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Table of 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.
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.