Earth Materials. John O'Brien
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Название: Earth Materials
Автор: John O'Brien
Издательство: John Wiley & Sons Limited
Жанр: География
isbn: 9781119512219
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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 [(Mg0.5,Fe0.5)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 two end member components. Point A on Figure 3.3 lies on the side opposite the magnesite apex and so contains no magnesium. Because it lies halfway between rhodochrosite and siderite, its composition may be written as Rc50Sd50 or as (Mn0.5,Fe0.5)CO3. Any point that lies within the triangle represents a solid solution that contains all three end member components. The precise composition of any three‐component solid solution can be determined by the distance from the point to the three apices of the triangle. Point B in Figure 3.3 lies closest to the rhodochrosite apex and farthest from the magnesite apex and so clearly contains more Mn than Fe and more Fe than Mg. Its precise composition can be expressed as Sd10Ms2Rc88 or as (Fe0.10,Mg0.02,Mn0.88)CO3. Many other examples of three‐component systems with complete solid solution exist; all may be represented in a similar fashion by their position on a triangular diagram.
3.1.2 Coupled (paired) ionic substitution
Coupled (paired) ionic substitution involves the simultaneous substitution of ions of different charges in two different structural sites in a way that preserves the electrical neutrality of the crystal lattice (Figure 3.4). The substitution of ions of different charge in one structural site changes the electric charge of the crystal lattice; this requires a second set of substitutions of ions in a second structural site to balance that change in charge. Many examples of coupled ionic substitution exist; none are more important than those that occur in the plagioclase feldspars, the most abundant mineral group in Earth's crust.
In the plagioclase feldspars, similar size ions of sodium (Na+1) and calcium (Ca+2) can substitute for one another in any proportion in the large cation coordination site. However, when calcium (Ca+2) substitutes for sodium (Na+1), the positive charge of the crystal lattice is increased, and when the reverse occurs, the positive charge of the lattice is decreased. These changes in charge are balanced by a second set of substitutions. This second set of substitutions occurs in the small tetrahedral cation coordination site where aluminum (Al+3) and silicon (Si+4) substitute for one another. When a sodium (Na+1) ion is added to the large cation coordination site, a silicon (Si+4) ion is added to the small cation structural site. The two sites together contain a total charge of +5 that is balanced by the anions in the plagioclase structure. When a calcium (Ca+2) is added to the large cation site, an aluminum (Al+3) is added to the small cation site. Once again, the two sites together contain a total charge of +5 which is balanced by the anions in the plagioclase structure. The two substitutions are paired. If a sodium (Na+1) ion replaces a calcium (Ca+2) ion in the first coordination site, a silicon (Si+4) ion must simultaneously replace an aluminum (Al+3) ion in the second structural site for the two sites to total +5, so that the electrical neutrality of the crystal lattice is maintained. Ideally all substitutions are paired and any change in the proportion of sodium to calcium (Na/Ca) in the large ion site is balanced by a similar change in the proportion of silicon to aluminum (Si/Al) in the small ion site. As a result, the general composition of plagioclase can be represented by the formula (Na,Ca)(Si,Al)AlSi2O8 to emphasize the nature of coupled ionic substitutions.