Read more
As the ability to produce nanomaterials advances, it becomes more important to understand how the energy of the atoms in these materials is affected by their reduced dimensions. Written by an acclaimed author team, Kinetics in Nanoscale Materials is the first book to discuss simple but effective models of the systems and processes that have recently been discovered. The text, for researchers and graduate students, combines the novelty of nanoscale processes and systems with the transparency of mathematical models and generality of basic ideas relating to nanoscience and nanotechnology.
List of contents
PREFACE ix
CHAPTER 1 INTRODUCTION TO KINETICS IN NANOSCALE MATERIALS 1
1.1 Introduction 1
1.2 Nanosphere: Surface Energy is Equivalent to Gibbs-Thomson Potential 3
1.3 Nanosphere: Lower Melting Point 6
1.4 Nanosphere: Fewer Homogeneous Nucleation and its Effect on Phase Diagram 10
1.5 Nanosphere: Kirkendall Effect and Instability of Hollow Nanospheres 13
1.6 Nanosphere: Inverse Kirkendall Effect in Hollow Nano Alloy Spheres 17
1.7 Nanosphere: Combining Kirkendall Effect and Inverse Kirkendall Effect on Concentric Bilayer Hollow Nanosphere 18
1.8 Nano Hole: Instability of a Donut-Type Nano Hole in a Membrane 19
1.9 Nanowire: Point Contact Reactions Between Metal and Silicon Nanowires 21
1.10 Nanowire: Nanogap in Silicon Nanowires 22
1.11 Nanowire: Lithiation in Silicon Nanowires 26
1.12 Nanowire: Point Contact Reactions Between Metallic Nanowires 27
1.13 Nano Thin Film: Explosive Reaction in Periodic Multilayered Nano Thin Films 28
1.14 Nano Microstructure in Bulk Samples: Nanotwins 30
1.15 Nano Microstructure on the Surface of a Bulk Sample: Surface Mechanical Attrition Treatment (SMAT) of Steel 32
References 33
Problems 35
CHAPTER 2 LINEAR AND NONLINEAR DIFFUSION 37
2.1 Introduction 37
2.2 Linear Diffusion 38
2.2.1 Atomic Flux 39
2.2.2 Fick's First Law of Diffusion 40
2.2.3 Chemical Potential 43
2.2.4 Fick's Second Law of Diffusion 45
2.2.5 Flux Divergence 47
2.2.6 Tracer Diffusion 49
2.2.7 Diffusivity 51
2.2.8 Experimental Measurement of the Parameters in Diffusivity 53
2.3 Nonlinear Diffusion 57
2.3.1 Nonlinear Effect due to Kinetic Consideration 58
2.3.2 Nonlinear Effect due to Thermodynamic Consideration 59
2.3.3 Combining Thermodynamic and Kinetic Nonlinear Effects 62
References 63
Problems 64
CHAPTER 3 KIRKENDALL EFFECT AND INVERSE KIRKENDALL EFFECT 67
3.1 Introduction 67
3.2 Kirkendall Effect 69
3.2.1 Darken's Analysis of Kirkendall Shift and Marker Motion 72
3.2.2 Boltzmann and Matano Analysis of Interdiffusion Coefficient 76
3.2.3 Activity and Intrinsic Diffusivity 80
3.2.4 Kirkendall (Frenkel) Voiding Without Lattice Shift 84
3.3 Inverse Kirkendall Effect 84
3.3.1 Physical Meaning of Inverse Kirkendall Effect 86
3.3.2 Inverse Kirkendall Effect on the Instability of an Alloy Nanoshell 88
3.3.3 Inverse Kirkendall Effect on Segregation in a Regular Solution Nanoshell 90
3.4 Interaction Between Kirkendall Effect and Gibbs-Thomson Effect in the Formation of a Spherical Compound Nanoshell 93
References 97
Problems 97
CHAPTER 4 RIPENING AMONG NANOPRECIPITATES 99
4.1 Introduction 99
4.2 Ham's Model of Growth of a Spherical Precipitate (Cr is Constant) 101
4.3 Mean-Field Consideration 103
4.4 Gibbs-Thomson Potential 105
4.5 Growth and Dissolution of a Spherical Nanoprecipitate in a Mean Field 106
4.6 LSW Theory of Kinetics of Particle Ripening 108
4.7 Continuity Equation in Size Space 113
4.8 Size Distribution Function in Conservative Ripening 114
4.9 Further Developments of LSW Theory 115
References 115
Problems 116
CHAPTER 5 SPINODAL DECOMPOSITION 118
5.1 Introduction 118
5.2 Implication of Diffusion Equation in Homogenization and Decomposition 121
5.3 Spinodal Decomposition 123
5.
About the author
KING-NING TU, PhD, is Professor in the Department of Materials Science and Engineering at the University of California, Los Angeles. His research focuses on kinetic processes in thin films, metal-silicon interfaces, electromigration, lead-free solder metallurgy, and point contact reactions on silicon nanowires.
ANDRIY M. GUSAK, PhD, is Chair and Professor in the Department of Physics at Cherkasy National University. His research explores nanomaterial science and kinetics of nanoscale systems, with an emphasis on the development of microelectronic materials.
Summary
As the ability to produce nanomaterials advances, it becomes more important to understand how the energy of the atoms in these materials is affected by their reduced dimensions.
