Page 124 - Materials Chemistry, Second Edition

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2.3. The Crystalline State

Figure 2.75. The Wigner-Seitz construction of a primitive unit cell for a 2-D lattice.

Figure 2.76. The first Brillouin zone of a fcc lattice, showing symmetry labels for high-symmetry lines
and points.

describe the electronic properties of crystalline solids. The BZ boundaries identify
where energy gaps occur along the k-axis. These are due to the finite lattice potential
that alters the energy-state continuum of the free-electron model to one in which
there are regions that have no energy states at all. It should be noted that for 3-D
arrays, the BZs are complex polyhedra; Figure 2.76 illustrates the Brillouin zone for
a fcc lattice, showing symmetry labels for relevant lines and points.
Figure 2.77 illustrates diffraction of an electron in a 2-D lattice, along with the
E-k relationship. When k x ¼ np/a, the electron wave will be diffracted by