Читать книгу Earth Materials - John O'Brien - Страница 105

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.