
Solitons in Crystalline Processes (2nd Edition) : Irreversible Thermodynamics of Structural Phase Transitions and Superconductivity.
Title:
Solitons in Crystalline Processes (2nd Edition) : Irreversible Thermodynamics of Structural Phase Transitions and Superconductivity.
Author:
Fujimoto, Minoru.
ISBN:
9780750325721
Personal Author:
Edition:
2nd ed.
Physical Description:
1 online resource (371 pages)
Series:
IOP Ebooks Series
Contents:
Intro -- Notes on the second edition -- Preface to the first edition -- Acknowledgments -- Author biography -- Minoru Fujimoto -- 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 -- 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 -- 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 -- 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 -- 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 -- 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 -- 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.
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 -- 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 -- 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 -- 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 -- 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 -- 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 -- 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 -- 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 -- 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 -- 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 -- 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.
Abstract:
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, the book examines structural transitions where the crystal symmetry changes, magnets and superconductors, and describes the role of nonlinear excitations in detail.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Genre:
Electronic Access:
Click to View