Handbook of Heterogenous Kinetics

Preface xxi

List of Symbols xxv

Chapter 1. Definitions and Experimental Approach 1

1.1. Thermal transformations of solids 1

1.2. Classification of transformations 2

1.3. Speed and rate of reaction 6

1.4. Reaction zones of a transformation 10

1.5. Chemical characterizations 12

1.6. Structural characterizations of the solids 13

1.7. Textural characterizations of the solids 14

1.8. Characterization of the evolution of the systems 17

1.9. Influence of various variables on speed 26

Chapter 2. The Real Solid: Structure Elements and Quasi-Chemical Reactions 29

2.1. Structure elements of a solid 30

2.2. Structure elements of a stoichiometric binary solid 35

2.3. Structure elements of a non-stoichiometric binary solid 36

2.4. Extension to non-binary compounds 44

2.5. Quasi-chemical reactions 46

2.6. Introduction of foreign elements into a solid 53

Chapter 3. Thermodynamics of Heterogenous Systems 59

3.1. Introduction: aims of thermodynamics 59

3.2. General survey of thermodynamics of equilibrium 60

3.3. Phenomena leading to solid-gas equilibriums 69

3.4. Thermodynamic approach of solid-gas systems 71

3.5. Thermodynamics of systems containing solid phases only 76

3.6. Specific study of quasi-chemical equilibriums 77

3.7. Thermodynamics of systems: water vapor-hydrated salts 85

3.8. Sequence of transformations, juxtaposition of stability area 93

3.9. Equilibrium of the formation of a solid from a solution 96

3.10. Variations in the equilibrium conditions with sizes of solid phases 100

Chapter 4. Elementary Steps in Heterogenous Reactions 105

4.1. Nature of elementary steps 107

4.2. Elementary reactions at solid-solid interfaces 114

4.3. Elementary reactions at gas-solid interfaces 122

4.4. The apparent energies of activation of interface reactions 130

4.5. The areal speed of an interface reaction 130

Chapter 5. Chemical Diffusion 131

5.1. Introduction: nature of diffusing particles in a solid 131

5.2. Flux of diffusion and velocity of diffusing particles 135

5.3. The laws of Fick136

5.4. Steady state obstructed diffusion 150

5.5. Diffusion under electric field 153

5.6. Diffusion in two mediums separated by a mobile interface 161

Chapter 6. Chemical Adsorption169

6.1. Definitions: physical adsorption and chemical adsorption 169

6.2. Adsorption thermodynamics and chemisorption equilibrium 170

6.3. Kinetics of chemisorption 178

6.4. Chemisorption and structure elements 181

Chapter 7. Mechanisms and Kinetics of a Process 195

7.1. Speeds and reactivities of reactions taking place in only a single zone 195

7.2. Transformations with several zones 201

7.3. Linear reaction mechanisms 210

7.4. Linear mechanisms in pseudo-steady state modes 213

7.5. Pure modes or modes with a rate-determining step 220

7.6. Mixed modes 234

7.7. Generalization, rate of a linear mechanism in pseudo-steady state mode 241

7.8. Mixed non-pseudo-steady state modes 242

7.9. Equivalent reaction of a linear subset in local pseudo-steady state mode 245

7.10. Reactions with separable rates 248

7.11. Influence of intensive variables on the kinetic laws 250

7.12. Distance from equilibrium for a reaction 252

7.13. Processes concerned in a heterogenous reaction 255

Chapter 8. Nucleation of a New Solid Phase 257

8.1. Clusters 258

8.2. Examples of nucleation diagram 258

8.3. Interfacial energy 260

8.4. Formation molar Gibbs energy of clusters 272

8.5. Kinetics of nucleation 285

Chapter 9. Growth of a Solid Phase 309

9.1. Description of the zones of growth 309

9.2. Direction of the development of phase B during the growth 311

9.3. Modes and models for growth 312

9.4. Relationship between the motion velocities of the interfaces and the chemical growth rate 315

9.5. Methodology to model growth 318

9.6. Expressions of the space functions for the growth of a grain 320

Chapter 10. Transformation by Surface Nucleation and Growth 337

10.1. Nucleation, growth, and experimental rate 338

10.2. One-process model with instantaneous nucleation and slow growth 339

10.3. Two-process models: nucleation and growth 347

10.4. Two-process model with surface nucleation-radial anisotropic growth 351

10.5. Two-process model with surface nucleation and isotropic growth 361

10.6. Non-isobaric and/or non-isothermal kinetics 370

10.7. Powders with granular distributions 375

10.8. Return to the first and second kind of changes of laws 376

10.9. Conclusion 377

Chapter 11. Modeling and Experiments 379

11.1. The adequacy between the experimental conditions and modeling 379

11.2. Expressions of experimental speeds 381

11.3. Derivation of the kinetic curves 388

11.4. The experimental verification of the assumptions 388

11.5. Determination of the morphological model for growth 395

11.6. Calculations of the reactivity of growth and the specific frequency of nucleation 398

11.7. Variations of the kinetic properties with the intensive variables 399

11.8. Methodology of a study 402

Chapter 12. Granular Coalescence 407

12.1. Qualitative description of the model 408

12.2. Morphological modeling 409

12.3. Structure of the coalescence mechanism 413

12.4. Determination of the space functions 416

12.5. Rate constants and radius of curvature 420

12.6. Reactivity of coalescence of a solid with a single component 423

12.7. Extensions to the coalescence of solids with several components 436

12.8. Relations between experiments and modeling 443

12.9. Oswald ripening and reduction in porosity 448

Chapter 13. Decomposition Reactions of Solids 449

13.1. Classifications of decomposition reactions 450

13.2. Extent measurement with the change of the mass 451

13.3. Observed experimental results 456

13.4. Kinetics of growth in decomposition reactions of solids 462

13.5. Nucleation in decomposition reactions of solids 478

13.6. Total kinetic curves 484

13.7. Influence of the granular distribution 484

13.8. Normal and abnormal growth 486

Chapter 14. Reactions Between Solids 489

14.1. Classification of the reactions between solids 490

14.2. The modeling assumptions 492

14.3. The experimental measure of the extent of the reactions 493

14.4. Reactivities of reactions between solids 494

14.5. Rates of the reactions between powders 508

14.6. Conclusion 541

Chapter 15. Gas-Solid Reactions 543

15.1. Classification of gas-solid reactions 544

15.2. Pure metal gas reactions 546

15.3. Growth process in the reduction of metallic oxides by hydrogen 585

15.4. Growth process of oxidation of metals by water vapor 596

Chapter 16. Transformations of Solid Solutions 603

16.1. General information on transformations of solid solutions 603

16.2. Oxidation of metal alloys 606

16.3. Variations of the composition of a solid solution with gas formation 640

16.4. Superposition of a variation of stoichiometry and decomposition 648

Chapter 17. Modeling of Mechanisms 651

17.1. Non-stoichiometry of iron oxide 651

17.2. Stability of calcium carbonate 658

17.3. Thermodynamics of a solid-solid reactions 665

17.4. Hydrates of alumina 669

17.5. Point defects in a metal sulfide 679

17.6. Point defects of an alkaline bromide 689

17.7. Diffusion of a metal into another metal 694

17.8. Generation of atmospheres with very low pressures 701

Chapter 18. Mechanisms and Kinetic Laws 709

18.1 Coalescence of anatase grains 709

18.2. Reaction of a cubic sample 713

18.3. Anisotropic growth 723

18.4. Gas-solid reaction with one-process model 732

18.5. The direction of the development of a layer 738

18.6. Mampel modeling by way of the point of inflection 747

18.7. Nucleation in a reaction of dehydration 753

18.8. Influence of particle size in nucleation-growth approach 759

18.9. Decomposition with slow nucleation and slow anisotropic growth determined by diffusion 767

19. Mechanisms and Reactivity 779

19.1. Competition oxidation – volatilization by TGA 779

19.2. Controlled rate thermal analysis (CRTA) 783

19.3. Sulfurization of a metal 789

19.4. Oxidation of a metal and some of its alloys 794

19.5. Reduction of octo-oxide of triuranium by dihydrogen 804

19.6. Dehydration of kaolinite 813

19.7. Decomposition of a carbonate of a metal 823

19.8. Reaction between two solids 837

Appendix 1 845

Appendix 2 847

Appendix 3 849

Appendix 4 853

Appendix 5 861

Appendix 6 867

Appendix 7 873

Appendix 8 875

Appendix 9 881

Appendix 10 899

Appendix 11 911

Bibliography 913

Index 919