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Kinetic Processes: Crystal Growth, Diffusion, and Phase Transformations in Materials

ISBN: 978-3-527-60495-1
424 pages
March 2006
Kinetic Processes: Crystal Growth, Diffusion, and Phase Transformations in Materials  (3527604952) cover image


The formation of solids is governed by kinetic processes, which are closely related to the macroscopic behaviour of the resulting materials. With the main focus on ease of understanding, the author begins with the basic processes at the atomic level to illustrate their connections to material properties. Diffusion processes during crystal growth and phase transformations are examined in detail. Since the underlying mathematics are very complex, approximation methods typically used in practice are the prime choice of approach. Apart from metals and alloys, the book places special emphasis on the growth of thin films and bulk crystals, which are the two main pillars of modern device and semiconductor technology. All the presented phenomena are tied back to the basic thermodynamic properties of the materials and to the underlying physical processes for clarity.
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Table of Contents


1. Introduction.

1.1 Arrhenius Plot.

1.2 The Relationship between Kinetics and Thermodynamics.

1.3 The Boltzmann Distribution.

1.4 Kinetic Theory of Gases.

1.5 Collisions.

2. Diffusion in Fluids.

2.1 Diffusion in a Gas.

2.2 Diffusion in Liquids.

3. Diffusion in Amorphous Materials.

3.1 Amorphous Materials.

3.2 Network Glass Formers.

3.3 The Glass Transition.

3.4 The Free-Volume Model.

3.5 Fictive Temperature.

3.6 Diffusion in Polymers.

3.7 The Stokes–Einstein Relationship.

4. Diffusion in Crystals.

4.1 Diffusion in a Crystal.

4.2 Diffusion Mechanisms in Crystals.

4.4 Equilibrium Concentration of Vacancies.

4.5 Simmons and Balluffi Experiment.

4.6 Ionic and Covalent Crystals.

4.7 Stoichiometry.

4.8 Measurement of Diffusion Coefficients.

4.9 Surface Diffusion.

4.10 Diffusion in Grain Boundaries.

4.11 Kirkendall Effect.

4.12 Whisker Growth.

4.13 Electromigration.

5. Diffusion in Semiconductors.

5.1 Introduction.

5.2.1 Vacancy Diffusion in Silicon.

5.2.2 Diffusion of Phosphorus in Silicon.

5.2.3 Diffusion of Arsenic in Silicon.

5.2.4 Diffusion of Boron in Silicon.

5.3 Diffusion of Zinc in GaAs.

5.4 Recombination-enhanced Diffusion.

5.5 Doping of Semiconductors.

5.6 Point-Defect Generation in Silicon during Crystal Growth.

5.7 Migration of Interstitials (and Liquid Droplets) in a Temperature Gradient.

5.8 Oxygen in Silicon.

5.9 Gettering.

5.10 Solid-State Doping.

6. Ion Implantation.

6.1 Introduction.

6.2 Ion Interactions.

6.3 Implantation Damage.

6.4 Rutherford Backscattering.

6.5 Channeling.

6.6 Silicon-on-Insulator.

7. Mathematics of Diffusion.

7.1 Random Walk.

7.2 The Diffusion Equation.

7.3 Solutions to the Diffusion Equation.

7.4 Numerical Methods.

7.5 Boltzmann–Matano Analysis.

8. Stefan Problems.

8.1 Steady-State Solutions to the Diffusion Equation.

8.2 Deal–Grove Analysis.

8.3 Diffusion-Controlled Growth of a Spherical Precipitate.

8.4 Diffusion-Limited Growth in Cylindrical Coordinates.

9. Phase Transformations.

9.1 Transformation-Rate-Limited Growth.

9.2 Diffusion-Limited Growth.

9.3 Thermally Limited Growth.

9.4 Casting of Metals.

9.5 Operating Point.

10. Crystal Growth Methods.

10.1 Melt Growth.

10.2 Solution Growth.

10.3 Vapor-Phase Growth.

10.4 Stoichiometry.

11. Segregation.

11.1 Segregation during a Phase Change.

11.2 Lever Rule.

11.3 Scheil Equation.

11.4 Zone Refining.

11.5 Diffusion at a Moving Interface.

11.6 Segregation in Three Dimensions.

11.7 Burton, Primm and Schlicter Analysis.

12. Interface Instabilities.

12.1 Constitutional Supercooling.

12.2 Mullins and Sekerka Linear Instability Analysis.

12.3 Anisotropic Interface Kinetics.

13. Chemical Reaction Rate Theory.

13.1 The Equilibrium Constant.

13.2 Reaction Rate Theory.

13.3 Reaction Rate Constant.

13.4 Transition State Theory.

13.5 Experimental Determination of the Order of a Reaction.

13.6 Net Rate of Reaction.

13.7 Catalysis.

13.8 Quasi-Equilibrium Model for the Rate of a First-Order phase Change.

14. Phase Equilibria.

14.1 First-Order Phase Changes.

14.2 Second-Order Phase Changes.

14.3 Critical Point between Liquid and Vapor.

15. Nucleation.

15.1 Homogeneous Nucleation.

15.2 Heterogeneous Nucleation.

15.3 Johnson–Mehl–Avrami Equation.

16. Surface Layers.

16.1.1 Langmuir Adsorption.

16.1.2 CVD Growth by a Surface-Decomposition Reaction.

16.1.3 Langmuir–Hinshelwood Reaction.

16.2 Surface Nucleation.

16.3 Thin Films.

16.4 Surface Reconstruction.

16.5 Amorphous Deposits.

16.6 Surface Modification.

16.7 Fractal Deposits.

16.8 Strain Energy and Misfit Dislocations.

16.9 Strained-Layer Growth.

17. Thin-Film Deposition.

17.1 Liquid Phase Epitaxy.

17.2 Growth Configurations for LPE.

17.3 Chemical Vapor Deposition.

17.4 Metal-Organic Chemical Vapor Deposition.

17.5 Physical Vapor Deposition.

17.6 Sputter Deposition.

17.7 Metallization.

17.8 Laser Ablation.

17.9 Molecular Beam Epitaxy.

17.10 Atomic Layer Epitaxy.

18. Plasmas.

18.1 Direct Current (DC) Plasmas.

18.2 Radio-Frequency Plasmas.

18.3 Plasma Etching.

18.4 Plasma Reactors.

18.5 Magnetron Sputtering.

18.6 Electron Cyclotron Resonance.

18.7 Ion Milling.

19. Rapid Thermal Processing.

19.1 Rapid Thermal Processing.

19.2 Rapid Thermal Processing Equipment.

19.3 Radiative Heating.

19.4 Temperature Measurement.

19.5 Thermal Stress.

19.6 Laser Heating.

20. Kinetics of First-Order Phase Transformations.

20.1 General Considerations.

20.2 The Macroscopic Shape of Crystals.

20.3 General Equation for the Growth Rate of Crystals.

20.4 Kinetic Driving Force.

20.5 Vapor-Phase Growth.

20.6 Melt Growth.

20.7 Molecular Dynamics Studies of Melt Crystallization Kinetics.

20.8 The Kossel–Stranski Model.

20.9 Nucleation of Layers.

20.10 Growth on Screw Dislocations.

20.11 The Fluctuation Dissipation Theorem.

21. The Surface-Roughening Transition.

21.1 Surface Roughness.

21.2 The Ising Model.

21.3 Cooperative Processes.

21.4 Monte Carlo Simulations of Crystallization.

21.5 Equilibrium Surface Structure.

21.6 Computer Simulations.

21.7 Growth Morphologies.

21.8 Kinetic Roughening.

21.9 Polymer Crystallization.

22. Alloys: Thermodynamics and Kinetics.

22.1 Crystallization of Alloys.

22.2 Phase Equilibria.

22.3 Regular Solution Model.

22.4 Near-Equilibrium Conditions.

22.5 Phase Diagrams.

22.6 The DLP Model.

23. Phase Separation.

23.1 Ordering versus Phase Separation.

23.2 Phase Separation.

23.3 Analytical Model for Spinodal Decomposition.

23.4 Microstructure Resulting from Phase Separation.

24. Non-Equilibrium Crystallization of Alloys.

24.1 Non-Equilibrium Crystallization.

24.2 Experiment.

24.3 Computer Modeling.

24.4 Analytical Model.

24.5 Comparison with Experiment.

24.6 Crystallization of Glasses.

25. Coarsening, Ripening.

25.1 Coarsening.

25.2 Free Energy of a Small Particle.

25.3 Coarsening in a Solution.

25.4 Coarsening of Dendritic Structures.

25.5 Sintering.

25.6 Bubbles.

25.7 Grain Boundaries.

25.8 Scratch Smoothing.

26. Dendrites.

26.1 Dendritic Growth.

26.2 Conditions for Dendritic Growth.

26.3 Simple Dendrite Model.

26.4 Phase Field Modeling.

26.5 Faceted Growth.

26.6 Distribution Coefficient.

27. Eutectics.

27.1 Eutectic Phase Diagram.

27.2 Classes of Eutectic Microstructures.

27.3 Analysis of Lamellar Eutectics.

27.4 Off-Composition Eutectics.

27.5 Coupled Growth.

27.6 Third-Component Elements.

28. Castings.

28.1 Grain Structure of Castings.

28.2 Dendrite Remelting.

Subject Index by Page.

Subject Index by Chapter Sections.

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Author Information

Kenneth A. Jackson is Professor in the Department of Materials Science and Engineering at the University of Arizona in Tucson, where he has been since 1989. He received his Ph.D. degree from Harvard University in 1956, and was an assistant Professor there until 1962, when he joined AT&T Bell Laboratories. At Bell Labs he was head of Materials Physics Research for many years. His major scientific interests are in the kinetic processes of crystal growth, and his scientific contributions include constitutional supercooling, the surface roughening transition, defect formation in crystals, and studies of alloy crystallization. He pioneered in computer simulation studies of the atomic scale processes during crystal growth. He has served as President for both the American Association for Crystal Growth and the Materials Research Society. He has received awards for his scientific contributions from both the American and the International Crystal Growth societies, and from the Materials Society of AIME, and has written and edited several books. He was elected to the National Academy of Engineering in 2005.
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"The book is written in a very educative manner and one cleary feels that Jackson is an excellent lecturer. ... this book is also a pleasure for lecturers in materials science and can be used as reference for lectures in materials science and engineering, physics or chemistry." (Prof. Ralf B. Wehrspohn, Nanophotonic Materials Group, Department of Physics, University Paderborn, ChemPhysChem, 1/2005)
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