PREFACE
CHAPTER 1 INTRODUCTION TO KINETICS IN NANOSCALE MATERIALS
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
5.3.1 Concentration Gradient in an Inhomogeneous Solid
Solution .......................................... 123
5.3.2 Energy of Mixing to Form a Homogeneous Solid
Solution .......................................... 124
5.3.3 Energy of Mixing to Form an Inhomogeneous Solid
Solution .......................................... 126
5.3.4 Chemical Potential in Inhomogeneous Solution ...... 129
5.3.5 Coherent Strain Energy ............................ 131
5.3.6 Solution of the Diffusion Equation ................ 134
References .................................................... 136
Problems ...................................................... 136
CHAPTER 6 NUCLEATION EVENTS IN BULK MATERIALS, THIN FILMS,
AND NANOWIRES ................................................. 138
6.1 Introduction ............................................. 138
6.2 Thermodynamics and Kinetics of Nucleation ................ 140
6.2.1 Thermodynamics of Nucleation ...................... 140
6.2.2 Kinetics of Nucleation ............................ 143
6.3 Heterogeneous Nucleation in Grain Boundaries of Bulk
Materials ................................................ 148
6.3.1 Morphology of Grain Boundary Precipitates ......... 150
6.3.2 Introducing an Epitaxial Interface to
Heterogeneous Nucleation .......................... 151
6.3.3 Replacive Mechanism of a Grain Boundary ........... 154
6.4 No Homogeneous Nucleation in Epitaxial Growth of Si
Thin Film on Si Wafer .................................... 156
6.5 Repeating Homogeneous Nucleation of Suicide in
Nanowires of Si .......................................... 160
6.5.1 Point Contact Reactions in Nanowires .............. 161
6.5.2 Homogeneous Nucleation of Epitaxial Suicide in
Nanowires of Si 164 References .................... 168
Problems ...................................................... 168
CHAPTER 7 CONTACT REACTIONS ON Si; PLANE, LINE, AND POINT
CONTACT REACTIONS ............................................. 170
7.1 Introduction ............................................. 170
7.2 Bulk Cases ............................................... 175
7.2.1 Kidson's Analysis of Diffusion-Controlled Planar
Growth ............................................ 175
7.2.2 Steady State Approximation in Layered Growth of
Multiple Phases ................................... 178
7.2.3 Marker Analysis ................................... 179
7.2.4 Interdiffusion Coefficient in Intermetallic
Compound .......................................... 182
7.2.5 Wagner Diffusivity ................................ 186
7.3 Thin Film Cases .......................................... 187
7.3.1 Diffusion-Controlled and Interfacial-Reaction-
Controlled Growth ................................. 187
7.3.2 Kinetics of Interfacial-Reaction-Controlled
Growth ............................................ 188
7.3.3 Kinetics of Competitive Growth of Two-Layered
Phases ............................................ 193
7.3.4 First Phase in Suicide Formation .................. 194
7.4 Nanowire Cases ........................................... 1%
7.4.1 Point Contact Reactions ........................... 197
7.4.2 Line Contact Reactions ............................ 202
7.4.3 Planar Contact Reactions .......................... 208
References .................................................... 208
Problems ...................................................... 209
CHAPTER 8 GRAIN GROWTH IN MICRO AND NANOSCALE ................ 211
8.1 Introduction ............................................. 211
8.2 How to Generate a Polycrystalline Microstructure ......... 213
8.3 Computer Simulation of Grain Growth ...................... 216
8.3.1 Atomistic Simulation Based on Monte Carlo Method .. 216
8.3.2 Phenomenological Simulations ...................... 217
8.4 Statistical Distribution Functions of Grain Size ......... 219
8.5 Deterministic (Dynamic) Approach to Grain Growth ......... 221
8.6 Coupling Between Grain Growth of a Central Grain and
the Rest of Grains ....................................... 225
8.7 Decoupling the Grain Growth of a Central Grain from the
Rest of Grains in the Normalized Size Space .............. 226
8.8 Grain Growth in 2D Case in the Normalized Size Space ..... 229
8.9 Grain Rotation ........................................... 231
8.9.1 Grain Rotation in Anisotropic Thin Films Under
Electromigration .................................. 232
References .................................................... 237
Problems ...................................................... 238
CHAPTER 9 SELF-SUSTAINED REACTIONS IN NANOSCALE MULTILAYERED
THIN FILMS .................................................... 240
9.1 Introduction ............................................. 240
9.2 The Selection of a Pair of Metallic Thin Films for SHS ... 243
9.3 A Simple Model of Single-Phase Growth in Self-Sustained
Reaction ................................................. 245
9.4 A Simple Estimate of Flame Velocity in Steady State
Heat Transfer ............................................ 250
9.5 Comparison in Phase Formation by Annealing and by
Explosive Reaction in Al/Ni .............................. 25T
9.6 Self-Explosive Silicidation Reactions .................... 251
References .................................................... 255
Problems ...................................................... 256
CHAPTER 10 FORMATION AND TRANSFORMATIONS OF NANOTWINS
IN COPPER ..................................................... 258
10.1 Introduction ............................................. 258
10.2 Formation of Nanotwins in Cu ............................. 260
10.2.1 First Principle Calculation of Energy of
Formation of Nanotwins ............................ 260
10.2.2 In Situ Measurement of Stress Evolution for
Nanotwin Formation During Pulse Electrodeposition
of Cu ............................................. 264
10.2.3 Formation of Nanotwin Cu in Through-Silicon Vias .. 266
10.3 Formation and Transformation of Oriented Nanotwins in
Cu ....................................................... 269
10.3.1 Formation of Oriented Nanotwins in Cu ............. 270
10.3.2 Unidirectional Growth of Cu-Sn Intermetallic
Compound on Oriented and Nanotwinned Cu ........... 270
10.3.3 Transformation of (111) Oriented and Nanotwinned
Cu to (100) Oriented Single Crystal of Cu ......... 274
10.4 Potential Applications of Nanotwinned Cu ................. 276
10.4.1 To Reduce Electromigration in Interconnect
Technology ........................................ 276
10.4.2 To Eliminate Kirkendall Voids in Microbump
Packaging Technology .............................. 277
References ............................................... 278
Problems ...................................................... 278
APPENDIX A LAPLACE PRESSURE IN NONSPHERICAL NANOPARTICLE ..... 280
APPENDIX В INTERDIFFUSION COEFFICIENT D = C8MG" .............. 282
APPENDIX С NONEQUILIBRIUM VACANCIES AND CROSS-EFFECTS ON
INTERDIFFUSION IN A PSEUDO-TERNARY ALLOY ...................... 285
APPENDIX D INTERACTION BETWEEN KIRKENDALL EFFECT AND GIBBS-
THOMSON EFFECT IN THE FORMATION OF A SPHERICAL COMPOUND
NANOSHELL ..................................................... 289
INDEX ......................................................... 293
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