Phase Diagrams and Thermodynamic Modeling of Solutions

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