Crystal Growth from Melts

Transcription

1 Crystal Growth from Melts Applications to Growth of Groups 1 and 2 Crystals Bimalendu Narayan Roy Sheffield City Polytechnic, UK JOHN WILEY & SONS Chichester New York Brisbane Toronto Singapore

2 Contents Preface Acknowledgements List of Symbols xv xvii xix 1 Introduction A Brief History of Crystal Growth High Temperature Crystal Growth Other Methods Growth from the pure melt Growth from the solid state Growth from aqueous solutions Growth from solvents other than water Growth from the vapour phase The hydrothermal method A Brief Review of the Advantages and Disadvantages of all of the Methods 5 References 7 2 Applications of Crystals and Methods of Crystal Growth General Applications of Crystals Grown from High Temperature Solutions Applications of Alkaline-earth Metal Crystals Classification of Crystal Growth Methods Growth from the melt Growth by evaporation Growth from seeds Growth from the solid state Growth from liquid metals : Temperature-gradient zone melting Growth from aqueous solution Crystal growth from non-aqueous solvents Hydrothermal growth Vapour-liquid-solid growth 17

3 2.4 Methods of Crystal Growth The Czochralski method The Bridgman-Stockbarger method Zone-melting methods The floating zone technique The gradient-freeze technique The hydrothermal growth method The flame fusion or Verneuil method Crystal growth by osmotic dewatering Preparation of Single Crystal Thin Films Vapour phase epitaxy Liquid phase epitaxy Molecular beam epitaxy Van der Waals epitaxy Metal-organic chemical vapour deposition Chemical beam epitaxy Langmuir-Blodgett thin film deposition 57 References 59 The Thermodynamics of Crystal Growth Introduction Mass Transfer in the Interface Chemical Equilibria in Crystal Growth Thermochemical Calculations Solubility and Phase Diagrams The dissolution-extraction method Quenching Hot-stage microscopy Differential thermal analysis Determination of the Solubility of Alkaline-earth Metal Salts Phase Diagrams of Alkaline-earth Metal Systems Binary systems Reciprocal ternary systems Quasi-binary systems Alkaline-earth metal salt-alkali metal chloride systems Alkaline-earth metal salt-alkali metal fluoride, borate, ferrite and molybdate systems Alkaline-earth metal salt-alkaline-earth metal fluoride, borate, ferrite and molybdate systems (with common cation) Alkaline-earth metal salt-alkali metal salt systems (with common anion) 79

4 3.7.8 Alkaline-earth metal salt-alkaline-earth metal chloride systems (with common cation) Solubilities of barium titanate in different solvents 81 References 85 4 The Physical Chemistry of Molten Salts Introduction Electrostatic Interaction and Structure Molten Salt Mixtures Diffusion in Salt Melts The Atomic Structure of Solid-Liquid Interfaces 92 References 94 5 Solvents and Solutes Introduction High Temperature Solvents Crystallisation Conditions Solute-Solvent Interactions Alkaline-earth metal oxide solutions in alkali metal chloride melts Alkaline-earth metal silicate solutions in alkaline-earth metal chloride melts Alkaline-earth metal titanate solutions in alkaline-earth metal chloride melts Alkaline-earth metal molybdate solutions in alkali metal chloride melts Alkaline-earth metal molybdate solutions in alkaline-earth metal chloride melts Alkaline-earth metal tungstate solutions in alkali metal chloride Alkaline-earth metal tungstate solutions in alkaline-earth metal chloride melts Alkaline-earth metal tungstate solutions in sodium tungstate melts 102 References Materials, Methods and Variables Introduction Furnace and Chemicals Methods of Crystallisation Crystallisation by hot-stage microscopy Crystallisation in platinum crucibles (by differential thermal analysis) 107 IX

5 X Crystallisation in alumina crucibles (in a high temperature furnace) Direct measurement of the degree of crystallisation Instrumental Analysis Infrared spectroscopy X-ray methods Particle Size Measurement Particle Size Distribution Standard Deviation and Standard Error Crystal Number (N) 124 References Theory of Crystallisation from Supersaturated Solutions at Constant Temperatures Introduction Supersaturation and Crystallisation Affinity The Thermodynamics of Nucleation The Kinetics of Nucleation Crystal Growth (and Growth Rates) The overall mechanism Growth processes The Overall Kinetics of Growth Heterogeneous nucleation Homogeneous nucleation Growth onto seeds Kinetic Equations for Growth Diffusion-controlled growth Surface nucleation-controlled growth 145 References Theory of Crystallisation with Continuous Development of Supersaturation Introduction Nucleation Critical Time and Critical Temperature Variation of N with S (or C) Overall Kinetics of Crystal Growth Systems with no induction period Systems with a short induction period Systems with a prolonged induction period Kinetic relationships at later stages 152 References 153

6 9 Preliminary General Studies on Crystallisation Introduction Crystallisation and Analysis Variation of Crystal Size and Number with Metal Salt Structure Crystallisation from lithium chloride melts Crystallisation from alkaline-earth metal chloride melts Crystallisation from sodium tungstate melts Variation of Crystal Size and Number with Rate of Cooling Crystallisation from lithium chloride melts Crystallisation from alkaline-earth metal chloride melts Crystallisation from sodium tungstate melts Variation of Crystal Size and Number with Initial Crystallisation Temperature (and Solute Solubility) Crystallisation from lithium chloride melts Crystallisation from alkaline-earth metal chloride melts Crystallisation from sodium tungstate melts Crystal Form Preliminary Differential Thermal Analysis Studies 168 References Crystallisation at Constant Temperatures Introduction Crystallisation Analysis and Characterisation of Crystals Crystal Size and Shape Crystal size Crystal size distribution Crystal form Crystal anisometry Alternative Methods Hot-stage microscopy Chemical analysis of the residual solution Differential thermal analysis Nucleation (Seed Number) Growth Degree of crystallisation (a t ) Course of growth Maximum length and width Kinetics of Growth Mechanism of Growth 192 XI

7 xii Kinetic relationships at early stages Kinetic relationships at later stages Rate Constants (for Diffusion-controlled Crystal Growth) Variation of rate constants with metal cation Variation of rate constants with temperature Diffusion Rate Constants and Diffusion Coefficients 198 References Crystallisation by Continuous Cooling from Lithium Chloride Melts in Alumina Crucibles Introduction Crystallisation Overall excess solute concentrations Residual excess solute concentrations Total crystal weights Methods of crystallisation Analysis and Characterisation of Crystals Crystal Size and Shape Crystal size Crystal size distribution Crystal form Crystal anisometry Shape factor (/ s ) Kinetics at Early Stages Degree of crystallisation Crystal length vs. time plots Nucleation Nucleation mechanism and kinetics Nucleation rate constants Nucleus number Induction periods Relationship betweentv and / Relationship between (N/t) and ДС Growth Kinetics Crystal length vs. growth time Growth-rates Mechanism of growth Rate Constants Rate Constants and Diffusion Coefficients Growth along major axes Growth along minor axes Factors Affecting Diffusion of Materials Non-ideal Diffusion-controlled Crystal Growth Crystal Anisometry 240

8 11.13 Final Crystal Size 240 References 241 XIII 12 Crystallisation by Continuous Cooling from Sodium Tungstate Melts in Alumina Crucibles Introduction Crystallisation Development of supersaturation Methods of crystallisation Crystal Size and Shape Crystal size Crystal form Crystal anisometry Shape factor (/ s ) Kinetics at Early Stages Degree of crystallisation (a t ) vs. time (t) plots Crystal length vs. time plots Crystal width Nucleation Variation with rate of cooling (RT) Variation with initial crystallisation temperature (To) Variation with metal cation Growth Kinetics Variation with initial crystallisation temperature (Го) Variation with rate of cooling (R T ) Mechanism of Growth Rate Constants (for Diffusion-controlled Growth) Rate Constants and Diffusion Coefficients Growth along the major axes Growth along the minor axes Non-ideal Diffusion-controlled Crystal Growth Crystal Anisometry Final Crystal Size 264 References Crystallisation by Differential Thermal Analysis Introduction Crystallisation Development of Supersaturation Overall excess solute concentrations Residual excess solute concentrations Total crystal weights 270

9 Critical time (t), critical temperature (Г) and critical excess solute concentration (AC) Overall Kinetics Degree of crystallisation (a t ) Crystal length Nucleation Variation of induction period with rate of cooling (R T ) Variation of induction period with initial crystallisation temperature (Г 0 ) Variation of induction period with metal cation Growth after the Induction Period Initial growth rates Average crystal length (l T ) /r vs. г relationships The final growth Mechanism of Growth Rate Constants 299 References 302 Kinetic Parameters and Thermodynamic Properties in Crystal Growth Introduction A Mathematical Model The Proximity of a Diffusing Particle and its Host Immediately before a Successful Diffusion Encounter Numerical Calculations of Kinetic Parameters and Thermodynamic Properties Crystallisation in Alumina Crucibles Activation energy The pre-exponential factor Activation enthalpy Free energy of activation Activation entropy Crystallisation in Platinum Crucibles The pre-exponential factor Activation energy Activation enthalpy Free energy of activation Activation entropy Proximity (du) between the Reacting Partners 317 References 318