1.02.1

Introduction

47

1.02.2

Intrinsic Point Defects in Ionic Materials

48

1.02.2.1

Point Defects Compared to Defects of Greater Spatial Extent

48

1.02.2.2

Intrinsic Disorder Reactions

48

1.02.2.3

Concentration of Intrinsic Defects

49

1.02.2.4

Kroger-Vink Notation

50

1.02.3

Defect Reactions

51

1.02.3.1

Intrinsic Defect Concentrations

51

1.02.3.2

Effect of Doping on Defect Concentrations

52

1.02.3.3

Decrease of Intrinsic Defect Concentration Through Doping

52

1.02.3.4

Defect Associations

52

1.02.3.5

Nonstoichiometry

53

1.02.3.6

Lattice Response to a Defect

55

1.02.3.7

Defect Cluster Structures

56

1.02.4

Electronic Defects

57

1.02.4.1

Formation

57

1.02.4.2

Concentration of Intrinsic Electrons and Holes

57

1.02.4.3

Band Gaps

58

1.02.4.4

Excited States

58

1.02.5

The Brouwer Diagram

60

1.02.6

Transport Through Ceramic Materials

61

1.02.6.1

Diffusion Mechanisms

61

1.02.6.2

Diffusion Coefficient

63

1.02.7

Summary

63

References

64

1.02.1 Introduction

electronic defects in order to maintain charge neutral-

ity.1,2 Such constraints on

the types and concentrations

The mechanical and electronic properties of crystalline

of point defects are the focus of this chapter.

ceramics are

dependent on the point defects that they

In the first section, we consider the intrinsic point

contain, and

as a consequence, it is necessary to under-

defects in ionic materials. This is followed by a dis-

stand their

structures, energies, and concentration

cussion of the defect reactions describing the effect

defects and their interactions.1,2 In terms of their crystal-

of doping, defect cluster formation, and nonstoichio-

lography, it is often convenient to characterize ceramic

metry. Thereafter, we

consider the importance of

materials by their anion and cation sublattices. Such

electronic defects and

their influence on ceramic

models lead

to some obvious expectations. It might,

properties. In the final

section, we examine solid-

for example, be energetically unfavorable for an anion

state diffusion in ceramic materials. Examples are

to occupy a site in the cation sublattice and vice versa.

used throughout to illustrate the extent and range of

This is because it would lead to anions having nearest

the point defects and associated processes occurring

neighbor anions with a substantial electrostatic energy

in ceramics. The subsequent chapters (see Chapter

penalty. Further, there should exist an equilibrium

1.03, Radiation-Induced Effects on Microstruc-

between the concentration of intrinsic defects (such as

ture and Chapter 1.06

, The Effects of Helium in

lattice vacancies), extrinsic defects (i. e., dopants), and

Irradiated Structural Alloys) will deal with defects