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Also called trigonal. In this case the spaced and mutually perpendicular, the unit cell is cubic. or a = b = c to one and at all c are another, vectors a, b, right angles equal = axial lengths = the = to values thus 90. a and giving special 7 By we can produce unit cells of various shapes and therefore of point lattices, since the points of the lattice are located at kinds various the cell corners. It turns out that only seven different kinds of cells are necessary to include all the possible point lattices.

We the Miller indices, which are defined as the reciprocals of the fractional intercepts which the plane makes with the crystallographic axes. For example, if the Miller indices of a plane are (AW), written in parentheses, then the plane makes fractional intercepts of I/A, I/A*, \/l with the plane in a lattice, the axial lengths are a, 6, c, the plane makes actual intercepts of a/A, b/k, c/l, as shown in Fig. 2-9(a). Parallel to any plane in any latone of which passes tice, there is a whole set of parallel equidistant planes, to that plane in refer through the origin; the Miller indices (hkl) usually if axes, and, nearest the origin, although they may be taken as referring other plane in the set or to the whole set taken together.

4-fold axis: AI becomes A\\ inversion center: A\ becomes A*. comes A%. (b) Rotation axes. 4-fold axis: (a) A\ becomes A^ 3-fold axis: * So called to distinguish them from certain microscopic symmetry operations with which we are not concerned here. The macrosopic elements can be deduced from the angles between the faces of a well-developed crystal, without any knowledge of the atom arrangement inside the crystal. The microscopic symmetry elements, on the other hand, depend entirely on atom arrangement, and their presence cannot be inferred from the external development of the crystal.

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Elements of X-Ray Diffraction . A Volume in Addison-Wesley Series in Metallurgy and Materials. by B. D. CULLITY

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