Читать книгу Solid State Chemistry and its Applications - Anthony R. West - Страница 27

We have already defined the d‐spacing of a set of planes as the perpendicular distance between any pair of adjacent planes in the set and it is this d value that appears in Bragg's law. For a cubic unit cell, the (100) planes simply have a d‐spacing of a, the value of the cell edge, Fig. 1.15(b). For (200) in a cubic cell, d = a/2. For orthogonal crystals (i.e. α = β = γ = 90°), the d‐spacing for any set of planes is given by

(1.1)

The equation simplifies for tetragonal crystals, in which a = b, and still further for cubic crystals with a = b = c:

(1.2)

As a check, for cubic (200): h = 2, k = l = 0; 1/d ² = 4/a ²; d = a/2.

Monoclinic and, especially, triclinic crystals have much more complicated d‐spacing formulae because each angle that is not equal to 90° is an additional variable. The formulae for d‐spacings and unit cell volumes of all crystal systems are given in Appendix A.