Page 49 - Materials Chemistry, Second Edition

36 2 Solid-State Chemistry

Figure 2.15. Schematic of the packing in an hcp unit cell, showing equivalent close-packed B sites. The
hexagon of A atoms is referred to as the basal plane, as this plane marks the top and bottom of a unit cell.
The fractional coordinates of each set of B sites are {(a, b, c): (1/3, 2/3, 1/2) shown, or (2/3, 1/3, 1/2)}.

not listed are not oversights, but may be further simplified. For instance, a “base-
centered tetragonal” unit cell does not appear as one of the 14 Bravais lattices. As
shown in Figure 2.17, a primitive unit cell may be defined from a base-centered
tetragonal array – the former is preferentially chosen due to its smaller volume.
A subclass of polymorphism known as polytypism is found for one-dimensional
close-packed and layered structures such as SiC, CdI 2 , ZnS, GaSe, and micas/
clay minerals such as kaolins. These crystal structures exhibit differing three-
dimensional lattices that vary depending on the stacking order of the two-dimensional
sheets that comprise the crystal, known as modular layers. Figure 2.18 illustrates the
crystal structures for two common polytypes of SiC, an important material used in
ceramic brakes, abrasive machining, and high-temperature electronic applications. [13]
Polytypes are defined by the Ramsdell notation <number><letter>, where the num-
ber indicates how many planes are stacked in a discrete unit cell, and the letter indicates
the crystal lattice type (C ¼ cubic, H ¼ hexagonal, R ¼ rhombohedral). Amazingly,
there are over 200 known polytypes of SiC; the most common include 3C (i.e., fcc with
ABC... packing), 2H, 4H, 6H, 8H, 9R, 10H, 14H, 15R, 19R, 20H, 21H, and 24R. [14]