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as hybrids or transitions between ionic and covalent bonds. Materials that possess such bonds commonly display properties that are transitional between those of ionically bonded substances and those of covalently bonded substances. Using the electronegativity difference – the difference between the electronegativities of the two elements sharing the bond – Pauling was able to predict the percentages of covalent and ionic bonding, that is, the percentages of electron sharing and electron transfer that characterize ionic–covalent transitional bonds. Figure 2.15 illustrates the relationship between electronegativity difference and the percentages of ionic and covalent bond character that typify the transitional ionic–covalent bonds.

      Where electronegativity differences in transitional ionic–covalent bonds are smaller than 1.68, the bonds are primarily electron‐sharing covalent bonds. Where electronegativity differences are larger than 1.68, the bonds are primarily electron‐transfer ionic bonds. Calculations of electronegativity and bond type lead to some interesting conclusions. For example, when an oxygen atom with En = 3.44 bonds with another oxygen atom with En = 3.44 to form O₂, the electronegativity difference (3.44 − 3.44 = 0.0) is zero and the resulting bond is 100% covalent. The valence electrons are completely shared by the two oxygen atoms. This will be the case whenever two highly electronegative, nonmetallic atoms of the same element bond together. On the other hand, when highly electronegative, nonmetallic atoms bond with strongly electropositive, metallic elements to form ionically bonded substances, the bond is never purely ionic. There is always at least a small degree of electron sharing and covalent bonding. For example, when sodium (Na) with En = 0.93 bonds with chlorine (Cl) with En = 3.6 to form sodium chloride (NaCl), the electronegativity difference (3.6 − 0.93 = 2.67) is 2.67 and the bond is only 83% ionic and 17% covalent. Although the valence electrons are largely transferred from sodium to chloride and the bond is primarily electrostatic (ionic), a degree of electron sharing (covalent bonding) exists. Even in this paradigm of ionic bonding, electron transfer is incomplete and a degree of electron sharing occurs. The bonding between silicon (Si) and oxygen (O), so important in silicate minerals, is very close to the perfect hybrid since the electronegativity difference is 3.44 − 1.90 = 1.54 and the bond is 45% ionic and 55% covalent.

Figure 2.15 Graph showing the electronegativity difference and bond type in covalent–ionic bonds. Percent covalent bonding is indicated by the black line and percent ionic bonding by the blue line.

This simple picture of transitional ionic–covalent bonding does not hold in bonds that involve transition metals. For example, the mineral galena (PbS) has properties that suggest its bonding is transitional between metallic and ionic. In this case some electrons are partially transferred from lead (Pb) to sulfur (S) in the manner characteristic of ionically bonded substances, but some electrons are weakly held in the manner characteristic of metallic bonds. As a result, galena displays both ionic properties (brittle and somewhat soluble) and metallic properties (soft, opaque and a metallic luster). Figure 2.16 utilizes a triangle, with pure covalent, ionic and metallic bonds at the apices, to depict the pure and transitional bonding characteristic of selected minerals, including those discussed above.

Figure 2.16 Triangular diagram representing the bond types of some common minerals.

      2.3.6 Van der Waals and hydrogen bonds

Because the distributions of electrons in the electron cloud are probabilistic and constantly changing, they may be, at any moment, asymmetrically distributed within the electron cloud. This asymmetry gives rise to weak electric dipoles on the surface of the electron cloud; areas of excess negative charge concentration where the electrons are located and areas of negative charge deficit (momentary positive charge) where they are absent. Areas of momentary positive charge on one atom attract electrons in an adjacent atom, thus inducing a dipole in that atom. The areas of excess negative charge on one atom are attracted to the areas of positive charge on an adjacent atom to form a very weak bond that holds the atoms together (Figure 2.17). Bonds that result from weak electric dipole forces that are caused by the asymmetrical distribution of electrons in the electron cloud are called van der Waals bonds. The presence of very weak van der Waals bonds helps to explain why minerals such as graphite and talc are extremely soft and have a “greasy” feel (Chapter 5).

Figure 2.17 Van der Waals bonding occurs when one atom becomes dipolar as the result of the random concentration of electrons in one region of an atom. The positively charged region of the atom attracts electrons in an adjacent atom causing it to become dipolar. Oppositely charged portions of adjacent dipolar atoms are attracted creating a weak van der Waals bond. Larger structures result from multiple bonds.

Figure 2.18 Diagram showing two water molecules joined by a hydrogen bond that links the hydrogen in one molecule to the oxygen in the other molecule.

Hydrogen bonds exist between electropositive hydrogen and electronegative ions such as oxygen in molecules such as water or hydroxyl ions. Because of the profound importance of water (H₂O) and hydroxyl ion (OH⁻¹), in both organic and inorganic compounds, this type of bond has been given its own separate designation (Figure 2.18). Hydrogen bonds are relatively weak bonds that occur in hydrated (water‐bearing) or hydroxide (hydroxyl‐bearing) minerals.

      Atoms are held together by a variety of chemical bonds. The type of bond that forms depends largely on the electron configurations of the combining elements, as expressed by their electronegativities, although environmental factors also play a role. Each bond type imparts certain sets of properties to Earth materials that contain those bonds. In the following section we will discuss factors that determine the three‐dimensional properties of the molecular units that result from such bonding. In Chapter 4 we will elaborate on the long‐range crystalline structures that form when these molecular units combine to produce crystals. Remember: it all starts with atoms, their electron properties and the way they bond together to produce crystals.

2.4 PAULING'S RULES AND COORDINATION POLYHEDRA

      2.4.1 Pauling's rules and radius ratios

      Linus Pauling (1929) established five rules, now called Pauling's rules, which describe cation–anion relationships in ionically bonded substances and are paraphrased below:

       Rule 1: A polyhedron of anions is formed about each cation, with the distance between a cation and an anion determined by the sum of their radii (radius sum).

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