Earth Materials. John O'Brien

University Press 621 pp.

Chapter 3 Atomic substitution, phase diagrams, and isotopes

      1  3.1 Atomic (ionic) substitutio

      2  3.2 Phase stability (equilibrium) diagrams

      3  3.3 Isotopes

3.1 ATOMIC (IONIC) SUBSTITUTION

      Minerals are composed of atoms or ions that occupy structural sites in a crystal structure (Chapter 2). Different ions can occupy the same structural site if (1) they have similar size, (2) have similar charge, and (3) are available in the environment in which the mineral is forming. This process of one ion replacing another ion is called ionic substitution. In mineral formulas, ions that commonly substitute for one another are generally placed within a single set of parentheses. In the olivine group, iron and magnesium can freely substitute for one another in the sixfold, octahedral site. As a result, the formula for olivine is commonly written as (Mg,Fe)₂SiO₄.

Substitution is favored for ions of similar ionic radius. In general, cation substitution at surface temperatures and pressures is limited when the larger cation radii exceed the smaller by 10–15% and becomes negligible for differences greater than 30%. Such ions are “too big” or “too small” to easily substitute for one another (Figure 3.1a), while ions of similar size are “just right.” Substitution of ions of significantly different radii distorts coordination polyhedra and decreases the stability of crystals. However, at higher temperatures, where the crystal structure is expanded, ions with larger differences in radius may more easily substitute for one another.

Substitution is favored for ions of similar charge. Where substitutions occur in only one coordination site, substitution is largely limited to ions with the same charge (Figure 3.1b). This enables the mineral to remain electrically neutral, which increases its stability. However, where substitution can occur in multiple coordination sites, ions of different charge may substitute for one another in one site so long as this charge difference is balanced by a second substitution of ions of different charge in a second coordination site.

Figure 3.1 Criteria for substitution are (a) similar size, (b) similar charge and (not shown) availability.

      Substitution is favored for ions that are widely available in the environment in which the mineral is growing (Figure 3.1). As minerals grow, coordination sites will preferentially select ions with the appropriate radii and charge that are available in the vicinity of the growing crystal. The ions that occupy a coordination site in a mineral provide vital clues to the chemical composition of the system and environmental conditions under which crystallization occurred.

      3.1.1 Simple ionic substitution

Simple, complete substitution exists when two or more ions of similar radii and the same charge may substitute for one another in a coordination site in any proportions. In such cases, it is convenient to define end members or components that have only one type of ion in the structural site in question. The olivine group illustrates complete substitution. In the olivine group, (Mg,Fe)₂SiO₄, Mg⁺² (radius = 0.66 Å) and Fe⁺² (radius = 0.74 Å) can substitute for one another in the octahedral site in any proportion. The two end members are the pure magnesium silicate component called forsterite [(Mg)₂SiO₄] and the pure iron silicate component called fayalite [(Fe)₂SiO₄]. Since these two end members can substitute for one another in any proportion in olivine, a complete solid solution series exists between them. As a result, the composition of any olivine can be expressed in terms of the proportions of forsterite (Fo) and/or fayalite (Fa). Simple two‐component, complete solid solution series are easily represented by a number line called a tie line between the two end members (Figure 3.2).

Compositions of any olivine can be represented in a number of different ways. For example, pure magnesium olivine can be represented by (1) a formula (Mg₂SiO₄), (2) a name (forsterite), (3) its position on the tie line (far right) or (4) the proportion of either end member (Fo₁₀₀ or Fa₀). Similarly, pure iron olivine can be represented by a formula (Fe₂SiO₄), a name (fayalite), its position on the tie line (far left) or the proportion of either end member (Fo₀ or Fa₁₀₀). Any composition in the olivine complete solid solution series can be similarly represented. For example, the composition of an olivine with equal amounts of the two end member components can be represented by the formula [(Mg_0.5,Fe_0.5)₂SiO₄], its position on the tie line (halfway between the ends), or the proportions of either end member (Fo₅₀ or Fa₅₀). Typically the forsterite component is used (e.g., Fo₅₀) and the fayalite (Fa) component (100 – Fo) is implied.

Figure 3.2 Olivine complete substitution solid solution series.

In cases where three ions substitute freely for one another in the same coordination site, it is convenient to define three end member components. Each of these end member components contains only one of the three ions in the structural site in which substitution occurs. For example, ferrous iron (Fe⁺²), magnesium (Mg⁺²), and manganese (Mn⁺²) can all substitute for one another in any proportions in the cation site of rhombohedral carbonates. The general formula for such carbonate minerals can be written as (Fe,Mg,Mn)CO₃.The three end member components are the “pure” minerals siderite (FeCO₃), magnesite (MgCO₃), and rhodochrosite (MnCO₃). On a three‐component diagram, the three pure end member components are plotted at the three apices of a triangle (Figure 3.3).

Figure 3.3 Compositions of carbonate minerals expressed in terms of the proportions of iron, magnesium, and manganese; that is of the three components: siderite (Sd), magnesite (Ms), and rhodochrosite (Rc) plotted on a ternary diagram.

Points on the apices of the triangle represent “pure” carbonate minerals with only one end member component. Percentages of any component decrease systematically from 100% at the apex toward the opposite side of the triangle where its percentage is zero. Each side of the triangle is a tie line connecting two end members. Points on the sides represent carbonate solid solutions between