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

Автор: John O'Brien
Издательство: John Wiley & Sons Limited
Серия:
Жанр произведения: География
Год издания: 0
isbn: 9781119512219
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ends of crystallographic axes (Figure 4.18a). Still others, with yet different orientations, intersect the positive ends of one or more axes and the negative ends of other crystallographic axes (Figure 4.18d, f). Given the myriad possibilities, a simple language is needed that allows one to visualize and communicate to others the relationship and orientation of any set of crystal planes to the crystallographic axes. The language for identifying and describing crystallographic planes involves the use of symbols called Miller indices, which has been employed since the 1830s and is explained in the following sections.

      4.6.3 Unit faces or planes

      In any crystal, the three crystallographic axes have a characteristic axial ratio, typically grounded in the cell edge lengths of the unit cell. No matter how large the mineral becomes during growth, even if it experiences preferred growth in a particular direction or inhibited growth in another, the axial ratio remains constant and corresponds to the axial ratio implied by the properties of the unit cell.

Schematic illustration of unit face (outlined in solid blue) in an orthorhombic crystal with three unequal unit cell edges and crystallographic axes that intersect at right angles.

      4.6.4 Weiss parameters

      Weiss parameters provide a method for describing the orientation of sets of crystal faces or planes in relationship to the crystallographic axes. They are always expressed in the sequence a : b : c, where a represents the relationship of the planes to the a‐axis (or a1‐axis), b represents the relationship between the planes and the b‐axis (or a2‐axis) and c depicts the relationship between the planes and the c‐axis (or a3‐axis). A unit face or plane that cuts all three crystallographic axes at ratios that correspond to their axial ratios has the Weiss parameters (1 : 1 : 1). Mathematically, if we divide the actual lengths at which the face or plane intercepts the three axes by the corresponding axial lengths, the three intercepts have the resulting ratio l : l : l, or unity, which is why such planes are called unit planes. Again, using the pseudo‐orthorhombic mineral staurolite as an example, if we divide the actual intercept distances by the axial lengths, the resulting ratios are 0.47/0.47 : 1.00/1.00 : 0.34/0.34 = 1 : 1 : 1. Even if we utilize the magnitudes of the dimensions, the three resulting numbers have the same dimensional magnitude, and so their ratio reduces to 1 : 1 : 1.

Schematic illustration of faces with different Weiss parameters on an orthorhombic crystal. Schematic illustration of (a) The darkened front crystal face possesses the Weiss parameters. (b) The face outlined in green possesses the Weiss parameters.