SILICATE CRYSTALS

Small cations form structures with coordination num-bers of 3 and 4 (Table 3.1). These cations are often highly charged and generate strong repulsions between adjacent triangles or tetrahedra. As a result, such struc-tures share only corners and possibly edges, but never faces, since to do so would bring the cations too close together. The radius of silicon is only 0.039 nm, whereas that of oxygen is 0.132 nm. Thus silicon and oxygen combine in tetrahedral coordination, with the silicon occupying the space at the center of the tetra-hedron formed by the four oxygens. The tetrahedral arrangement satisfies both the directionality of the bonds (the Si–O bond is about half covalent and half ionic) and the geometry imposed by the radius ratio.

Silicon is very abundant in Earth’s crust, amounting to about 25 percent by weight, but only 0.8 percent by volume. Almost half of igneous rock by weight and 91.8 percent by volume is oxygen.

Silica tetrahedra join only at their corners, and sometimes not at all. Thus many crystal structures are possible, and there is a large number of silicate min-erals. Silicate minerals are classified according to how the silica tetrahedra (SiO₄)^4⫺associate with each other, as shown in Fig. 3.8. The tetrahedral combinations in-crease in complexity from the beginning to the end of the figure. The structural stability increases in the same direction.

Island (independent) silicates are those in which the tetrahedra are not joined to each other. Instead, the four excess oxygen electrons are bonded to other positive ions in the crystal structure. In the olivine group, the minerals have the composition R₂^2⫹ _ SiO₄^4⫺. Garnets contain cations of different valences and coordination numbers R₃^2⫹_R₂^3⫹(SiO₄)₃. The negative charge of the SiO₄group in zircon is all balanced by the single Zr^4⫹. Ring and chain silicates are formed when corners of tetrahedra are shared. The formulas for these structures

contain (SiO₃)^2⫺. The pyroxene minerals are in this class. Enstatite, MgSiO₃, is a simple member of this group. Some of the positions normally occupied by Si^4⫹in single-chain structures may be filled by Al^3⫹.

Substitution of ions of one kind by ions of another type, having either the same or different valence, but the same crystal structure, is termed isomorphous sub-stitution. The term substitution implies a replacement whereby a cation in the structure is replaced at some time by a cation of another type. In reality, however, the replaced cations were never there, and the mineral was formed with its present proportions of the different cations in the structure.

Double chains of indefinite length may form with (Si₄O₁₁)^6⫺as part of the structure. The amphiboles fall into this group (Fig. 3.8). Hornblendes have the same basic structure, but some of the Si^4⫹positions are filled by Al^3⫹. The cations Na^⫹and K^⫹ can be incorporated into the structure to satisfy electrical neutrality; Al^3⫹, Fe^3⫹, Fe^2⫹, and Mn^2⫹ can replace part of the Mg^2⫹ in sixfold coordination, and the (OH)^⫺ group can be re-placed by F^⫺.

In sheet silicates three of the four oxygens of each tetrahedron are shared to give structures containing (Si₂O₅)^2⫺. The micas, chlorites, and many of the clay minerals contain silica in a sheet structure. Framework silicates result when all four of the oxygens are shared with other tetrahedra. The most common example is quartz. In quartz, the silica tetrahedra are grouped to form spirals. The feldspars also have three-dimensional framework structures. Some of the silicon positions are filled by aluminum, and the excess negative charge thus created is balanced by cations of high coordina-tion such as potassium, calcium, sodium, and barium.

Differences in the amounts of this isomorphous sub-stitution are responsible for the different members of the feldspar family.

3.9 SURFACES

All liquids and solids terminate at a surface, or phase boundary, on the other side of which is matter of a different composition or state. In solids, atoms are bonded into a three-dimensional structure, and the ter-mination of this structure at a surface, or phase bound-ary, produces unsatisfied force fields. In a fine-grained particulate material such as clay soil the surface area may be very large relative to the mass of the material, and, as is emphasized throughout this book, the influ-ences of the surface forces on properties and behavior may be very large.

Unsatisfied forces at solid surfaces may be balanced in any of the following ways:

Figure 3.8 Silica tetrahedral arrangements in different silicate mineral structures. Reprinted Gillott (1968) with permission from Elsevier Science Publishers BV.

SURFACES 47

Figure 3.8 (Continued )

1. Attraction and adsorption of molecules from the adjacent phase

2. Cohesion with the surface of another mass of the same substance

3. Solid-state adjustments of the structure beneath the surface.

Each unsatisfied bond force is significant relative to the weight of atoms and molecules. The actual mag-nitude of 10^⫺11 N or less, however, is infinitesimal compared to the weight of a piece of gravel or a grain of sand. On the other hand, consider the effect of re-ducing particle size. A cube 10 mm on an edge has a

surface area of 6.0 _⫻ 10^⫺4 m². If it is cut in half in the three directions, eight cubes result, each 5 mm on an edge. The surface area now is 12.0 _⫻ 10^⫺4 m². If the cubes are further divided to 1m on an edge, the surface becomes 6.0 m² for the same 1000 mm³ of material. Thus, as a solid is subdivided into smaller and smaller units, the proportion of surface area to weight becomes larger and larger. For a given particle shape, the ratio of surface area to volume is inversely proportional to some effective particle diameter.

For many materials when particle size is reduced to 1 or 2 m or less the surface forces begin to exert a distinct influence on the behavior. Study of the behav-ior of particles of this size and less requires consider-ations of colloidal and surface chemistry. Most clay particles behave as colloids, both because of their small size and because they have unbalanced surface electrical forces as a result of isomorphous substitu-tions within their structure.

Montmorillonite, which is one of the members of the smectite clay mineral group (see Section 3.17), may break down into particles that are only 1 unit cell thick (1.0 nm) when in a dispersed state and have a specific surface area of 800 m²/ g. If all particles con-tained in about 10 g of this clay could be spread out side by side, they would cover a football field.

3.10 GRAVEL, SAND, AND SILT PARTICLES