Calculation of interplanar spacings and angles
Although there are tabulations of lattice spacings37 and parameters38,39 which assist the identification of unknown materials, it is equally necessary, especially with spot patterns, to have tables of interplanar and interzonal angles. It is often found useful to re-arrange or extend tables of spacings. Table 1 summarizes the formulae used to obtain any d-spacing or angle. Tables 2 to 7 show applications of these formulae to give the angles between certain planes in the tetragonal and hexagonal systems, and cover a wide range of interaxial ratios. Tables 3 and 7 are included in Part 2 because they are specific examples of the general tables. Table 9 covers all the angles between crystallographic planes in the cubic crystal system for h, k and l ≦ 5. Massalski and King40,41 have published tables for quick calculation of d-spacings in the tetragonal and hexagonal systems for given c/a ratios. Cubic d-spacings can be easily calculated to slide-rule accuracy.