Earth Materials. John O'Brien

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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:

      Pauling's rules provide important tools for understanding crystal structures. Especially important is the rule concerning radius ratio and coordination polyhedra. Coordination polyhedra provide a powerful means for visualizing crystal structures and their relationship to crystal chemistry. In fact, they provide a fundamental link between the two. When atoms and ions combine to form crystals, they bond together into geometric patterns in which each atom or ion is bonded to a number of nearest neighbors. The number of nearest neighbor ions or atoms is called the coordination number (CN). Clusters of atoms or ions bonded to other coordinating atoms produce coordination polyhedron structures. Polyhedrons include triangles, cubes, octahedra, tetrahedra, and other geometric forms.

      When ions of opposite charge combine to form minerals, each cation attracts as many nearest neighbor anions as can fit around it as approximate “spheres in contact”. In this way, the basic units of crystal structure are formed which grow into crystals as multiples of such units are added to the existing structure. One can visualize crystal structures in terms of different coordinating cations and coordinated anions that together define a simple three‐dimensional polyhedron structure. As detailed in Chapters 3 and 4, complex polyhedral structures develop by linking of multiple coordination polyhedra.

The number of nearest neighbor anions that can be coordinated with a single cation “as spheres in contact” depends on the radius ratio (RR = Rc/Ra) which is the radius of the smaller cation (Rc) divided by the radius of the larger anion (Ra). For very small, highly charged cations coordinated with much larger, highly charged anions, the radius ratio (RR) and the coordination number (CN) are small. This is analogous to fitting basketballs as spheres in contact around a small marble. Only two basketballs can fit as spheres in contact with the marble. For cations of smaller charge coordinated with anions of smaller charge, the coordination number is larger. This is analogous to fitting golf balls around a larger marble. One can fit a larger number of golf balls around a large marble as spheres in contact because the radius ratio is larger.

Table 2.5 Relationship between radius ratio, coordination number, and coordination polyhedra.