Phase Diagrams and Thermodynamic Modeling of Solutions

Description

Cover......Page 1 PHASE DIAGRAMS AND THERMODYNAMIC MODELING OF SOLUTIONS ......Page 3 Copyright......Page 4 Dedication......Page 5 Acknowledgement......Page 6 Introduction......Page 7 List of Websites......Page 8 Part I: Phase Diagrams and Thermodynamics ......Page 9 1. Introduction......Page 10 List of Websites......Page 90 List of Websites......Page 15 2. Thermodynamics Fundamentals......Page 16 The First Law......Page 17 The Second Law......Page 18 The Fundamental Equation of Thermodynamics......Page 19 Enthalpy......Page 20 Gibbs Energy......Page 23 Equilibria Involving a Gaseous Phase......Page 25 A Note on Nonideal Gases......Page 27 Predominance Diagrams......Page 29 Measuring Gibbs Energy Change......Page 32 Measuring Entropy-The Third Law of Thermodynamics......Page 33 Gibbs Energy of a Pure Compound as a Function of Temperature......Page 34 Auxiliary Functions......Page 35 The Chemical Potential......Page 36 The Gibbs-Duhem Equation......Page 37 List of Websites......Page 38 3. The Gibbs Phase Rule......Page 39 The Phase Rule and Binary Temperature-Composition Phase Diagrams......Page 41 Three-Phase Invariants in Binary Temperature-Composition Phase Diagrams......Page 43 Other Examples of Applications of the Phase Rule......Page 44 Reference......Page 46 Gibbs Energy of Mixing......Page 47 Partial Molar Properties......Page 49 Relative Partial Molar Properties......Page 50 A Note on Standard States......Page 51 Ideal Raoultian Solutions......Page 52 Excess Properties......Page 54 Activity Coefficients......Page 55 Regular Solution Theory......Page 56 List of Websites......Page 58 Temperature-Composition Phase Diagrams in Systems with Complete Solid and Liquid Miscibility......Page 59 Binary Pressure-Composition Phase Diagrams......Page 64 Minima and Maxima in Two-Phase Regions......Page 65 Miscibility Gaps......Page 67 Simple Eutectic Systems......Page 69 Thermodynamic Origin of Simple Binary Phase Diagrams Illustrated by Regular Solution Theory......Page 71 Immiscibility-Montectics......Page 73 Intermediate Phases......Page 76 Limited Mutual Solubility-Ideal Henrian Solutions......Page 79 Henry's Law, Raoult's Law and Standard States......Page 82 Single Ion Activities......Page 84 The ``Activity´´ of a Solution......Page 85 Geometry of Binary Temperature-Composition Phase Diagrams......Page 86 Effects of Grain Size, Coherency, and Strain Energy......Page 89 The Ternary Composition Triangle......Page 91 Ternary Space Model......Page 92 Polythermal Projections of Liquidus Surfaces......Page 94 Ternary Isothermal Sections......Page 97 Topology of Ternary Isothermal Sections......Page 99 Ternary Isopleths (Constant Composition Sections)......Page 101 Quasibinary Phase Diagrams......Page 102 First-Melting (Solidus) Projections of Ternary Systems......Page 103 Liquidus Projections......Page 105 Solidus Projections......Page 106 List of Websites......Page 108 7. General Phase Diagram Sections......Page 109 Corresponding Potentials and Extensive Variables......Page 110 The Law of Adjoining Phase Regions......Page 111 Nodes in Phase Diagram Sections......Page 113 Zero Phase Fraction Lines......Page 114 General Algorithm to Calculate Any Phase Diagram Section......Page 115 Choice of Variables to Ensure That Phase Diagram Sections are Single-Valued......Page 116 Corresponding Phase Diagrams......Page 120 Enthalpy-Composition Phase Diagrams......Page 123 The Thermodynamics of General Phase Diagram Sections......Page 124 Interpreting Phase Diagrams of Oxide Systems and Other Systems Involving Two or More Oxidation States of a Metal......Page 128 Choice of Components and Choice of Variables......Page 133 Phase Diagrams of Reciprocal Systems......Page 134 Choice of Variables to Ensure Straight Tie-Lines......Page 135 Other Sets of Corresponding Variable Pairs......Page 136 References......Page 137 Equilibrium Solidification......Page 138 General Nomenclature for Invariant and Other Reactions......Page 139 Quasi-Invariant Reactions......Page 140 Nonequilibrium Scheil-Gulliver Solidification......Page 141 Binary Systems......Page 142 Ternary Systems......Page 145 Topology and Calculation of Scheil-Gulliver Constituent Diagrams......Page 152 List of Websites......Page 153 9. Paraequilibrium Phase Diagrams and Minimum Gibbs Energy Diagrams......Page 154 The Geometry of Paraequilibrium Phase Diagram Sections......Page 155 Minimum Gibbs Energy Phase Diagrams......Page 160 References......Page 163 10 Second-Order and Higher-Order Transitions......Page 164 Equations for Thermodynamic Properties due to Magnetic Ordering......Page 168 References......Page 169 List of Websites......Page 295 Evaporation Paths......Page 170 Eh-pH Diagrams......Page 172 True Aqueous Phase Diagrams......Page 177 Other Examples of True Aqueous Phase Diagram Sections......Page 181 Re-plotting the Diagrams in Eh-pH Coordinates......Page 185 Summary......Page 186 List of Websites......Page 187 Phase Diagram Compilations......Page 188 References......Page 189 List of Websites......Page 190 Part II: Thermodynamic Modeling of Solutions ......Page 191 13. Introduction......Page 192 List of Websites......Page 194 14. Single-Lattice Random-Mixing (Bragg-Williams-BW) Models......Page 195 Ideal Raoultian Solutions......Page 196 Regular Solution Theory: Binary Systems......Page 197 Polynomial Expansion of the Excess Gibbs Energy: Binary Systems......Page 198 Respecting the Gibbs-Helmholz Equation......Page 199 A Shortcoming of Polynomial Expansions......Page 200 A Caveat for Optimizations When Data Are Available Only Over a Limited Composition Range......Page 201 Asymmetric Common-Ion Molten Salt Solutions: Temkin Model......Page 202 Solutions With Limited Solubility: Lattice Stabilities......Page 203 Darken's Quadratic Formalism......Page 204 Introduction to Coupled Thermodynamic/Phase Diagram Optimization: Binary Systems......Page 205 Use of ``Virtual Data´´......Page 208 Multicomponent Systems......Page 209 Kohler Model vs Muggianu Model......Page 214 Sample Calculation: The KF-LiF-NaF System......Page 215 Ternary Polynomial Terms......Page 216 Binary Terms......Page 218 Ternary Terms......Page 220 Liquid Solutions: Coordination Equivalent Fractions......Page 221 Wagner's Interaction Parameter Formalism and the Unified Interaction Parameter Formalism......Page 224 Approximation for 23......Page 226 Interaction Parameter Formalism With Molar Ratios......Page 227 References......Page 228 15. Multiple-Sublattice Random-Mixing (Bragg-Williams-BW) Models......Page 230 Case of a Two-Sublattice (A,B)(X,Y) Solution......Page 232 Reciprocal Excess Terms......Page 236 Activities of the End-Members......Page 240 Interstitial Solutions......Page 241 Nonstoichiometric Compounds......Page 242 Ceramic Solutions......Page 247 Asymmetric Molten Ionic Solutions: Temkin Model......Page 250 Solid vs Liquid Asymmetric Ionic Solutions......Page 252 List of Website......Page 253 16. Single-Lattice Models With Short-Range Ordering (SRO)......Page 254 Associate Models......Page 258 The Modified Quasichemical Model (MQM)......Page 261 Combining the Quasichemical and Bragg-Williams Models......Page 265 Expansion of ΔgAB as a Polynomial......Page 269 Composition-Dependent Coordination Numbers......Page 270 Example of an Optimization Using the MQM-The Mg-Sn System......Page 271 Second-Nearest-Neighbor Short-Range Ordering in Ionic Liquids......Page 273 Complex Anion Model......Page 274 Short-Range Ordering and Positive Deviations From Ideal Mixing......Page 275 Approximating Short-Range Ordering with a Polynomial Expansion......Page 278 Modified Quasichemical Model-Multicomponent Systems......Page 279 When Δgmn in a Binary System is Given by Eq. (16.50) or (16.51)......Page 281 Symmetric Model......Page 282 Multicomponent Solutions......Page 283 Symmetric Model......Page 285 Multicomponent Solutions......Page 286 The MQM Equations in Closed Explicit Form......Page 287 Combining Bragg-Williams and MQM Models in One Multicomponent Database......Page 288 Comparison of the Bragg-Williams, Associated and Modified Quasichemical Models in Predicting Ternary Properties Fro .........Page 289 The Two-Sublattice ``Ionic Liquid´´ Model......Page 293 Introduction......Page 296 Definitions, Coordination Numbers......Page 297 Formal Treatment of Quadruplets as ``Complexes´´ or ``Molecules´´......Page 301 Choice of Zij/klm......Page 303 Gibbs Energy Equation......Page 304 The Configurational Entropy......Page 306 Default Values of zetai/j......Page 308 Second-Nearest-Neighbor Interaction Terms......Page 309 The Quasichemical Model in a ``Complex´´ Formalism......Page 313 Combining Different Models in One Database......Page 314 Summary of Model......Page 315 Sample Calculations......Page 318 References......Page 319 Molten Oxide Solutions......Page 320 The Modified Quasichemical Model (MQM)......Page 325 Associate Model......Page 326 Reciprocal Ionic Liquid Model......Page 327 The Charge Compensation Effect: Amphoteric Oxides......Page 328 Other Network Forming (Acidic) Oxides......Page 329 Nonoxide Anions in Oxide Melts......Page 331 Order-Disorder Transitions......Page 334 Liquid Solutions With More Than One Composition of Short-Range Ordering......Page 342 Deoxidation Equilibria in Steel......Page 343 Limiting Liquidus Slope in Dilute Solutions......Page 347 List of Websites......Page 351 Exercise 3 (Chapter 2)......Page 352 Exercise 6 (Chapter 2)......Page 353 Exercise 10 (Chapter 2)......Page 354 Exercise 14 (Chapter 4)......Page 355 Exercise 18 (Chapters 2 and 4)......Page 356 Exercise 22 (Chapters 4 and 5)......Page 357 Exercise 26 (Chapter 5)......Page 358 Exercise 30 (Chapter 14)......Page 359 Exercise 33 (Chapter 14)......Page 361 Exercise 36 (Chapter 15)......Page 362 Exercise 38 (Chapter 16)......Page 363 Exercise 3......Page 364 Exercise 5......Page 365 Exercise 7......Page 366 Exercise 9......Page 367 Exercise 11......Page 368 Exercise 15......Page 369 Exercise 19......Page 370 Exercise 23......Page 371 Exercise 26......Page 372 Exercise 30......Page 373 Exercise 33......Page 374 Exercise 36......Page 375 Exercise 38......Page 376 C......Page 378 G......Page 379 M......Page 380 P......Page 381 S......Page 382 T......Page 383 Z......Page 384 Back Cover......Page 385