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The Resource Solitons in crystalline processes : statistical thermodynamics of structural phase transitions and mesoscopic disorder, Minoru Fujimoto

Solitons in crystalline processes : statistical thermodynamics of structural phase transitions and mesoscopic disorder, Minoru Fujimoto

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Author
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Summary
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
Language
eng
Work
Publication
Extent
1 PDF (various pagings)
Note
"Version: 20171101"--Title page verso
Contents
  • 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 approximation
  • part 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 correlations
  • 2. 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 variables
  • 3. 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 clusters
  • 4. 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 pinning
  • part 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 experiments
  • 6. Magnetic resonance studies on critical anomalies -- 6.1. Magnetic resonance -- 6.2. Magnetic resonance in modulated crystals -- 6.3. Examples of transition anomalies
  • 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 pseudospins -- 7.4. Temperature dependence of soft-mode frequencies -- 7.5. Cochran's model of a ferroelectric transition -- 7.6. Symmetry change at Tc
  • part 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 crystals
  • 9. 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 transitions
  • 10. 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 analysis
  • 11. 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 lattices
  • 12. Transversal correlations and the domain structure -- 12.1. The Klein-Gordon equation 2 for phase modulation -- 12.2. The Bäcklund transformation and domain boundaries -- 12.3. Computational studies of the Bäcklund 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 polymers
  • part 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 statistics
  • 14. Soliton theory of superconducting transitions -- 14.1. The Fröhlich condensate -- 14.2. The Cooper pair and superconducting transition -- 14.3. Persistent supercurrent -- 14.4. Critical energy gap and the superconducting ground state
  • 15. High-Tc superconductors -- 15.1. Superconducting transitions under isothermal conditions -- 15.2. Protonic superconducting transitions under high-pressure conditions -- 15.3. Summary: superconducting transitions
  • 16. 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 transitions
  • 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 ferromagnetic states -- 17.9. Fluctuations in ferromagnetic and antiferromagnetic states
  • Concluding remarks -- Appendices -- A. A note on liquid crystals -- B. A note on computational studies -- C. Hyperbolic and elliptic functions
Isbn
9780750315128
Instance
Label
Solitons in crystalline processes : statistical thermodynamics of structural phase transitions and mesoscopic disorder
Title
Solitons in crystalline processes
Title remainder
statistical thermodynamics of structural phase transitions and mesoscopic disorder
Statement of responsibility
Minoru Fujimoto
Title variation
Statistical thermodynamics of structural phase transitions and mesoscopic disorder
Creator
Contributor
Author
Publisher
Subject
Language
eng
Summary
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
Member of
Additional physical form
Also available in print.
Biographical or historical data
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.
Cataloging source
CaBNVSL
http://library.link/vocab/creatorName
Fujimoto, Minoru
Dewey number
548/.86
Illustrations
illustrations
Index
no index present
LC call number
QD937
LC item number
.F847 2017eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Institute of Physics (Great Britain)
Series statement
  • IOP release 4
  • IOP Expanding Physics,
http://library.link/vocab/subjectName
  • Crystals
  • Statistical thermodynamics
  • Phase transformations (Statistical physics)
  • Solitons
  • Physics
  • SCIENCE / Physics / Mathematical & Computational
  • Crystals
  • Phase transformations (Statistical physics)
  • Solitons
  • Statistical thermodynamics
Target audience
adult
Label
Solitons in crystalline processes : statistical thermodynamics of structural phase transitions and mesoscopic disorder, Minoru Fujimoto
Instantiates
Publication
Note
"Version: 20171101"--Title page verso
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 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 approximation
  • part 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 correlations
  • 2. 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 variables
  • 3. 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 clusters
  • 4. 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 pinning
  • part 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 experiments
  • 6. Magnetic resonance studies on critical anomalies -- 6.1. Magnetic resonance -- 6.2. Magnetic resonance in modulated crystals -- 6.3. Examples of transition anomalies
  • 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 pseudospins -- 7.4. Temperature dependence of soft-mode frequencies -- 7.5. Cochran's model of a ferroelectric transition -- 7.6. Symmetry change at Tc
  • part 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 crystals
  • 9. 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 transitions
  • 10. 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 analysis
  • 11. 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 lattices
  • 12. Transversal correlations and the domain structure -- 12.1. The Klein-Gordon equation 2 for phase modulation -- 12.2. The Bäcklund transformation and domain boundaries -- 12.3. Computational studies of the Bäcklund 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 polymers
  • part 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 statistics
  • 14. Soliton theory of superconducting transitions -- 14.1. The Fröhlich condensate -- 14.2. The Cooper pair and superconducting transition -- 14.3. Persistent supercurrent -- 14.4. Critical energy gap and the superconducting ground state
  • 15. High-Tc superconductors -- 15.1. Superconducting transitions under isothermal conditions -- 15.2. Protonic superconducting transitions under high-pressure conditions -- 15.3. Summary: superconducting transitions
  • 16. 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 transitions
  • 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 ferromagnetic states -- 17.9. Fluctuations in ferromagnetic and antiferromagnetic states
  • Concluding remarks -- Appendices -- A. A note on liquid crystals -- B. A note on computational studies -- C. Hyperbolic and elliptic functions
Control code
1015235221
Dimensions
unknown
Extent
1 PDF (various pagings)
File format
multiple file formats
Form of item
online
Isbn
9780750315128
Media category
electronic
Media MARC source
isbdmedia
Other control number
10.1088/978-0-7503-1514-2
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
9780750315142
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1015235221
System details
  • Mode of access: World Wide Web
  • System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader
Label
Solitons in crystalline processes : statistical thermodynamics of structural phase transitions and mesoscopic disorder, Minoru Fujimoto
Publication
Note
"Version: 20171101"--Title page verso
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 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 approximation
  • part 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 correlations
  • 2. 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 variables
  • 3. 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 clusters
  • 4. 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 pinning
  • part 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 experiments
  • 6. Magnetic resonance studies on critical anomalies -- 6.1. Magnetic resonance -- 6.2. Magnetic resonance in modulated crystals -- 6.3. Examples of transition anomalies
  • 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 pseudospins -- 7.4. Temperature dependence of soft-mode frequencies -- 7.5. Cochran's model of a ferroelectric transition -- 7.6. Symmetry change at Tc
  • part 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 crystals
  • 9. 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 transitions
  • 10. 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 analysis
  • 11. 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 lattices
  • 12. Transversal correlations and the domain structure -- 12.1. The Klein-Gordon equation 2 for phase modulation -- 12.2. The Bäcklund transformation and domain boundaries -- 12.3. Computational studies of the Bäcklund 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 polymers
  • part 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 statistics
  • 14. Soliton theory of superconducting transitions -- 14.1. The Fröhlich condensate -- 14.2. The Cooper pair and superconducting transition -- 14.3. Persistent supercurrent -- 14.4. Critical energy gap and the superconducting ground state
  • 15. High-Tc superconductors -- 15.1. Superconducting transitions under isothermal conditions -- 15.2. Protonic superconducting transitions under high-pressure conditions -- 15.3. Summary: superconducting transitions
  • 16. 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 transitions
  • 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 ferromagnetic states -- 17.9. Fluctuations in ferromagnetic and antiferromagnetic states
  • Concluding remarks -- Appendices -- A. A note on liquid crystals -- B. A note on computational studies -- C. Hyperbolic and elliptic functions
Control code
1015235221
Dimensions
unknown
Extent
1 PDF (various pagings)
File format
multiple file formats
Form of item
online
Isbn
9780750315128
Media category
electronic
Media MARC source
isbdmedia
Other control number
10.1088/978-0-7503-1514-2
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
9780750315142
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1015235221
System details
  • Mode of access: World Wide Web
  • System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader

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