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Deformation of Earth Materials Much of the recent progress in the solid Earth sciences is based on the interpretation of a range of geophysical and geological observations in terms of the properties and deformation of Earth materials. One of the greatest challenges facing geoscientists in achieving this lies in finding a link between physical processes operating in minerals at the smallest length scales to geodynamic phenomena and geophysical observations across thousands of kilometers. This graduate textbook presents a comprehensive and unified treatment of the materials science of deformation as applied to solid Earth geophysics and geology. Materials science and geophysics are integrated to help explain important recent developments, including the discovery of detailed structure in the Earth’s interior by high-resolution seismic imaging, and the discovery of the unexpectedly large effects of high pressure on material properties, such as the high solubility of water in some minerals. Starting from fundamentals such as continuum mechanics and thermodynamics, the materials science of deformation of Earth materials is presented in a systematic way that covers elastic, anelastic, and viscous deformation. Although emphasis is placed on the fundamental underlying theory, advanced discussions on current debates are also included to bring readers to the cutting edge of science in this interdisciplinary area. Deformation of Earth Materials is a textbook for graduate courses on the rheology and dynamics of the solid Earth, and will also provide a much-needed reference for geoscientists in many fields, including geology, geophysics, geochemistry, materials science, mineralogy, and ceramics. It includes review questions with solutions which allow readers to monitor their understanding of the material presented. Shun-ichiro Karato is a Professor in the Department of Geology and Geophysics at Yale University. His research interests include experimental and theoretical studies of the physics and chemistry of minerals, and their applications to geophysical and geological problems. Professor Karato is a Fellow of the American Geophysical Union and a recipient of the Alexander von Humboldt Prize (1995), the Japan Academy Award (1999), and the Vening Meinesz medal from the Vening Meinesz School of Geodynamics in The Netherlands (2006). He is the author of more than 160 journal articles and has written edited seven other books. Deformation of Earth Materials An Introduction to the Rheology of Solid Earth Shun-ichiro Karato Yale University, Department of Geology & Geophysics, New Haven, CT, USA CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org 9780521844048 © S. Karato 2008 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2008 ISBN-13 978-0-511-39478-2 ISBN-13 978-0-521-84404-8 eBook (NetLibrary) hardback Contents Preface Part I General background 1 Stress and strain 1.1 Stress 1.2 Deformation, strain 2 Thermodynamics 2.1 Thermodynamics of reversible processes 2.2 Some comments on the thermodynamics of a stressed system 2.3 Thermodynamics of irreversible processes 2.4 Thermally activated processes 3 Phenomenological theory of deformation 3.1 Classification of deformation 3.2 Some general features of plastic deformation 3.3 Constitutive relationships for non-linear rheology 3.4 Constitutive relation for transient creep 3.5 Linear time-dependent deformation Part II Materials science of deformation 4 Elasticity 4.1 Introduction 4.2 Elastic constants 4.3 Isothermal versus adiabatic elastic constants 4.4 Experimental techniques 4.5 Some general trends in elasticity: Birch’s law 4.6 Effects of chemical composition 4.7 Elastic constants in several crystal structures 4.8 Effects of phase transformations 5 Crystalline defects 5.1 Defects and plastic deformation: general introduction 5.2 Point defects 5.3 Dislocations 5.4 Grain boundaries 6 Experimental techniques for study of plastic deformation 6.1 Introduction 6.2 Sample preparation and characterization 6.3 Control of thermochemical environment and its characterization 6.4 Generation and measurements of stress and strain 6.5 Methods of mechanical tests 6.6 Various deformation geometries 7 Brittle deformation, brittle–plastic and brittle–ductile transition 7.1 Brittle fracture and plastic flow: a general introduction 7.2 Brittle fracture 7.3 Transitions between different regimes of deformation 8 Diffusion and diffusional creep 8.1 Fick’s law 8.2 Diffusion and point defects 8.3 High-diffusivity paths 8.4 Self-diffusion, chemical diffusion 8.5 Grain-size sensitive creep (diffusional creep, superplasticity) 9 Dislocation creep 9.1 General experimental observations on dislocation creep 9.2 The Orowan equation 9.3 Dynamics of dislocation motion 9.4 Dislocation multiplication, annihilation 9.5 Models for steady-state dislocation creep 9.6 Low-temperature plasticity (power-law breakdown) 9.7 Deformation of a polycrystalline aggregate by dislocation creep 9.8 How to identify the microscopic mechanisms of creep 9.9 Summary of dislocation creep models and a deformation mechanism map 10 Effects of pressure and water 10.1 Introduction 10.2 Intrinsic effects of pressure 10.3 Effects of water 11 Physical mechanisms of seismic wave attenuation 11.1 Introduction 11.2 Experimental techniques of anelasticity measurements 11.3 Solid-state mechanisms of anelasticity 11.4 Anelasticity in a partially molten material 12 Deformation of multi-phase materials 12.1 Introduction 12.2 Some simple examples 12.3 More general considerations 12.4 Percolation 12.5 Chemical effects 12.6 Deformation of a single-phase polycrystalline material 12.7 Experimental observations 12.8 Structure and plastic deformation of a partially molten material 13 Grain size 13.1 Introduction 13.2 Grain-boundary migration 13.3 Grain growth 13.4 Dynamic recrystallization Contents 13.5 Effects of phase transformations 13.6 Grain size in Earth’s interior Part III Geological and geophysical applications 17 Composition and structure of Earth’s interior 17.1 Gross structure of Earth and other terrestrial planets 17.2 Physical conditions of Earth’s interior 17.3 Composition of Earth and other terrestrial planets 17.4 Summary: Earth structure related to rheological properties 18 Inference of rheological structure of Earth from time-dependent deformation 18.1 Time-dependent deformation and rheology of Earth’s interior 18.2 Seismic wave attenuation 18.3 Time-dependent deformation caused by a surface load: post-glacial isostatic crustal rebound 18.4 Time-dependent deformation caused by an internal load and its gravitational signature 18.5 Summary 19 Inference of rheological structure of Earth from mineral physics 19.1 Introduction 19.2 General notes on inferring the rheological properties in Earth’s interior from mineral physics 19.3 Strength profile of the crust and the upper mantle 19.4 Rheological properties of the deep mantle 19.5 Rheological properties of the core 20 Heterogeneity of Earth structure and its geodynamic implications 20.1 Introduction 20.2 High-resolution seismology 20.3 Geodynamical interpretation of velocity (and attenuation) tomography Seismic anisotropy and its geodynamic implications 21.1 Introduction 21.2 Some fundamentals of elastic wave propagation in anisotropic media 21.3 Seismological methods for detecting anisotropic structures 21.4 Major seismological observations 21.5 Mineral physics bases of geodynamic interpretation of seismic anisotropy 21.6 Geodynamic interpretation of seismic anisotropy References Materials index Subject index The colour plates are between pages 118 and 119. Preface Understanding the microscopic physics of deformation, materials science of deformation of minerals and rocks over various time-scales is critical in many branches of solid Earth science. Long-term geological processes are described in addition to short-term phenomena. Ключевые слова: e, r, o