Geochemistry. William M. White

Figure 1.8 (a) Geometry of the water molecule. (b) Hydrogen bonds between water molecules. The δ+ and δ– indicate partial positive and negative charges, respectively.

      Geometry becomes enormously important for organic molecules and life. For example, C₁₂H₂₂O₁₁ is the chemical formula for both lactose and sucrose, as well as several other disaccharide carbohydrates, but the atoms are stitched together differently and as a result they have quite different properties. Among other things, all adults (and essentially all animals) can readily digest sucrose, but many adult humans (and most adult mammals) cannot digest lactose. In other molecules, even slight variations in structure, for example, a molecular structure and its mirror image can have quite different properties – a topic we'll explore briefly in Chapter 12.

      Molecules are not necessarily static entities. An important feature of some molecules is the ability to dissociate. This is particularly true of both water and carbonic acid, which can give up hydrogen atoms. Acidity reflects the balance between H⁺ (strictly speaking H₃O⁺) and OH^– ions; these must be equal in pure water, but a solution of CO₂ in water will have an excess of H⁺ and hence be acidic. These hydrogen ions can also reassociate with their parent molecules and do so when H ions become abundant.

The bonds between atoms in molecules are also not static, but rather bond lengths and bond angles continually oscillate about their mean values. For example, the water molecule has three fundamental modes of vibration: two stretching vibrations of the O-H bond (one symmetric, one asymmetric) and a bending vibration in which the bond angle changes. Vibrational frequencies are proportional to bond strength and increase with increasing temperature (in stepwise fashion, as they are quantized), although many molecules remain in the ground state vibrational frequencies over the range of temperatures at the Earth's surface. These vibrations are responsible for some of the interaction of molecules with light. For example, the frequencies of the stretching vibrations of water and CO₂ correspond to near-infrared electromagnetic frequencies and as a consequence both molecules absorb infrared photons, and hence both are important greenhouse gases.

       1.5.5.2 Crystals

      The solid Earth, however, is not made up of molecules. Instead, it is made up almost entirely of minerals. By definition, a mineral is a crystalline solid. Crystals are infinitely repeating lattice structures that define the fixed positions of atoms and the geometric relationships between them (but just as in molecules, atoms vibrate in crystals). Just as the chemical formula of molecule, for example C₁₂H₂₂O₁₁, does not tell us all we need to know about that compound, a chemical formula of a crystal such as quartz, SiO₂, does not tell us everything we need to know about that crystal as SIO₂ has several polymorphs, such as cristobalite and tridymite. Nothing demonstrates this better than the difference between the two polymorphs of carbon: graphite and diamond, which differ only in the way carbon atoms are bound together.

The most abundant elements in the Earth are O and Fe (both close to 32%), Mg (∼15%), Si (∼14%), Ni (∼1.8%), Ca (1.7%), and Al (1.6%). The majority of the Earth's Fe and Ni are in the core. The remaining rocky part of the Earth, the mantle and crust, consists of ∼44% O, ∼23% Mg, ∼21% Si, ∼8% Fe, ∼2.5% Ca, and ∼2.4% Al. As a consequence, the outer part of the Earth consists almost entirely of silicate minerals, in which the basic structural unit is , in which four oxygens are arranged around the silicon atom to form a tetrahedron (Figure 1.9a). The simplest of silicates is quartz, with a chemical formula of SiO₂.

How do we go from to the chemical formula of SiO₂? Each oxygen atom shared by two silicon atoms; that is, each is part of two tetrahedra. These linked tetrahedra are repeated infinitely to produce a quartz crystal (Figure 1.9b). We can define a unit cell that contains all the necessary information to describe both the chemical and structural elements of quartz (Figure 1.9c). The unit cell of lattice is defined by the length of three axes and the angles between them. In the case of quartz, the lattice cell has the chemical formula of Si₃O₆ and axes of lengths: a = 0.49 nm, b = 0.49 nm, and c = 0.54 nm, with the b–c and b–a angles are equal to 90° and the angle between the a and c axes equal to 120°. The quartz crystal is built up by repetition of the unit cell along its principal axes.

Figure 1.9 (a) The silica tetrahedron,

, consists of a silicon atom surrounded by four oxygens. This is the basic building block of silicate minerals. (b) In quartz, each oxygen (gray) is shared between two tetrahedra to produce a three-dimensional structure. (c) The quartz unit cell consists of a central Si atom whole within the cell and with four Si atoms on the edges that are shared by adjacent unit cells, hence it contains 1 + 4 × ½ Si = 3 Si (faded silicon atoms are outside the cell). Six oxygens are wholly within the cell, so the chemical formula of the cell is Si₃O₆; a, b, and c are the crystallographic axes.

      Crystals have varying degrees of symmetry that can be divided into seven different systems, which, with decreasing symmetry, are cubic, hexagonal, trigonal, tetragonal, orthorhombic, monoclinic, and triclinic (sometimes trigonal is included with hexagonal to give only six systems). The cubic system has the highest symmetry, with all three axes of equal length and all three angles equal to 90°; triclinic has the lowest, with no axes of equal length and no angles of 90°. Diamond is an example of a cubic mineral. Quartz, with two equal length axes and one 120° angle, is an example of a trigonal mineral. Graphite, in its most common form, is hexagonal. Since all axes are equal in cubic crystals, they transmit light and vibrations, sound, and seismic waves, equally in all directions. Hexagonal, trigonal, and tetragonal have one unique crystallographic axis that transmits light and sound at different velocities than the other two and are said to be uniaxial. The least symmetric classes, orthorhombic, monoclinic, and triclinic as said to be biaxial and transmit light and sound at three different velocities along the three axes.

Minerals are by definition naturally occurring inorganic crystalline solids. Most minerals are “ionic solids” that consist of cations, metals or metalloids, bound to nonmetals or anionic radicals (although the bonds can have a partly covalent character; in quartz for example, bonds between the oxygens and silicon are roughly 50% covalent and quite strong). In the majority of minerals, several metals are present and only a single anion, most often oxygen. For these kinds of crystals, rules elaborated by Linus Pauling in 1929, known as Pauling's rules, dictate crystal structure. The first of these is that the ratio of cation to anion radius determines

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