Microscopic theory of crystal growth:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Akad.-Verl.
1989
|
| Schriftenreihe: | Physical research
11. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 400 S. |
| ISBN: | 3055006844 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804117901705216000 |
|---|---|
| adam_text | MICROSCOPIC THEORY OF CRYSTAL GROWTH BY HUBERT^PFEIFFER THOMAS KLUPSCH
WERNER HAUBENREISSER WITH 73 FIGURES AND 5 TABLES AKADEMIE-VERLAG BERLIN
1989 CONTENTS 1. INTRODUCTION 15 2. LATTIOE MODEL OF CRYSTAL GROWTH 23
2.1. PRELIMINARIES 23 2.2. DESCRIPTION OF THE INTERFAOE AND THE
ELEMENTARY PROCESSES WITHIN THE LATTIOE MODE?. 26 2.3. BASIC VARIABLES,
HAMILTONIAN, AND FREE ENERGY 30 2.4. MATHEMATICAL BACKGROUND. MASTER
EQUATION APPROACH 34 2.4.1. MONTE-CARLO SIMULATION 37 2.4.2. ORDER
PARAMETER CONCEPT 38 2.4.3. KINETIC EQUATIONS 41 2.5. ONE-COMPONENT
SYSTEMS 44 2.5.1. ROUGHENING TRANSITION - LATERAL AND NORMAL GROWTH 47
2.5.2. MASTER EQUATION APPROACH IN MICROVARIABLES 49 2.5.2.1.
FORMULATION IN SITE VARIABLES (SPIN VARIABLES) 49 2.5.2.1.1. RATE
EQUATIONS IN BRAGG-WILLIAMS APPROXIMATION 52 2.5.2.1.2. CONTINUUM
APPROXIMATION 55 2.5.2.1.3. STEP GROWTH AND SURFACE DIFFUSION 62
2.5.2.2. FORMULATION IN COLUMN VARIABLES 67 2.5.2.2.1. THE GROWTH OF
STEPS 68 2.5.2.2.1.1. HAMILTONIAN AND MASTER EQUATION 69 2.5.2.2.1.2.
THE CRITICAL NUCLEUS 77 2.5.2.2.1.3. KINETIC EQUATION 80 2.5.2.2.1.4.
ANISOTROPY OF STEP GROWTH 83 2.5.2.2.1.5. INFLUENCE OF THE SECOND
NEAREST NEIGHBOUR INTERACTION 93 2.5.2.2.1.6. INCLUSION OF DIFFUSION 95
2.5.2.2.1.7. TWO-PARTICLE RELAXATION PROCESSES 99 2.5.2.2.2. -THE GROWTH
OF FACES 102 2.5.2.2.2.1. MASTER EQUATION APPROACH IN JUMP VARIABLES 103
2.5.2.2.2.2. INFLUENCE OF DIFFUSION 111 2.5.3. MASTER EQUATION APPROACH
IN MACROVARIABL ES 113 2.6. SUMMARY AND RELATION TO EXPERIMENT 120
2.6.1. STEP GROWTH ON SINGULAR (HO)-GARNET PACES 121 2.6.2.
DETERMINATION OF THE JACKSON-TEMKIN FACTOR 124 2.7. TWO-COMPONENT
SYSTEMS 128 2.7.1. INTRO DUCT ORY REMARKS 128 2.7.2. MASTER EQUATION
APPROACH IN ZLICROVARIABLES 129 2.7.2.1. FORMULATION IN SITE VARIABLES
129 2.7.2.1.1. KINETIC EQUATIONS 132 2.7.2.1.2. EVALUATION OF THE
KINETIC EQUATIONS IN PAIR APPROXIMATION - 136 2.7.2.1.3. INFLUENCE OF
THE DIFFUSION IN THE MELT 140 2.7.2.1.4. KINETICS OF ORDERING IN BINARY
CRYSTALS 143 2.7.2.2. FORMULATION IN COLUMN VARIABLES 147 2.7.2.2.1.
INCORPORATION OF IMPURITIES 150 2.7.2.2.2. THE GROWTH OF CRYSTALS BEING
ORDERED 152 2.7.3. FORMULATION IN MACROVARIABLES 155 2.7.3.1.
MACROSTATES AND MACROVARIABLES 155 2.7.3.2. FREE ENERGY AND HASTER
EQUATION 157 8 RATE EQUATIONS IN .BRAGG-WILLIAMS APPRO- XIMATION 160
EQUILIBRIUM 164 HONEQUILIBRIUM 165 IMPURITY INCORPORATION 168 TREATMENT
IN BRAGG-WILLIAMS APPROXIMATIO 170 MODIFIED BRAGG-WILLIAMS APPROXIMATION
173 DISCUSSION AND RELATION TO EXPERIMENT 181 IMPURITY TRAPPING 182
GROWTH-INDUCED MAGNETIC ANISOTROPY ,184 FINAL ASSESMENT OF THE LATTICE
MODEL 188 PRINCIPLES OF A MOLECULAR THEORY OF CRYSTAL GROWTH 189
PRELIMINARY REMARKS: GENERAL CONCEPTS 191 MICROSCOPIC MODEL 191
HEWTONIAN DYNAMICS 191 INTERACTION POTENTIAL, MICROSCOPIC AND EXTER- NAL
PARAMETERS 193 DESCRIPTION OF STRUCTURE 197 MOLECULAR EQUILIBRIUM
DISTRIBUTION FUNCTIONS 197 HOMOGENEOUS FLUID STATE 198 IDEAL CRYSTALLINE
STATE 199 SOME COMMENTS ON INLIOMOGENEOUS SYSTEMS 201 MATHEMATICAL
TREATMENT: SOME GENERAL CONCEPTS 203 9 3. 3. 3. 3. 3, 3. 3, 3. 3, .1.
.1, ,1, ,1, ,2, ,2, ,2, ,2, .2, .3. .3. .3, .3. 1 .1. .2. .3. .4. 1 2 3
4 PHASE TRANSITIONS AND PHASE COEXISTENOE 203 INTERFAOE 206 DENSITY
PUNOTIONAL THEORY 207 SOME CONCLUSIONS 210 MOLECULAR EQUILIBRIUM
DISTRIBUTION FUNOTIONS 211 CANONICAL ENSEMBLE: STRICT DEFINITION 211
BORN-BOGOLYUBOV-GREEN-KIRKWOOD-YVON (BB&KY) HIERARCHY 214 FREE ENERGY
FUNCTIONAL AND EFFECTIVE POTENTIAL 215 DIRECT CORRELATION FUNCTIONS,
ORNSTEIN-ZERNIKE AND PERCUS-YEVICK EQUATION 218 3.3. THEORY OF THE
CRYSTAL-LIQUID INTERFACE OF SIMPLE ONE-COMPONENT SYSTEMS AT THERMAL
EQUILIBRIUM 221 3.3.1. FREE ENERGY FUNCTIONAL FOR BENNARD-JONES SYSTEMS
221 3.3.1.1. PERTURBATION THEORETICAL SOLUTION OF THE COUP- LED
ORNSTEIN-ZERNIKE AND PERCUS-YEVICK EQUA- TIONS 221 3.3.1.2 SINGLE
PARTICLE DENSITY ANSATZ 222 3.3.1.3. DIRECT CORRELATION FUNCTION 225
3.3.1.4. FREE ENERGY FUNCTIONAL SUBDIVISION 227 3.3.1.5. LIQUID PART 229
3.3.1.6. SOLID PART 231 3.3.1.7. ORDER PARAMETERS AND CONTINUUM
APPROXIMATION 234 3.3.2. CRYSTAL-LIQUID COEXISTENCE AND INTERFACIAL PRO-
PERTIES FROM ORNSTEIN-ZERNIKE AND PEROUS-YEVIOK EQUATIONS 236 3.3.2.1.
MINIMIZATION OF THE FREE ENERGY FUNCTIONAL 236 3.3.2.2. PHASE
COEXISTENCE PROPERTIES NEAR THE TRIPLE POINT AND COMPARISON WITH OTHER
RESULTS 239 3.3.2.3. INTERFAOIAL PROPERTIES NEAR THE TRIPLE POINT AND
COMPARISON WITH OTHER RESULTS 243 10 3.3.3. OTHER THEORETIOAL CONCEPTS
248 3.4. EFFECTIVE LATTICE MODEL DESCRIPTION OF SIMPLE CRYSTAL-MELT
SYSTEMS 251 3.4W1. GENERAL REMARKS 251 3.4.2. SUBSEQUENT APPROXIMATION
STEPS 252 3.4.2.1. BASIC CELL STATES 252 3.4.2.2. FREE ENERGY FUNCTIONAL
AND EFFECTIVE POTENTIAL 255 3.4.3. QUADRATIC APPROACH 260 3.4.3.1.
SYMMETRY CONDITION 260 3.4.3.2. QUADRATIC HAMILTONIAN AND MEAN FIELD
APPROACH 262 3.4.3.3. NUMERICAL ESTIMATION OF THE COEFFICIENTS:
BENNARD-JONES SYSTEMS NEAR THE TRIPLE POINT 263 3.4.4. THE
JACKSON-TEMKIN MODEL REVISED 265 3.4.4.1. TRANSITION TO A RESTRICTED
S.C. LATTICE MODEL 265 3.4.4.2. ESTIMATION OF THE JACKSON-TEMKIN FACTOR
269 3.4.4.3. DISCUSSION 270 3.5. KINETICS OF THE CRYSTAL-MELT INTERFACE:
GENERAL ASPECTS OF THE MOLECULAR THEORY 272 3.5.1. PRELIMINARY REMARKS
272 3.5.2 4 . REDUCED DISTRIBUTION FUNCTIONS AND THE DYNAMICAL
BBGKT-HIERARCHY 273 3.5.3. CHARACTERISTIC TIME SCALES, PARTICLE CORRELA-
TIONS, AND LOCAL EQUILIBRIUM 277 3.5.4. INHOMOGENEOUS SYSTEMS 281 3.5.5.
STOCHASTIC SINGLE PARTICLE MOTION AND THERMODY- NAMICS OF IRREVERSIBLE
PROCESSES ON MOLECULAR BEVEL 283 11 3.6. STOCHASTIC SINGLE PARTICLE
MOTION AT THE INTERFACE 287 3.6.1. BASIC MODELS AND EQUATIONS 287
3*6.1.1. BANGEVIN EQUATION AND FOKKER-PLANCK EQUATION 287 3.6.1.2.
EFFECTIVE LIQUID MODEL 290 3.6.1.3. APPROXIMATE CALCULATION OF KINETIC
COEFFI- CIENTS 292 3.6.2. FRICTION AND SELF DIFFUSION COEFFICIENT AT THE
INTERFACE 296 3.6.2.1. MEAN SQUARED FLUCTUATING FORCE 296 3.6.2.2. SOME
BASIC ESTIMATIONS 300 3.6.2.3. NUMERICAL RESULTS 303 3.6.3. SOLID-LIQUID
FLUCTUATION TIME 305 3.6.3.1. DEFINITION 305 3.6.3.2. SMOLUCHOWSKI
EQUATION OF SOLID - LIQUID TRANSITION 305 3.6.3.3. CALCULATION OF THE
SOLID-LIQUID FLUCTUATION TIME 309 3.6.3.4. CHARACTERISTIC FLUCTUATION
FREQUENCY 311 3.6.4. DYNAMICS OF THE EFFECTIVE LATTICE MODEL 312
3.6.4.1. ELEMENTARY KINETIC EVENTS: MASTER EQUATION 312 3.6.4.2.
DETERMINATION OF COEFFICIENTS 314 3.7. GLOBAL INTERFAOIAL KINETICS
AND THE ABSOLUTE KINETIC COEFFICIENT 318 3.7.1. TIME-DEPENDENT ORDER
PARAMETER THEORIES 318 3.7.1.1. CONDITIONS SUMMARIZED 318 3.7.1.2.
SEPARATION OF BOUNDARY LAYER EFFECTS 319 3.7.1.3. TIME-DEPENDENT SINGLE
PARTICLE DENSITY: SMOLUCHOWSKI EQUATION 321 12 3.7.2. EFFECTIVE KINETIC
LATTICE MODEL AND TIME-DE- PENDENT GINZBURG-LANDAU EQUATION 324
3.7.2.1. ORDER PARAMETER AND LOOAL EQUILIBRIUM STATE 324 3.7.2.2.
ELEMENTARY KINETIC PROCESSES UNDER LOCAL EQUI- LIBRIUM CONDITIONS 326
3.7.2.3. KINETICS OF ORDER-PARAMETER: LANGER-TYPE MASTER EQUATION 327
3.7.2.4. GENERALIZED TIME-DEPENDENT GINZBURG-LANDAU EQUATION 332 3.7.3.
GROWTH VELOCITY AND INTERFACIAL KINETIC CO- EFFICIENT 334 3.7.3.1.
SOLITARY SOLUTIONS OF THE GENERALIZED TIME- DEPENDENT GINZBURG-LANDAU
EQUATION 334 3.7.3.2. APPROXIMATIONS NEAR THERMAL EQUILIBRIUM 336
3.7.3.3. NUMERICAL RESULTS 339 3.7.4. DISCUSSION . 340 3.7.4.1. GROWTH
VELOCITY: COMPARISON WITH OTHER THEO- RIES AND EXPERIMENTAL VALUES 340
3.7.4.2. ASPECTS OF A MANY-ORDER PARAMETER THEORY: STRUCTURAL RELAXATION
AND GROWTH ENHANCE- MENT 343 3.7.4.3. MAXIMUM GROWTH VELOCITIES AND
BREAKDOWN OF ORDER PARAMETER THEORIES 344 APPENDIX: ON THE JOINT
MOLECULAR THEORETICAL DESCRIP- TION OF THE CRYSTALLINE AND FLUID STATE
347 A..1. GENERAL CONCEPT AND UNIFIED PARTITION FUNC- TION 347 A.2.
CANONICAL ENSEMBLE: MEAN FIELD APPROACH OF THE CRYSTALLINE STATE AND
THEORY OF BAZAROV 354 13 A.3. GRAND CANONICAL ENSEMBLE: DERIVATION OF
UNIFIED CLOSURE RELATIONS 360 A.4. SOLUTION OF THE COUPLED
ORNSTEIN-ZERNIKE AND PERCUS-YEVIOK EQUATIONS FOR SYSTEMS WITH EXTREME
INHOMOGENEITIES 363 A.5. SOME PROPERTIES OF THE UNIFIED FREE ENERGY
FUNCTIONAL FROM THE GRAND CANONIOAL ENSEMBLE FORMALISM 369 REFERENCES
375 SUBJECT INDEX 388 BIST OF IMPORTANT SYMBOLS 392 14
|
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| author | Pfeiffer, Hubert Klupsch, Thomas Haubenreißer, Werner |
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| author_sort | Pfeiffer, Hubert |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 548 - Crystallography |
| dewey-raw | 548/.5 |
| dewey-search | 548/.5 |
| dewey-sort | 3548 15 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik |
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| id | DE-604.BV003552435 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:01:46Z |
| institution | BVB |
| isbn | 3055006844 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002258898 |
| oclc_num | 21487059 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-20 DE-29T DE-634 DE-83 |
| owner_facet | DE-384 DE-703 DE-20 DE-29T DE-634 DE-83 |
| physical | 400 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Akad.-Verl. |
| record_format | marc |
| series | Physical research |
| series2 | Physical research |
| spelling | Pfeiffer, Hubert Verfasser aut Microscopic theory of crystal growth by Hubert Pfeiffer ; Thomas Klupsch ; Werner Haubenreißer Berlin Akad.-Verl. 1989 400 S. txt rdacontent n rdamedia nc rdacarrier Physical research 11. Mathematisches Modell Crystal growth Crystal lattices Crystals Mathematical models Molecular crystals Phase transformations (Statistical physics) Modell (DE-588)4039798-1 gnd rswk-swf Kinetik (DE-588)4030665-3 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Kristallgitter (DE-588)4139853-1 gnd rswk-swf Kristallsymmetrie (DE-588)4136175-1 gnd rswk-swf Simulation (DE-588)4055072-2 gnd rswk-swf Grenzfläche (DE-588)4021991-4 gnd rswk-swf Kristallwachstum (DE-588)4123579-4 gnd rswk-swf Kristallwachstum (DE-588)4123579-4 s DE-604 Simulation (DE-588)4055072-2 s 1\p DE-604 Grenzfläche (DE-588)4021991-4 s 2\p DE-604 Monte-Carlo-Simulation (DE-588)4240945-7 s 3\p DE-604 Kristallsymmetrie (DE-588)4136175-1 s 4\p DE-604 Kinetik (DE-588)4030665-3 s 5\p DE-604 Modell (DE-588)4039798-1 s 6\p DE-604 Kristallgitter (DE-588)4139853-1 s 7\p DE-604 Klupsch, Thomas Verfasser aut Haubenreißer, Werner Verfasser aut Physical research 11. (DE-604)BV000651253 11. GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002258898&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pfeiffer, Hubert Klupsch, Thomas Haubenreißer, Werner Microscopic theory of crystal growth Physical research Mathematisches Modell Crystal growth Crystal lattices Crystals Mathematical models Molecular crystals Phase transformations (Statistical physics) Modell (DE-588)4039798-1 gnd Kinetik (DE-588)4030665-3 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Kristallgitter (DE-588)4139853-1 gnd Kristallsymmetrie (DE-588)4136175-1 gnd Simulation (DE-588)4055072-2 gnd Grenzfläche (DE-588)4021991-4 gnd Kristallwachstum (DE-588)4123579-4 gnd |
| subject_GND | (DE-588)4039798-1 (DE-588)4030665-3 (DE-588)4240945-7 (DE-588)4139853-1 (DE-588)4136175-1 (DE-588)4055072-2 (DE-588)4021991-4 (DE-588)4123579-4 |
| title | Microscopic theory of crystal growth |
| title_auth | Microscopic theory of crystal growth |
| title_exact_search | Microscopic theory of crystal growth |
| title_full | Microscopic theory of crystal growth by Hubert Pfeiffer ; Thomas Klupsch ; Werner Haubenreißer |
| title_fullStr | Microscopic theory of crystal growth by Hubert Pfeiffer ; Thomas Klupsch ; Werner Haubenreißer |
| title_full_unstemmed | Microscopic theory of crystal growth by Hubert Pfeiffer ; Thomas Klupsch ; Werner Haubenreißer |
| title_short | Microscopic theory of crystal growth |
| title_sort | microscopic theory of crystal growth |
| topic | Mathematisches Modell Crystal growth Crystal lattices Crystals Mathematical models Molecular crystals Phase transformations (Statistical physics) Modell (DE-588)4039798-1 gnd Kinetik (DE-588)4030665-3 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Kristallgitter (DE-588)4139853-1 gnd Kristallsymmetrie (DE-588)4136175-1 gnd Simulation (DE-588)4055072-2 gnd Grenzfläche (DE-588)4021991-4 gnd Kristallwachstum (DE-588)4123579-4 gnd |
| topic_facet | Mathematisches Modell Crystal growth Crystal lattices Crystals Mathematical models Molecular crystals Phase transformations (Statistical physics) Modell Kinetik Monte-Carlo-Simulation Kristallgitter Kristallsymmetrie Simulation Grenzfläche Kristallwachstum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002258898&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000651253 |
| work_keys_str_mv | AT pfeifferhubert microscopictheoryofcrystalgrowth AT klupschthomas microscopictheoryofcrystalgrowth AT haubenreißerwerner microscopictheoryofcrystalgrowth |