Book contents
- Frontmatter
- Contents
- Preface
- Part I General background
- Part II Materials science of deformation
- 4 Elasticity
- 5 Crystalline defects
- 6 Experimental techniques for study of plastic deformation
- 7 Brittle deformation, brittle–plastic and brittle–ductile transition
- 8 Diffusion and diffusional creep
- 9 Dislocation creep
- 10 Effects of pressure and water
- 11 Physical mechanisms of seismic wave attenuation
- 12 Deformation of multi-phase materials
- 13 Grain size
- 14 Lattice-preferred orientation
- 15 Effects of phase transformations
- 16 Stability and localization of deformation
- Part III Geological and geophysical applications
- References
- Materials index
- Subject index
- Plate section
4 - Elasticity
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Part I General background
- Part II Materials science of deformation
- 4 Elasticity
- 5 Crystalline defects
- 6 Experimental techniques for study of plastic deformation
- 7 Brittle deformation, brittle–plastic and brittle–ductile transition
- 8 Diffusion and diffusional creep
- 9 Dislocation creep
- 10 Effects of pressure and water
- 11 Physical mechanisms of seismic wave attenuation
- 12 Deformation of multi-phase materials
- 13 Grain size
- 14 Lattice-preferred orientation
- 15 Effects of phase transformations
- 16 Stability and localization of deformation
- Part III Geological and geophysical applications
- References
- Materials index
- Subject index
- Plate section
Summary
This chapter provides a brief summary of the physics of elastic constants that has important applications for the inference of the constitution of Earth's interior (Chapter 17) as well as for understanding the origin of lateral heterogeneity in seismic wave velocities (Chapter 20) and seismic anisotropy (Chapter 21). Elasticity is one of the key properties of materials that control seismic wave propagation. To the extent that elastic constants reflect the nature of chemical bonding and crystal structure, the elasticity of a given material also influences its plastic properties. Starting from the definition of elastic constants and their symmetry properties, a brief summary of the experimental techniques of measurements of elastic constants and some materials science (solid-state physics) fundamentals of elastic constants are discussed including the origin of the variation of the elastic constant with pressure and temperature (anharmonicity) and the influence of chemical composition and phase transformations on elastic constants. Birch's law on the relationship between density and elastic wave velocities and the Debye model of lattice vibration provide a unified framework to understand the relationship among various anharmonic parameters although these relations (or models) are only approximately satisfied in real materials.
Key words Hooke's law, elastic constants, bulk modulus, shear modulus, Lamé constants, Poisson's ratio, Cauchy relation, X-ray diffraction, Brillouin scattering, ultrasonic wave techniques, Birch's law, Grüneisen parameter, Anderson–Grüneisen parameter, Debye model, soft mode, polyhedral model, Pauling's rule.
Introduction
Although the main emphasis of this book is plastic deformation, an understanding of elastic deformation is important for two reasons.
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- Deformation of Earth MaterialsAn Introduction to the Rheology of Solid Earth, pp. 51 - 74Publisher: Cambridge University PressPrint publication year: 2008