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# Elements of X-Ray Diffraction . A Volume in Addison-Wesley by B. D. CULLITY

By B. D. CULLITY

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Sample text

Some of the points so generated are shown in the figure, at the EI, , ends of dashed lines, in order to exhibit the hexagonal symmetry of the The third axis a 3 lattice, which has a 6-fold rotation axis parallel to c. , lying in the basal plane of the hexagonal prism, so symmetrically related to EI and a 2 that it is often used in conjunction with the other two. Thus the indices of a plane in the hexagonal system, called Miller-Bra vais is and are written (hkil). The index i is the reciproon the a 3 axis.

It is The equally true in three dimensions. /, measa function both of the plane indices The exact relation der, a, 0, 7). system involved and for the cubic system takes on form the relatively simple crystal d hk (Cubic) = i (2-5) -^-JL===. In the tetragonal system the spacing equation naturally involves both a and c since these are not generally equal : (Tetragonal) d h ki Interplanar spacing equations for 2-7 Crystal structure. So of mathematical (geometrical) far = all (2-0) systems are given in Appendix 1 .

Also that in these, as in all other structures, the operation of any symmetry element possessed by the lattice must bring similar atoms or For example, in Fig. 2-18(b), 90 rotation about ions into coincidence. the 4-fold [010] rotation axis shown brings the chlorine ion at coincidence with the chlorine ion at ^11, the sodium ion at the sodium ion at 1 1 \ into with 1 1 1 1, etc. Elements and compounds often have closely similar structures. 2-19 shows the unit cells of diamond and the zinc-blende form Both are face-centered cubic.