At non-zero temperatures, there is hardly a perfect solid and imperfections or defects in solids not only exist, but also play a crucial role in the dynamics of atoms in crystals as well as catalysis. The defects include vacancies, substitutional impurities, interstitial impurities, self
interstitial
dislocation, edge dislocations and grain boundaries. Some of these examples are shown in Fig 17.7. If
E is the energy required to create one impurity or vacancy, then the fraction of vacancies or impurities ( f ) is given by
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