Page 42 - Materials Chemistry, Second Edition

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2.3. The Crystalline State

2.3.2. Crystal Structures
A crystal is comprised of an infinite 3-D lattice of repeating units, of which the
smallest building block is known as the asymmetric unit. When acted upon by crystal
symmetry operations such as rotation axes or mirror planes (see Section 2.3.2), the
asymmetric unit is duplicated to produce the contents of a unit cell (Figure 2.7). For
any crystal lattice, it is possible to define an infinite number of possible unit cells
(Figure 2.8). However, by convention, this unit is chosen to be a repeatable unit that

Figure 2.7. Illustration of the asymmetric unit of a unit cell.

Figure 2.8. Representation of some unit cell selections from a two-dimensional array. The triangle
and smaller rhombus selections are known as “primitive” unit cells, as each contains one object per unit cell
(3 1/3for the triangle,4 1/4for the rhombus).Bycontrast,there arefour objectsper unit cellforthelarger
rhombus (4 1/4 for corner objects; 4 1/2 for those on the edges; one in the center). When each of these
selections is translated along the two-dimensionalaxes, theyreproduce the positions of allobjects in the lattice.