P.A. Cox - Inorganic chemistry (793955), страница 26
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One procedure is to look for the minimum value in the electron density distribution betweenneighboring ions, but apart from the experimental difficulties involved such measurements do not really support theassumption of constant radius. Sets of ionic radii are therefore all based ultimately on somewhat arbitrary assumptions.Several different sets have been derived, the most widely used being those of Shannon and Prewitt, based on theassumed radius of 140 pm for O2− in six-coordination. Values for a selection of ions are shown in Table 1.Any consistent set of radii should be able to give estimates of the total anioncation distance and hence the unit celldimensions if the structure is known. It is essential not to mix values from different sets.
Although the values maydiffer, all sets show the same trends.112D4—BINARY COMPOUNDS: FACTORS INFLUENCING STRUCTURETable 1. Ionic radii (pm) for six-coordination, based on a value of 140 pm for O2−(i) For isoelectronic ions, radii decrease with increasing positive charge (e.g. Na+>Mg2+>Al3+) or decreasingnegative charge (e.g.
O2−>F−).(ii) Radii increase down each group (e.g. Li+<Na+< etc.).(iii) For elements with variable oxidation state (not shown in Table 1) radius decreases with increasing positive charge(e.g. Fe2+>Fe3+).(iv) Most anions are larger than most cations.(v) Ionic radii increase with coordination number (CN). For example, the Shannon and Prewitt radii (in pm)for K+ with different CN (shown in parenthesis) are: 138 (6); 151 (8); 159 (10); 160 (12).Trends (i)–(iv) follow the changes expected in the radii of atomic orbitals (see Topic A5). The variation with CN is,however, very important and shows that ions cannot be regarded as hard spheres but have an effective size depending ontheir environment. This is expected because the equilibrium distance between ions involves a balance of attractive andrepulsive forces.
Repulsive forces come from the overlap of closed shells and their net importance increases inproportion to the CN. Attractive forces are electrostatic and depend on the long-range summation of the interactionsbetween many ions (see Topic D6). Although they increase with CN the change is much less than for short-rangerepulsion. Increasing the CN therefore changes the balance in favor of repulsive forces and leads to an increase indistance.Radius ratiosAn ionic solid should achieve maximum electrostatic stability when (i) each ion is surrounded by as many as possibleions of opposite charge, and (ii) the anioncation distance is as short as possible.
There is, however, a play-off betweenthese two factors. Consider an octahedral hole in a close-packed array of anions (see Topic D3). The minimum radius ofthe hole, obtained when the anions are in contact, is 0.414 times the anion radius. A cation smaller than this will not beable achieve the minimum possible anion-cation distance in octahedral coordination, and a structure with lowercoordination (e.g. tetrahedral) may be preferred. These considerations lead to the radius ratio rules, which predictthe likely CN for the smaller ion (usually the cation) in terms of the ratio r</r> where r< is the smaller and r> the largerof the two radii.
The approximate radius ratios for different CN are:SECTION D—STRUCTURE AND BONDING IN SOLIDSr</r>>0.70.4–0.70.2–0.4CN864113The rules provide a useful qualitative guide to the way structures change with the size of ions. For example, the radiusratios and the observed CN of the metal ions M2+ in some group 2 fluorides are:BeF2:MgF2:CaF2:r</r>=0.20r</r>=0.54r</r>=0.75CN=4CN=6CN=8However, radius ratio arguments are not quantitatively reliable, and they even fail to account for the structures of somealkali halides.
The predicted coordination number is four in LiI and eight in RbCl, although both compounds have therocksalt structure (CN=6) at normal temperature and pressure.The fact that radius ratio arguments do not always predict the correct structure is sometimes regarded as a seriousfailure of the ionic model, and an indication that nonionic forces must be involved in bonding. Given the uncertainties indefinition of ionic radii, however, and the fact that they are known to vary with CN, it is hardly surprising thatpredictions based on the assumption of hard spheres are unreliable.
It also appears that for some compounds thedifference in energy between different structure types is very small, and the observed structure may change withtemperature or pressure.Ion polarizabilityThe polarizability of an ion refers to the ability of an applied electric field to distort the electron cloud and so inducean electric dipole moment. The most polarizable ions are large ones, especially anions from later periods (e.g. S2−, Br−,I−). ‘Polarization’ is a term often used loosely as meaning ‘covalency’ but the purely electrostatic polarizability of ionshas effects that are entirely separate. In layer and chain structures (see Topic D3) anions are generally in asymmetricenvironments and experience a strong net electric field from neighboring ions.
Polarization lowers the energy of an ionin this situation, giving a stabilizing effect not possible when the coordination is symmetrical. It is notable that layerstructures occur frequently with disulfides and dichlorides (and with heavier anions lower in the same groups), butalmost never with dioxides and difluorides: compare TiO2 and FeF2 (both rutile structure) with TiS2 and FeI2 (bothCdI2 structure). Cs2O is a rare example of the anti-CdI2 structure, with adjacent layers of Cs+; the high polarizability ofthe Cs+ ion must be a contributing factor.Another consequence of polarizability is the existence of van der Waals’ forces between ions (see Topic C10).They are considerably weaker than ionic forces but can have an influence on structures, especially with large ions of highpolarizability. Being short-ranged (varying with distance R as R−6) compared with Coulomb energies (R−1) they favorthe maximum number of near-neighbors, irrespective of charge.
It is very likely that the occurrence of the 8:8 CsClstructure with cesium halides (except CsF) is influenced by this effect. Van der Waals’ forces between adjacent anionsare also responsible for holding together layers and chains, which is another reason why ion polarizability is importantfor such structures.114D4—BINARY COMPOUNDS: FACTORS INFLUENCING STRUCTURECovalent bondingPurely electrostatic forces between ions are nondirectional, but with increasing covalent character the directionalproperties of valence orbitals become more important. Compounds between nonmetallic elements have predominantlycovalent bonding and the structures can often be rationalized from the expected CN and bonding geometry of the atomspresent (see Topics C2 and C6).
Thus in SiC both elements have tetrahedral coordination; in SiO2 silicon also forms fourtetrahedral bonds, and oxygen two bonds with a nonlinear geometry.Compounds of less electropositive metals also show structural effects that can be attributed to partial covalentbonding. CuCl and ZnO have structures with tetrahedral coordination although from radii the (octahedral) rocksaltstructure would seem more likely. Partial covalent bonding involves some transfer of electrons back from the anions,into the empty 4s and 4p orbitals on Cu+ and Zn2+. Tetrahedral coordination is the normal bonding geometry when acomplete set of s and p orbitals is used in this way (see Topics C2 and C6). Mercury forms an extreme example of thelower coordination numbers often found with post-transition metals: HgII compounds are of generally low ioniccharacter, and two-coordination is common (see Topic G4).Covalent bonding effects sometimes dictate less regular structures than those shown by Cu+ and Zn2+.
Specific delectron effects operate in compounds such as CuO and PdO (see Topics H4 and H5), and some post-transition metalcompounds such as SnO and PbO apparently show the structural influence of nonbonding electron pairs on the cation(see Topic G6).Covalent bonding interactions can also occur between atoms of the same element.
Section D5 describes some structuresthat can arise in this way. Here it is worthwhile noting that the NiAs structure (see Topic D3), never expected forpurely ionic compounds because cations are closer together than in the rocksalt structure, is often found with transitionmetals in combination with less electronegative nonmetals such as S, P and As.
The compounds formed are of low ioniccharacter and frequently show metallic conduction. The close contacts between metal atoms facilitate direct bondinginteraction.Section D—Structure and bonding in solidsD5MORE COMPLEX SOLIDSKey NotesHomoelement bondingTernary structuresMicroporous solidsIntercalation andinsertion compoundsRelated topicsBinary solids with bonds between atoms of the same type includecompounds with ions such asZintl compounds formedbetween electropositive metals and p-block elements of period 3 andbelow, and compounds with metal-metal bonding often formed by 4dand 5d transition metals.Some ternary oxides and halides may have discrete complex ions suchasothers have structures with no such discrete ions. Silicatesshow a range of intermediate possibilities. The compound formulaalone does not indicate the structure type.Zeolites are solids with aluminosilicate frameworks having pores andchannels.
When these are occupied by hydrated ions the compoundsare used as ion exchangers; when the pores are empty they haveuseful catalytic properties.Intercalation compounds are formed from layered structures withadditional atoms or molecules between the layers, insertioncompounds when atoms enter a three-dimensional framework. Manyof these compounds are nonstoichiometric.Inorganic reactions andOxygen (F7)synthesis (B6)Binary compounds: simplestructures (D3)Homoelement bondingBonding between atoms of the same kind may often be present when a binary compound shows an apparently anomalousstoichiometry.
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