## 4.2. Tetragonal and hexagonal structures

For tetragonal and hexagonal structures an extra variable - the axial ratio, c/a - is involved and therefore the problem is more complicated. For tetragonal structures, eq. (5) is replaced by

 (6)

Now no precise rules can be given, but the values of sin2 may give some hints. For example, if l = 0, the values of sin2 are in the ratios 1, 2, 4, 5 corresponding to indices 100, 110, 200, 210 If we find a set of values in these ratios we can assume that the indices are as shown, and then we have to find l from the lines that are not in this sequence. The ratio 1:2 particularly should be looked for.

For hexagonal structures, or trigonal structures referred to hexagonal axes, eq. (5) is modified to

 (7)
and the dominant factor is 1:3. Again, if some of the simpler lines can be accounted for in this way, trial-and-error can be applied to the others. Graphical and numerical methods have been applied to these problems; a summary is given by Lipson and Steeple (1970).

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