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As we discussed in lecture, we can apply selection rules to determine what kind of crystal structure a sample has. For each of the Bravais lattices, selection rules tell us which planes have coherent scattering and which do not:
24 de nov. de 2022 · The Body-Centered Cubic (BCC) crystal structure is important because it is extremely common in metals, and results in interesting properties like the ductile-to-brittle transformation temperature (DBTT) and high melting points.
What we find is that the reciprocal lattice of a face-centred cubic lattice is itself a body-centred cubic lattice in reciprocal space, a result that we met in Lecture 1. It is a good
Table 1.1 summarizes the selection rules (or extinction conditions as they are also known) for cubic lattices. According to these selection rules, the h2 + J<2 + [2 values for the different cubic lattices follow the sequence Primitive I, 2, 3,4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, ... Body-centered 2,4, 6, 8, 10, 12, 14, 16, ...
When h+k+l is even F = non-zero → reflection. When h+k+l is odd F = 0 → no reflection. Consider the previous body-centered unit cell containing two atoms of the same kind located at origin, uvw=000 and uvw=1⁄2, 1⁄2, 1⁄2 basis. (S = h2+k2+l2) (001) planes are out of phase and cancel whereas (002) planes are allowed.
Bond charges in covalent solid. (1/8,1/8,1/8), (3/8,3/8,1/8),(1/8,3/8,3/8) and (3/8,1/8,3/8). Bond charges form a "crystal" with a fcc lattice with 4 "atoms" per unit cell. origin : (1/8,1/8,1/8). Bond charge position: (0,0,0), (1/4,1/4,0),(0,1/4,1/4) and (1/4,0,1/4).
