Callister - An introduction - 8th edition

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Chapter 5 Diffusion The photograph at the top of this page is of a steel gear that has been case hardened. Its outer surface layer was selectively hardened by a high-temperature heat treatment during which carbon from the surrounding atmosphere diffused into the surface. The “case” appears as the dark outer rim of that segment of the gear that has been sectioned. This increase in the carbon content raises the surface hardness (as explained in Section 10.7), which in turn leads to an improvement of wear resistance of the gear. In addition, residual compressive stresses are introduced within the case region; these give rise to an enhancement of the gear’s resistance to failure by fatigue while in service (Chapter 8). Case-hardened steel gears are used in automobile transmissions, similar to the one shown in the photograph directly below the gear. (Top: courtesy of Surface Division Midland-Ross; center: courtesy Ford Motor Company; bottom right: © BRIAN KERSEY/UPI/Landov LLC; bottom inset: © iStockphoto.) 122 •
WHY Study Diffusion? Materials of all types are often heat-treated to improve their properties. The phenomena that occur during a heat treatment almost always involve atomic diffusion. Often an enhancement of diffusion rate is desired; on occasion measures are taken to reduce it. Heat-treating temperatures and times and/or cooling rates are often predictable using the mathematics of diffusion and appropriate diffusion constants. The steel gear shown on page 122 (top) has been case hardened (Section 8.10); that is, its hardness and resistance to failure by fatigue have been enhanced by diffusing excess carbon or nitrogen into the outer surface layer. In the processing/structure/properties/performance scheme, reasons for studying diffusion are as follows: • Diffusional processes (conducted at elevated temperatures) are often utilized to introduce impurity atoms into silicon semiconductors. Thus, a knowledge of the time and temperature dependences of appropriate diffusion parameters is necessary. • Likewise, the heat treatment of steels (and the development of their mechanical properties) involves diffusion. Learning Objectives After studying this chapter you should be able to do the following: 1. Name and describe the two atomic mechanisms concentration of diffusing species at the of diffusion. surface is held constant. Define all parameters 2. Distinguish between steady-state and nonsteadystate diffusion. 4. Calculate the diffusion coefficient for some in this equation. 3. (a) Write Fick’s first and second laws in equation form and define all parameters. appropriate diffusion constants. material at a specified temperature, given the (b) Note the kind of diffusion for which each of these equations is normally applied. 4. Write the solution to Fick’s second law for diffusion into a semi-infinite solid when the 5.1 INTRODUCTION Many reactions and processes that are important in the treatment of materials rely on the transfer of mass either within a specific solid (ordinarily on a microscopic diffusion level) or from a liquid, a gas, or another solid phase.This is necessarily accomplished by diffusion, the phenomenon of material transport by atomic motion. This chapter discusses the atomic mechanisms by which diffusion occurs, the mathematics of diffusion, and the influence of temperature and diffusing species on the rate of diffusion. The phenomenon of diffusion may be demonstrated with the use of a diffusion couple, which is formed by joining bars of two different metals together so that there is intimate contact between the two faces; this is illustrated for copper and nickel in Figure 5.1, which includes schematic representations of atom positions and composition across the interface. This couple is heated for an extended period at an elevated temperature (but below the melting temperature of both metals) and cooled to room temperature. Chemical analysis will reveal a condition similar to that represented in Figure 5.2—namely, pure copper and nickel at the two extremities of the couple, separated by an alloyed region. Concentrations of • 123
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Characteristics of Selected Element
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E IGHTH E DITION Materials Science
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viii • Preface FEATURES THAT ARE
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x • Preface 2. Answers to Concept
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Appreciation is expressed to those
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xiv • Contents 3. The Structure o
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xvi • Contents 9.12 Development o
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xviii • Contents 15.14 Factors Th
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xx • Contents 21.14 Optical Fiber
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xxii • List of Symbols HK Knoop
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Chapter 1 Introduction A familiar i
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1.2 Materials Science and Engineeri
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1.4 Classification of Materials •
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1.5 Advanced Materials • 11 aeros
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1.6 Modern Materials’ Needs • 1
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STEELS Processing Diffusion ➣ Rec
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Question • 17 REFERENCES Ashby, M
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WHY STUDY Atomic Structure and Inte
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2.3 Electrons in Atoms • 21 Orbit
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2.3 Electrons in Atoms • 23 Table
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2.3 Electrons in Atoms • 25 Table
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2.4 The Periodic Table • 27 Metal
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2.5 Bonding Forces and Energies •
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2.6 Primary Interatomic Bonds • 3
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2.6 Primary Interatomic Bonds • 3
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2.7 Secondary Bonding or van der Wa
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2.7 Secondary Bonding or van der Wa
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Summary • 39 Primary Interatomic
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Questions and Problems • 41 QUEST
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Questions and Problems • 43 Sprea
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WHY STUDY The Structure of Crystall
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lattice 3.4 Metallic Crystal Struct
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3.4 Metallic Crystal Structures •
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3.5 Density Computations • 51 EXA
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3.7 Crystal Systems • 53 Another
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3.8 Point Coordinates • 55 Concep
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3.9 Crystallographic Directions •
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3.10 Crystallographic Planes • 63
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3.12 Close-Packed Crystal Structure
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Page 109 and 110: Summary • 81 Point Coordinates Cr
Page 111 and 112: Processing/Structure/Properties/Per
Page 113 and 114: Questions and Problems • 85 118.7
Page 115 and 116: Questions and Problems • 87 3.40
Page 117 and 118: Questions and Problems • 89 Inten
Page 119 and 120: WHY STUDY Imperfections in Solids?
Page 121 and 122: self-interstitial increases exponen
Page 123 and 124: 2. Crystal structure. For appreciab
Page 125 and 126: 4.4 Specification of Composition
Page 127 and 128: 4.5 Dislocations—Linear Defects
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Page 131 and 132: 4.6 Interfacial Defects • 103 Ang
Page 133 and 134: 4.6 Interfacial Defects • 105 MAT
Page 135 and 136: the order of 10 13 vibrations per s
Page 137 and 138: 4.10 Microscopic Techniques • 109
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Page 141 and 142: 4.11 GRAIN SIZE DETERMINATION grain
Page 143 and 144: Summary • 115 Specification of Co
Page 145 and 146: Summary • 117 List of Symbols Sym
Page 147 and 148: Questions and Problems • 119 (a)
Page 149: Design Problems • 121 (a) at a ma
Page 153 and 154: 5.2 Diffusion Mechanisms • 125 se
Page 155 and 156: 5.3 Steady-State Diffusion • 127
Page 157 and 158: 5.4 Nonsteady-State Diffusion • 1
Page 159 and 160: 5.4 Nonsteady-State Diffusion • 1
Page 161 and 162: 5.5 Factors That Influence Diffusio
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Page 171 and 172: Summary • 143 Diffusion in Semico
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Page 175 and 176: Diffusion coefficient (m 2 /s) 10 -
Page 177 and 178: Design Problems • 149 the process
Page 179 and 180: WHY STUDY The Mechanical Properties
Page 181 and 182: 6.2 Concepts of Stress and Strain
Page 183 and 184: 6.2 Concepts of Stress and Strain
Page 185 and 186: 6.3 Stress-Strain Behavior • 157
Page 187 and 188: 6.4 Anelasticity • 159 Figure 6.8
Page 189 and 190: 6.5 Elastic Properties Of Materials
Page 191 and 192: 6.6 Tensile Properties • 163 Figu
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6.9 Compressive, Shear, and Torsion
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Table 6.5 Hardness-Testing Techniqu
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Brinell Hardness Tests 15 6.10 Hard
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6.10 Hardness • 179 are contained
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6.11 Variability Of Material Proper
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6.12 Design/Safety Factors • 183
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Summary • 185 • For an isotropi
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Summary • 187 6.15 s T F True st
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Questions and Problems • 189 a lo
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Questions and Problems • 191 tens
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Questions and Problems • 193 modu
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Design Problems • 195 (a) Determi
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Chapter 7 Dislocations and Strength
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Dislocations and Plastic Deformatio
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7.3 Characteristics of Dislocations
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7.4 Slip Systems • 203 D B A (a)
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7.5 Slip in Single Crystals • 205
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7.5 Slip in Single Crystals • 207
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7.6 Plastic Deformation of Polycrys
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7.7 Deformation by Twinning • 211
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7.9 Solid-Solution Strengthening
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7.10 Strain Hardening • 215 (a) (
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7.10 Strain Hardening • 217 600 2
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7.11 RECOVERY recovery 7.12 RECRYST
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7.12 Recrystallization • 221 (e)
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7.12 Recrystallization • 223 DESI
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Summary • 225 Figure 7.25 The log
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Summary • 227 Strain Hardening
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Questions and Problems • 229 Iron
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Questions and Problems • 231 and
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Design Problems • 233 Spreadsheet
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WHY STUDY Failure? The design of a
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8.3 Ductile Fracture • 237 Figure
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8.4 Brittle Fracture • 239 8.4 BR
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8.4 Brittle Fracture • 241 SEM Mi
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8.5 Principles of Fracture Mechanic
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8.6 Fracture Toughness Testing •
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8.6 Fracture Toughness Testing •
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8.7 Cyclic Stresses • 255 Most ce
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8.8 The S-N Curve • 257 fatigue l
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8.9 Crack Initiation and Propagatio
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8.9 Crack Initiation and Propagatio
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8.10 Factors that Affect Fatigue Li
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8.12 Generalized Creep Behavior •
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8.13 Stress and Temperature Effects
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8.15 Alloys For High-Temperature Us
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Summary • 271 Ductile Fracture
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Summary • 273 • The presence of
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fatigue limit fatigue strength frac
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Questions and Problems • 277 Cycl
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Design Problems • 279 8.31 A cyli
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Chapter 9 Phase Diagrams The graph
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Definitions and Basic Concepts 9.2
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9.5 PHASE EQUILIBRIA equilibrium fr
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phases is along curve aO—likewise
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9.8 Interpretation of Phase Diagram
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9.9 Development of Microstructure i
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9.10 Mechanical Properties of Isomo
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9.11 Binary Eutectic Systems • 29
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9.12 Development of Microstructure
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9.13 Equilibrium Diagrams Having In
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9.14 Eutectoid and Peritectic React
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9.15 Congruent Phase Transformation
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9.17 The Gibbs Phase Rule • 317 F
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The Iron-Carbon System 9.18 The Iro
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9.18 The Iron-Iron Carbide (Fe-Fe 3
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Summary • 331 SUMMARY Introductio
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Summary • 333 Development of Micr
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Questions and Problems • 335 Impo
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Questions and Problems • 337 (b)
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Questions and Problems • 339 Figu
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Questions and Problems • 341 9.54
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WHY STUDY Phase Transformations? Th
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10.3 The Kinetics of Phase Transfor
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10.4 Metastable versus Equilibrium
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10.5 Isothermal Transformation Diag
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10.6 Continuous Cooling Transformat
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10.6 Continuous Cooling Transformat
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10.7 Mechanical Behavior of Iron-Ca
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10.7 Mechanical Behavior of Iron-Ca
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10.8 TEMPERED MARTENSITE In the as-
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10.8 Tempered Martensite • 377 (b
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10.9 Review of Phase Transformation
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Summary • 381 Figure 10.37. Of co
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Summary • 383 Spheroidite—is co
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Questions and Problems • 385 Stee
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Questions and Problems • 389 (c)
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Chapter 11 Applications and Process
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11.2 Ferrous Alloys • 393 Types o
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11.2 Ferrous Alloys • 395 Table 1
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11.2 Ferrous Alloys • 397 Table 1
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11.2 Ferrous Alloys • 399 is exte
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11.2 Ferrous Alloys • 401 (c) 20
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Table 11.5 Designations, Minimum Me
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11.2 Ferrous Alloys • 405 is pres
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11.3 Nonferrous Alloys • 407 Tabl
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Table 11.9 Compositions, Mechanical
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11.3 Nonferrous Alloys • 415 or n
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11.4 Forming Operations • 417 Met
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11.5 Casting • 419 that have rath
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11.6 Miscellaneous Techniques • 4
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11.7 Annealing Processes • 423 ox
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modification of mechanical properti
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11.8 Heat Treatment of Steels • 4
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11.9 Precipitation Hardening • 43
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Summary • 443 Forming Operations
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Summary • 445 PROCESSING Recrysta
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Questions and Problems • 447 REFE
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Design Problems • 449 and temperi
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Chapter 12 Structures and Propertie
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12.2 Crystal Structures • 453 Con
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12.2 Crystal Structures • 455 Tab
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12.2 Crystal Structures • 457 Fur
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12.2 Crystal Structures • 459 VMS
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12.2 Crystal Structures • 461 Tet
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12.2 Crystal Structures • 463 EXA
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12.3 Silicate Ceramics • 465 Si 4
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12.3 Silicate Ceramics • 467 Figu
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12.4 Carbon • 469 Figure 12.16 Sc
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Another molecular form of carbon ha
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12.5 Imperfections in Ceramics •
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12.5 Imperfections in Ceramics •
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12.7 Ceramic Phase Diagrams • 477
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12.7 Ceramic Phase Diagrams • 479
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12.8 Brittle Fracture of Ceramics
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12.8 Brittle Fracture of Ceramics
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flexural strength Flexural strength
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12.10 Mechanisms of Plastic Deforma
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viscosities at ambient temperatures
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Summary • 491 Table 12.6 Vickers
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Summary • 493 • Diagrams for Al
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Questions and Problems • 495 visc
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Questions and Problems • 497 does
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Questions and Problems • 499 Stre
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Chapter 13 Applications and Process
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13.3 Glass-Ceramics • 503 Ceramic
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13.5 Refractories • 505 Glass-cer
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13.6 Abrasives • 507 (2910F). Thu
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13.8 Advanced Ceramics • 509 Seve
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13.8 Advanced Ceramics • 511 opti
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13.9 Fabrication and Processing of
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13.11 Powder Pressing • 523 a sca
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13.12 Tape Casting • 525 Figure 1
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Summary • 527 • Requirements fo
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Summary • 529 This chapter also d
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13.12 Compare the softening points
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WHY STUDY Polymer Structures? A rel
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14.3 Polymer Molecules • 535 Tabl
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14.4 The Chemistry of Polymer Molec
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14.4 The Chemistry of Polymer Molec
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Figure 14.3 Hypothetical polymer mo
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14.5 Molecular Weight • 543 Table
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14.7 Molecular Structure • 545 Fi
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14.8 Molecular Configurations • 5
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14.8 Molecular Configurations • 5
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14.10 Copolymers • 551 adjacent c
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14.11 Polymer Crystallinity • 553
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For copolymers, as a general rule,
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14.12 Polymer Crystals • 557 ~ 10
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14.14 Diffusion in Polymeric Materi
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Summary • 561 PET is permeable to
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Equation Summary Summary • 563 Po
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Important Terms and Concepts Questi
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Questions and Problems • 567 age
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Chapter 15 Characteristics, Applica
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15.2 Stress-Strain Behavior • 571
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15.3 Macroscopic Deformation • 57
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15.4 Viscoelastic Deformation • 5
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15.4 Viscoelastic Deformation • 5
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15.5 Fracture of Polymers • 579 F
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15.7 Deformation of Semicrystalline
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t 0 t t 0 t 0 Stage 1 Stage 2 (a) (
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15.8 Factors That Influence the Mec
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15.8 Factors That Influence the Mec
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15.9 Deformation of Elastomers •
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15.10 Crystallization • 591 Norma
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15.13 Melting and Glass Transition
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15.14 Factors That Influence Meltin
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15.15 Plastics • 597 Table 15.3 (
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15.16 Elastomers • 599 ing phenol
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15.18 Miscellaneous Applications
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15.19 Advanced Polymeric Materials
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15.19 Advanced Polymeric Materials
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The tensile modulus of this TPE mat
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15.20 Polymerization • 609 Additi
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15.22 Forming Techniques for Plasti
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15.22 Forming Techniques for Plasti
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15.24 Fabrication of Fibers and Fil
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Factors That Influence the Mechanic
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Summary • 619 Equation Summary Eq
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Questions and Problems • 621 McCr
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Questions and Problems • 623 Tens
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Design Questions • 625 Elastomers
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3.1 Hardness • 627 WHY STUDY Comp
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16.1 Introduction • 629 Dispersed
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16.2 Large-Particle Composites •
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16.2 Large-Particle Composites •
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Critical fiber length—dependence
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16.5 Influence of Fiber Orientation
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ut, because s/E, 16.5 Influence o
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16.6 The Fiber Phase • 645 Applic
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eactions with the environment. Such
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16.8 Polymer-Matrix Composites •
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16.8 Polymer-Matrix Composites •
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16.9 Metal-Matrix Composites • 65
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The high-temperature creep and rupt
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16.12 HYBRID COMPOSITES hybrid comp
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16.13 Processing of Fiber-Reinforce
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16.15 Sandwich Panels • 661 Figur
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Summary • 663 they remain separat
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Summary • 665 When l l c , Equat
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References • 667 List of Symbols
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Design Problems • 671 to be align
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Chapter 17 Corrosion and Degradatio
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Corrosion of Metals 17.2 Electroche
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17.2 Electrochemical Considerations
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17.4 Prediction of Corrosion Rates
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17.5 Passivity • 691 to further c
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17.7 Forms of Corrosion • 693 sur
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17.7 Forms of Corrosion • 695 Fig
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sodium chloride. Dilute sulfuric ac
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17.10 Oxidation • 703 Zinc coatin
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17.10 Oxidation • 705 Table 17.3
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Ceramic materials are frequently us
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17.12 Bond Rupture • 709 17.12 BO
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Summary • 711 marily a result of
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Summary • 713 Corrosion Preventio
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Questions and Problems • 715 REFE
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Chapter 18 Electrical Properties (b
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18.3 Electrical Conductivity • 72
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18.5 Energy Band Structures in Soli
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valence band conduction band energy
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covalent) and relatively weak, whic
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18.8 Electrical Resistivity of Meta
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18.9 Electrical Characteristics of
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18.10 Intrinsic Semiconduction •
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18.10 Intrinsic Semiconduction •
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18.11 Extrinsic Semiconduction •
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18.11 Extrinsic Semiconduction •
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18.12 The Temperature Dependence of
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18.13 Factors That Affect Carrier M
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DESIGN EXAMPLE 18.1 Acceptor Impuri
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18.14 The Hall Effect • 747 Depen
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18.15 Semiconductor Devices • 749
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18.16 Conduction in Ionic Materials
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ands that overlap the valence and c
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18.19 Field Vectors and Polarizatio
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18.19 Field Vectors and Polarizatio
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ionic polarization Electric dipole
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18.23 Dielectric Materials • 765
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Summary • 767 + + + + + + + + +
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Summary • 769 • With these mate
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Summary • 771 18.11 r i Ac i 11
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Summary • 773 One common use for
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Questions and Problems • 775 Elec
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Questions and Problems • 777 The
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Design Problems • 779 DESIGN PROB
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Chapter 19 Thermal Properties (a) (
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19.2 Heat Capacity • 783 Figure 1
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19.3 Thermal Expansion • 785 Tabl
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19.3 Thermal Expansion • 787 For
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19.4 THERMAL CONDUCTIVITY Thermal c
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19.4 Thermal Conductivity • 791 F
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19.5 Thermal Stresses • 793 speci
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Summary • 795 • Coefficient-of-
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Design Problems • 799 rod be fabr
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WHY STUDY the Magnetic Properties o
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20.2 Basic Concepts • 803 I B 0 =
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20.3 Diamagnetism and Paramagnetism
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20.4 Ferromagnetism • 807 Table 2
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20.5 Antiferromagnetism and Ferrima
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20.5 Antiferromagnetism and Ferrima
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20.6 The Influence of Temperature o
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20.7 Domains and Hysteresis • 815
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20.7 Domains and Hysteresis • 817
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20.9 Soft Magnetic Materials • 81
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20.9 Soft Magnetic Materials • 82
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20.10 Hard Magnetic Materials • 8
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20.11 Magnetic Storage • 825 requ
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20.11 Magnetic Storage • 827 Figu
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20.12 Superconductivity • 829 Ele
Page 859 and 860:
20.12 Superconductivity • 831 Tab
Page 861 and 862:
Summary • 833 • For cubic ferri
Page 863 and 864:
Questions and Problems • 835 List
Page 865 and 866:
Questions and Problems • 837 with
Page 867 and 868:
Design Problems • 839 H C 1T 2 H
Page 869 and 870:
WHY STUDY the Optical Properties of
Page 871 and 872:
21.3 Light Interactions with Solids
Page 873 and 874:
21.4 Atomic and Electronic Interact
Page 875 and 876:
21.5 Refraction • 847 Velocity of
Page 877 and 878:
21.7 ABSORPTION Nonmetallic materia
Page 879 and 880:
21.7 Absorption • 851 Reaction de
Page 881 and 882:
21.9 Color • 853 21.9 COLOR color
Page 883 and 884:
21.11 Luminescence • 855 Figure 2
Page 885 and 886:
21.11 Luminescence • 857 n- and p
Page 887 and 888:
21.13 Lasers • 859 Ruby Flash lam
Page 889 and 890:
21.13 Lasers • 861 Partially refl
Page 891 and 892:
21.4 Optical Fibers in Communicatio
Page 893 and 894:
Summary • 865 Input impulse Outpu
Page 895 and 896:
Summary • 867 Transparent nonmeta
Page 897 and 898:
Questions and Problems • 869 Impo
Page 899 and 900:
Design Problem • 871 fiber glass
Page 901 and 902:
WHY STUDY Economic, Environmental,
Page 903 and 904:
Environmental and Societal Consider
Page 905 and 906:
Environmental and Societal Consider
Page 907 and 908:
22.5 Recycling Issues in Materials
Page 909 and 910:
Page 911 and 912:
Page 913:
Design Questions • 885 Environmen
Page 916 and 917:
A2 • Appendix A / The Internation
Page 918 and 919:
A4 • Appendix B / Properties of S
Page 920 and 921:
Page 922 and 923:
Page 924 and 925:
A10 • Appendix B / Properties of
Page 926 and 927:
Page 928 and 929:
Page 930 and 931:
Page 932 and 933:
Page 934 and 935:
Page 936 and 937:
Page 938 and 939:
Page 940 and 941:
Page 942 and 943:
Page 944 and 945:
Page 946 and 947:
A32 • Appendix C / Costs and Rela
Page 948 and 949:
A34 • Appendix C / Costs and Rela
Page 950 and 951:
Appendix D Repeat Unit Structures f
Page 952 and 953:
A38 • Appendix D / Repeat Unit St
Page 954 and 955:
Appendix E Glass Transition and Mel
Page 956 and 957:
G2 • Glossary atomic mass units (
Page 958 and 959:
G4 • Glossary according to unit c
Page 960 and 961:
G6 • Glossary Fick’s first law.
Page 962 and 963:
G8 • Glossary J Jominy end-quench
Page 964 and 965:
G10 • Glossary alternating layers
Page 966 and 967:
G12 • Glossary stock; also, elong
Page 968 and 969:
G14 • Glossary tempered martensit
Page 970 and 971:
Answers to Selected Problems Chapte
Page 972 and 973:
S2 • Answers to Selected Problems
Page 974:
S4 • Answers to Selected Problems
Page 977 and 978:
plane strain fracture toughness, 24
Page 979 and 980:
Clay, characteristics, 518-519 Clay
Page 981 and 982:
Die casting, 419 Dielectric breakdo
Page 983 and 984:
Fatigue life, 258, G4 factors that
Page 985 and 986:
Heat treatable, definition of, 406
Page 987 and 988:
modulus of elasticity, 486 thermal
Page 989 and 990:
Nanotubes, carbon, 13, 471 Natural
Page 991 and 992:
fatigue behavior (PET), 580 magneti
Page 993 and 994:
single crystal, 451 structure of, 4
Page 995 and 996:
Stabilized zirconia, 478, 655 Stabi
Page 997 and 998:
Transparency, 844, G13 Transverse b
Page 999 and 1000:
Power 1 W 0.239 cal/s 1 cal/s 4.1
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Callister - An introduction - 8th edition

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