Solitons in Crystalline Processes: Irreversible Thermodynamics of Structural Phase Transitions and Superconductivity

Description

An introduction to the statistical thermodynamics of phase transitions in crystallized solids, polymers and liquid crystals. Written as an introductory treatise with respect to the soliton concept, from structural transitions where the crystal symmetry changes, to magnets and superconductors, describing the role of nonlinear excitations in detail. PRELIMS.pdf Notes on the second edition Preface to the first edition Acknowledgments Author biography Minoru Fujimoto INTRO.pdf 0 Introduction 0.1 The internal energy of equilibrium crystals 0.2 Microscopic order variables and their fluctuations 0.3 Collective order variables in propagation 0.4 Crystal surfaces and entropy production 0.5 Lattice symmetry and the internal energy in crystals 0.6 Timescales for sampling modulated structure and thermodynamic measurements 0.7 Statistical theories and the mean-field approximation 0.7.1 Probabilities and the domain structure 0.7.2 Short-range correlations and the mean-field approximation 0.7.3 The Bragg–Williams theory 0.7.4 Ferromagnetic order and the Weiss field 0.8 Remarks on notations in mesoscopic states Exercises References CH001.pdf Chapter 1 Phonons and lattice stability 1.1 The space symmetry group and the internal energy in crystals 1.2 Normal modes in a monatomic lattice 1.3 Quantized normal modes 1.4 Phonon field and momentum 1.5 Specific heat of monatomic crystals 1.6 Approximate phonon distributions 1.6.1 Einstein’s model 1.6.2 Debye’s model 1.7 Phonon correlations Exercises References CH002.pdf Chapter 2 Displacive order variables in collective mode and adiabatic Weiss’ potentials 2.1 One-dimensional ionic chain 2.2 Practical examples of displacive order variables 2.3 The Born–Oppenheimer approximation and adiabatic Weiss’ potentials 2.4 The Bloch theorem for collective order variables 2.4.1 Reciprocal lattice and renormalized coordinates 2.4.2 The Bloch theorem 2.4.3 The Brillouin zone Exercises References CH003.pdf Chapter 3 Pseudospin clusters and the Born–Huang principle: coherent order-variables as solitons in crystals 3.1 Pseudospins for binary displacements 3.1.1 Binary displacements 3.1.2 Ising’s model of a pseudospin at Tc 3.1.3 Pseudospin correlations below Tc 3.1.4 Boson statistics for modulated pseudospins 3.2 The Born–Huang principle and pseudospin clusters 3.3 Properties of pseudospin clusters 3.4 Examples of pseudospin clusters 3.4.1 Cubic-to-tetragonal transition in SrTiO3 3.4.2 Monoclinic crystals of TSCC 3.4.3 Remarks on pseudospin coupling constants Exercises References CH004.pdf Chapter 4 The mean-field theories and critical phase fluctuations at transition temperatures 4.1 Landau’s theory and Curie–Weiss’ law 4.1.1 Landau’s theory of binary transitions 4.1.2 Curie–Weiss law of susceptibilities 4.2 Fluctuations of pseudospin clusters in adiabatic potentials 4.2.1 Initial pinning of pseudospin fluctuations 4.2.2 Critical fluctuations 4.2.3 Energy transfer to the lattice at Tc 4.3 Observing critical phase anomalies 4.4 Intrinsic and extrinsic pinning 4.4.1 Point defects 4.4.2 Electric field pinning 4.4.3 Surface pinning Exercises References CH005.pdf Chapter 5 Scattering experiments on critical anomalies 5.1 X-ray diffraction 5.2 Diffuse diffraction from a modulated lattice 5.3 Neutron inelastic scatterings 5.4 Light scattering experiments 5.4.1 Brillouin scatterings 5.4.2 Raman spectroscopy of soft modes References CH006.pdf Chapter 6 Magnetic resonance studies on critical anomalies 6.1 Magnetic resonance 6.1.1 Nuclear magnetic resonance and relaxation 6.1.2 Paramagnetic resonance with impurity probes 6.1.3 The spin-Hamiltonian and a crystal field 6.1.4 Hyperfine interactions 6.2 Magnetic resonance in modulated crystals 6.3 Examples of transition anomalies 6.3.1 Mn2+ spectra in TSCC 6.3.2 Mn2+ spectra in BCCD 6.3.3 VO2+ spectra in BCCD 6.3.4 Comments on the temperature-dependence of critical spectra References CH007.pdf Chapter 7 Soft modes of lattice displacements 7.1 The Lyddane–Sachs–Teller relation in dielectric crystals 7.2 Soft modes in perovskite oxides 7.3 Lattice response to collective pseudopins 7.3.1 Energy dissipation of soft modes 7.3.2 Susceptibility analysis of soft modes 7.3.3 Central peaks 7.4 Temperature dependence of soft mode frequencies 7.5 Cochran’s model of a ferroelectric transition 7.6 Symmetry change at Tc Exercises References CH008.pdf Chapter 8 Nonlinear dynamics in finite crystals: displacive waves, complex adiabatic potentials and pseudopotentials 8.1 Internal pinning of collective pseudospins 8.2 Transverse components and the cnoidal potential 8.3 Finite crystals and the domain structure 8.4 Lifshitz’ incommensurability in mesoscopic phases 8.5 Klein–Gordon equation for the Weiss potential 8.6 Pseudopotentials in mesoscopic phases Exercises References CH009.pdf Chapter 9 Opposite Weiss fields for nonlinear order variables and entropy production: the Korteweg–deVries equation for transitions between conservative states 9.1 Dispersive equations in asymptotic approximation 9.2 The Korteweg–deVries equation 9.3 Thermodynamic solutions of the Korteweg–deVries equation 9.4 Isothermal transitions in the Eckart potential 9.5 Condensate pinning by the Eckart potentials 9.6 Elemental solitons as Boson particles 9.7 Riccati’s thermodynamic transitions Exercises References CH010.pdf Chapter 10 Soliton mobility in dynamical phase space: time–temperature conversion for thermal processes 10.1 Bargmann’s theorem 10.1.1 One-soliton solution 10.1.2 Two-soliton solution 10.2 Riccati’s theorem and the modified Korteweg–deVries equation 10.2.1 Riccati’s theorem 10.2.2 Modified Korteweg–deVries equation 10.3 Soliton mobility studied by computational analysis Exercises References CH011.pdf Chapter 11 Toda’s theorem of the soliton lattice 11.1 The Toda lattice 11.1.1 Theorem of dual chains for condensates 11.1.2 Discovering the exponential potential 11.1.3 The Toda lattice 11.1.4 Nonlinear waves in finite crystals 11.2 Developing nonlinearity with Toda’s correlation potentials 11.3 Infinite periodic lattice 11.4 Scattering and capture by singular soliton potentials 11.4.1 Reflection and transmission 11.4.2 Capture at singularities 11.5 The Gel’fand–Levitan–Marchenko theorem 11.6 Entropy production at soliton singularities 11.6.1 Energy transfer at singularities 11.6.2 Soliton potentials at singularities 11.7 The Toda lattice and the Korteweg–deVries equation 11.8 Topological strain mapping of mesoscopic Toda lattices Exercises References CH012.pdf Chapter 12 Phase solitons in adiabatic processes: topological correlations in the domain structure 12.1 The sine-Gordon equation 12.2 The Bäcklund transformation and domain boundaries 12.3 Computational studies of Bäcklund transformation 12.4 Trigonal structural transitions 12.4.1 The sine-Gordon equation 12.4.2 Observing adiabatic fluctuations 12.5 Toda’s theory of domain stability 12.6 Kac’s theory of nonlinear development and domain boundaries 12.7 Domain separation: thermal and quasi-adiabatic transitions 12.7.1 Domain separation in finite crystals 12.7.2 Entropy production in isothermal and quasi-adiabatic transitions Exercises References CH013.pdf Chapter 13 Phonons, solitons and electrons in modulated lattices 13.1 Phonon statistics in metallic states 13.2 Solitons in modulated metals 13.3 Conduction electrons in normal metals 13.3.1 The Pauli principle for electrons 13.3.2 The Coulomb interaction of electrons in metals 13.3.3 The Bloch theorem for single electrons in periodic structure 13.4 The multi-electron system 13.5 The Fermi–Dirac statistics Exercises References CH014.pdf Chapter 14 Soliton theory of superconducting transitions 14.1 The Fröhlich condensate and the Meissner effect 14.2 The Cooper pair and superconducting transition 14.3 Persistent supercurrents 14.4 Critical energy gap and the superconducting ground state 14.4.1 Energy gap between normal- and superconducting states 14.4.2 Anderson’s pseudospins for the Cooper pair Exercise References CH015.pdf Chapter 15 High-Tc superconductors 15.1 Superconducting transitions under isothermal conditions 15.1.1 Layer structure of YBaCuO superconductors: cuprates 15.1.2 The Cooper pair in high-Tc superconductors of cuprate layers 15.1.3 Layer structure in YBaCuO and other cuprate superconductors 15.1.4 Layer structure of high Tc superconductors 15.2 Protonic superconducting transitions under high pressure conditions 15.2.1 Metallic hydrogen sulfide 15.2.2 Order variables in hydrogen sulfide Exercises References CH016.pdf Chapter 16 Superconducting phases in metallic crystals 16.1 Meissner’s diamagnetism 16.1.1 The Meissner effect 16.1.2 Specific-heat anomalies of superconducting transitions 16.1.3 Thermodynamic analysis 16.2 Electromagnetic properties of superconductors 16.3 The Ginzburg–Landau equation 16.4 Field theories of superconducting transitions 16.4.1 Bardeen–Cooper–Schrieffer ground states 16.4.2 Superconducting states at finite temperatures Exercises References CH017.pdf Chapter 17 Magnetic crystals 17.1 Microscopic magnetic moments 17.2 Brillouin’s formula 17.3 Spin–spin exchange correlations 17.4 Collective propagation of Larmor’s precession 17.5 Magnetic Weiss field 17.6 Spin waves 17.7 Magnetic anisotropy 17.8 Antiferromagnetic and ferrimagnetic states 17.9 Fluctuations in ferromagnetic and antiferromagnetic states 17.9.1 Ferromagnetic resonance 17.9.2 Antiferromagnetic resonance References CH018.pdf Chapter 18 Crystalline polymers and liquid crystals 18.1 Transversal correlations in crystalline polymers 18.1.1 Polyvinylidene fluoride 18.1.2 Numerical evidence of transverse correlations in β-PVDF 18.2 Liquid crystals 18.2.1 Lattice-like structure of liquid crystals and the correlation energy between parallel layers 18.2.2 Onsager’s order variables 18.2.3 Optical observation of the mesoscopic structure 18.2.4 Static distortions in liquid crystals Exercises References CH019.pdf Chapter 19 Concluding remarks APP1.pdf Chapter A.1 Hyperbolic functions A.2 Elliptic integrals A.3 Jacobi’s elliptic function Reference books Online references