Laurent Maveyraud <laurent.maveyr...@ipbs.fr> writes: > this is explained in details in table 2.2.4.1 of vol A of > International Tables of Crystallography (p 18 in my edition). > > For trigonal/hexagonal, the primary direction is along c, along the > 3-fold (6-fold axis). It's the same in tetragonal (obviously for the > 4-fold axis !).. > > The secondary directions for trigonal/hexagonal are [100], the a > vector, [010], the b vector, and [-1-10] the diagonal direction > between -a and -b vectors (and therefore of between the a and b > vectors). > In tetragonal, the secondary directions are only [100], a, and [010], b. > > The tertiary direction for trigonal/hexagonal are [120] and [-2-10] > which are directions perpendicular to a and to b, respectively, and > [1-10]. None of these directions are the diagonal of a and b vectors. > In tetragonal, the tertiary directions are [110], the diagonal of the > a and b vectors, and [1-10], the diagonal of the a and -b vectors. >
I find it less confusing in these cases—not everyone might agree—to use three equivalent axes ⟂ to Z: X, Y and U, and hence four‐index denotations for directions, h k i l where h + k + i = 0. Someone has borrowed my copy of McKie and McKie, and not brought it back, but I’ve made the enclosed badly‐drawn diagram from memory.
-- Ian ◎
