TABLE OF CONTENTS Defects in solids exert significant effects in kinetic phenomena, as well as on the thermodynamic properties of semiconductors and ionic materials. We consider the thermodynamics of defects in this chapter. Applications involving defects in kinetic phenomena are considered in later chapters.
The defects that we consider in this section are vacancies and interstitials. Figure 6.1 defines these defects and also makes the point that a vacancy is sometimes called a Schottky defect while the combination of the two defects (Figure 6.1(c)) is called a Frenkel defect. Let us determine the concentration of vacancies that may be expected in a monatomic solid containing N atoms at equilibrium. By the definition of equilibrium, the Gibbs free energy must be at a minimum with respect to a variation in the concentration of vacancies. Hence, we formulate the Gibbs free energy of the monatomic solid containing vacancies. If the increase in free energy of the solid on the introduction of one vacancy into some particular site in the lattice by transfer of the atom at this site to a surface site [*] is g v, then the free energy of the system containing N v vacancies is
where g is the free energy per atom in the absence of vacancies and W is the number of different complexions of N v vacancies and N atoms (see equation 1.2b and note the change in symbol to prevent misinterpretation of the symbols).
