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| Length-scale in solidification analysis | |
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| Thermodynamics of solidification | |
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| Equilibrium | |
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| The undercooling requirement | |
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| Kinetic undercooling | |
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| Curvature undercooling | |
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| Thermal undercooling | |
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| Constitutional undercooling | |
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| Pressure undercooling | |
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| Hierarchy of equilibrium | |
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| Local interface equilibrium | |
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| Interface non-equilibrium | |
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| References | |
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| Macro-scale phenomena - formation of macrostructure | |
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| Relevant transport equations | |
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| Introduction to the mathematics of diffusive transport | |
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| The differential equation for macroscopic heat transport | |
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| Solutions of the heat conduction equation | |
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| References | |
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| Macro-mass transport | |
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| Solute diffusion controlled segregation | |
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| Analysis of solute redistribution | |
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| Equilibrium solidification | |
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| No diffusion in solid, complete diffusion in liquid (the Gulliver-Scheil model) | |
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| No diffusion in solid, limited diffusion in liquid | |
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| Limited diffusion in solid, complete diffusion in liquid | |
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| Limited diffusion in liquid and solid | |
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| Partial mixing in liquid, no diffusion in solid | |
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| Zone melting | |
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| Fluid flow controlled segregation | |
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| Shrinkage flow | |
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| Natural convection | |
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| Flow through the mushy zone | |
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| Fluid flow/solute diffusion controlled segregation | |
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| Fluid dynamics during mold filling | |
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| Fluid dynamics during casting solidification--macro shrinkage formation | |
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| References | |
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| Macro-Energy Transport | |
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| Governing equation for energy transport | |
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| Boundary conditions | |
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| Analytical solutions for steady-state solidification of castings | |
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| Analytical solutions for non-steady-state solidification of castings | |
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| Resistance in the mold | |
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| Resistance at the mold/solid interface | |
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| The heat transfer coefficient | |
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| Resistance in the solid | |
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| Resistance in the solid and in the mold | |
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| References | |
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| Macro-modeling of solidification; Numerical approximation methods | |
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| Problem formulation | |
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| Discretization of governing equations | |
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| Taylor series and numerical differentiation | |
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| Finite difference discretization of the heat conduction equation | |
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| Control volume formulation | |
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| Solution of the discretized equations | |
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| Applications of macro-modeling of solidification | |
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| Model deliverables | |
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| Criteria functions | |
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| Scaling relationships for criteria functions | |
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| References | |
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| Micro-scale phenomena and interface dynamics | |
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| Problem formulation | |
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| Nucleation | |
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| Heterogeneous nucleation models | |
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| Dynamic nucleation models | |
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| Micro-solute redistribution in alloys and microsegregation | |
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| Interface stability | |
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| Thermal instability | |
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| Solutal instability | |
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| Thermal, solutal and surface energy driven morphological instability | |
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| Influence of convection on interface stability | |
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| References | |
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| Cellular and dendritic growth | |
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| Morphology of primary phases | |
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| Interface undercooling and growth velocity models for dendrites | |
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| Tip velocity models | |
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| Solute diffusion controlled growth (isothermal growth) | |
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| Thermal diffusion controlled growth | |
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| Solutal, thermal, and capillary controlled growth | |
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| Interface anisotropy and the dendrite tip selection parameter | |
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| Effect of fluid flow on dendrite tip velocity | |
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| Multicomponent alloys | |
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| Dendritic arrays models | |
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| Volume averaged dendrite models | |
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| Complex geometry models | |
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| Dendritic arm spacing and coarsening | |
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| Primary spacing | |
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| Secondary arm spacing | |
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| The columnar-to-equiaxed transition | |
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| References | |
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| Eutectic solidification | |
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| Types of eutectics | |
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| Cooperative eutectics | |
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| Model of eutectic growth assuming only diffusion parallel to the interface | |
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| Model of eutectic growth assuming diffusion parallel and perpendicular to the interface; the Jackson-Hunt model | |
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| Operating point of cooperative eutectics | |
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| The extremum criterion | |
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| Growth at the limit of morphological stability | |
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| Divorced eutectics | |
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| Modification of eutectics | |
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| Interface stability of eutectics | |
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| Competitive growth of eutectic and dendritic phases | |
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| Equiaxed eutectic grain growth | |
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| References | |
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| Peritectic and monotectic solidification | |
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| Peritectic solidification | |
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| The Peritectic Reaction | |
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| The Peritectic Transformation | |
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| Monotectic Solidification | |
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| References | |
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| Solidification in the presence of a third phase | |
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| Interaction of solid inclusions with the solid/liquid interface | |
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| Particle interaction with a planar interface | |
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| Thermodynamic models | |
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| Thermal properties criterion models | |
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| Kinetic models | |
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| Particle interaction with a cellular/dendritic interface | |
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| Microshrinkage | |
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| The physics of microshrinkage formation | |
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| Modeling of microshrinkage formation | |
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| Prevention of microshrinkage | |
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| References | |
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| Atomic scale phenomena: nucleation and growth | |
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| Homogeneous nucleation | |
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| Heterogeneous nucleation | |
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| Growth kinetics | |
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| Types of interfaces | |
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| Continuous growth | |
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| Lateral growth | |
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| References | |
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| Stochastic modeling of solidification | |
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| Monte-Carlo grain growth models | |
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| Dendrite envelope growth models | |
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| Eutectic S/L interface growth models | |
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| Cellular automaton models | |
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| Cellular automaton grain growth models | |
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| Cellular automaton dendrite growth models | |
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| References | |
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| Macro-micro modeling of solidification of some commercial alloys | |
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| Steel | |
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| Nucleation of primary dendrites | |
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| Growth of primary dendrites | |
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| Micro/macro-segregation | |
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| Inclusions | |
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| Cast iron | |
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| Nucleation and growth of austenite dendrites | |
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| Crystallization of graphite from the liquid | |
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| Eutectic solidification | |
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| Microsegregation | |
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| The gray-to-white structural transition | |
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| Room temperature microstructure and mechanical properties | |
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| Aluminum-silicon alloys | |
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| Nucleation and growth of primary aluminum dendrites | |
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| Eutectic solidification | |
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| Superalloys | |
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| References | |
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| Appendix A | |
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| Appendix B | |
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| Subject Index | |
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| About the Author | |