Solitons in crystalline processes :statistical thermodynamics of structural phase transitions and mesoscopic disorder /

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Solitons in crystalline processes :statistical thermodynamics of structural phase transitions and mesoscopic disorder /

Fujimoto, Minoru, - Personal Name; Institute of Physics (Great Britain), - Personal Name;

"Version: 20171101"--Title page verso.Includes bibliographical references.Preface -- 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. Timescales for sampling modulated structure and thermodynamic measurements -- 0.6. Statistical theories and the mean-field approximationpart I. Binary transitions -- 1. Phonons and internal energies of stable lattices -- 1.1. Symmetry group 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 -- 1.7. Phonon correlations2. Displacive order variables in collective mode and adiabatic potentials -- 2.1. One-dimensional ionic chain -- 2.2. Displacive order variables -- 2.3. Born-Oppenheimer's asymptotic approximation and adiabatic potentials -- 2.4. The Bloch theorem for collective order variables3. Pseudospin clusters and the Born-Huang principle -- 3.1. Pseudospins for binary displacements -- 3.2. The Born-Huang principle and pseudospin clusters -- 3.3. Properties of pseudospin clusters -- 3.4. Examples of pseudospin clusters4. Critical phase fluctuations of pseudospin modes -- 4.1. Landau's theory and Curie-Weiss' law -- 4.2. Fluctuations of pseudospin clusters in adiabatic potentials -- 4.3. Observing critical anomalies -- 4.4. Extrinsic pinningpart II. Experimental studies on critical anomalies and soft modes -- 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 experiments6. Magnetic resonance studies on critical anomalies -- 6.1. Magnetic resonance -- 6.2. Magnetic resonance in modulated crystals -- 6.3. Examples of transition anomalies7. 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 pseudospins -- 7.4. Temperature dependence of soft-mode frequencies -- 7.5. Cochran's model of a ferroelectric transition -- 7.6. Symmetry change at Tcpart III. Soliton theory of lattice dynamics -- 8. Displacive waves and complex adiabatic potentials in finite crystals -- 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 -- 8.5. The Klein-Gordon equation 1 -- 8.6. Pseudopotentials in crystals9. The Weiss field of soliton potentials for developing nonlinearity -- 9.1. Dispersive equations in asymptotic approximation -- 9.2. The Korteweg-de Vries equation -- 9.3. Solutions of the Korteweg-de Vries equation -- 9.4. Thermodynamic transitions and the Eckart potential -- 9.5. Condensate pinning by the Eckart potentials -- 9.6. Elemental solitons at singular transitions -- 9.7. Riccati's thermodynamic transitions10. Soliton mobility in time-temperature conversion -- 10.1. Bargmann's theorem of amplitude modulation -- 10.2. Riccati's theorem and the modified Korteweg-de Vries equation -- 10.3. Soliton mobility studied by computational analysis11. Toda's theorem of soliton lattice -- 11.1. The Toda lattice -- 11.2. Developing nonlinearity with Toda's correlation potentials -- 11.3. Infinite periodic lattice -- 11.4. Scattering and capture by singular adiabatic potentials -- 11.5. The Gelfand-Levitan-Marchenko theorem -- 11.6. Entropy production at singularities -- 11.7. The Toda lattice and the Korteweg-de Vries equation -- 11.8. Topological strain mapping of mesoscopic Toda lattices12. Transversal correlations and the domain structure -- 12.1. The Klein-Gordon equation 2 for phase modulation -- 12.2. The B?acklund transformation and domain boundaries -- 12.3. Computational studies of the B?acklund transformation -- 12.4. Trigonal structural transitions -- 12.5. Toda's theory of domain stability -- 12.6. Kac's theory of nonlinear development and boundary instability -- 12.7. Domain separation; thermal and quasi-adiabatic transitions -- 12.8. Transversal correlations in crystalline polymerspart IV. Superconducting and magnetic systems -- 13. Phonons, solitons and electrons in finite metallic phases -- 13.1. Phonon statistics in metallic states -- 13.2. Solitons in modulated metals -- 13.3. Conduction electrons in normal metallic states -- 13.4. The multi-electron system -- 13.5. The Fermi-Dirac statistics14. Soliton theory of superconducting transitions -- 14.1. The Fr?ohlich condensate -- 14.2. The Cooper pair and superconducting transition -- 14.3. Persistent supercurrent -- 14.4. Critical energy gap and the superconducting ground state15. High-Tc superconductors -- 15.1. Superconducting transitions under isothermal conditions -- 15.2. Protonic superconducting transitions under high-pressure conditions -- 15.3. Summary: superconducting transitions16. Superconducting states in metallic crystals -- 16.1. Meissner's diamagnetism -- 16.2. Electromagnetic properties of superconductors -- 16.3. The Ginzburg-Landau equation -- 16.4. Field theories of superconducting transitions17. 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 ferromagnetic states -- 17.9. Fluctuations in ferromagnetic and antiferromagnetic statesConcluding remarks -- Appendices -- A. A note on liquid crystals -- B. A note on computational studies -- C. Hyperbolic and elliptic functions.Solitons in Crystalline Processes is an introduction to the statistical thermodynamics of phase transitions in crystallized solids. This book is 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.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Minoru Fujimoto is a retired professor of University of Guelph, Ontario, Canada. Engaged in experimental work on magnetic resonance on structural phase transitions, he has published a number of books including Introduction to the Mathematical Physics of Nonlinear Waves in 2014 with IOP Publishing.Title from PDF title page (viewed on December 11, 2017).

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Series Title: -
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Publisher: : .,
Collation: 1 online resource (various pagings) :illustrations.
Language: English
ISBN/ISSN: 9780750315142
Classification: 548/.86
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Subject(s): SCIENCE / Physics / Mathematical & Computational.
Physics.
Crystals
Statistical thermodynamics.
Phase transformations (Statistical physics)
Solitons.
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Statement of Responsibility: Minoru Fujimoto.

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