Fundamentals of Crystal Growth I

The intrinsic properties of a solid, i. e. , the properties that result from its specific structure, can be largely modified by crystallographic and chem­ ical defects. The formation of these defects is governed by the heat and mass transfer conditions which prevail on and near a crystal-nutrient in­ terface during crystallization. Hence, both the growth of highly perfect crystals and the preparation of samples having predetermined defect-induced (extrinsic) properties require a thorough understanding of the reaction and transport mechanisms that govern crystallization from vapors, solutions and melts. Crystal growth, as a science, is therefore mostly concerned with the chemistry and physics of heat and mass transport in these fluid-solid phase transitions. Solid-solid transitions are, at this time, not widely employed for high quality single-crystal production. Transport concepts are largely built upon equilibrium considerations, i. e. , on thermodynamic and phase equilibrium concepts. Hence to supply a "workable" foundation for the succeeding discussions, this text begins in Chapter 2 with a concise treatment of thermodynamics which emphasizes applications to mate­ rials preparation. After working through this chapter, the reader should feel at ease with often (particularly among physicists) unfamiliar entities such as chemical potentials, fugacities, activities. etc. Special sections on ther­ mochemical calculations (and their pitfalls) and compilations of thermochemi­ cal data conclude the second chapter. Crystal growth can be called. in a wide sense, the science and technology of controlling phase transitions that lead to (single crystalline) solids.

Contenu

1. Introduction.- 2. Thermodynamics.- 2.1 Systems.- 2.2 State Variables.- 2.3 Equations of State.- 2.4 First Law of Thermodynamics.- 2.5 Second Law of Thermodynamics.- 2.6 Thermal Efficiency.- 2.7 Reversibility and Entropy.- 2.8 Chemical Potential.- 2.9 Thermodynamic Potentials.- 2.10 Equilibrium.- 2.10.1 General criteria.- 2.10.2 Interphase mass transfer.- 2.11 Chemical Equilibrium.- 2.12 Thermochemical Calculations.- 2.12.1 General discussion and approximations.- 2.12.2 Sources for thermochemical data.- Problems.- 3. Phase Equilibria and Phase Diagrams.- 3.1 Clausius-Clapeyron Relation.- 3.2 Gibbs Phase Rule.- 3.3 Monocomponent Systems.- 3.4 Binary Systems.- 3.4.1 Definitions and general remarks.- 3.4.2 Ideal solutions.- 3.4.3 Real solutions.- 3.4.4 Invariant transitions.- 3.4.5 Ordered and intermediate phases.- 3.4.6 Congruent and incongruent melting.- 3.4.7 Vapor-liquid-solid equilibria.- 3.5 Ternary Systems.- 3.6 Sources for Phase Diagrams and Solubility Data.- Problems.- 4. Crystal Growth and Phase Diagrams.- 4.1 The Ideal System.- 4.2 Classification of Fluid to Solid Processes.- 4.3 Liquid-Solid Equilibria.- 4.3.1 Congruent and incongruent solidification.- 4.3.2 Crystallization from solutions.- 4.4 Vapor-Condensed Phase Equilibria.- 4.4.1 Vapor composition control.- 4.4.2 Vapor-solid equilibria.- 4.5 Container Materials.- Problems.- 5. Mass Transport and Heat Transfer.- 5.1 Fluxes and References Frames.- 5.2 Diffusion.- 5.2.1 Driving potentials.- 5.2.2 Concentration or ordinary diffusion.- 5.2.3 Diffusion coefficients.- 5.2.4 Thermal diffusion.- 5.2.5 Pressure diffusion.- 5.2.6 Forced diffusion (electromigration).- 5.3 Forced Convective Flow.- 5.3.1 Equations of change.- 5.3.2 Flow near solid-fluid interfaces.- 5.3.3 Viscosities.- 5.4 Convective-Diffusive Mass Transfer.- 5.5 Non-Radiative Heat Transfer.- 5.5.1 Basic equations for non-radiative transfer.- 5.5.2 Coupled interfacial heat and mass transfer.- 5.5.3 Correlations of solutions to mass and heat transfer problems.- 5.5.4 Thermal diffusivities and boundary layers.- 5.6 Radiative Heat Transfer.- 5.6.1 Fundamental concepts.- 5.6.2 Applications of the radiative transfer concepts.- 5.6.3 Combined conductive-convective-radiative heat transfer.- 5.7 Stefan Problems.- 5.8 Free Convection.- 5.8.1 Introductory Remarks.- 5.8.2 Buoyancy-driven convection.- 5.8.3 Surface-Tension-Driven Convection.- Problems.- 6. Segregation.- 6.1 Segregation Coefficients.- 6.2 Equilibrium Segregation.- 6.2.1 Thermodynamics of segregation.- 6.2.2 Experimental observations.- 6.3 Steady-State Segregation.- 6.3.1 Segregation in growth from a nutrient of uniform density.- 6.3.2 Segregation in growth from a nutrient of non-uniform density.- 6.3.3 Experimental observations.- 6.4 Macrodistribution.- 6.4.1 Normal freezing.- 6.4.2 Zone melting.- 6.4.3 Uniform composition.- 6.5 Microdistribution.- 6.5.1 Non-steady segregation.- 6.5.2 Non-equilibrium segregation.- Problems.- Appendices.- A. Universal Gas Constant.- B. Thermodynamic Functions.- C. Derivations of some Relations Used in Sect. 5.2.- References.