Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Frequently used symbols
- 1 Introduction
- 2 Basic elements of linear elasticity
- 3 Methods
- 4 Green's functions for unit point force
- 5 Interactions between defects and stress
- 6 Inclusions in infinite homogeneous regions
- 7 Interactions between inclusions and imposed stress
- 8 Inclusions in finite regions – image effects
- 9 Inhomogeneities
- 10 Point defects in infinite homogeneous regions
- 11 Point defects and stress – image effects in finite bodies
- 12 Dislocations in infinite homogeneous regions
- 13 Dislocations and stress – image effects in finite regions
- 14 Interfaces
- 15 Interactions between interfaces and stress
- 16 Interactions between defects
- Appendix A Relationships involving the ∇ operator
- Appendix B Integral relationships
- Appendix C The tensor product of two vectors
- Appendix D Properties of the delta function
- Appendix E The alternator operator
- Appendix F Fourier transforms
- Appendix G Equations from the theory of isotropic elasticity
- Appendix H Components of the Eshelby tensor in isotropic system
- Appendix I Airy stress functions for plane strain
- Appendix J Deviatoric stress and strain in isotropic system
- References
- Index
10 - Point defects in infinite homogeneous regions
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Frequently used symbols
- 1 Introduction
- 2 Basic elements of linear elasticity
- 3 Methods
- 4 Green's functions for unit point force
- 5 Interactions between defects and stress
- 6 Inclusions in infinite homogeneous regions
- 7 Interactions between inclusions and imposed stress
- 8 Inclusions in finite regions – image effects
- 9 Inhomogeneities
- 10 Point defects in infinite homogeneous regions
- 11 Point defects and stress – image effects in finite bodies
- 12 Dislocations in infinite homogeneous regions
- 13 Dislocations and stress – image effects in finite regions
- 14 Interfaces
- 15 Interactions between interfaces and stress
- 16 Interactions between defects
- Appendix A Relationships involving the ∇ operator
- Appendix B Integral relationships
- Appendix C The tensor product of two vectors
- Appendix D Properties of the delta function
- Appendix E The alternator operator
- Appendix F Fourier transforms
- Appendix G Equations from the theory of isotropic elasticity
- Appendix H Components of the Eshelby tensor in isotropic system
- Appendix I Airy stress functions for plane strain
- Appendix J Deviatoric stress and strain in isotropic system
- References
- Index
Summary
Introduction
Point defects in crystals can exist in many configurations. Substitutional point defects occupy substitutional lattice sites and include single vacancies (unoccupied substitutional sites) and single foreign solute atoms occupying substitutional sites in dilute solution. Interstitial point defects correspond to atoms occupying interstitial sites, i.e., sites in the interstices between substitutional sites. The interstitial atoms may be either foreign solute atoms, or the host atoms themselves: defects of the latter type are often referred to as self-interstitial defects. Small clusters at the atomic scale of any of these defect types also qualify as point defects. These clusters may consist entirely of substitutional atoms or entirely of interstitial atoms or may be of mixed character. For example, an undersized solute atom of one type may occupy a substitutional site and be bound to an undersized atom of another type occupying an adjacent interstitial site.
A common feature of all these defects is that they generally distort the host lattice and generate corresponding long-range stress and strain fields around them. If, for example, an embedded solute atom has a larger ion core radius than its host atoms it will, on average, push outwards against its near neighbors, causing a net expansion of the surrounding crystal, i.e., it will act as a positive center of dilatation. Conversely, a smaller solute atom will behave as a negative center. An interstitial atom is usually larger than the interstice in the lattice that it occupies and therefore acts as a positive center. On the other hand, the atoms around a vacancy often tend to relax inwards towards the vacant site causing the vacancy to act as a negative center. The symmetry of the surrounding stress field depends upon the symmetry of the point defect, as discussed later.
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- Information
- Introduction to Elasticity Theory for Crystal Defects , pp. 201 - 214Publisher: Cambridge University PressPrint publication year: 2012