Physical Metallurgy Second Edition Physical Metallurgy Second Edition William F. Hosford CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2010 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-13: 978-1-4398-1361-4 (Ebook-PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface .................................................................................................................. xv Author ................................................................................................................ xvii Chapter 1 Introduction .................................................................................... 1 1.1 Metallic Elements ................................................................ 1 1.2 Price and Abundance ............................................................. 4 1.3 Miscellany .............................................................................. 5 Problems ......................................................................................... 6 Reference .......................................................................................... 8 Chapter 2 Freezing ............................................................................................ 9 2.1 Introduction ........................................................................... 9 2.2 Liquid Metals ......................................................................... 9 2.3 Nucleation .............................................................................. 9 2.4 Growth ................................................................................. 15 2.5 Ingot Structure ..................................................................... 16 2.6 Segregation during Freezing ............................................... 18 2.7 Zone Refi ning ...................................................................... 20 2.8 Steady-State Freezing .......................................................... 23 2.9 D endritic Growth ................................................................. 23 2.10 Length and Spacing of Dendrite Arms ............................... 25 2.11 Consequences of Dendritic Growth .................................... 27 2.12 Gas Solubility and Gas Porosity .......................................... 27 2.13 Growth of Single Crystals ................................................... 29 2.14 Eutectic Solidifi cation ......................................................... 29 2.15 Peritectic Freezing ............................................................... 30 2.16 Metal Glasses ....................................................................... 31 2.17 Miscellany ........................................................................... 33 Problems ......................................................................................... 34 References ...................................................................................... 36 Chapter 3 Diffusion ......................................................................................... 37 3.1 Fick’s First Law ...................................................................... 37 3.2 Fick’s Second Law ............................................................... 37 3.3 Solutions of Fick’s Second Law ........................................... 39 v vi Contents 3.3.1 Addition of Material to or Removal from a Surface ................................................................... 39 3.3.2 Junction of Two Solid Solutions ............................... 40 3.3.3 Homogenization ....................................................... 41 3.4 Mechanisms of Diffusion .................................................... 42 3.5 Kirkendall Effect ................................................................. 44 3.6 Special Diffusion Paths ........................................................ 45 3.7 Darken’s Equation ................................................................ 47 3.8 Diffusion in Systems with More than One Phase ................ 47 3.9 Miscellany ............................................................................ 51 Problems ......................................................................................... 52 References ...................................................................................... 52 Chapter 4 Surface Tension and Surface Energy ............................................. 53 4.1 Direct Measurements of Surface Energy ............................. 53 4.2 Measurements of Relative Surface Energies ....................... 55 4.3 Wetting Angles .................................................................... 56 4.4 Relation of Surface Energy to Bonding ............................... 56 4.5 Anisotropy of Surface Energy ............................................. 57 4.6 Segregation to Surfaces ........................................................ 60 4.6.1 Note .......................................................................... 61 4.7 Miscellany ............................................................................ 61 Problems ......................................................................................... 61 Appendix: Data on Various Systems .............................................. 62 References ..........................................................................................64 Chapter 5 Solid Solutions ................................................................................ 65 5.1 Types of Solid Solutions ...................................................... 65 5.2 Electron-to-Atom Ratio ....................................................... 65 5.3 Entropy of Mixing ............................................................... 66 5.4 Enthalpy of Mixing .............................................................. 68 5.5 Free Energy Change on Mixing ........................................... 69 5.5.1 Solubility in Dilute Solutions ................................... 70 5.6 Equilibrium Vacancy and Interstitial Concentrations ......... 71 5.7 Ordered versus Random Solid Solutions ............................. 71 5.8 Miscellany ............................................................................ 72 Problems ......................................................................................... 74 References ...................................................................................... 75 Chapter 6 Intermediate Phases ....................................................................... 77 6.1 Hume-Rothery or Electron Phases ....................................... 77 6.2 Covalent Compounds ........................................................... 77 6.3 Ionic Compounds ................................................................. 77 Contents vii 6.4 I nterstitial Compounds ......................................................... 78 6.5 Laves Phases ........................................................................ 78 6.6 Miscellany ............................................................................ 81 Problems ......................................................................................... 81 References ...................................................................................... 81 Chapter 7 Phase Diagrams .............................................................................. 83 7.1 Review of Binary Phase Diagrams ...................................... 83 7.2 Invariant Reactions .............................................................. 83 7.3 Lever Law ............................................................................ 84 7.4 Gibbs’ Phase Rule ................................................................ 84 7.4.1 Equalities .................................................................. 85 7.4.2 Variables ................................................................... 86 7.4.3 Degrees of Freedom ................................................. 86 7.5 Ternary Phase Diagrams ...................................................... 88 7.5.1 Two-Phase Regions .................................................. 89 7.5.2 Three-Phase Regions ................................................ 90 7.5.3 Vertical Sections ....................................................... 91 7.6 Miscellany ............................................................................ 92 Problems ......................................................................................... 93 References ...................................................................................... 93 Chapter 8 Dislocations .................................................................................... 95 8.1 The Nature of Dislocations .................................................. 95 8.2 Energy of a Screw Dislocation ............................................. 97 8.3 Burgers Vector Notation .................................................... 100 8.4 Reactions between Parallel Dislocations and Frank’s Rule ................................................................ 100 8.5 Stress Fields around Dislocations ...................................... 101 8.6 Forces on Dislocations ....................................................... 103 8.7 Partial Dislocations in fcc Crystals .................................... 104 8.8 Stacking Faults ................................................................... 106 8.9 C ross Slip ........................................................................... 109 8.10 M iscellany .......................................................................... 110 8.10.1 Postulation of Dislocations ..................................... 110 8.10.2 Discovery of the Strength of Whiskers .................. 111 Problems ....................................................................................... 111 References .................................................................................... 113 Chapter 9 Annealing ..................................................................................... 115 9.1 General ............................................................................... 115 9.2 Recovery ............................................................................ 115 9.3 Recrystallization ................................................................ 118 viii Contents 9.4 Avrami Kinetics ................................................................. 124 9.5 Grain Growth ..................................................................... 125 9.6 Limiting Grain Size ........................................................... 129 9.6.1 Summary of Grain Growth .................................... 132 9.7 Chapter Summary .............................................................. 132 9.8 Miscellany .......................................................................... 133 Problems ....................................................................................... 133 References .................................................................................... 135 Chapter 10 Phase Transformations ................................................................. 137 10.1 Classifi cation of Solid–State Phase Transformations ....................................................... 137 10.2 M artensitic Transformations .............................................. 137 10.3 Spinodal Decomposition .................................................... 140 10.4 Nucleation Kinetics ............................................................ 143 10.5 Growth ............................................................................... 143 10.6 O verall Kinetics ................................................................. 144 10.7 Precipitation from a Supersaturated Solid Solution .............................................................................. 145 10.8 Precipitation Hardening Kinetics ...................................... 145 10.9 Precipitate Growth ............................................................. 147 10.10 P recipitation Kinetics ......................................................... 148 10.11 Strain Energy ..................................................................... 148 10.12 Hardening Mechanism ....................................................... 149 10.13 O stwald Ripening .............................................................. 150 10.14 Practical Age-Hardening Treatments ................................ 150 10.15 Aluminum–Copper Alloys ................................................ 154 10.16 Habit ................................................................................... 155 10.17 Miscellany .......................................................................... 157 Problems ....................................................................................... 158 References ........................................................................................160 Chapter 11 Crystallographic Textures ............................................................ 161 11.1 Stereographic Projection .................................................... 161 11.2 Construction of a Standard Cubic Projection .................... 163 11.3 Locating the HKL Pole in the Standard Stereographic Projection of a Cubic Crystal ............................................. 164 11.4 Orientation Representation ................................................ 165 11.5 Pole Figures ........................................................................ 166 11.6 Inverse Pole Figures ........................................................... 167 11.7 Orientation Distribution Functions .................................... 167 11.8 Origins of Texture .............................................................. 168 11.9 Recrystallization Textures ................................................. 170 11.10 Effect of Texture on Mechanical Properties ...................... 170 Contents ix 11.11 Effect of Texture on the Microstructure of Wires of BCC Metals .................................................... 172 11.12 Miscellany .......................................................................... 177 Problems ....................................................................................... 179 References .................................................................................... 179 Chapter 12 Aluminum and Its Alloys ............................................................. 181 12.1 Uses .................................................................................... 181 12.2 Alloys ................................................................................. 181 12.3 Wrought Alloys .................................................................. 184 12.3.1 Temper Designations .............................................. 184 12.4 Casting Alloys .................................................................... 188 12.5 Powder Processing ............................................................. 190 12.6 Corrosion Resistance ......................................................... 191 12.7 Aluminum–Lithium Alloys ............................................... 193 12.8 Foams ................................................................................. 196 12.9 Miscellany .......................................................................... 196 Problems ....................................................................................... 197 References ...................................................................................... 199 Chapter 13 Copper and Nickel Alloys ............................................................ 201 13.1 Electrical Properties ........................................................... 201 13.2 Commercial Grades of Copper .......................................... 201 13.3 Commercial Copper Alloys ............................................... 207 13.4 Brass ................................................................................... 207 13.5 Other Copper-Based Alloys ............................................... 211 13.6 Casting of Copper Alloys ................................................... 215 13.7 Corrosion of Copper Alloys ............................................... 217 13.8 Nickel-Based Alloys .......................................................... 219 13.9 Miscellany .......................................................................... 221 Problems ....................................................................................... 222 References .................................................................................... 223 Chapter 14 Hexagonal Close-Packed Metals .................................................. 225 14.1 General ............................................................................... 225 14.2 Z inc .................................................................................... 225 14.3 Magnesium ......................................................................... 227 14.4 Titanium ............................................................................. 232 14.5 Z irconium .......................................................................... 241 14.6 Beryllium ........................................................................... 241 14.7 M iscellany .......................................................................... 241 Problems ....................................................................................... 242 References ...................................................................................... 243