Physical Metallurgy Principles This page intentionally left blank Fourth Edition Physical Metallurgy Principles Reza Abbaschian Lara Abbaschian Robert E. Reed-Hill Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States 00FM.qxd 11/6/08 3:28 PM Page iv Physical Metallurgy Principles, Fourth Edition © 2009, 1994 Cengage Learning Reza Abbaschian, Lara Abbaschian, ALL RIGHTS RESERVED. No part of this work covered by the copyright Robert E. Reed-Hill herein may be reproduced, transmitted, stored, or used in any form or by any means—graphic, electronic, or mechanical, including but not limited to Director, Global Engineering Program: photocopying, recording, scanning, digitizing, taping, Web distribution, Chris Carson information networks, information storage and retrieval systems, or in any Senior Developmental Editor: Hilda Gowans other manner—except as may be permitted by the license terms herein.
Editorial Assistant: Jennifer Dinsmore For product information and technology assistance, contact us at Marketing Specialist: Lauren Betsos Cengage Learning Customer & Sales Support, 1-800-354-9706. Senior Content Project Manager: For permission to use material from this text or product, submit all Kim Kusnerak requests online at www. Production Service: RPK Editorial Services Further permissions questions can be emailed to permissionrequest@cengage. Copyeditor: Patricia Daly Proofreader: Martha McMaster Library of Congress Control Number: 2008940048 Indexer: Shelly Gerger-Knechtl U.
Student Edition: Compositor: Integra ISBN-13: 978-0-495-08254-5 ISBN-10: 0-495-08254-6 Senior Art Director: Michelle Kunkler Cengage Learning Internal Designer: Jen2Design 200 First Stamford Place, Suite 400 Cover Designer: Andrew Adams Stamford, CT 06902 USA Cover Images: Top/Middle: © iStock, Inc. Cengage Learning is a leading provider of customized learning solutions Bottom: © Fedor-o/Dreamstime.com with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan. Locate your local office at: Photo/Text Permissions Researcher: international. Natalie Barrington Cengage Learning products are represented in Canada by Senior First Print Buyer: Doug Wilke Nelson Education Ltd.
For your course and learning solutions, visit www. Purchase any of our products at your local college store or at our preferred online store www. Printed in the United States of America 1 2 3 4 5 6 7 12 11 10 09 08 Dedication We wish to dedicate this edition to honor Professor Robert E. Reed-Hill, who spent a lifetime to advance physical metallurgy.
We also give special thanks to Janette and Cyrus for their support and care. This page intentionally left blank 00FM.qxd 11/6/08 3:28 PM Page vii Contents CHAPTER 1 THE STRUCTURE OF METALS 1 1.1 The Structure of Metals, 1 1.3 The Body-Centered Cubic Structure (BCC), 3 1.4 Coordination Number of the Body-Centered Cubic Lattice, 4 1.5 The Face-Centered Cubic Lattice (FCC), 4 1.6 The Unit Cell of the Hexagonal Closed-Packed (HCP) Lattice, 5 1.7 Comparison of the Face- Centered Cubic and Close-Packed Hexagonal Structures, 6 1.8 Coordination Number of the Systems of Closest Packing, 7 1.10 Textures or Preferred Orientations, 8 1.12 Crystal Structures of the Metallic Elements, 14 1.13 The Stereographic Projection, 15 1.14 Directions that Lie in a Plane, 16 1.15 Planes of a Zone, 17 1.16 The Wulff Net, 17 1.18 The Standard Stereographic Triangle for Cubic Crystals, 24 Problems, 26 References, 28 CHAPTER 2 CHARACTERIZATION TECHNIQUES 29 2.1 The Bragg Law, 30 2.3 The Rotating-Crystal Method, 35 2.4 The Debye-Scherrer or Powder Method, 36 2.5 The X-Ray Diffractometer, 39 2.6 The Transmission Electron Microscope, 40 2.7 Interactions Between the Electrons in an Electron Beam and a Metallic Specimen 46 2.11 The Scanning Electron Microscope, 48 2.13 The Picture Element Size, 53 2.14 The Depth of Focus, 54 2.15 Microanalysis of Specimens, 55 2.16 Electron Probe X-Ray Microanalysis, 55 2.17 The Characteristic X-Rays, 56 2.18 Auger* Electron Spectroscopy (AES), 58 2.19 The Scanning Transmission Electron Microscope (STEM), 60 Problems, 60 References 61 CHAPTER 3 CRYSTAL BINDING 62 3.1 The Internal Energy of a Crystal, 62 3.3 The Born Theory of Ionic Crystals, 63 3.4 Van Der Waals Crystals, 68 3.8 The Lattice Energy of an Inert-Gas Solid, 71 3.9 The Debye Frequency, 72 3.10 The Zero-Point Energy, 73 3.11 Dipole-Quadrupole and Quadrupole-Quadrupole Terms, 75 3.13 Refinements to the Born Theory of Ionic Crystals, 75 3.14 Covalent and Metallic Bonding, 76 Problems 80 References, 81 vii 00FM.qxd 11/6/08 3:28 PM Page viii viii Contents CHAPTER 4 INTRODUCTION TO DISLOCATIONS 82 4.1 The Discrepancy Between the Theoretical and Observed Yield Stresses of Crystals, 82 4.3 The Burgers Vector, 93 4.4 Vector Notation for Dislocations, 95 4.5 Dislocations in the Face-Centered Cubic Lattice, 96 4.6 Intrinsic and Extrinsic Stacking Faults in Face-Centered Cubic Metals, 101 4.7 Extended Dislocations in Hexagonal Metals, 102 4.8 Climb of Edge Dislocations, 102 4.10 The Stress Field of a Screw Dislocation, 107 4.11 The Stress Field of an Edge Dislocation, 109 4.12 The Force on a Dislocation, 111 4.13 The Strain Energy of a Screw Dislocation, 114 4.14 The Strain Energy of an Edge Dislocation, 115 Problems, 116 References, 118 CHAPTER 5 DISLOCATIONS AND PLASTIC DEFORMATION 119 5.1 The Frank-Read Source, 119 5.2 Nucleation of Dislocations, 120 5.5 Slip Planes and Slip Directions, 127 5.7 Critical Resolved Shear Stress, 129 5.8 Slip on Equivalent Slip Systems, 133 5.9 The Dislocation Density, 133 5.10 Slip Systems in Different Crystal Forms, 133 5.13 Double Cross-Slip, 141 5.14 Extended Dislocations and Cross-Slip, 143 5.15 Crystal Structure Rotation During Tensile and Compressive Deformation, 144 5.16 The Notation for the Slip Systems in the Deformation of FCC Crystals, 147 5.19 The Relation Between Dislocation Density and the Stress, 151 5.21 The Orowan Equation, 153 Problems, 154 References, 157 CHAPTER 6 ELEMENTS OF GRAIN BOUNDARIES 158 6.2 Dislocation Model of a Small-Angle Grain Boundary, 159 6.3 The Five Degrees of Freedom of a Grain Boundary, 161 6.4 The Stress Field of a Grain Boundary, 162 6.5 Grain-Boundary Energy, 165 6.6 Low-Energy Dislocation Structures, LEDS, 167 6.8 Surface Tension of the Grain Boundary, 172 6.9 Boundaries Between Crystals of Different Phases, 175 6.10 The Grain Size, 178 6.11 The Effect of Grain Boundaries on Mechanical Properties: Hall-Petch Relation, 180 6.12 Grain Size Effects in Nanocrystalline Materials, 182 6.13 Coincidence Site Boundaries, 185 6.14 The Density of Coincidence Sites, 186 6.15 The Ranganathan Relations, 186 6.16 Examples Involving Twist Boundaries, 187 6.17 Tilt Boundaries, 189 Problems, 192 References, 193 CHAPTER 7 VACANCIES 194 7.1 Thermal Behavior of Metals, 194 7.5 Gibbs Free Energy, 197 00FM.qxd 11/6/08 3:28 PM Page ix Contents ix 7.6 Statistical Mechanical Definition of Entropy, 199 7.9 Interstitial Atoms and Divacancies, 211 Problems, 214 References, 215 CHAPTER 8 ANNEALING 216 8.1 Stored Energy of Cold Work, 216 8.2 The Relationship of Free Energy to Strain Energy, 217 8.3 The Release of Stored Energy, 218 8.5 Recovery in Single Crystals, 221 8.7 Dislocation Movements in Polygonization, 226 8.8 Recovery Processes at High and Low Temperatures, 229 8.10 The Effect of Time and Temperature on Recrystallization, 230 8.12 The Effect of Strain on Recrystallization, 233 8.13 The Rate of Nucleation and the Rate of Nucleus Growth, 234 8.14 Formation of Nuclei, 235 8.15 Driving Force for Recrystallization, 237 8.16 The Recrystallized Grain Size 237 8.17 Other Variables in Recrystallization, 239 8.18 Purity of the Metal, 239 8.19 Initial Grain Size, 240 8.22 Three-Dimensional Changes in Grain Geometry, 244 8.23 The Grain Growth Law, 245 8.24 Impurity Atoms in Solid Solution, 249 8.25 Impurities in the Form of Inclusions, 250 8.26 The Free-Surface Effects, 253 8.27 The Limiting Grain Size, 254 8.30 Strain-Induced Boundary Migration 257 Problems, 258 References, 259 CHAPTER 9 SOLID SOLUTIONS 261 9.3 Interstitial Solid Solutions, 262 9.4 Solubility of Carbon in Body-Centered Cubic Iron, 263 9.5 Substitutional Solid Solutions and the Hume-Rothery Rules, 267 9.6 Interaction of Dislocations and Solute Atoms, 267 9.8 The Formation of a Dislocation Atmosphere, 269 9.9 The Evaluation of A, 270 9.10 The Drag of Atmospheres on Moving Dislocations, 271 9.11 The Sharp Yield Point and Lüders Bands, 273 9.12 The Theory of the Sharp Yield Point, 275 9.14 The Cottrell-Bilby Theory of Strain Aging, 277 9.15 Dynamic Strain Aging 282 Problems, 285 References, 286 CHAPTER 10 PHASES 287 10.1 Basic Definitions, 287 10.2 The Physical Nature of Phase Mixtures, 289 10.3 Thermodynamics of Solutions, 289 10.4 Equilibrium Between Two Phases, 292 10.5 The Number of Phases in an Alloy System, 293 10.6 Two- Component Systems Containing Two Phases, 303 10.7 Graphical Determinations of Partial-Molal Free Energies, 304 10.8 Two-Component Systems with Three Phases in Equilibrium, 306 10.9 The Phase Rule, 307 10.10 Ternary Systems, 309 Problems, 310 References, 311 00FM.qxd 11/6/08 3:28 PM Page x x Contents CHAPTER 11 BINARY PHASE DIAGRAMS 312 11.2 Isomorphous Alloy Systems, 312 11.3 The Lever Rule, 314 11.4 Equilibrium Heating or Cooling of an Isomorphous Alloy, 317 11.5 The Isomorphous Alloy System from the Point of View of Free Energy, 319 11.6 Maxima and Minima, 320 11.10 The Microstructures of Eutectic Systems, 329 11.11 The Peritectic Transformation, 334 11.13 Other Three-Phase Reactions, 338 11.15 The Copper-Zinc Phase Diagram, 341 11.16 Ternary Phase Diagrams, 343 Problems, 346 References, 347 CHAPTER 12 DIFFUSION IN SUBSTITUTIONAL SOLID SOLUTIONS 348 12.1 Diffusion in an Ideal Solution, 348 12.2 The Kirkendall Effect, 352 12.5 Fick’s Second Law, 360 12.6 The Matano Method, 363 12.7 Determination of the Intrinsic Diffusivities, 366 12.8 Self-Diffusion in Pure Metals, 368 12.9 Temperature Dependence of the Diffusion Coefficient, 370 12.10 Chemical Diffusion at Low-Solute Concentration, 372 12.11 The Study of Chemical Diffusion Using Radioactive Tracers, 374 12.12 Diffusion Along Grain Boundaries and Free Surfaces, 377 12.13 Fick’s First Law in Terms of a Mobility and an Effective Force, 380 12.14 Diffusion in Non-Isomorphic Alloy Systems, 382 Problems, 386 References, 388 CHAPTER 13 INTERSTITIAL DIFFUSION 389 13.1 Measurement of Interstitial Diffusivities, 389 13.2 The Snoek Effect, 391 13.3 Experimental Determination of the Relaxation Time, 398 13.5 Anelastic Measurements at Constant Strain, 405 Problems, 406 References, 407 CHAPTER 14 SOLIDIFICATION OF METALS 408 14.1 The Liquid Phase, 408 14.4 Crystal Growth from the Liquid Phase, 420 14.5 The Heats of Fusion and Vaporization, 421 14.6 The Nature of the Liquid-Solid Interface, 423 14.9 Stable Interface Freezing, 428 14.10 Dendritic Growth in Pure Metals, 429 14.11 Freezing in Alloys with Planar Interface, 432 14.12 The Scheil Equation, 434 14.13 Dendritic Freezing in Alloys, 437 14.14 Freezing of Ingots, 439 14.15 The Grain Size of Castings, 443 14.20 Eutectic Freezing, 454 Problems, 459 References, 461 00FM.qxd 11/6/08 3:28 PM Page xi Contents xi CHAPTER 15 NUCLEATION AND GROWTH KINETICS 463 15.1 Nucleation of a Liquid from the Vapor, 463 15.2 The Becker-Döring Theory, 471 15.4 Solid-State Reactions, 475 15.7 Diffusion Controlled Growth, 484 15.8 Interference of Growing Precipitate Particles, 488 15.9 Interface Controlled Growth, 488 15.10 Transformations That Occur on Heating, 492 15.11 Dissolution of a Precipitate, 493 Problems, 495 References, 497 CHAPTER 16 PRECIPITATION HARDENING 498 16.1 The Significance of the Solvus Curve, 499 16.2 The Solution Treatment, 500 16.3 The Aging Treatment, 500 16.4 Development of Precipitates, 503 16.5 Aging of Al-Cu Alloys at Temperatures Above 100°C (373 K), 506 16.6 Precipitation Sequences in Other Aluminum Alloys, 509 16.7 Homogeneous Versus Heterogeneous Nucleation of Precipitates, 511 16.9 Theories of Hardening, 515 16.10 Additional Factors in Precipitation Hardening, 516 Problems, 518 References, 519 CHAPTER 17 DEFORMATION TWINNING AND MARTENSITE REACTIONS 521 17.2 Formal Crystallographic Theory of Twinning, 524 17.5 Accommodation of the Twinning Shear, 533 17.6 The Significance of Twinning in Plastic Deformation, 534 17.7 The Effect of Twinning on Face- Centered Cubic Stress-Strain Curves, 535 17.9 The Bain Distortion, 538 17.10 The Martensite Transformation in an Indium-Thallium Alloy, 540 17.11 Reversibility of the Martensite Transformation, 541 17.13 Phenomenological Crystallographic Theory of Martensite Formation, 542 17.14 Irrational Nature of the Habit Plane, 548 17.15 The Iron-Nickel Martensitic Transformation, 549 17.16 Isothermal Formation of Martensite, 551 17.18 Nucleation of Martensite Plates, 552 17.19 Growth of Martensite Plates, 553 17.20 The Effect of Stress, 553 17.21 The Effect of Plastic Deformation, 554 17.22 Thermoelastic Martensite Transformations, 554 17.23 Elastic Deformation of Thermoelastic Alloys, 556 17.24 Stress-Induced Martensite (SIM), 556 17.25 The Shape-Memory Effect, 557 Problems, 559 References, 560 CHAPTER 18 THE IRON-CARBON ALLOY SYSTEM 562 18.1 The Iron-Carbon Diagram, 562 18.