Nucleation in Condensed Matter (eBook)

Applications in Materials and Biology

Alan Lindsay Greer, Ken Kelton (Autoren)

eBook Download: EPUB

2010 | 1. Auflage
756 Seiten
Elsevier Science (Verlag)
978-0-08-091264-6 (ISBN)

Infos

In Nucleation in Condensed Matter, key theoretical models for nucleation are developed and experimental data are used to discuss their range of validity. ,A central aim of this book is to enable the reader, when faced with a phenomenon in which nucleation appears to play a role, to determine whether nucleation is indeed important and to develop a quantitative and predictive description of the nucleation behavior. The third section of the book examines nucleation processes in practical situations, ranging from solid state precipitation to nucleation in biological systems to nucleation in food and drink. Nucleation in Condensed Matter is a key reference for an advanced materials course in phase transformations. It is also an essential reference for researchers in the field.

• Unified treatment of key theories, experimental evaluations and case studies


• Complete derivation of key models


• Detailed discussion of experimental measurements


• Examples of nucleation in diverse systems

Inhalt

Front Cover 1
Nucleation in Condensed Matter 4
Copyright Page 5
Dedication 6
Contents 8
Preface 14
Symbols 16
Abbreviations and Acronyms 30
Chapter 1. Introduction 34
1. What is Nucleation? 34
2. Historical Background 36
3. The Aim and Plan of this Book 45
References 47
PART I: Theory 50
Chapter 2. The Classical Theory 52
1. The Nucleation Barrier 52
2. Thermodynamics of Cluster Formation 54
3. Kinetic Model for Cluster Formation 61
4. Computation of the Rate Constants 63
5. Kinetic Potential — An Alternative to the Constrained Equilibrium Hypothesis 66
6. Numerical Exploration of the Consequences of the Kinetic Model for Nucleation 68
7. Steady-State Homogeneous Nucleation — Discrete Cluster Model 72
8. Estimate of the Steady-State Nucleation Rate in a Condensed System 75
9. Zeldovich–Frenkel Equation — Continuous Cluster Model 77
10. Alternative Master Equations 80
11. The Nucleation Theorem 81
12. Summary 84
References 85
Chapter 3. Time-Dependent Effects Within the Classical Theory 88
1. Qualitative Discussion of Time-Dependent Nucleation 88
2. Numerical Analysis of Time-Dependent Nucleation 92
3. Analytical Solutions to the Discrete Coupled Differential Equations 98
4. Analytical Solutions of the Zeldovich–Frenkel Equation 102
5. Limits of Applicability of Selected Analytical Expressions 110
6. Summary 115
References 116
Chapter 4. Beyond the Classical Theory 118
1. Introduction 118
2. A Statistical–Mechanical Treatment of Cluster Formation 119
3. Diffuse-Interface Theory 122
4. Density-Functional Theory 126
5. Nonclassical Formulations of Nucleation Kinetics 145
6. Summary 152
References 154
Chapter 5. Multi-Component Systems 158
1. Introduction 158
2. Work of Cluster Formation 159
3. Multi-Component Kinetic Models for Nucleation (General Considerations) 162
4. Interface-Limited Nucleation 163
5. Coupled Interface/Diffusion Nucleation 177
6. Summary 193
References 196
Chapter 6. Heterogeneous Nucleation 198
1. Introduction 198
2. Nucleation on Interfaces 199
3. Nucleation on Dislocations 238
4. Nucleation on Atomic-Scale Heterogeneities 245
5. Pattern and Competition 249
6. Summary 254
References 256
PART II: Experimental Measurements 260
Chapter 7. Crystallization in Liquids and Colloidal Suspensions 262
1. Introduction 262
2. Maximum-Supercooling Studies 263
3. Measurements of the Nucleation Rate 291
4. Crystallization in Colloidal Suspensions 296
5. Nucleation near a Magnetic Phase Transition 299
6. Summary 306
References 307
Chapter 8. Crystallization in Glasses 312
1. Introduction 312
2. The Glassy State 314
3. Nucleation in Glass Formation 315
4. Devitrification Mechanisms 320
5. Measuring the Nucleation Rate 321
6. Homogeneous Nucleation of Polymorphic Crystallization 326
7. Time-Dependent Nucleation 341
8. Crystallization to Quasicrystals — A Low Nucleation Barrier 348
9. Primary Crystallization 349
10. Heterogeneous Nucleation 351
11. Summary 355
References 356
Chapter 9. Precipitation in Crystalline Solids 364
1. Phase Transformations in the Solid State 364
2. Precipitation in Cu–Co 365
3. Oxygen Precipitation in Silicon 379
4. Summary 390
References 391
Chapter 10. Computer Models 396
1. Introduction 396
2. Overview of Computer Methods 397
3. Steady-State Nucleation 400
4. Time-Dependent Nucleation Rate 408
5. Cluster Properties 411
6. Coupled Phase Transitions 414
7. Impact of Diffusion on Nucleation 416
8. Summary 420
References 421
PART III: Further Topics and Applications 424
Chapter 11. Crystallization in Polymeric and Related Systems 426
1. Introduction 426
2. Homogeneous Nucleation 430
3. Memory Effects 437
4. Orientation-Induced Nucleation 438
5. Nucleation on Foreign Particles 441
6. Secondary Nucleation: The Lauritzen–Hoffman theory 444
7. Rigid Molecules: Isotropic-to-Nematic Transition 447
8. Summary 450
References 451
Chapter 12. Dislocation-Mediated Transformations 456
1. Introduction 456
2. Nucleation of Dislocations 457
3. Recrystallization 470
4. Twinning and Martensitic Transformations 478
5. Summary 488
References 490
Chapter 13. Solidification 494
1. Introduction 494
2. Microstructure of Castings 496
3. Grain Refinement by Inoculation 502
4. Nucleation Laws for Solidification Modeling 525
5. Grain Refinement Without Inoculation 526
6. Porosity 534
7. Summary 537
References 538
Chapter 14. Transformations in the Solid Phase 544
1. Introduction 544
2. Devitrification 545
3. Melting 561
4. Metallurgical Control of Nucleation 570
5. Radiation Damage and Voids 598
6. Summary 610
References 610
Chapter 15. Interfacial and Thin-Film Reactions 620
1. Introduction 620
2. Evidence for Nucleation 622
3. Nucleation on a Moving Interface 630
4. Driving Force for Transformation in Nonuniform Composition 633
5. Phase Growth and Stability Influenced by Interdiffusion Fluxes 641
6. Summary 651
References 652
Chapter 16. Biology and Medicine 656
1. Introduction 656
2. Nucleation of Ice 657
3. Nucleation of Gas Bubbles 670
4. Biomineralization 673
5. Pathological Mineralization 685
6. Neurodegenerative Disease 690
7. Summary 695
References 696
Chapter 17. Food and Drink 706
1. Phase Transformations in Foods 706
2. Sugars 707
3. Chocolate 710
4. Carbonated Drinks 714
5. Summary 719
References 719
Chapter 18. Key Themes and Prospects 722
1. Emerging Themes 722
2. Length Scales in Nucleation 724
3. Time Scales in Nucleation 726
4. Prospects 728
Appendix: Models Used for Analysis of Liquid and Glass Nucleation Data 730
Author index 734
A 734
B 734
C 735
D 735
E 736
F 736
G 736
H 737
I 737
J 737
K 738
L 738
M 739
N 739
O 739
P 740
Q 740
R 740
S 741
T 742
U 742
V 742
W 742
X 743
Y 743
Z 743
Subject index 744
A 744
B 744
C 745
D 747
E 748
F 748
G 749
H 750
I 750
J 751
K 751
L 751
M 752
N 753
O 753
P 753
Q 754
R 754
S 755
T 757
U 758
V 758
W 758
Y 759
Z 759

Textauszug

Chapter 1

Introduction

K.F. Kelton    Washington University in St. Louis, USA

A.L. Greer    University of CambridgeAmsterdam

Publisher Summary

This chapter discusses the classical theories of steady-state and time-dependent nucleation. The classical theory is appropriate for cases in which the nucleation kinetics is governed by processes that occur at the interface between the original and new phases. The ways in which the classical theory might be extended to take account of coupling between interfacial and long-range diffusion kinetic fluxes are reviewed and computer simulations that increasingly provide valuable new “experimental” insights into nucleation processes are discussed. The chapter introduces the particles that catalyze nucleation (heterogeneous nucleation) for grain refinement in the solidification of the liquids of metallurgical importance and the tailoring of annealing treatments to produce conventional precipitation-hardened alloys as well as micro- and nano-structured composites in ceramic and metallic glasses. The importance of nucleation in the food and drink industry as well as the emerging view of the importance of nucleation processes in biology and medicine is discussed.

1 What is Nucleation?

The word nucleus, defined by the Oxford English Dictionary as “the central and most important part of an object, movement, or group, forming the basis for its activity and growth” [1], was introduced into English usage early in the eighteenth century, derived from the Latin for kernel or inner part. In the nineteenth century, it was adopted to describe a small region of a new phase appearing during a phase change such as melting or freezing. Such phase transitions (also known, particularly in metallurgy, as phase transformations) are ubiquitous in the natural world and are hence important in a very wide range of scientific disciplines, including astrophysics, metallurgy, materials science, electronic engineering, atmospheric physics, mineralogy, chemical engineering, biology, food science, and medicine.

Statistical fluctuations generate nuclei through the transient appearance and disappearance of small regions of a new phase within an original (or “parent”) phase. The lifetime of a fluctuation is related to its size. Only when a “critical” size is exceeded is the dissolution probability small enough for the fluctuation to evolve into a macroscopic region of the new phase. The stochastic behavior of shrinkage and growth is consistent with the existence of a barrier to the phase transition — the nucleation barrier. Familiar examples of nucleation-limited phase transformations are the condensation of vapors, the crystallization of liquids, and precipitation in liquids and solids. Nucleation can also be central to less familiar processes, such as phase separation, magnetic domain formation, dislocation formation, star and galaxy formation, and even the emergence of matter in the primordial universe. A growing realization, discussed in the later chapters of this book, is that nucleation can be important even in biological processes. In whatever field, the nucleation mechanism can be complex and often proceeds in stages; it may involve coupled phase transitions, coupled kinetic fluxes, and coupled fluctuations in different order parameters that characterize the original and new phases.

Sometimes the term nucleation is applied loosely to any appearance of a new phase. In many of these cases, the precise definition of a nucleation process is not satisfied. For example, the new phase may grow by irreversible aggregation, rather than by stochastic formation and dissolution. Some processes can mimic nucleation arbitrarily closely. On holding at an elevated temperature, a dispersion of one solid phase in another may show coarsening in which larger particles of the dispersed phase grow while smaller particles shrink and disappear. In this way, the dispersion evolves to contain fewer larger particles with a smaller total interfacial area between the two phases. This coarsening, often called Ostwald ripening, does not involve nucleation, although a critical size exists, above which particles grow and below which they shrink. While this is analogous to a critical nucleus, it is so large that molecular-scale fluctuations are insignificant; growth and shrinkage are by-and-large deterministic. On the other hand, fluctuations might play a role if the particles were sufficiently fine, such as nanocrystallites grown in an amorphous phase.

In other cases, nucleation is essential, but is not the controlling factor in initiating the overall transformation. For nucleation occurring on catalyst surfaces, for example, subsequent growth may be characterized by a competition (likely to be mediated by heat or solute) in which only some nuclei can participate in the overall transformation. Microstructural development is then controlled largely by growth. Nucleation can be observed only within a limited window of thermodynamic and kinetic conditions. It may be, then, that in some cases nucleation plays a hidden but still central role. In such cases, details of the phase transformation mechanisms and of the role of nucleation may be very difficult or impossible to determine.

Since nucleation is the initial step in many phase transformations, the ability to control that process is often of significant practical concern. It is the key, for example, to the production of desired microstructures that are tailored to technological needs and it is fundamental for the survival of some biological organisms (Chapter 16). The pattern shown in Figure 1 is a decorative example of nucleation control, where the potter has controlled conditions to produce a pleasing pattern of crystalline areas in an otherwise amorphous glaze. Each crystalline area grew from a distinct initiation event; the pattern is determined by the sequence of events and by the growth of those nuclei to consume the amorphous phase.

Fig. 1 A vase coated with a glaze that has been partially crystallized during firing. A distribution of crystal sizes is observed, with the larger crystallites having nucleated first; growth has led to crystal impingement. For further examples, see Ref [2]. (Photo courtesy of Brian Barber.)

The phenomenological evidence for nucleation, the development of theoretical models, measurement methods, the use of the resulting data in evaluating nucleation models, and examples of nucleation control in practical situations are the themes developed in Chapters 2–17 of this book. Before beginning that discussion, however, it is useful to examine briefly the experimental observations and theoretical understanding that form the basis of our knowledge of nucleation processes.

2 Historical Background

2.1 Experimental observations

In 1721, Fahrenheit discovered a tendency for water cooled to below its freezing temperature (a supercooled or undercooled liquid) to resist the formation of the crystalline phase, ice. In 1724, he reported the results of a systematic set of experiments in which sealed containers of boiled water were set outside on winter evenings when the temperature of the surroundings was lower than the freezing point of the water (thirty-two degrees at standard atmospheric pressure in the units of his new temperature scale, i.e. 32°F) [3]. Surprisingly, he found that the water remained a fluid, even when left outside overnight in an air temperature of 15°F. When small ice particles were introduced into the supercooled water, however, crystallization followed immediately, with the temperature of the ice–water mixture rising to 32°F. Further, he reported that when carrying a glass vial of the supercooled water from his bedchamber to a nearby room, he stumbled on the stairs connecting the rooms, agitating the liquid, and it immediately crystallized.

These observations were reproduced and extended to other liquids by Triewald, Musschenbroek, Brugmanns, and Mairan [4, 5], Lowitz [6], and others; a critical review was written as early as 1775 (see [7]). The amount of supercooling can be considerable. For water, Fahrenheit reported a maximum supercooling of 17°F (∼8 K). In 1820, Kaemtz [8] achieved a supercooling of 19 K and in a series of papers from 1844 to 1847, Regnault reported 32.8 K, a value not equaled or exceeded until almost a century later. Gay-Lussac demonstrated the generality of supercooling and confirmed Fahrenheit's report that mechanical vibration could induce crystallization in supercooled liquids [9, 10].

The degree of supercooling was often variable. Schröder, von Dusch, and Violette recognized that this was due largely to airborne particles and particles residing in the containers [11–13]. Eliminating these particles improved the reproducibility of the observed supercooling [14, 15]. The structure and chemistry of the particles were identified as critical factors for catalyzing crystallization. Lowitz observed that the introduction of small particles of the primary crystallizing phase into supercooled liquids readily initiated crystallization, while the introduction of particles of unrelated phases often had little influence [6]. Ostwald demonstrated that the effectiveness of nucleation was out of...

Produkt-Details

• Erscheint lt. Verlag: 19.3.2010
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Chemie ► Physikalische Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-091264-8 / 0080912648
• ISBN-13: 978-0-08-091264-6 / 9780080912646