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2.20). The electrostatic valency of each bond is given by EV = Z/CN = +4/4 = +1. What this means is that each bond between the coordinating silicon ion (Si⁺⁴) and the coordinated oxygen ions (O⁻²) balances a charge of +1. Another way to look at this is to say that each bond involves an electrostatic attraction between ions of opposite charge of one charge unit. Since there are four Si–O bonds, each balancing a charge of +1, the +4 charge on the silicon ion is fully neutralized by the four nearest neighbor anions to which it is bonded. However, although the +4 charge on the coordinating silicon ion is fully satisfied, the −2 charge on each of the coordinated ions is not. Since each has a −2 charge, a single bond involving an electrostatic attraction of one charge unit neutralizes only half their charge. They must attract and bond to one or more additional cations, with an additional total electrostatic valency of one, in order to have their charges effectively neutralized. So it is that during mineral growth, cations attract anions and anions attract additional cations of the appropriate charge and radius which in turn attract additional anions of the appropriate charge and radius as the mineral grows. In this manner minerals retain their essential geometric patterns and their ions are neutralized as the mineral grows. In the following section we will introduce the major mineral groups and see how their crystal chemistry forms the basis of the mineral classification.

Figure 2.19 Common coordination polyhedra: (a) cubic closest packing, (b) cubic, (c) octahedral, (d) tetrahedral, (e) triangular, (f) linear.

      Source: Wenk and Bulakh (2004). © Cambridge University Press.

Table 2.6 Variations in ionic radius (in angstroms) with coordination number (CN) for some common cations.

Ion	CN = 4	CN = 6	CN = 8
Na+1	0.99	1.02	1.18
K+1		1.38	1.51
Rb+1		1.52	1.61
Cs+1		1.67	1.74
Mg+2	0.57	0.72
Al+3	0.39	0.48
Si+4	0.26	0.40
P+5	0.17	0.38
S+6	0.12	0.29

2.5 THE CHEMICAL CLASSIFICATION OF MINERALS

The formation and growth of most minerals can be modeled by the attractive forces between cations and anions, the formation of coordination polyhedra with unsatisfied negative charges and the attraction of additional ions to build additional coordination polyhedra ad infinitum, until the conditions for growth cease to exist. It is useful to visualize minerals in terms of major anions and anion groups and/or radicals bonded to various cations that effectively neutralize their charge during the formation and growth of minerals. One common way to group or classify minerals is to do so in terms of the major anion group in the mineral structure. Those that contain (SiO₄)⁻⁴ silica tetrahedra, discussed in the previous section, are silicate minerals, by far the most common minerals in Earth's crust and upper mantle. Those that do not contain silica tetrahedra are nonsilicate minerals and are further subdivided on the basis of their major anions. Table 2.7 summarizes the common mineral groups according to this classification system. These groups are discussed in more detail in Chapter 5.

Figure 2.20 A silica tetrahedron is formed when four oxygen ions (O⁻²) bond to one silicon ion (Si⁺⁴) in the form of a tetrahedron. The electrostatic valency of each silicon–oxygen bond in the silica tetrahedron is one charge unit, which fully neutralizes the charge on the central silicon ion (four = four), while leaving the charge on the oxygen ions only partially neutralized (one is one‐half of two).

Table 2.7 Mineral classification based on the major anion groups.

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Mineral group	Major anion groups	Mineral group	Major anion groups
Native elements	None	Nitrates	(NO3)−1
Halides	F−1, Cl−1, Br−1	Borates	(BO3)−3 and (BO4)−5
Sulfides	S−2, S−4	Sulfates	(SO4)−2
Arsenides	As−2, As−3	Phosphates	(PO4)−3
Sulfarsendies	As−2 or As−3 and S−2 or S−4	Chromates	(CrO4)−5
Selenides	Se−2	Arsenates	(AsO4)−3
Tellurides	Te−2	Vanadates	(VO4)−3
Oxides	O−2