Inorganic Chemistry

(more correctly known as a clinographic projection), which is 
the most common way of showing a unit cell. 
(b) Figure 1b shows a projection down one axis of the cell. The position of an atom on the hidden 
axis is given by specifying a fractional coordinate (e.g. 0.5 for the central atom showing it is halfway 
up). No coordinate is given for atoms at the base of the cell. 
(c) Figure 1c shows the atoms shifted relative to the unit cell, and emphasizes the fact that what is 
important about a unit cell is its size and shape; its origin is arbitrary because of the way in which it 
is repeated to fill space. 
(d) In Figure. 1d the drawing has been extended to show some repeated positions of the central 
atom. This helps in seeing the coordination of the corner atom (see below). 
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Fig. 1. Alternative views of the CsCl structure (see text). 
Nonstoichiometry 
Whereas a pure molecular substance has a definite stoichiometry, this is not always true for solids. 
Defects in crystals can include vacancies (atoms missing from their expected sites) and interstitials 
(extra atoms in sites normally vacant in the unit cell). An imbalance of defects involving different 
elements can introduce nonstoichiometry. This is common in compounds of transition metals, 
where variable oxidation states are possible (see Topics D5 and H4). For example, the sodium 
tungsten bronzes are formulated as NaxWO3, where x can have any value in the range 0\u20130.9. 
Another form of nonstoichiometry arises from the partial replacement of one element by another 
in a crystal. It is common in natural minerals, such as the aluminosilicate feldspars (Na,Ca)(Al,Si)
4O8. The notation (Na,Ca) means that Na and Ca can be present in the same crystal sites in varying 
proportions. Simultaneous (Si,Al) replacement ensures that all elements remain in their normal 
oxidation states. Even this formulation is approximate, as several other elements may be present in 
smaller proportions. 
Chemical classification 
Solids are often classified according to their chemical bonding, structures and properties (see Topic 
B1): 
Molecular solids contain discrete molecular units held by relatively weak intermolecular forces (see 
Topic C10). 
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Metallic solids have atoms with high coordination numbers, bound by delocalized electrons that 
give metallic conduction. 
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Although these broad distinctions are useful, many solids show a degree of intermediate character, or 
even several types of bonding simultaneously. Metallic and covalent interactions both arise from 
overlapping atomic orbitals (see Topics C4\u2013C7) and the distinction in physical properties arises from 
the energy distribution of electronic levels (see Topic D7). The structures and electronic properties 
of elements show a gradation in character at the metal-nonmetal borderline (see Topics B2 and D2). 
A similar gradation is seen between ionic and covalent compounds as the electronegativity 
difference between two elements changes (see Topics B1 and D4). Furthermore, solids with 
predominantly ionic bonding between some atoms can also have covalent bonds between others (see 
Topic D5). 
Covalent or polymeric solids have atoms bound by directional covalent bonds, giving relatively low 
coordination numbers in a continuous one-, two- or three-dimensional network. 
Ionic solids are bound by electrostatic attraction between anions and cations, with structures where 
every anion is surrounded by cations and vice versa. 
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Section D\u2014Structure and bonding in solids 
D2 
ELEMENT STRUCTURES 
Sphere packing 
Element structures where chemical bonding is nondirectional are best introduced by considering the 
packing of equal spheres. Close-packed structures are ones that fill space most efficiently. In two 
dimensions this is achieved in a layer with each sphere surrounded hexagonally by six others. Three-
dimensional structures are developed by stacking these layers so that the spheres in one layer fall 
over the hollows in the one below, as shown in Fig. 1a. Having placed two layers, labeled A and B, 
there are alternative positions for the spheres in the third layer. They could be placed directly over 
spheres in the first layer A to give a sequence denoted ABA. Alternatively, the spheres in the third 
layer can be placed in positions where there are gaps in layer A; two such spheres labeled C are 
shown in Fig. 1a. A regular packing based on this latter arrangement would then place the fourth 
layer directly over layer A, giving a sequence denoted ABCA. The simplest three-dimensional close-
packed structures are based on these two regular sequences of layer positions: 
These structures are illustrated in Fig. 1b and c, respectively. In the ccp arrangement, successive 
close-packed layers are placed along the body diagonal of a cube. The unit cell shown is based on a 
cube with atoms in the face positions, and the structure is also known commonly as face-centered 
cubic (fcc). 
Key Notes 
Sphere 
packing 
Spheres of equal size may be packed in three dimensions to give hexagonal close-packed 
(hcp) and cubic close-packed (ccp, also known as face-centered cubic, fcc) structures. The 
body-centered cubic (bcc) structure is slightly less efficiently close packed. 
Metallic 
elements 
Many metallic elements have hcp, fcc or bcc structures. There are some clear group trends in 
structure, although there are exceptions to these and some metals have less regular structures, 
especially in the p block. 
Nonmetallic 
elements 
Most nonmetallic elements have structures that can be understood using simple electron-pair 
bonding models. C, N and O can form multiple bonds and are exceptional in their groups. 
Related topics Chemical periodicity (B2) Introduction to nonmetals (F1) 
ABABABAB\u2026gives hexagonal close packing (hcp); 
ABCABCABC\u2026gives cubic close packing (ccp).
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Fig. 1. Close-packed structures, (a) Stacking of layers showing the sequence ABC (see 
text); (b) the hcp structure; (c) one unit cell of the fcc structure. 
In both fcc and hcp structures each sphere is surrounded by 12 others at the same near-neighbor 
distance. (There are six in the same close-packed layer, and three each in the layers above and 
below.) If the spheres are in contact both structures give 74% filling of space by the spheres, with the 
remaining 26% outside them. This is the optimum space filling possible with equal spheres. 
Similarly close-packed structures can be constructed from more complicated sequences of layers 
such as ABABCABABC\u2026, or even with random sequences. Although these are sometimes found, 
most close-packed structures are of the simple fcc or hcp types. 
Another structure that gives fairly efficient space filling (68% compared with 74% above) is the 
body-centered cubic (bcc) one illustrated in Fig. 2. Each atom has eight near-neighbors, but there 
are six others (also shown in the figure) slightly further away. 
 
Fig. 2. Bcc structure. 
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Metallic elements 
A high proportion of metallic elements have one of the three structures ccp, hcp or bcc just 
described. The factors that determine the