that coordinate the cation and the shape of the coordinated polyhedron of anions. Smaller cations will be surrounded by few anions, larger cations will be coordinated by more anions (Figure 1.10). When the cation/anion radius ratio is <0.22, three anions will coordinate each anion, forming a triangular polyhedron; when the ratio is >0.22 and <0.414, four anions coordinate the cation; the radius Si4+ is 40 pm, that of O2– is 126 pm, so the ratio is 0.317. As a result, the four oxygens form a tetrahedron around silicon. For a ratio >0.414 and <0.73, six anions surround the cation in octahedral coordination, as in halite, which has a Na+/Cl– radius ratio is 0.56. If the ratio is ≥0.73, eight coordinating anions will form a cube. Pauling's second rule is that the electrostatic bond strength between the cation and each coordinating anion is equal to the cation charge divided by the number of coordinating anions. So highly charged, small cations are more strongly bond than large ones with smaller charge.
Figure 1.10 Geometric relationships between cations and their coordinating anions. Because they have fewer electrons relative to protons, cations tend to be small, while anions, with excess electrons, tend to be large. The number of anions that immediately surround and bond to a cation depends on the relative radii. Small cations, such as B3+ in the borate ion, are coordinated by only three oxygens, Si in quartz by four, and Na in halite by six; if Na+ is replace by Cs+, a much larger ion, the coordination number increases to eight.
Another of Pauling's rules is that in a crystal containing different cations, those of high valency and small coordination number tend not to share polyhedron elements with one another. Most silicate minerals contain more than one cation; like quartz, the Si tetrahedron is the basic structural unit, but unlike quartz, not all oxygens are shared. In orthosilicates, the silica tetrahedra are either completely independent or form dimers – that is, two linked tetrahedra. A good example of a mineral of this type is olivine, whose structure is illustrated in Figure 1.11a. The chemical formula for olivine is (Mg,Fe)2SiO4. The notation (Mg,Fe) indicates that either magnesium or iron or both may be present. Olivine is an example of a solid solution between the Mg end-member, forsterite (Mg2SiO4), and the Fe end-member, fayalite (Fe2SiO4). Such solid solutions are quite common among silicates. As the formula indicates, there are two magnesium or iron atoms for each silica tetrahedron. Since each Mg or Fe has a charge of +2, their charge balances the −4 charge of each silica tetrahedron. Olivine constitutes roughly 50% of the Earth's upper mantle and is thus one of the most abundant minerals on Earth.
In chain silicates, the silica tetrahedra are linked together to form infinite chains (Figure 1.11b and c), with two bridging oxygen per tetrahedron. Oxygens shared by two silicons are called bridging oxygens. Minerals of this group are known as pyroxenes and have the general formula XSiO3 where X is some metal, most commonly Ca, Mg, or Fe, which is located between the chains. Two pyroxenes, orthopyroxene ((Mg,Fe)SiO3) and clinopyroxene (Ca(Mg,Fe)Si2O6) are very abundant in the Earth's upper mantle as well as in mafic igneous rocks. The pyroxenes wollastonite (CaSiO3) and jadeite (NaAlSi2O6) are found exclusively in metamorphic rocks.
Figure 1.11 Silicate mineral structures. (a) In orthosilicates such as olivine, the tetrahedra are separate and each oxygen is also bound to other metal ions that occupy interstitial sites between the tetrahedra. (b) In pyroxenes, the tetrahedra each share two oxygens and are bound together into chains. (c) Metal ions are located between the chains in pyroxenes. (d) In sheet silicates, such as talc, mica, and clays, the tetrahedra each share three oxygens and are bound together into sheets.
In double chain silicates, an additional one-half bridging oxygen per tetrahedra joins two chains together. Minerals of this group are known as amphiboles, which occur widely in both igneous and metamorphic rocks. Among the important minerals in this group are hornblende (Ca2Na(Mg,Fe)4Al3Si8O22(OH)2), tremolite-actinolite (Ca2(Mg,Fe)5Si8O22(OH)2), and glaucophane (Ca2(Mg,Fe)3Al3Si8O22(OH)2). These minerals all contain OH as an essential component (Cl or F sometimes substitutes for OH). They are thus examples of hydrous silicates.
Sharing of a third oxygen links the tetrahedra into sheets, forming the sheet silicates (Figure 1.11d). This group includes micas such as biotite (K(Mg,Fe)3AlSi3O10(OH)2) and muscovite (KAl3Si3O10 (OH)2), talc (Mg3Si4O10(OH)2), and clay minerals such as kaolinite (Al2Si2O5(OH)4). As in amphiboles, OH is an essential component of sheet silicates. Many of these minerals form through weathering and are thus primary sedimentary minerals. Many of them are found in igneous and metamorphic rocks as well.
When all four oxygens are shared between tetrahedra, the result is a framework. The simplest framework silicate is quartz (SiO2), which consists solely of linked SiO4 tetrahedra. The other important group of framework silicates is the feldspars, of which there are three end-members: sanidine (KAlSi3O8), albite (NaAlSi3O8), and anorthite (CaAl2Si2O8). The calcium and sodium feldspars form the plagioclase solid solution, which is stable through a large temperature range. Sodium and potassium feldspars, collectively called alkali feldspar, form more limited solid solutions, as we will find in Chapter 4. Feldspars are the most abundant minerals in the Earth's crust.
Because only a single anion or anionic group is present in the common minerals (the presence of OH– in many kinds of silicates is an important exception), minerals are classified compositionally by the nature of the anion or anionic group. Silicates, as we noted, are the most abundant compositional class. Other classes of minerals include oxides, in which one or more metals are bound to oxygen, for example, magnetite (Fe3O4) and ilmenite (FeTiO3), Carbonates are a particularly important and abundant class of minerals at the Earth's surface, of which calcite (CaCO3) is by far the most important. Other important groups include sulfates, such as gypsum (CaSO4.2H2O), hydroxides such as gibbsite (Al(OH)3), sulfides such as pyrite FeS2, halides, such as halite (NaCl) and fluorite (CaF), and phosphates, of which only one, apatite (Ca5(PO4)3(OH,F,Cl) is common. There are others as well, such as “native” minerals, consisting of a single element such as diamond, borates, arsenates, etc.
1.6
