E-raamat: Methods for Phase Diagram Determination

Preface		vii
1 Introduction to Phase Diagrams		1
John F. Smith
1 Introduction		1
2 J. Willard Gibbs and the First Equilibrium Diagram		3
3 Twentieth Century Developments		5
4 The CALPHAD Method and Its Need for Data		8
5 Thermodynamic Constraints on Phase Diagrams		10
6 Experimental Considerations		17
2 The Role of Phase Transformation Kinetics in Phase Diagram Determination and Assessment		22
J.-C. Zhao
1 Introduction		22
2 Phase Transformation Kinetics During Cooling and Heating as Related to Phase Diagram Determination		24
2.1 Shifting of Transformation-Start Temperature with Cooling Rate		26
2.2 Formation of Metastable Phases During Cooling		27
2.3 Shifting of Transformation-Start Temperature with Heating Rate		30
2.4 Analyses of Examples from Cooling and Heating Experiments		35
3 Isothermal Phase Transformation Kinetics as Related to Phase Diagram Determination		41
3.1 Precipitation of Phases from Quenched Alloys		41
3.2 Kinetics and Phase Formation in Diffusion Couples/Multiples		46
4 Concluding Remarks		48
3 Correct and Incorrect Phase Diagram Features		51
Hiroaki Okamoto and Thaddeus B. Massalski
1 Introduction		52
2 Phase Rule Violations		53
2.1 Typical Phase Rule Violations		53
3 Guidelines for Finding Less Obvious Phase Diagram Errors		56
3.1 Problems Connected with Phase Boundary Curvatures		56
3.2 Summary of Improbable Phase Diagram Situations		57
3.3 Van't Hoff Relationship and Charles' Law		59
3.4 Form of the Liquidus of a Compound Near a Pure Element Side		61
3.5 Sharpness of the Liquidus of a Compound and its Relation to a Possible Eutectoid Temperature		63
3.6 Two Compounds with Very Similar Compositions Are Unlikely to Coexist in a Wide Temperature Range		65
3.7 Asymmetry of the Liquidus Around the Melting Point of a Compound		65
3.8 Narrowing of the Width of a Two-Phase Field When the Boundaries Are Extrapolated Toward Higher Temperatures		68
3.9 An Abrupt Change of Slope		70
3.10 An Excessive Slope Change Associated with a Polymorphic Transformation		72
3.11 Shape of a Miscibility Gap		73
3.12 Displaced Miscibility Gap		74
3.13 An Inverse Miscibility Gap		76
3.14 Almost Symmetric Syntectic Reaction		76
3.15 Metastable Melting Point of a Pure Element		77
4 Examples of Phase Diagrams with Improbable Features		79
4.1 Ag–Pr		80
4.2 Al–B		80
4.3 Al–Mn		82
4.4 Al–Pu		82
4.5 Al–Se		83
4.6 Au–La		83
4.7 Au–U		84
4.8 B–Bi		86
4.9 B–W		86
4.10 C–Ge		87
4.11 Ca–Eu		87
4.12 Ce–Pr		87
4.13 Cr–Ni		89
4.14 Cu–Hf		90
4.15 Ir–Rh		92
4.16 Lu–Th		92
4.17 Mg–Sb		92
4.18 Mn–Y		94
4.19 Mo–Ru		94
4.20 Nd–Pu		96
4.21 Ni–Sr		96
4.22 Np–Zr		97
4.23 Pd–Zr		97
4.24 Pt–Zr		99
5 Unusual but Correct Phase Diagrams		100
5.1 Apparent Four-Phase Equilibrium		100
5.2 Apparent Five-Phase Equilibrium		100
5.3 Pointed Liquidus		102
5.4 A Straight Line Liquidus		102
5.5 Off-Stoichiometric Melting		104
6 Phase Diagram Below 0°C		105
7 Conclusion		105
4 Determination of Phase Diagrams Using Equilibrated Alloys		108
Yong Zhong Zhan, Yong Du and Ying Hong Zhuang
1 Introduction		108
2 Alloy Preparation		109
2.1 High-Temperature Melting of Alloys		109
2.2 Arc Melting		110
2.3 Induction Melting		111
2.4 Powder Metallurgy Method		112
3 Homogenization Heat Treatment		113
4 Determination of Phase Equilibria: Isothermal Experiments vs. Cooling/Heating Experiments		114
4.1 Analysis of Quenched Samples to Construct Isothermal Sections (Static Method)		115
4.2 Analysis of Samples by Heating and Cooling Experiments to Construct Vertical Sections and Liquid Projections (Dynamic Method)		122
5 Examples of Phase Diagram Determination Using Equilibrated Alloys		129
5.1 The Cu–Nd Binary System		130
5.2 The Al–Be–Si Ternary System		131
5.3 The Al–Mn–Si Ternary System		135
5.4 Multicomponent Phase Diagram and the Al–C–Si–Ti System		137
6 Crystal Structure Identification of New Phases		140
7 Pitfalls		145
7.1 Verification of the Establishment of True Equilibrium		145
7.2 Inconsistency Between the Result from DTA Measurement and that from XRD and Microscopy Observation		147
7.3 Identification of Degenerated Phase Equilibrium		148
5 DTA and Heat-Flux DSC Measurements of Alloy Melting and Freezing		151
William J. Boettinger, Ursula R. Kattner, Kil-Won Moon and John H. Perepezko
1 Introduction		152
1.1 Focus of this Chapter		152
1.2 Information Sought from DTA/Heat-Flux DSC Measurements		153
1.3 Relevant Standards		154
1.4 Major Points		155
2 Instruments and Operation		155
2.1 Variations Among Instruments		155
2.2 Samples		159
2.3 Reference Materials		164
2.4 Calibration and DTA Signal from Pure Metals		164
2.5 Major Points		169
3 Analysis of DTA Data for Binary Alloys		170
3.1 General Behavior for a Binary Eutectic System: Example Ag–Cu Alloy Melting		171
3.2 Problems with Solidus Determination on Heating		176
3.3 Problems with Liquidus Determination on Heating		180
3.4 Supercooling Problem with Liquidus Determination on Cooling		186
3.5 Eutectic Reactions vs. Peritectic Reactions		191
3.6 Major Points		192
4 Analysis of DTA Data for Ternary Alloys		194
4.1 Al-Rich Corner of Al–Cu–Fe Phase Diagram		194
4.2 Al-20% Cu–0.5% Fe		195
4.3 Al-6% Cu–0.5% Fe		197
4.4 Major Points		198
5 Concluding Remarks		198
Appendix A Glossary		201
Appendix B Recommended Reading		204
Appendix C Model for Simulating DTA Response for Melting and Solidification of Materials with Known or Assumed Enthalpy vs. Temperature Relations. Also Method for Determining Thermal Lag Time Constants of DTA/DSC Instruments		205
Appendix D Expressions for the Rate Dependence of Melting Onset Temperatures for a Pure Metal		205
Appendix E Enthalpy vs. Temperature Relations for Dilute Binary Solid Solution Alloy		211
Appendix F Binary Phase Diagrams and DTA Response		213
Appendix G Tutorial on Melting and Freezing of Multicomponent Alloys		213
G.1 Aluminum Alloy 2219		213
G.2 Udimet 700		218
6 Application of Diffusion Couples in Phase Diagram Determination		222
A.A. Kodentsov, Guillaume F. Bastin and Frans J.J. van Loo
1 Introduction		222
2 General Principles of the Diffusion Couple Method		223
3 Experimental Procedures		225
3.1 Preparation of Diffusion Couples		225
3.2 Analytical Techniques and Specimen Preparation		226
3.3 Preparation of Diffusion Couple Specimens for EPMA		227
4 Variations of the Diffusion Couple Technique		228
5 Error Sources Encountered in the Diffusion Couple Experiments		236
6 Concluding Remarks		244
7 Phase Diagram Determination Using Diffusion Multiples		246
J.-C. Zhao
1 Introduction		246
2 Diffusion-Multiple Fabrication		248
3 Analysis of Diffusion Multiples and Extraction of Phase Diagram Data		256
3.1 Imaging Examination and Phase Analysis		256
3.2 EPMA Profiling		257
3.3 Extraction of Equilibrium Tie Lines		259
4 Sources of Errors		266
5 Concluding Remarks		269
8 Application of Computational Thermodynamics to Rapidly Determine Multicomponent Phase Diagrams		273
Y. Austin Chang and Ying Yang
1 Introduction		273
2 Ternary Mg—Al—Sr System		275
2.1 Experimental Method		276
2.2 Thermodynamic Models		276
2.3 Experimental Results and Discussion		277
3 Quaternary Mo—Si—B—Ti System		282
4 Concluding Remarks		289
9 Determination of Phase Diagrams with Reactive or Volatile Elements		292
Cezary Guminski
1 Introduction		293
2 Solid–Solid Equilibria		299
2.1 Thermal Analysis		299
2.2 Zone Melting		300
2.3 Microstructural Analysis of Quenched Samples		301
2.4 X-Ray Diffraction		302
2.5 Densitometry		302
2.6 Dilatometry		303
2.7 Interdiffusion		303
2.8 Hardness		304
2.9 Calorimetry		304
2.10 Electrical Resistivity		305
2.11 Superconductivity		305
2.12 Electromotive Force		306
2.13 Coulometric Titration		307
2.14 Galvanic Polarization		309
2.15 Magnetic Susceptibility		310
2.16 Vapor Pressure		311
2.17 Gaseous Thermal Extraction		314
3 Solid–Liquid Equilibria		315
3.1 Weight Loss of a Solid After Equilibration with a Liquid		315
3.2 Chemical Analysis of a Separated Liquid		316
3.3 Chemical Analysis of Quenched Samples		318
3.4 Thermal Analysis		319
3.5 Electromotive Force		320
3.6 Electrical Resistivity		321
3.7 Anodic Oxidation		321
3.8 Magnetic Susceptibility		323
3.9 Densitometry		325
3.10 Enthalpy of Dilution		325
3.11 Kinetics of Alloy Decomposition or Formation		325
3.12 Diffusion Coefficient		327
3.13 Vapor Pressure		327
3.14 X-Ray Absorption Spectrometry		328
3.15 Viscosity		328
3.16 Optical Reflectivity		328
3.17 Corrosion Tests		328
3.18 Motion of Liquid Metal Inclusions in Ionic Crystals		330
4 Liquid—Liquid Equilibria		330
4.1 Chemical Analysis of Separated Liquids		330
4.2 Thermal Analysis		330
4.3 Calorimetry		331
4.4 Densitometry by X-Ray Attenuation		332
4.5 Neutron Transmission		332
4.6 Electromotive Force		332
4.7 Electrical Resistivity		332
4.8 Magnetic Susceptibility		333
4.9 Vapor Pressure		333
5 Solid—Vapor Equilibria		334
5.1 Vapor Pressure		334
5.2 Thermogravimetry		335
6 Liquid—Vapor Equilibria		336
6.1 Vapor Pressure		336
7 Liquid—Fluid Equilibria		337
8 Concluding Remarks		337
10 Phase Diagram Determination of Ceramic Systems		341
Doreen Edwards
1 Introduction		341
2 Ex Situ Methods		342
2.1 Sample Preparation and Equilibration		343
2.2 Phase and Compositional Analysis		350
2.3 Identification of New Phases		354
3 In Situ Methods		354
3.1 Thermal Analysis		355
3.2 Coulometric Titration		356
3.3 High-Temperature X-Ray Diffraction		358
3.4 Thermomicroscopy and Other Optical Techniques		358
3.5 Oscillation Method of Phase Analysis		358
3.6 In Situ Electrical, Dielectric, and Magnetic Measurements		359
4 Concluding Remarks		359
11 Determination of Phase Diagrams Involving Order—Disorder Transitions		361
Ryosuke Kainuma, Ikuo Ohnuma and Kiyohito Ishida
1 Introduction		361
2 ER and Thermal Analysis Methods		362
2.1 ER Method (Resistometric Study)		362
2.2 Thermal Analysis		364
3 Singular Point Method		366
3.1 Origin of Singularity		366
3.2 Examples of SPM		368
4 Concentration Gradient Method		374
4.1 Basics of CGM		376
4.2 Examples of CGM		376
5 Concluding Remarks		380
12 Determination of Phase Diagrams Involving Magnetic Transitions		383
Ichiro Takeuchi and Samuel E. Lofland
1 Introduction		383
2 The Basics of Magnetism and the Traditional Methods of Mapping Magnetic Phase Diagrams		384
2.1 Basics of Magnetism		384
2.2 Measurements of Magnetism		385
2.3 Effects of Magnetism on Phase Diagrams		389
3 Combinatorial and High-Throughput Mapping of Magnetic Phase Diagrams		396
3.1 Introduction to the Combinatorial Approach		396
3.2 Combinatorial Mapping of Magnetic Phase Diagrams in Metallic Systems		396
3.3 Combinatorial Mapping of Oxide Systems		404
4 Concluding Remarks		409
13 Determination of Pressure-Dependent Phase Diagrams		412
Surendra K. Saxena and Yanbin Wang
1 Introduction		412
2 High-Pressure Devices		413
2.1 Diamond-Anvil Cells		413
2.2 Large-Volume Presses		416
3 Pressure Measurement		418
3.1 Pressure Measurement Using Ruby Fluorescence		418
3.2 Pressure Measurement Using X-Rays		419
4 High Pressure and Temperature		421
4.1 X-Rays at High Pressure		421
4.2 Heating at High Pressure in a DAC		422
5 Examples of Phase Diagrams Determined Using LVPs		431
5.1 Phase Relations in Univariant Systems		431
5.2 Phase Relations in Complex Systems		434
6 Phase Diagrams Using DAC		435
7 Industrial Solids		438
14 The Determination of Phase Diagrams for Slag Systems		442
David R. Gaskell
1 Introduction		442
2 The CaO—Al2O3—SiO2 System		443
2.1 The CaO—SiO2 System		443
2.2 The Al2O3—SiO2 System		447
2.3 The CaO—Al2O3—SiO2 System		452
3 The CaO—"FeO"—SiO2 System		453
4 The FeO—Fe2O3—SiO2 System		455
15 Determination of Phase Diagrams for Hydrogen-Containing Systems		459
Ted B. Flanagan and Weifang Luo
1 Introduction		459
2 Phase Diagram Representations of M–H Systems		462
2.1 Binary M–H Systems		462
2.2 Multi-component Systems		466
3 Some Useful Rules Relating Phase Diagrams and Reaction Enthalpies for M–H Systems		471
4 Techniques Employed for Phase Diagram Determination of M–H Systems		473
4.1 Open Systems		474
4.2 Closed Systems		477
4.3 Electron Diffraction and TEM		480
4.4 Magnetic Susceptibility		480
4.5 Electric Resistivity		480
4.6 Dilatometry		480
16 Miscellaneous Topics on Phase Diagrams		483
J.-C. Zhao and Jack H. Westbrook
1 Introduction		483
2 Ever-Increasing Interplay of Modeling and Experiment		484
3 Phase Diagrams for Functional Materials		485
4 High-Throughput Approaches to Phase Diagram Determination		486
5 Low-Temperature Phase Diagrams		487
6 Phase Diagram Determination: A Never-Ending Task		488
7 Some Suggestions		489
Further Reading		490
General Phase Diagram Introduction		490
Specimen Purity and Preparation		490
Diffusion as Related to Phase Diagrams and Phase Diagram Determination		490
Interplay of Ordering, Magnetic Transitions, and Phase Equilibria		491
Ceramic Phase Diagram Determination		491
Theoretical/Modeling Work		491
The CALPHAD Approach		491
Miscellaneous Recommended Papers on Phase Diagram Determination		491
Some Current Phase Diagram Compilations		492
Elemental and Metallic Systems		493
Ceramic Systems		493
Other Miscellaneous Compilations/Books		493
Some Useful Websites		493

Prof. J.-C. Zhao joined the Department of Materials Science and Engineering at The Ohio State University (OSU) in January 2008 after 12 years (1995 to 2007) as a materials scientist and project/team leader at GE Global Research in Niskayuna/Schenectady, NY. He obtained his PhD degree in materials science and engineering from Lehigh University in 1995. His research focuses are on high-throughput materials science methodologies, phase diagrams, computational thermodynamics, diffusion, design of advanced alloys and coatings, and hydrogen storage materials. In addition to many materials innovations, he developed a diffusion-multiple approach and co-developed several associated materials property microscopy tools for accelerated materials discovery and development. Zhao has received several honors including the Geisler Award from ASM International, the Hull Award from GE Global Research and the Lumley Interdisciplinary Research Award from OSU, and was elected a Fellow of ASM International in 2003. He has published about 100 papers and edited/co-edited three books and two theme issues of MRS Bulletin.