Page 93 - Materials Chemistry, Second Edition

80 2 Solid-State Chemistry

Figure 2.49. Illustration of a unit cell of an ionic crystal with Frenkel and Schottky defects.

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(e.g.,O ) to balance the crystal charge. This is the mode of activity for solid
electrolytes used for fuel cell, supercapacitor, battery, and sensory applications – the
topic of this end-of-chapter “Important Materials Application.”
When the composition of a crystal is defined by a distinct chemical formula (e.g.,
SiO 2 ), it is known as a stoichiometric compound. If the composition of the crystal is
altered upon doping or thermal treatment, the resulting solid may deviate from the
original chemical formula, forming a nonstoichiometric solid. Nonstoichiometry
and the existence of point defects in a solid are often closely related, and are
prevalent for transition metal (e.g., W, Zn, Fe) and main group (e.g., Si, Al) oxides.
For instance, the formation of x anion vacancies per each quartz (SiO 2 ) unit cell will
result in the nonstoichiometric compound SiO 2 x .
Bulk defects are produced through the propagation of the microscopic flaws in the

lattice. For crystals with a planar defect such as polycrystalline solids, the grain
boundary marks the interface between two misaligned portions of the bulk crystal
(Figure 2.50). The size of the individual microcrystals (or grains) that comprise a
larger aggregate greatly affects many properties of the bulk crystal. Both optical
microscopy and X-ray diffraction are used to determine the grain sizes; most
commercial metals and alloys consist of individual crystallites with diameters
ranging from 10 to 100 mm, each corresponding to millions of individual metal
atoms. Since energy is required to form a surface, grains tend to grow in size at the
expense of smaller grains to minimize energy. This growth process occurs by
diffusion, which is accelerated at high temperatures.
A decrease in the size of these microscopic grains or crystallites results in an
increase in both strength and hardness of the bulk material, due to closer packing
among neighboring grains. The density of atoms at a solid surface, or in the
region surrounding a grain boundary is always smaller than the bulk value. This is
due to atoms at these regions containing dangling bonds, known as coordinatively