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chapter 4 imperfections in solids 4.1 Inteoduction in the previous chapter we investigated the structure of crystalline materials on a unit-cell level. We must recognize,however,that engineering materials are composed of very large numbers of atoms in small volumes. Thus far it has been tacitly assumed that perfect order exists throughout crystalline materials on an atomic scale.However,such an idealized solid does not exist;all contain large numbers of various defects or imperfections.As a matter of fact,many of the properties of materials are profoundly sensitive to deviations from crystalline perfection;the influence is not always adverse,and often specific characteristics are deliberately fashioned by the introduction of controlled amounts or numbers of particular defects. By “crystalline defect”is meant a lattice irregularity having one or more of its dimensions on the order of an atomic diameter.Classification of crystalline imperfections is frequently made according to geometry or dimensionality of the defect.Several different imperfections are discussed in this chapter,including point defects those associated with one or two atomic positions),linear (or one-dimensional) defects,as well as interfacial defects,or boundaries,which are two-dimensional.Impurities in solids are also discussed,since impurity atoms may exist as point defects.Finally,we will discuss the grain size determination. 4.2 Point Defects 4.2.1 Vacancies and self-interstitials The simplest of the point defects is a vacancy,or vacant lattice site,one normally occupied from which an atom is missing (Figure 4.1).All crystalline solids contain vacancies and,in fact,it is not possible to create such a material that is free of these defects.The necessity of the existence of vacancies is explained using principles of thermodynamics;in essence,the presence of vacancies increases the entropy (i.e.,the randomness) of the crystal. The equilibrium number of vacancies for a given quantity of material