Verfügbarkeit: The atomistic nature of crystal growth

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Bibliographische Detailangaben
Beteilige Person:	Mutaftschiev, Boyan 1932- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 2001
Schriftenreihe:	Springer series in materials science 43
Schlagwörter:	Cristaux - Croissance Crystal growth Keimbildung Kristallwachstum
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009194327&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XIII, 368 S. Ill., graph. Darst.
ISBN:	3540664963

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DE-BY-TUM_call_number	0001 08.2003 A 37 0202 PHY 802f 2002 A 4672
DE-BY-TUM_katkey	1215137
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adam_text	CONTENTS PART I INTRODUCTION AND BACKGROUND 1. INTRODUCTION .............................................. 3 2. THERMODYNAMICS ......................................... 7 2.1 SOME DEFINITIONS ....................................... 7 2.2 THE PRINCIPLES OF THERMODYNAMICS ....................... 8 2.3 INTERNAL ENERGY ........................................ 9 2.4 OTHER THERMODYNAMIC FUNCTIONS; MAXWELLS RELATIONS ...... 10 2.5 WORK AND EQUILIBRIUM .................................. 13 2.6 INTEGRATED EQUATIONS .................................... 16 2.7 CHEMICAL POTENTIALS AND SUPERSATURATION .................. 17 2.7.1 SUPERSATURATED VAPOR (IDEAL GAS) .................. 18 2.7.2 SUPERSATURATED SOLUTION ........................... 18 2.7.3 UNDERCOOLED CONDENSED PHASE ..................... 19 2.8 THE SURFACE PHASE* .................................... 19 3. STATISTICAL THERMODYNAMICS .............................. 23 3.1 PARTITION FUNCTIONS; GENERAL ............................. 23 3.2 PARTITION FUNCTION IN A CONTINUUM PHASE SPACE ............ 24 3.3 EXAMPLES OF SIMPLE PARTITION FUNCTIONS ................... 26 3.3.1 TRANSLATIONAL MOTION ............................. 26 3.3.2 HARMONIC OSCILLATOR .............................. 26 3.3.3 FREE ROTATION .................................... 30 3.4 CANONICAL PARTITION FUNCTIONS OF PURE PHASES; FREE ENERGY AND CHEMICAL POTENTIAL ...................... 32 3.4.1 THE IDEAL GAS ................................... 32 3.4.2 THE LATTICE GAS ................................ 32 3.4.3 THE MONATOMIC EINSTEIN CRYSTAL ................... 33 3.4.4 THE ONE-DIMENSIONAL NON-EINSTEIN CRYSTAL .......... 34 3.5 PARTITION FUNCTION OF ASSOCIATED VAPOR .................... 38 X CONTENTS PART II EQUILIBRIA 4. EQUILIBRIUM BETWEEN LARGE PHASES; THE VAPOR PRESSURE OF SOLIDS ............................. 43 4.1 THE CLAUSIUSCLAPEYRON EQUATION ........................ 43 4.2 STATISTICAL-THERMODYNAMIC TREATMENT .................... 45 4.3 REPETITIVE-STEP; THERMODYNAMIC FREQUENCY ............... 45 4.4 KINETIC TREATMENT OF THE EQUILIBRIUM CRYSTAL-VAPOR ........ 49 4.5 EQUILIBRIUM IN THE DIFFERENT SITES ON THE CRYSTAL SURFACE .... 51 4.6 ADSORBED AND INCORPORATED MOLECULES; THE DIFFERENT TYPES OF CRYSTAL FACE ....................... 55 5. THE SURFACE TENSION OF CRYSTALS .......................... 61 5.1 THE BROKEN-BOND APPROACH TO THE SURFACE ENERGY OF A SOLID: THE BORNSTERN PROCEDURE ............................... 61 5.2 SURFACE STRESS .......................................... 65 5.3 INTERFACIAL TENSION ...................................... 67 5.4 STEFANS RULE .......................................... 70 6. EQUILIBRIUM BETWEEN LARGE THREE- AND TWO-DIMENSIONAL PHASES: ADSORPTION PHENOMENA .... 73 6.1 PARTITION FUNCTION AND CHEMICAL POTENTIAL OF AN ADSORBED LAYER ................................... 73 6.1.1 THE ISING MODEL ................................. 75 6.1.2 THE MEAN FIELD APPROXIMATION .................... 77 6.2 DESORPTION WORK ....................................... 78 6.3 FRUMKINFOWLERS ADSORPTION ISOTHERM .................... 79 6.4 MULTILAYER ADSORPTION ................................... 84 6.5 TWO-DIMENSIONAL PHASE TRANSITIONS; SPREADING PRESSURE ..... 88 6.6 TWO-DIMENSIONAL VERSUS THREE DIMENSIONAL PHASES; A LINK TO WETTING ...................................... 93 6.7 DISPLACEMENT AND MIXING OF CONDENSED TWO-DIMENSIONAL PHASES .................... 94 7. THIN FILMS, SURFACE ROUGHENING, AND SURFACE ALLOYS ...... 103 7.1 CHEMISORBED VERSUS PHYSISORBED LAYERS; THIN SOLID FILMS .. 103 7.2 SURFACE ROUGHNESS CONSIDERED AS A SPECIAL CASE OF ADSORPTION .......................................... 106 7.3 ADSORPTION ON A THERMALLY ROUGH SUBSTRATE: SURFACE ALLOYING ........................................ 113 7.4 SURFACE MELTING ........................................ 119 CONTENTS XI 8. EQUILIBRIUM BETWEEN A SMALL AND A LARGE PHASE .......... 123 8.1 THE GIBBS POTENTIAL OF A SMALL PHASE; THE CAPILLARITY APPROXIMATION ........................... 123 8.2 THE SIZE-DEPENDENT CHEMICAL POTENTIAL ................... 128 8.2.1 DROPLETS IN A VAPOR ............................... 129 8.2.2 GAS BUBBLES IN A LIQUID ........................... 130 8.2.3 SOLID CLUSTERS IN A MELT ........................... 132 8.3 STATISTICAL MECHANICAL TREATMENT OF THE FREE ENERGY OF A SOLID CLUSTER ....................................... 133 8.4 CAPILLARITY APPROXIMATION VERSUS MODEL CALCULATIONS ....... 138 9. EQUILIBRIUM SHAPES OF CRYSTALS ........................... 147 9.1 CURIEWULFFS CONDITION AND WULFFS THEOREM ............. 148 9.2 HERRINGS -PLOT ........................................ 151 9.3 FACETING OF A K FACE .................................... 156 9.4 EQUILIBRIUM SHAPE ON A FOREIGN SUBSTRATE ................. 158 9.5 EQUILIBRIUM SHAPE OF A DROPLET ON A SUBSTRATE: YOUNGS EQUATION ...................................... 161 9.6 ENTROPY EFFECTS ON SURFACE FREE ENERGY AND EQUILIBRIUM SHAPE .................................. 163 9.7 EQUILIBRIUM OF SMALL ANISOTROPIC PHASES; THE THERMODYNAMIC APPROACH ........................... 166 9.8 EQUILIBRIUM OF SMALL ANISOTROPIC PHASES; THE ATOMISTIC APPROACH ................................. 168 9.9 THE INFLUENCE OF FOREIGN ADSORPTION ON THE EQUILIBRIUM SHAPE ............................... 174 9.9.1 THE DIFFERENT TYPES OF CRYSTAL FACE ................ 177 9.9.2 THE EQUILIBRIUM SHAPE ........................... 179 9.9.3 FACETING ......................................... 180 PART III NUCLEATION 10. HOMOGENEOUS NUCLEATION; THE PHASE APPROACH ........... 183 10.1 THE CLASSICAL NUCLEATION WORK. DROPLETS IN A VAPOR ........ 184 10.2 BUBBLES IN LIQUIDS: BOILING AND CAVITATION ................ 189 10.2.1 BOILING UNDER POSITIVE EXTERNAL PRESSURE ............ 190 10.2.2 BOILING UNDER NEGATIVE EXTERNAL PRESSURE ........... 192 10.3 ANISOTROPIC EMBRYOS; THE THERMODYNAMIC APPROACH ....... 193 10.4 ANISOTROPIC EMBRYOS; THE ATOMISTIC APPROACH ............. 194 10.5 THE VOLMERWEBER TREATMENT OF NUCLEATION KINETICS ....... 196 11. HOMOGENEOUS NUCLEATION; THE CHEMICAL APPROACH ........ 201 11.1 EQUILIBRIUM IN ASSOCIATED VAPOR ......................... 201 11.2 FRENKELS SIZE DISTRIBUTION ............................... 207 XII CONTENTS 11.3 FRENKELS TREATMENT OF STEADY STATE NUCLEATION KINETICS ..... 210 11.4 THE BECKERD¨ ORING TREATMENT OF STEADY STATE NUCLEATION KINETICS ..................................... 215 11.5 NUCLEATION KINETICS IN CONDENSED SYSTEMS ................. 221 11.6 CLUSTER ISOMERS AND EQUILIBRIUM SHAPE ................... 223 12. NUCLEATION ON A FOREIGN SUBSTRATE ........................ 227 12.1 NUCLEATION ON A FOREIGN SOLID SUBSTRATE ................... 227 12.2 NUCLEATION ON THE INTERFACE BETWEEN TWO FLUIDS ............ 233 12.3 TWO-DIMENSIONAL NUCLEATION ............................. 235 12.4 ROLE OF THE STRUCTURE IN SUBSTRATE NUCLEATION: EPITAXY ...... 239 12.4.1 EPITAXY BY CLASSICAL THREE-DIMENSIONAL NUCLEATION ... 240 12.4.2 EPITAXY BY NON-CLASSICAL* THREE-DIMENSIONAL NUCLEATION ....................................... 241 12.4.3 EPITAXY BY TWO-DIMENSIONAL NUCLEATION ............ 242 12.5 NUCLEATION ON FOREIGN PARTICLES .......................... 244 12.5.1 NUCLEATION ON PERFECTLY WETTED SPHERICAL PARTICLES ................................ 245 12.5.2 NUCLEATION ON BETTER-THAN-PERFECTLY-WETTED SPHERICAL PARTICLES ................................ 247 13. SOME SPECIFIC CASES OF NUCLEATION ........................ 249 13.1 NUCLEATION ON CHARGED PARTICLES .......................... 249 13.2 SOLIDIFICATION OF SMALL DROPLETS ........................... 251 13.3 NUCLEATION IN A SMALL VOLUME ............................ 255 13.4 NUCLEATION AND OSTWALDS RULE ........................... 257 13.5 NUCLEATION IN A BINARY ALLOY ............................. 262 13.5.1 THREE-DIMENSIONAL BINARY ALLOYS ................... 262 13.5.2 TWO-DIMENSIONAL (SURFACE) ALLOYS .................. 265 14. TIME-DEPENDENT NUCLEATION KINETICS ..................... 267 14.1 THE TIME LAG IN NUCLEATION ............................. 267 14.2 NON-CLASSICAL NUCLEATION ON A SUBSTRATE ................... 270 PART IV CRYSTAL GROWTH 15. ELEMENTARY PROCESSES ON THE SURFACE OF A CRYSTAL ......... 279 15.1 STICKING ............................................... 281 15.2 SURFACE MIGRATION ...................................... 283 15.3 MEAN DIFFUSION LENGTH .................................. 285 16. GROWTH OF A PERFECT* K FACE ............................ 291 16.1 KINETICS OF GROWTH OF A PLANAR K FACE .................... 292 16.1.1 THE MAXIMUM GROWTH RATE ....................... 292 CONTENTS XIII 16.1.2 INCOMPLETE STICKING; KINETIC COEFFICIENTS ............ 294 16.1.3 A SIMPLE CASE OF DIFFUSION-CONTROLLED GROWTH ....... 295 16.2 DIFFUSION VERSUS CAPILLARITY: MORPHOLOGICAL STABILITY ........ 297 17. GROWTH OF AN F FACE OF A PERFECT CRYSTAL ................. 303 17.1 THE TRANSITION FROM LAYER-BY-LAYER TO CONTINUOUS GROWTH .. 303 17.2 A ONE-DIMENSIONAL K FACE: THE MONOMOLECULAR STEP ....... 308 17.3 RATE OF PROPAGATION OF A SINGLE STRAIGHT STEP .............. 314 17.3.1 ADVANCEMENT CONTROLLED BY SURFACE DIFFUSION ........ 314 17.3.2 ADVANCEMENT CONTROLLED BY VOLUME DIFFUSION ........ 318 17.4 RATE OF ADVANCEMENT OF A CURVED STEP .................... 320 17.5 GROWTH BY TWO-DIMENSIONAL NUCLEATION; MONONUCLEAR GROWTH ................................... 323 17.6 GROWTH BY TWO-DIMENSIONAL NUCLEATION; POLYNUCLEAR GROWTH ..................................... 326 18. GROWTH OF AN F FACE OF AN IMPERFECT CRYSTAL ............. 331 18.1 RATE OF PROPAGATION OF A TRAIN OF EQUIDISTANT STEPS ........ 332 18.1.1 ADVANCEMENT CONTROLLED BY SURFACE DIFFUSION ........ 332 18.1.2 ADVANCEMENT CONTROLLED BY VOLUME DIFFUSION ........ 333 18.2 GROWTH SPIRALS ......................................... 336 18.2.1 GROWTH GOVERNED BY SURFACE DIFFUSION .............. 339 18.2.2 GROWTH GOVERNED BY VOLUME DIFFUSION .............. 340 19. CONCLUSION ............................................... 341 APPENDICES ................................................... 343 A.LEGENDRE TRANSFORMATIONS ............................... 343 B.METHOD OF LAGRANGE MULTIPLIERS .......................... 344 C.EULERS THEOREM ........................................ 344 D.STIRLINGS APPROXIMATION ................................ 345 E.MAXIMUM TERM APPROXIMATION .......................... 345 F.INTEGRALS OF THE TYPE * * 0 X N EXP( * *X 2 )D X . . . . . . . . . . . . . . . . . 347 REFERENCES .................................................... 349 INDEX ......................................................... 357
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indexdate	2024-12-20T10:47:56Z
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isbn	3540664963
language	English
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physical	XIII, 368 S. Ill., graph. Darst.
publishDate	2001
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publisher	Springer
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series	Springer series in materials science
series2	Springer series in materials science Physics and astronomy online library
spellingShingle	Mutaftschiev, Boyan 1932- The atomistic nature of crystal growth Springer series in materials science Cristaux - Croissance Crystal growth Keimbildung (DE-588)4201506-6 gnd Kristallwachstum (DE-588)4123579-4 gnd
subject_GND	(DE-588)4201506-6 (DE-588)4123579-4
title	The atomistic nature of crystal growth
title_auth	The atomistic nature of crystal growth
title_exact_search	The atomistic nature of crystal growth
title_full	The atomistic nature of crystal growth Boyan Mutaftschiev
title_fullStr	The atomistic nature of crystal growth Boyan Mutaftschiev
title_full_unstemmed	The atomistic nature of crystal growth Boyan Mutaftschiev
title_short	The atomistic nature of crystal growth
title_sort	the atomistic nature of crystal growth
topic	Cristaux - Croissance Crystal growth Keimbildung (DE-588)4201506-6 gnd Kristallwachstum (DE-588)4123579-4 gnd
topic_facet	Cristaux - Croissance Crystal growth Keimbildung Kristallwachstum
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009194327&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000683335
work_keys_str_mv	AT mutaftschievboyan theatomisticnatureofcrystalgrowth

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