Verfügbarkeit: Equilibrium statistical physics

Equilibrium statistical physics: phases of matter and phase transitions ; with ... 8 tables

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Hauptverfasser:	Baus, Marc (VerfasserIn), Tejero, Carlos F. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	[Berlin] Springer 2008
Schlagworte:	Phase rule and equilibrium Phase transformations (Statistical physics) Statistische Thermodynamik Lehrbuch
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XIV, 364 S. Ill., graph. Darst.
ISBN:	9783540746317 9783540746324

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adam_text	Contents Part I Basics 1 Mechanics ..................................................... 3 1.1 Classical Mechanics ........................................ 3 1.2 Hamilton s Equations ....................................... 4 1.3 External Parameters ........................................ 5 1.4 Dynamical Functions ....................................... 7 1.5 Quantum Mechanics ........................................ 9 1.6 Self-adjoint Operators ....................................... 10 1.7 Eigenvalue Equation ........................................ 11 1.8 Sehrödinger s Equation ...................................... 13 1.8.1 Free Particle ........................................ 14 1.8.2 Harmonic Oscillator .................................. 16 1.8.3 Particle in a Magnetic Field ............................ 16 1.9 System of Identical Particles ................................. 18 References ..................................................... 20 2 Thermodynamics .............................................. 21 2.1 Fundamental Equation ...................................... 21 2.2 Intensive Variables ......................................... 23 2.3 Law of Entropy Increase ..................................... 25 2.4 Thermodynamic Potentials ................................... 26 2.5 Equilibrium Conditions ..................................... 28 2.6 Stability Conditions ........................................ 29 2.7 Coexistence Conditions ..................................... 32 2.8 Phase Diagrams ............................................ 33 2.8.1 Gibbs Free Energy ................................... 33 2.8.2 Helmholtz Free Energy ............................... 37 2.8.3 van der Waals Loop .................................. 39 2.8.4 An Example of a Phase Diagram ....................... 41 References ..................................................... 43 x Contents 3 Statistical Physics .............................................. 45 3.1 Dynamical Functions and Fields .............................. 46 3.2 Liouville s Equation ........................................ 48 3.3 Systems in Equilibrium ..................................... 49 3.4 Density Operator ........................................... 51 3.5 Ergodicity ................................................. 53 3.6 Thermodynamic Limit ...................................... 55 3.7 Symmetry Breaking ........................................ 61 References ..................................................... 63 Partii Ideal Systems 4 Microcanonical Ensemble ....................................... 67 4.1 Classical Microcanonical Ensemble ........................... 67 4.2 Classical Ideal Gas ......................................... 69 4.3 Entropy and the Gibbs Paradox ............................... 71 4.4 Temperature and Thermal Equilibrium ......................... 75 4.5 Ideal Systems .............................................. 77 4.6 Equipartition Theorem ...................................... 78 4.7 Equation of State ........................................... 79 4.8 Entropy and ¡ireversibility ................................... 81 4.9 Quantum Microcanonical Ensemble ........................... 83 4.10 Absolute Negative Temperatures .............................. 86 References ..................................................... 88 5 Canonical Ensemble ............................................ 89 5.1 Classical Canonical Ensemble ................................ 89 5.2 Mean Values and Fluctuations ................................ 91 5.3 Helmholtz Free Energy ...................................... 93 5.4 Classical Ideal Gas ......................................... 94 5.5 Ideal Gas in an External Potential ............................. 95 5.6 Equipartition Theorem ...................................... 97 5.7 Classical Theory of Radiation ................................ 99 5.8 Classical Theory of Solids ................................... 101 5.9 Quantum Canonical Ensemble ................................ 103 5.10 Ideal Quantum Systems ..................................... 105 5.11 Maxwell-Boltzmann Statistics ............................... 106 5.12 Maxwell-Boltzmann s Ideal Gas .............................. 108 5.13 Brillouin s Paramagnetism ...................................109 5.14 Photon Gas ................................................ Ill 5.15 Phonon Gas ...............................................114 References .....................................................119 Contents xi 6 Grand Canonical Ensemble.....................................121 6.1 Classical Grand Canonical Ensemble..........................121 6.2 Mean Values and Fluctuations ................................125 6.3 Grand Potential ............................................127 6.4 Classical Ideal Gas .........................................128 6.5 Classical Ideal Gas in an External Potential .....................129 6.6 Two-Particle Distribution Function ............................131 6.7 Density Fluctuations ........................................133 6.8 Correlations at the Critical Point ..............................135 6.9 Quantum Grand Canonical Ensemble ..........................138 6.10 Bose-Einstein and Fermi-Dirac Statistics ......................139 6.11 Virial Expansions in the Classical Limit ........................142 6.12 Boson Gas: Bose-Einstein Condensation .......................144 6.12.1 Specific Heat ........................................147 6.12.2 Equation of State ....................................150 6.13 Fermion Gas ...............................................152 References .....................................................158 Part III Non-ideal Systems 7 Classical Systems with Interactions ..............................163 7.1 Thermodynamic Integration ..................................163 7.2 Thermodynamic Perturbation Theory ..........................165 7.3 Virial Expansions ..........................................167 7.4 Direct Correlation Function ..................................171 7.5 Density Functional Theory ...................................173 7.6 Mean Field Theory .........................................175 7.7 Numerical Simulations ......................................177 7.7.1 Molecular Dynamics .................................178 7.7.2 Monte Carlo Method .................................179 References .....................................................183 8 Phases of Matter ..............................................185 8.1 Crystals ...................................................186 8.1.1 Crystal Structure .....................................186 8.1.2 Cell Theory .........................................188 8.1.3 van der Waals Theory .................................191 8.1.4 Variational Theory ...................................192 8.2 Fluids ....................................................196 8.2.1 Dense Fluids ........................................196 8.2.2 Fluid Structure ......................................199 8.2.3 Fluids and Glasses ...................................203 8.2.4 Vapor and Liquid ....................................206 Contents 8.3 Mixtures ..................................................209 8.3.1 Binary Mixtures .....................................209 8.3.2 Colloidal Suspensions ................................211 8.3.3 Asakura-Oosawa Potential ............................213 8.3.4 DLVO Potential .....................................215 8.4 Liquid Crystals ............................................216 8.4.1 Maier-Saupe Theory .................................217 8.4.2 Onsager Theory .....................................220 8.5 Polymers .................................................223 8.5.1 Radius of Gyration ...................................224 8.5.2 Flory-Huggins Theory ................................226 References .....................................................231 Phase Transitions ..............................................233 9.1 Structural Transitions .......................................233 9.1.1 Fluid-Solid Transition ................................234 9.1.2 Isotropic-Nematic Transition ..........................237 9.2 Isostructural Transitions .....................................239 9.2.1 Liquid-Vapor Transition ..............................239 9.2.2 Solid-Solid Transition ................................241 9.3 Symmetry Breaking and Order Parameters .....................242 9.4 Landau Theory .............................................245 9.4.1 Continuous Transitions ...............................247 9.4.2 Discontinuous Transitions .............................247 9.5 Bifurcation Theory .........................................248 9.6 Critical Points .............................................251 9.6.1 Isolated Critical Points ................................251 9.6.2 Liquid-Vapor Critical Point ...........................253 9.6.3 Solid-Solid Critical Point .............................254 9.6.4 Consolute Critical Point ..............................256 9.6.5 Critical Lines .......................................259 9.7 Summary .................................................261 9.8 Triple Points ...............................................262 9.8.1 Ordinary Triple Point .................................262 9.8.2 Critical Endpoint....................................263 9.8.3 Bicritical Point ......................................264 9.8.4 Tricritical Point ......................................265 References .....................................................265 Contents xiii Part IV More Advanced Topics 10 Critical Phenomena ............................................269 10.1 Classical Theory ...........................................269 10.2 Critical Exponents ..........................................270 10.3 Scaling Hypothesis .........................................273 10.4 Correlation Length and Universality ...........................275 10.5 Renormalization Group (RG) Idea ............................278 10.6 Critical Exponents and the Flory Exponent .....................278 10.7 RG-Calculation of the Flory Exponent .........................280 10.7.1 RG-Transformations .................................280 10.7.2 Fixed-Points of the RG ...............................281 10.7.3 Non-classical Flory Exponent ..........................282 10.7.4 Critical Dimension ...................................283 10.7.5 ε -Expansion........................................ 283 10.7.6 Differential RG-Equations .............................284 10.7.7 Stability of the Fixed Points ...........................286 10.7.8 Numerical Value of the Flory Exponent ..................287 10.8 Numerical Values of the Critical Exponents .....................288 References .....................................................289 11 Interfaces .....................................................291 11.1 Non-uniform Systems .......................................292 11.2 Density Profile .............................................294 11.3 Pressure Profile ............................................298 11.4 Surface Tension ............................................303 References .....................................................306 12 Topological Defects .............................................307 12.1 Frustration ................................................308 12.2 Elastic Deformations ........................................309 12.3 Schlieren Texture ...........................................310 References .....................................................313 13 Phase Transformation Kinetics ..................................315 13.1 Homogeneous Nucleation ...................................315 13.1.1 Becker-Döring Theory ...............................316 13.1.2 Zeldovich-Frenkel Theory ............................322 13.1.3 Avrami Theory ......................................327 13.2 Heterogeneous Nucleation ...................................328 13.3 Spinodal Decomposition ....................................330 13.4 Glass Transition ............................................332 References .....................................................334 xiv Contents Part V Appendices A Legendre Transformations ......................................337 A. 1 Case of One Variable .......................................337 A.2 Case of и Variables .........................................340 A.2. 1 Some Examples .....................................341 Reference ......................................................342 В Random Variables .............................................343 B.I One-Dimensional Random Variable ...........................343 B. 1.1 Some Examples .....................................344 B.2 Approximation Methods .....................................345 B.3 н -Dimensional Random Variable ..............................346 Reference ......................................................349 С Functional and Functional Derivative ............................351 C. 1 Definition of a Functional ....................................351 C.2 The Functional Derivative ...................................351 C.3 Some Examples ............................................352 References .....................................................354 D A Quasicrystalline Lattice .......................................355 D. 1 Forbidden Symmetries of Periodic 2D Lattices ..................355 D.2 A Quasiperiodic 2D Lattice ..................................356 References .....................................................358 Index .............................................................359
adam_txt	Contents Part I Basics 1 Mechanics . 3 1.1 Classical Mechanics . 3 1.2 Hamilton's Equations . 4 1.3 External Parameters . 5 1.4 Dynamical Functions . 7 1.5 Quantum Mechanics . 9 1.6 Self-adjoint Operators . 10 1.7 Eigenvalue Equation . 11 1.8 Sehrödinger's Equation . 13 1.8.1 Free Particle . 14 1.8.2 Harmonic Oscillator . 16 1.8.3 Particle in a Magnetic Field . 16 1.9 System of Identical Particles . 18 References . 20 2 Thermodynamics . 21 2.1 Fundamental Equation . 21 2.2 Intensive Variables . 23 2.3 Law of Entropy Increase . 25 2.4 Thermodynamic Potentials . 26 2.5 Equilibrium Conditions . 28 2.6 Stability Conditions . 29 2.7 Coexistence Conditions . 32 2.8 Phase Diagrams . 33 2.8.1 Gibbs Free Energy . 33 2.8.2 Helmholtz Free Energy . 37 2.8.3 van der Waals Loop . 39 2.8.4 An Example of a Phase Diagram . 41 References . 43 x Contents 3 Statistical Physics . 45 3.1 Dynamical Functions and Fields . 46 3.2 Liouville's Equation . 48 3.3 Systems in Equilibrium . 49 3.4 Density Operator . 51 3.5 Ergodicity . 53 3.6 Thermodynamic Limit . 55 3.7 Symmetry Breaking . 61 References . 63 Partii Ideal Systems 4 Microcanonical Ensemble . 67 4.1 Classical Microcanonical Ensemble . 67 4.2 Classical Ideal Gas . 69 4.3 Entropy and the Gibbs Paradox . 71 4.4 Temperature and Thermal Equilibrium . 75 4.5 Ideal Systems . 77 4.6 Equipartition Theorem . 78 4.7 Equation of State . 79 4.8 Entropy and ¡ireversibility . 81 4.9 Quantum Microcanonical Ensemble . 83 4.10 Absolute Negative Temperatures . 86 References . 88 5 Canonical Ensemble . 89 5.1 Classical Canonical Ensemble . 89 5.2 Mean Values and Fluctuations . 91 5.3 Helmholtz Free Energy . 93 5.4 Classical Ideal Gas . 94 5.5 Ideal Gas in an External Potential . 95 5.6 Equipartition Theorem . 97 5.7 Classical Theory of Radiation . 99 5.8 Classical Theory of Solids . 101 5.9 Quantum Canonical Ensemble . 103 5.10 Ideal Quantum Systems . 105 5.11 Maxwell-Boltzmann Statistics . 106 5.12 Maxwell-Boltzmann's Ideal Gas . 108 5.13 Brillouin's Paramagnetism .109 5.14 Photon Gas . Ill 5.15 Phonon Gas .114 References .119 Contents xi 6 Grand Canonical Ensemble.121 6.1 Classical Grand Canonical Ensemble.121 6.2 Mean Values and Fluctuations .125 6.3 Grand Potential .127 6.4 Classical Ideal Gas .128 6.5 Classical Ideal Gas in an External Potential .129 6.6 Two-Particle Distribution Function .131 6.7 Density Fluctuations .133 6.8 Correlations at the Critical Point .135 6.9 Quantum Grand Canonical Ensemble .138 6.10 Bose-Einstein and Fermi-Dirac Statistics .139 6.11 Virial Expansions in the Classical Limit .142 6.12 Boson Gas: Bose-Einstein Condensation .144 6.12.1 Specific Heat .147 6.12.2 Equation of State .150 6.13 Fermion Gas .152 References .158 Part III Non-ideal Systems 7 Classical Systems with Interactions .163 7.1 Thermodynamic Integration .163 7.2 Thermodynamic Perturbation Theory .165 7.3 Virial Expansions .167 7.4 Direct Correlation Function .171 7.5 Density Functional Theory .173 7.6 Mean Field Theory .175 7.7 Numerical Simulations .177 7.7.1 Molecular Dynamics .178 7.7.2 Monte Carlo Method .179 References .183 8 Phases of Matter .185 8.1 Crystals .186 8.1.1 Crystal Structure .186 8.1.2 Cell Theory .188 8.1.3 van der Waals Theory .191 8.1.4 Variational Theory .192 8.2 Fluids .196 8.2.1 Dense Fluids .196 8.2.2 Fluid Structure .199 8.2.3 Fluids and Glasses .203 8.2.4 Vapor and Liquid .206 Contents 8.3 Mixtures .209 8.3.1 Binary Mixtures .209 8.3.2 Colloidal Suspensions .211 8.3.3 Asakura-Oosawa Potential .213 8.3.4 DLVO Potential .215 8.4 Liquid Crystals .216 8.4.1 Maier-Saupe Theory .217 8.4.2 Onsager Theory .220 8.5 Polymers .223 8.5.1 Radius of Gyration .224 8.5.2 Flory-Huggins Theory .226 References .231 Phase Transitions .233 9.1 Structural Transitions .233 9.1.1 Fluid-Solid Transition .234 9.1.2 Isotropic-Nematic Transition .237 9.2 Isostructural Transitions .239 9.2.1 Liquid-Vapor Transition .239 9.2.2 Solid-Solid Transition .241 9.3 Symmetry Breaking and Order Parameters .242 9.4 Landau Theory .245 9.4.1 Continuous Transitions .247 9.4.2 Discontinuous Transitions .247 9.5 Bifurcation Theory .248 9.6 Critical Points .251 9.6.1 Isolated Critical Points .251 9.6.2 Liquid-Vapor Critical Point .253 9.6.3 Solid-Solid Critical Point .254 9.6.4 Consolute Critical Point .256 9.6.5 Critical Lines .259 9.7 Summary .261 9.8 Triple Points .262 9.8.1 Ordinary Triple Point .262 9.8.2 Critical Endpoint.263 9.8.3 Bicritical Point .264 9.8.4 Tricritical Point .265 References .265 Contents xiii Part IV More Advanced Topics 10 Critical Phenomena .269 10.1 Classical Theory .269 10.2 Critical Exponents .270 10.3 Scaling Hypothesis .273 10.4 Correlation Length and Universality .275 10.5 Renormalization Group (RG) Idea .278 10.6 Critical Exponents and the Flory Exponent .278 10.7 RG-Calculation of the Flory Exponent .280 10.7.1 RG-Transformations .280 10.7.2 Fixed-Points of the RG .281 10.7.3 Non-classical Flory Exponent .282 10.7.4 Critical Dimension .283 10.7.5 ε -Expansion. 283 10.7.6 Differential RG-Equations .284 10.7.7 Stability of the Fixed Points .286 10.7.8 Numerical Value of the Flory Exponent .287 10.8 Numerical Values of the Critical Exponents .288 References .289 11 Interfaces .291 11.1 Non-uniform Systems .292 11.2 Density Profile .294 11.3 Pressure Profile .298 11.4 Surface Tension .303 References .306 12 Topological Defects .307 12.1 Frustration .308 12.2 Elastic Deformations .309 12.3 Schlieren Texture .310 References .313 13 Phase Transformation Kinetics .315 13.1 Homogeneous Nucleation .315 13.1.1 Becker-Döring Theory .316 13.1.2 Zeldovich-Frenkel Theory .322 13.1.3 Avrami Theory .327 13.2 Heterogeneous Nucleation .328 13.3 Spinodal Decomposition .330 13.4 Glass Transition .332 References .334 xiv Contents Part V Appendices A Legendre Transformations .337 A. 1 Case of One Variable .337 A.2 Case of и Variables .340 A.2. 1 Some Examples .341 Reference .342 В Random Variables .343 B.I One-Dimensional Random Variable .343 B. 1.1 Some Examples .344 B.2 Approximation Methods .345 B.3 н -Dimensional Random Variable .346 Reference .349 С Functional and Functional Derivative .351 C. 1 Definition of a Functional .351 C.2 The Functional Derivative .351 C.3 Some Examples .352 References .354 D A Quasicrystalline Lattice .355 D. 1 Forbidden Symmetries of Periodic 2D Lattices .355 D.2 A Quasiperiodic 2D Lattice .356 References .358 Index .359
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spelling	Baus, Marc Verfasser (DE-588)1270656198 aut Equilibrium statistical physics phases of matter and phase transitions ; with ... 8 tables Marc Baus ; Carlos F. Tejero [Berlin] Springer 2008 XIV, 364 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Phase rule and equilibrium Phase transformations (Statistical physics) Statistische Thermodynamik (DE-588)4126251-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistische Thermodynamik (DE-588)4126251-7 s DE-604 Tejero, Carlos F. Verfasser (DE-588)1270657364 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016068779&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Baus, Marc Tejero, Carlos F. Equilibrium statistical physics phases of matter and phase transitions ; with ... 8 tables Phase rule and equilibrium Phase transformations (Statistical physics) Statistische Thermodynamik (DE-588)4126251-7 gnd
subject_GND	(DE-588)4126251-7 (DE-588)4123623-3
title	Equilibrium statistical physics phases of matter and phase transitions ; with ... 8 tables
title_auth	Equilibrium statistical physics phases of matter and phase transitions ; with ... 8 tables
title_exact_search	Equilibrium statistical physics phases of matter and phase transitions ; with ... 8 tables
title_exact_search_txtP	Equilibrium statistical physics phases of matter and phase transitions ; with ... 8 tables
title_full	Equilibrium statistical physics phases of matter and phase transitions ; with ... 8 tables Marc Baus ; Carlos F. Tejero
title_fullStr	Equilibrium statistical physics phases of matter and phase transitions ; with ... 8 tables Marc Baus ; Carlos F. Tejero
title_full_unstemmed	Equilibrium statistical physics phases of matter and phase transitions ; with ... 8 tables Marc Baus ; Carlos F. Tejero
title_short	Equilibrium statistical physics
title_sort	equilibrium statistical physics phases of matter and phase transitions with 8 tables
title_sub	phases of matter and phase transitions ; with ... 8 tables
topic	Phase rule and equilibrium Phase transformations (Statistical physics) Statistische Thermodynamik (DE-588)4126251-7 gnd
topic_facet	Phase rule and equilibrium Phase transformations (Statistical physics) Statistische Thermodynamik Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016068779&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT bausmarc equilibriumstatisticalphysicsphasesofmatterandphasetransitionswith8tables AT tejerocarlosf equilibriumstatisticalphysicsphasesofmatterandphasetransitionswith8tables

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