adjacent close-packed layers.Table 1. Some binary structures based on close-packed arrays of anionsabLayer structures.Filling the holes changes the symmetry; the rutile unit cell is not hexagonal.When only a fraction of the holes of a given type are occupied there are several possibilities. The most symmetrical wayof filling half the tetrahedral holes gives the zinc blende structure with ccp, and the very similar 4:4 wurtzite (ZnO)D3—BINARY COMPOUNDS: SIMPLE STRUCTURES109structure with hcp.
Both the rutile and CdI2 structures can be derived by filling half the octahedral holes in hcp. Theformer gives a more regular coordination of the anions (see above) although the resulting structure is no longerhexagonal. The CdI2 structure arises from alternately occupying every octahedral hole between two adjacent closepacked planes, and leaving the next layer of holes empty. It is an example of a layer structure based on BAB‘sandwiches’ that are stacked with only B-B contacts between them.
The CdCl2 structure is based in a similar way onccp (rather than hcp) anions, and many other layer structures with formulae such as AB3 can be formed by only partialfilling of the holes between two layers.Linked polyhedraAn alternative way of analyzing binary structures is to concentrate on the coordination polyhedra of one type ofatom, and on the way these are linked together. This approach is generally useful in structures with covalent bonding,and/or ones that are more open than those derived from close packing.If two tetrahedral AB4 units share one B atom in common (1) we talk of corner sharing.
A corner-shared pair hasstoichiometry A2B7 and is found in (molecular) Cl2O7 and occasionally in silicates. Tetrahedra each sharing corners withtwo others generate a chain or a ring (2) of stoichiometry AB3, as found with SO3 and commonly in silicates (seeTopics D5 and G4).
These structures are often represented by drawing the tetrahedra without showing the atomsexplicitly. Rings and chains with two corners shared are shown in this way (Fig. 3a and b). Sharing three corners makes alayer or a tetrahedral cluster of stoichiometry A2O5; such layers occur in silicates, and the clusters as P4O10 molecules(see Topic F6, Structure 5). Tetrahedra sharing all four corners with others generate a 3D framework ofstoichiometry AB2, found in the various (crystalline and glassy) structures of SiO2.Tetrahedra with two B atoms in common are said to be edge sharing: examples of isolated edge-sharing pairs areB2H6 and Al2Cl6 (see Topic C8, Structure 2).
A chain of tetrahedra each sharing two edges with others has astoichiometry AB2 and is found as the chain structures of BeH2 and SiS2, shown in Fig. 3c and in Topic G3, Structure3. Face sharing is also possible but is almost never found with tetrahedra as the A atoms would be very close together.Similar ideas can be used with octahedra. Chains of corner-sharing octahedra are found in WOBr4 and of edgesharing octahedra in NbI4. If octahedra share all six corners, the 3D ReO3 structure results (see Fig.
3d. compare Fig. 1).110SECTION D—STRUCTURE AND BONDING IN SOLIDSFig. 3. Structures derived from linking of polyhedra (see text).Section D—Structure and bonding in solidsD4BINARY COMPOUNDS: FACTORS INFLUENCING STRUCTUREKey NotesIonic radiiRadius ratiosIon polarizabilityCovalent bondingRelated topicsIonic radii are derived from a somewhat arbitrary division of the observedanion-cation distances.
Different assumptions lead to different values, but allsets show similar trends. Ionic radii vary with coordination number.Simple geometrical arguments based on hard-sphere ions give predictions ofstructure according to the ratio of ionic radii. These are qualitatively usefulbut not quantitatively reliable.The electrostatic polarizability of ions increases with its radius and may bepartly responsible for the adoption of structures where coordinationgeometries are unsymmetrical, and of structures with high coordinationnumbers.When covalent bonding predominates the coordination numbers andgeometries are often those expected by analogy with molecules.
Somedegree of covalency in ‘ionic’ compounds can influence the structure, oftenleading to coordination numbers less than expected.Electronegativity and bond typeBinary compounds: simple(B1)structures (D3)Ionic radiiThe experimentally measured anion-cation distances in highly ionic solids can be interpreted on the assumption thateach ion has a nearly fixed radius. For example, the difference in anion-cation distance between the halides NaX and KXis close to 36 pm irrespective of the anion X, and it is natural to attribute this to the difference in radii between Na+ andK+. To separate the observed distances into the sum of two ionic radii is, however, difficult to do in an entirelysatisfactory way.
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