Earth Materials. John O'Brien. Читать онлайн. Newlib. NEWLIB.NET

Автор: John O'Brien
Издательство: John Wiley & Sons Limited
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Жанр произведения: География
Год издания: 0
isbn: 9781119512219
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target="_blank" rel="nofollow" href="#ulink_db4eb72b-b86d-569e-a9c2-c7ca7a0c78b7">Figure 4.15 A pyritohedron, a closed form in which all faces have the same general relationship to the crystallographic axes.

Schematic illustration of different types of dipyramid forms in the trigonal, tetragonal, and hexagonal systems.

      Source: Klein and Hurlbut (1985). © John Wiley & Sons.

      The most common crystal forms in each system are discussed later in this chapter, after we have presented the language used to describe them. More detailed discussions are available in Nesse (2016) and Klein and Dutrow (2007).

      4.6.1 Axial ratios

      Whatever their respective lengths, the proportional lengths or axial ratios of the three crystallographic axes (a : b : c) can be calculated. The standard method for expressing axial ratios is to express their lengths relative to the length of the b‐axis (or a2‐axis) which is taken to be unity so that the ratio is expressed as a : b : c; b = 1. This is accomplished by dividing the lengths of all three axes by the length of the b‐axis (a/b: b/b: c/b). An example from the monoclinic system, the pseudo‐orthorhombic mineral staurolite, will illustrate how axial ratios are calculated. In staurolite, the unit cell edges have average dimensions expressed in angstrom (Å) units of: a = 7.87 Å, b = 16.58 Å, and c = 5.64 Å. The axial ratios are calculated from a/b : b/b : c/b = 7.87/16.58 Å : 16.58/16.58 Å : 5.64/16.58 Å. The average axial ratios of staurolite are 0.47 : 1.00 : 0.34.

      Axial ratios are essential to understanding how crystallographic planes and crystal forms are described or indexed by reference to the crystallographic axes as discussed in the section that follows.

      4.6.2 Crystal planes and crystallographic axes

Schematic illustration of (a) Common open forms: pedions, pinacoids, domes, sphenoids, and pyramids. (b) Different types of prisms that characterize the orthorhombic, trigonal, tetragonal, and hexagonal systems.

      Source: Klein and Hurlbut (1985). © John Wiley & Sons.

      In addition, any set of parallel planes in a crystal is ideally characterized by a particular molecular content; all the parallel planes in the set possess closely similar molecular units, spacing, and arrangement. A molecular image of one of these planes is sufficient to depict the general molecular content of all the planes that are parallel to it. All planes in a set of parallel planes have the same general spatial relationship to the three crystallographic axes. This means that they can be collectively identified in terms of their spatial relationship to the three crystallographic axes. This is true for crystal faces, for cleavage surfaces, for X‐ray reflecting planes or for any set of parallel crystallographic planes that we wish to identify. A universally utilized language has evolved that uses the relationship between the planar features in minerals and the crystallographic axes to identify different sets of planes. A discussion of this language and its use follows.

Schematic illustration of representative crystal faces that cut one, two or three crystallographic axes.

      Of course, some sets of planes or their projections intersect the positive ends of crystallographic axes (Figure 4.18b, c, and e). Others, with