Phase Transitions and Crystal Symmetry
|
|
|
- Emily Joseph
- 5 years ago
- Views:
Transcription
1 Phase Transitions and Crystal Symmetry by Yu. A. IZYUMOV and V. N. SYROMYATNIKOV Institute of Metal Physics, Ural Division of the U.S.S.R. Academy of Sciences, Sverdlovsk, U.S.S.R. KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
2 Contents Preface Preface to the English Edition Notation xiii xvii xix Chapter 1. Introduction to Phenomenological Phase Transition Theory 1 1. Fundamentals of Landau's Thermodynamic Theory 1 Elementary thermodynamic analysis (1). Spontaneous symmetry breaking at a continuous phase transition (7). The Landau condition for a second-order phase transition (9). Further development of Landau's theory (10). 2. Prerequisites on Space-group Representations 12 Space-group irreducible representations (12). Irreducible representations and their decomposition (15). References 17 Chapter 2. Physical Realization of the Order Parameters at a Microscopic Level of Description Tensor Representation of the Space Group on a Basis of Localized Atomic Functions 19 Constructing crystal space group reducible representations (20). The stabilizer method (24). Constructing basis functions for star arms (27). 4. Permutational Representation and its Basis 28 A summary of formulas (28). The OP for ordering in AB type alloys (29). The OP for ordering in Nb-H and Ta-H hydrides (30).
3 VI CONTENTS 5. Vector Representation and its Basis 36 A summary of formulas (36). The OP at a structural phase transition in A-15 compounds (38). The OP at a structural phase transition in C-15 compounds (43). 6. Pseudovector Representation and its Basis 45 A description of the magnetically ordered state (45). The OP at a magnetic phase transition in a garnet (47). References 51 Chapter 3. Symmetry Change at Phase Transitions Change in Translational Symmetry 52 The Brillouin zone and the symmetric points in it (52). Arm mixing and the transition channel (56). Magnetic lattices (72). 8. The Total Symmetry Change 74 Principles for finding the symmetry group of a new phase (74). An example of a group-theoretic method of searching for dissymmetric phases (77). 9. Domains 82 Domains as a consequence of the Curie principle (82). A symmetry classification of domains (83). Arm, orientational and antiphase domains (85). Examples of an analysis of the domain structure (87). 10. The Paraphase 91 The initial phase and the paraphase (91). Major criteria for paraphase search (93). An example of choosing the paraphase (94). References 98 Chapter 4. Analysis of the Thermodynamic Potential Invariant Expressions of the Thermodynamic Potential 100 A straightforward (direct) method of constructing polynomial invariants (100). Constructing the Ф for the structural phase transition in C-15 compounds (101). Constructing the Ф for the structural phase transition in A-15 compounds (102). 12. Integral Rational Basis of Invariants 104 General remarks (104). The IRBI construction algorithm (105). Solvability of the group and the minimal IRBI (110). 13. Examples of the Construction of an IRBI 112 Constructing the IRBI for the structural transition in C-15 compounds (112). Construction of the IRBI for the structural transition
4 CONTENTS vii in A-15 compounds (114). Constructing the IRBI for the structural transition in MnAs (117). 14. Irreducible Representation Images and Thermodynamic Potential Types 118 General information on the / groups (118). Two- and three-component order parameters (119). A multicomponent order parameter (121). I groups and rotation groups in multidimensional space (121). Universal classes (123). References 130 Chapter 5. Phase Diagrams in the Space of Thermodynamic Potential Parameters Theoretical Fundamentals of the Phase Diagram Construction Method 131 Major physical principles (131). Requisite theorems from the algebra of polynomials (134). 16. The One-Component Order Parameter 137 The form of the thermodynamic potential (137). The if model (137). The rf model (139). Succession of solutions to equations of state (146). 17. The Two-Component Order Parameter 148 The if model (148). The rf model (152). Cubic invariants in the rf model (156). Cubic invariants in the if model (159). 18. The Three-Component Order Parameter 161 The phases and the stability conditions (161). The phase diagram in the»7 4 model (164). 19. The Role of the IRBI in the Construction of Phase Diagrams The two-component order parameter (166). The three-component order parameter (167). 20. Coupling Order Parameters 168 The interplay of two one-component order parameters (168). Phase transitions in MnAs (170). Phase transitions in KMnFe (173). Orientation transitions (178). References 186
5 viii CONTENTS Chapter 6. Macroscopic Order Parameters Transformation Properties of the Order Parameters 188 Physical realization of the macroparameters (188). Construction of basis functions (191). Constructing the thermodynamic potential (192). 22. Interplay of Micro- and Macroparameters 197 Constructing the thermodynamic potential (197). Improper transitions (198). Examples of structural transitions in perovskite-type crystals (199). 23. Ferroics 202 Classification of dissymmetric phases according to macroproperties (202). Ferroelectrics (204). Ferroelastics (205). Ferrobielectrics and ferrobimagnetics (205). Higher-order ferroics (206). 24. Non-ferroics 211 Crystal-class-preserving phase transitions (211). Examples of nonferroics (212). References 214 Chapter 7. Phase Transitions in an External Field Phase Diagrams 215 Constructing a potential for a system in an external field (215). Phase diagram for the rf model (216). Phase diagram for the rf model (217). Singular points on the phase diagram (222). Multicomponent order parameter (222). Splitting of a phase transition described by a microparameter in an external field (226). 26. Features Peculiar to the Temperature Behavior of Susceptibility in the Vicinity of the Second-Order Phase Transition 227 Classification of the singularities by the Aizu indices (227). Catastrophe indices (231). 27. Calculation of Susceptibilities for Second-Order Phase Transitions 233 Proper phase transitions (233). Improper phase transitions (234). Pseudoproper phase transitions (238). 28. Singularities of the Susceptibility in the Vicinity of the First-Order Phase Transition 239 Classification of the first-order transitions (239). Classifying the singularities of susceptibilities (240). Calculating the susceptibilities (243).
6 CONTENTS ix 29. Domains in an External Field 244 A thermodynamic description of the domains (244). Effect of an external field on domains (247). References 249 Chapter 8. Martensite Transformations Reconstructive Structural Transitions 250 Transitions without group-subgroup relation (250). Geometric relation of direct lattices (253). The b.c.c.-f.c.c. transition (255). The b.c.c.-h.c.p. transition (256). The f.c.c.-h.c.p. transition (257). Orientation relations (258). Interrelationship of reciprocal lattices (261). 31. Thermodynamic Analysis of the Homogeneous State 266 Describing the martensitic transition in terms of deformation (266). Thermodynamic potential and phase diagram (268). Behavior in an external field (270). Shape memory effect (274). 32. Inhomogeneous States in the Vicinity of the Phase Transition Thermodynamic potential with gradient terms (275). Equations of motion (277). Tetragonal-strain phase transition (278). Phase transition with shear strain (282). Square lattice (288). 33. The Omega Phase 292 Interrelationship between the lattices at the b.c.c.-w-phase transformation (292). Thermodynamic potential (295). Inhomogeneous states (296). References 298 Chapter 9. Incommensurate Periodicity Phases General Approach to the Problem 301 Commensurate and incommensurate phases (301). Expansion of a thermodynamic potential with continuous order parameters (303). 35. Phases without Linear Gradient Terms in Free Energy 304 One-component order parameter (304). Two-component order parameter (309). Three-component order parameter (311). Lifschitz point (316). 36. Phases with Linear Gradient Terms 318 The soliton lattice (318). Soliton lattice stability (323). The devil's staircase (328). Stochastic regime (331).
7 X CONTENTS 37. Multi-K-structures 332 Conditions for many-arm structures to be thermodynamically favorable (332). Multi-K-structure in СеАЬ (334). Multi-/c-structure in Nd (336). 38. Incommensurate Phases in External Fields 340 Helical structure in an external field (340). Effect of external fields on the wave-vector of incommensurate phases (343). 39. The Thermodynamics of Phase Transitions to Incommensurate Phases 347 Constructing a thermodynamic potential for non-lifschitz stars (347). Phase transition from incommensurate to commensurate phase (350). Concomitant order parameters and incommensurate-phase symmetry (351). Peculiarities of susceptibilities in incommensurate phases (353). References 355 Chapter 10. Color Symmetry and its Role in Phase Transition Theory Color Symmetry in the Theory of Magnetic Structures 358 Magnetic structures and their symmetries. Geometric aspect (358). Color symmetry and the thermodynamic-potential model (360). The hierarchy of approximations for describing the magnetic structure of FeGe 2 (362). 41. Supersymmetry of Incommensurate Structures 365 Incommensurate structures and the paradox of the Cheshire cat (365). Phase symmetry of the thermodynamic potential and the symmetry of incommensurate structures (367). 42. Icosahedral Symmetry of Crystals. Quasicrystals 372 A new type of atomic ordering (372). The geometric aspect (374). The thermodynamic aspect (379). The symmetry of quasicrystal structures (385). Al 86 Mn 14 : A Fibonacci structure or a quasicrystal? (387). Conclusion (388). 43. Color Groups in the Theory of Systems with a Quantum Mechanical Order Parameter 390 The quantum mechanical order parameter (390). Classification of ordered phases on the basis of color sub-groups of the normal-phase
8 CONTENTS xi symmetry group (391). OP symmetry and the behavior of the gap in к space (394). Thermodynamic potentials (399). References 401 Chapter 11. Fluctuations and Symmetry Fundamentals of the Fluctuation Phase Transitions Theory Critical indices (404). The renormalization-group and e-expansion method (406). The isotropic model (413). 45. Critical Behavior of Anisotropic Systems 415 Universal classes (415). Cubic anisotropy (417). Examples of systems with multicomponent order parameters (419). 46. Fluctuation-Induced Break-Down to First-Order Phase Transitions. 423 The absence of stable fixed points (423). First-order transitions in magnetic systems (424). 47. Fluctuations in the Vicinity of Multicritical Points 426 Systems with coupled order parameters. Bicritical and tetracritical points (426). Lifschitz point (434). References 437 Appendix 439 Index 441
ELECTRODYNAMICS OF CONTINUOUS MEDIA
ELECTRODYNAMICS OF CONTINUOUS MEDIA by L. D. LANDAU and E. M. LIFSHITZ Institute of Physical Problems, USSR Academy of Sciences Volume 8 of Course of Theoretical Physics Translated from the Russian by
Ferroelectric Phenomena in Crystals
В. А. Strukov А. Р. Levanyuk Ferroelectric Phenomena in Crystals Physical Foundations With 153 Figures and 14 Tables Springer Contents 1. General Characteristics of Structural Phase Transitions in Crystals
Preface Introduction to the electron liquid
Table of Preface page xvii 1 Introduction to the electron liquid 1 1.1 A tale of many electrons 1 1.2 Where the electrons roam: physical realizations of the electron liquid 5 1.2.1 Three dimensions 5 1.2.2
Electron Correlation
Series in Modern Condensed Matter Physics Vol. 5 Lecture Notes an Electron Correlation and Magnetism Patrik Fazekas Research Institute for Solid State Physics & Optics, Budapest lb World Scientific h Singapore
Structure and Dynamics : An Atomic View of Materials
Structure and Dynamics : An Atomic View of Materials MARTIN T. DOVE Department ofearth Sciences University of Cambridge OXFORD UNIVERSITY PRESS Contents 1 Introduction 1 1.1 Observations 1 1.1.1 Microscopic
On conservation of the of crystal lattice symmetry in transition at Curie point in exchange magnets Khisa Sh. Borlakov * and Albert Kh.
On conservation of the of crystal lattice symmetry in transition at Curie point in exchange magnets Khisa Sh. Borlakov * and Albert Kh. Borlakov North Caucasian State Humanitarian and Technological Academy,
Symmetries in Physics
W. Ludwig C. Falter Symmetries in Physics Group Theory Applied to Physical Problems With 87 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Contents 1. Introduction 1 2. Elements
The Superfluid Phase s of Helium 3
The Superfluid Phase s of Helium 3 DIETER VOLLHARD T Rheinisch-Westfälische Technische Hochschule Aachen, Federal Republic of German y PETER WÖLFL E Universität Karlsruhe Federal Republic of Germany PREFACE
Differential Geometry, Lie Groups, and Symmetric Spaces
Differential Geometry, Lie Groups, and Symmetric Spaces Sigurdur Helgason Graduate Studies in Mathematics Volume 34 nsffvjl American Mathematical Society l Providence, Rhode Island PREFACE PREFACE TO THE
ELASTOPLASTICITY THEORY by V. A. Lubarda
ELASTOPLASTICITY THEORY by V. A. Lubarda Contents Preface xiii Part 1. ELEMENTS OF CONTINUUM MECHANICS 1 Chapter 1. TENSOR PRELIMINARIES 3 1.1. Vectors 3 1.2. Second-Order Tensors 4 1.3. Eigenvalues and
Group Theory and Its Applications in Physics
T. Inui Y Tanabe Y. Onodera Group Theory and Its Applications in Physics With 72 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Contents Sections marked with
The Oxford Solid State Basics
The Oxford Solid State Basics Steven H. Simon University of Oxford OXFORD UNIVERSITY PRESS Contents 1 About Condensed Matter Physics 1 1.1 What Is Condensed Matter Physics 1 1.2 Why Do We Study Condensed
Physics 127b: Statistical Mechanics. Landau Theory of Second Order Phase Transitions. Order Parameter
Physics 127b: Statistical Mechanics Landau Theory of Second Order Phase Transitions Order Parameter Second order phase transitions occur when a new state of reduced symmetry develops continuously from
M.S. Dresselhaus G. Dresselhaus A. Jorio. Group Theory. Application to the Physics of Condensed Matter. With 131 Figures and 219 Tables.
M.S. Dresselhaus G. Dresselhaus A. Jorio Group Theory Application to the Physics of Condensed Matter With 131 Figures and 219 Tables 4) Springer Contents Part I Basic Mathematics 1 Basic Mathematical Background:
FUNDAMENTALS OF POLARIZED LIGHT
FUNDAMENTALS OF POLARIZED LIGHT A STATISTICAL OPTICS APPROACH Christian Brosseau University of Brest, France A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. New York - Chichester. Weinheim. Brisbane
Contents. Acknowledgments
MAGNETIC MATERIALS Fundamentals and Applications Second edition NICOLA A. SPALDIN University of California, Santa Barbara CAMBRIDGE UNIVERSITY PRESS Contents Acknowledgments page xiii I Basics 1 Review
PHYSICAL PROPERTIES OF CRYSTALS
PHYSICAL PROPERTIES OF CRYSTALS THEIR REPRESENTATION TENSORS AND MATRICES BY By J. F. NYE, F.R.S. CLARENDON PRESS OXFORD NOTATION INTRODUCTION xiii xv PART 1. GENERAL PRINCIPLES I. THE GROUNDWORK OF CRYSTAL
Landau-Ginzburg model for antiferroelectric phase transitions based on microscopic symmetry
PHYSICAL REVIEW B VOLUME 62, NUMBER 2 1 JULY 2000-II Landau-Ginzburg model for antiferroelectric phase transitions based on microscopic symmetry Richard A. Hatt Materials Research Laboratory, The Pennsylvania
2.3 Band structure and lattice symmetries: example of diamond
2.2.9 Product of representaitons Besides the sums of representations, one can also define their products. Consider two groups G and H and their direct product G H. If we have two representations D 1 and
Classification of Solids, Fermi Level and Conductivity in Metals Dr. Anurag Srivastava
Classification of Solids, Fermi Level and Conductivity in Metals Dr. Anurag Srivastava Web address: http://tiiciiitm.com/profanurag Email: profanurag@gmail.com Visit me: Room-110, Block-E, IIITM Campus
Roger Johnson Structure and Dynamics: Displacive phase transition Lecture 9
9.1. Summary In this Lecture we will consider structural phase transitions characterised by atomic displacements, which result in a low temperature structure that is distorted compared to a higher temperature,
Principles of Equilibrium Statistical Mechanics
Debashish Chowdhury, Dietrich Stauffer Principles of Equilibrium Statistical Mechanics WILEY-VCH Weinheim New York Chichester Brisbane Singapore Toronto Table of Contents Part I: THERMOSTATICS 1 1 BASIC
Principles of Condensed matter physics
Principles of Condensed matter physics P. M. CHAIKIN Princeton University T. C. LUBENSKY University of Pennsylvania CAMBRIDGE UNIVERSITY PRESS Preface xvii 1 Overview 1 1.1 Condensed matter physics 1 1.2
SOLID STATE PHYSICS. Second Edition. John Wiley & Sons. J. R. Hook H. E. Hall. Department of Physics, University of Manchester
SOLID STATE PHYSICS Second Edition J. R. Hook H. E. Hall Department of Physics, University of Manchester John Wiley & Sons CHICHESTER NEW YORK BRISBANE TORONTO SINGAPORE Contents Flow diagram Inside front
Physics of Materials: Classification of Solids On The basis of Geometry and Bonding (Intermolecular forces)
Physics of Materials: Classification of Solids On The basis of Geometry and Bonding (Intermolecular forces) Dr. Anurag Srivastava Atal Bihari Vajpayee Indian Institute of Information Technology and Manegement,
Mathematics for Engineers and Scientists
Mathematics for Engineers and Scientists Fourth edition ALAN JEFFREY University of Newcastle-upon-Tyne B CHAPMAN & HALL University and Professional Division London New York Tokyo Melbourne Madras Contents
Statistical Mechanics
Franz Schwabl Statistical Mechanics Translated by William Brewer Second Edition With 202 Figures, 26 Tables, and 195 Problems 4u Springer Table of Contents 1. Basic Principles 1 1.1 Introduction 1 1.2
Table of Contents. Chapter 1. Dielectricity, Piezoelectricity, Pyroelectricity and Ferroelectricity... 1
Preface... General Introduction... xiii xvii Chapter 1. Dielectricity, Piezoelectricity, Pyroelectricity and Ferroelectricity.... 1 1.1. Crystal structure... 1 1.1.1. Crystal = lattice + pattern... 1 1.1.2.
Contents. I Introduction 1. Preface. xiii
Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................
Contents. Appendix A Strong limit and weak limit 35. Appendix B Glauber coherent states 37. Appendix C Generalized coherent states 41
Contents Preface 1. The structure of the space of the physical states 1 1.1 Introduction......................... 1 1.2 The space of the states of physical particles........ 2 1.3 The Weyl Heisenberg algebra
Preface. Preface to the Third Edition. Preface to the Second Edition. Preface to the First Edition. 1 Introduction 1
xi Contents Preface Preface to the Third Edition Preface to the Second Edition Preface to the First Edition v vii viii ix 1 Introduction 1 I GENERAL THEORY OF OPEN QUANTUM SYSTEMS 5 Diverse limited approaches:
Symmetries in Quantum Physics
Symmetries in Quantum Physics U. Fano Department of Physics and James Franck Institute University of Chicago Chicago, Illinois A. R. P. Rau Department of Physics and Astronomy louisiana State University
Damping of magnetization dynamics
Damping of magnetization dynamics Andrei Kirilyuk! Radboud University, Institute for Molecules and Materials, Nijmegen, The Netherlands 1 2 Landau-Lifshitz equation N Heff energy gain:! torque equation:
Crystallographic Point Groups and Space Groups
Crystallographic Point Groups and Space Groups Physics 251 Spring 2011 Matt Wittmann University of California Santa Cruz June 8, 2011 Mathematical description of a crystal Definition A Bravais lattice
Chapter 1. Crystal structure. 1.1 Crystal lattices
Chapter 1 Crystal structure 1.1 Crystal lattices We will concentrate as stated in the introduction, on perfect crystals, i.e. on arrays of atoms, where a given arrangement is repeated forming a periodic
Quantum Mechanics: Foundations and Applications
Arno Böhm Quantum Mechanics: Foundations and Applications Third Edition, Revised and Enlarged Prepared with Mark Loewe With 96 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo
QUANTUM WELLS, WIRES AND DOTS
QUANTUM WELLS, WIRES AND DOTS Theoretical and Computational Physics of Semiconductor Nanostructures Second Edition Paul Harrison The University of Leeds, UK /Cf}\WILEY~ ^INTERSCIENCE JOHN WILEY & SONS,
The Non-Linear Field Theories of Mechanics
С. Truesdell-W.Noll The Non-Linear Field Theories of Mechanics Second Edition with 28 Figures Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Hong Kong Barcelona Budapest Contents. The Non-Linear
Tianyou Fan. Mathematical Theory of Elasticity of Quasicrystals and Its Applications
Tianyou Fan Mathematical Theory of Elasticity of Quasicrystals and Its Applications Tianyou Fan Mathematical Theory of Elasticity of Quasicrystals and Its Applications With 82 figures Author Tianyou Fan
STOCHASTIC PROCESSES IN PHYSICS AND CHEMISTRY
STOCHASTIC PROCESSES IN PHYSICS AND CHEMISTRY Third edition N.G. VAN KAMPEN Institute for Theoretical Physics of the University at Utrecht ELSEVIER Amsterdam Boston Heidelberg London New York Oxford Paris
Microstructural Randomness and Scaling in Mechanics of Materials. Martin Ostoja-Starzewski. University of Illinois at Urbana-Champaign
Microstructural Randomness and Scaling in Mechanics of Materials Martin Ostoja-Starzewski University of Illinois at Urbana-Champaign Contents Preface ix 1. Randomness versus determinism ix 2. Randomness
Lecture 10 Phase transitions.
Lecture 10 Phase transitions. 1 Introduction The study of phase transitions is at the very core of structural condensed-matter physics, to the point that one might consider all we have learned in the previous
PRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in
LONDON BEIJING HONG TSINGHUA Report and Review in Physics Vol2 PRINCIPLES OF PHYSICS From Quantum Field Theory to Classical Mechanics Ni Jun Tsinghua University, China NEW JERSEY \Hp SINGAPORE World Scientific
INTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition
INTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition Kerson Huang CRC Press Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group an Informa
NON-EQUILIBRIUM THERMODYNAMICS
NON-EQUILIBRIUM THERMODYNAMICS S. R. DE GROOT Professor of Theoretical Physics University of Amsterdam, The Netherlands E MAZUR Professor of Theoretical Physics University of Leiden, The Netherlands DOVER
THEORY OF GROUP REPRESENTATIONS AND APPLICATIONS
THEORY OF GROUP REPRESENTATIONS AND APPLICATIONS ASIM 0. BARUT Institute for Theoretical Physics, University of Colorado, Boulder, Colo., U.S.A. RYSZARD RATJZKA Institute for Nuclear Research, Warszawa,
Continuum Mechanics and Theory of Materials
Peter Haupt Continuum Mechanics and Theory of Materials Translated from German by Joan A. Kurth Second Edition With 91 Figures, Springer Contents Introduction 1 1 Kinematics 7 1. 1 Material Bodies / 7
GROUP REPRESENTATION THEORY FOR PHYSICISTS
GROUP REPRESENTATION THEORY FOR PHYSICISTS JIN-QUAN CHEN Vfe World Scientific wl Singapore New Jersey London Hong Kong Contents Foreword Preface Glossary v vii xix Introduction 1 Chapter 1 Elements of
3. General properties of phase transitions and the Landau theory
3. General properties of phase transitions and the Landau theory In this Section we review the general properties and the terminology used to characterise phase transitions, which you will have already
Nonlinear Problems of Elasticity
Stuart S. Antman Nonlinear Problems of Elasticity With 105 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest Contents Preface vn Chapter I. Background
Symmetry Properties of Superconductors
Australian Journal of Basic and Applied Sciences, 6(3): 81-86, 2012 ISSN 1991-8178 Symmetry Properties of Superconductors Ekpekpo, A. Department of Physics, Delta State University, Abraka, Nigeria. Abstract:
most easily accessible to experiments and to computer simulations PACS numbers: e, Fh, h
Surface-induced order and disorder: Critical phenomena at first-order phase transitions (invited) R. Lipowsky Sektion Physik der Universität München, Theresienstr. 37, 8000 München 2, West Germany Recent
INTERNATIONAL SCHOOL ON FUNDAMENTAL CRYSTALLOGRAPHY AND WORKSHOP ON STRUCTURAL PHASE TRANSITIONS. 30 August - 4 September 2017
INTERNATIONAL SCHOOL ON FUNDAMENTAL CRYSTALLOGRAPHY AND WORKSHOP ON STRUCTURAL PHASE TRANSITIONS 30 August - 4 September 2017 ROURKELA INTERNATIONAL CRYSTALLOGRAPHY SCHOOL BILBAO CRYSTALLOGRAPHIC SERVER
FINITE ELEMENT ANALYSIS OF COMPOSITE MATERIALS
FINITE ELEMENT ANALYSIS OF COMPOSITE MATERIALS Ever J. Barbero Department of Mechanical and Aerospace Engineering West Virginia University USA CRC Press Taylor &.Francis Group Boca Raton London New York
Algebraic Curves and Riemann Surfaces
Algebraic Curves and Riemann Surfaces Rick Miranda Graduate Studies in Mathematics Volume 5 If American Mathematical Society Contents Preface xix Chapter I. Riemann Surfaces: Basic Definitions 1 1. Complex
Walsh Series and Transforms
Walsh Series and Transforms Theory and Applications by B. Golubov Moscow Institute of Engineering, A. Efimov Moscow Institute of Engineering, and V. Skvortsov Moscow State University, W KLUWER ACADEMIC
Constructing Landau-Ginzburg-Devonshire Type Models for Ferroelectric Systems Based on Symmetry
701 GFER A 3395 October 18, 008 11:19 GFER #3395, VOL 375, ISS 1 Constructing Landau-Ginzburg-Devonshire Type Models for Ferroelectric Systems Based on Symmetry WENWU CAO QUERY SHEET This page lists questions
H = 1 2 τψ gψ4, (0.0.1)
32.1 Landau theory We have derived the Ginzburg-Landau Hamiltonian in Lecture 18. If we apply the mean field theory, that is, if we ignore fluctuations, then H = 1 2 τψ2 + 1 4 gψ4, (0.0.1) should be interpreted
Boundary. DIFFERENTIAL EQUATIONS with Fourier Series and. Value Problems APPLIED PARTIAL. Fifth Edition. Richard Haberman PEARSON
APPLIED PARTIAL DIFFERENTIAL EQUATIONS with Fourier Series and Boundary Value Problems Fifth Edition Richard Haberman Southern Methodist University PEARSON Boston Columbus Indianapolis New York San Francisco
Excitonic Condensation in Systems of Strongly Correlated Electrons. Jan Kuneš and Pavel Augustinský DFG FOR1346
Excitonic Condensation in Systems of Strongly Correlated Electrons Jan Kuneš and Pavel Augustinský DFG FOR1346 Motivation - unconventional long-range order incommensurate spin spirals complex order parameters
GROUP THEORY IN PHYSICS
GROUP THEORY IN PHYSICS Wu-Ki Tung World Scientific Philadelphia Singapore CONTENTS CHAPTER 1 CHAPTER 2 CHAPTER 3 CHAPTER 4 PREFACE INTRODUCTION 1.1 Particle on a One-Dimensional Lattice 1.2 Representations
1. Group Theory Permutations.
1.1. Permutations. 1. Group Theory Problem 1.1. Let G be a subgroup of S n of index 2. Show that G = A n. Problem 1.2. Find two elements of S 7 that have the same order but are not conjugate. Let π S 7
Nematic and Magnetic orders in Fe-based Superconductors
Nematic and Magnetic orders in Fe-based Superconductors Cenke Xu Harvard University Collaborators: Markus Mueller, Yang Qi Subir Sachdev, Jiangping Hu Collaborators: Subir Sachdev Markus Mueller Yang Qi
Partial Fractions. Prerequisites: Solving simple equations; comparing coefficients; factorising simple quadratics and cubics; polynomial division.
Prerequisites: olving simple equations; comparing coefficients; factorising simple quadratics and cubics; polynomial division. Maths Applications: Integration; graph sketching. Real-World Applications:
The Boltzmann Equation and Its Applications
Carlo Cercignani The Boltzmann Equation and Its Applications With 42 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo CONTENTS PREFACE vii I. BASIC PRINCIPLES OF THE KINETIC
Solid Surfaces, Interfaces and Thin Films
Hans Lüth Solid Surfaces, Interfaces and Thin Films Fifth Edition With 427 Figures.2e Springer Contents 1 Surface and Interface Physics: Its Definition and Importance... 1 Panel I: Ultrahigh Vacuum (UHV)
Modern Geometric Structures and Fields
Modern Geometric Structures and Fields S. P. Novikov I.A.TaJmanov Translated by Dmitry Chibisov Graduate Studies in Mathematics Volume 71 American Mathematical Society Providence, Rhode Island Preface
Understanding. Solid State Physics. Sharon Ann Holgate. CRC Press Taylor & Francis Group Boca Raton London NewYork
Understanding Solid State Physics Sharon Ann Holgate (И CRC Press Taylor & Francis Group Boca Raton London NewYork CRC Press is an imprint of the Taylor & Francis Group, an informa business A TAYLORS FRANCIS
Applied Asymptotic Analysis
Applied Asymptotic Analysis Peter D. Miller Graduate Studies in Mathematics Volume 75 American Mathematical Society Providence, Rhode Island Preface xiii Part 1. Fundamentals Chapter 0. Themes of Asymptotic
Numerical Methods with MATLAB
Numerical Methods with MATLAB A Resource for Scientists and Engineers G. J. BÖRSE Lehigh University PWS Publishing Company I(T)P AN!NTERNATIONAL THOMSON PUBLISHING COMPANY Boston Albany Bonn Cincinnati
Luigi Paolasini
Luigi Paolasini paolasini@esrf.fr LECTURE 5: MAGNETIC STRUCTURES - Mean field theory and magnetic order - Classification of magnetic structures - Collinear and non-collinear magnetic structures. - Magnetic
PROPERTIES OF POLYMERS
PROPERTIES OF POLYMERS THEIR CORRELATION WITH CHEMICAL STRUCTURE; THEIR NUMERICAL ESTIMATION AND PREDICTION FROM ADDITIVE GROUP CONTRIBUTIONS Third, completely revised edition By D.W. VÄN KREVELEN Professor-Emeritus,
Antiferromagnetic Textures
Antiferromagnetic Textures This image cannot currently be displayed. ULRICH K. RÖSSLE IFW DRESDEN SPICE Workshop Antiferromagnetic Spintronics 26.-30/09/2016 Schloss Waldthausen u.roessler@ifw-dresden.de
Emergent Frontiers in Quantum Materials:
Emergent Frontiers in Quantum Materials: High Temperature superconductivity and Topological Phases Jiun-Haw Chu University of Washington The nature of the problem in Condensed Matter Physics Consider a
Natural Boundary Integral Method and Its Applications
Natural Boundary Integral Method and Its Applications By De-hao Yu State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing
STATISTICS; An Introductory Analysis. 2nd hidition TARO YAMANE NEW YORK UNIVERSITY A HARPER INTERNATIONAL EDITION
2nd hidition TARO YAMANE NEW YORK UNIVERSITY STATISTICS; An Introductory Analysis A HARPER INTERNATIONAL EDITION jointly published by HARPER & ROW, NEW YORK, EVANSTON & LONDON AND JOHN WEATHERHILL, INC.,
Phys 412 Solid State Physics. Lecturer: Réka Albert
Phys 412 Solid State Physics Lecturer: Réka Albert What is a solid? A material that keeps its shape Can be deformed by stress Returns to original shape if it is not strained too much Solid structure
5 Symmetries and point group in a nut shell
30 Phys520.nb 5 Symmetries and point group in a nut shell 5.1. Basic ideas: 5.1.1. Symmetry operations Symmetry: A system remains invariant under certain operation. These operations are called symmetry
Classes of Linear Operators Vol. I
Classes of Linear Operators Vol. I Israel Gohberg Seymour Goldberg Marinus A. Kaashoek Birkhäuser Verlag Basel Boston Berlin TABLE OF CONTENTS VOLUME I Preface Table of Contents of Volume I Table of Contents
Crystal Structure. Dr Bindu Krishnan
Solid State Physics-1 Crystal Structure Dr Bindu Krishnan CRYSTAL LATTICE What is crystal (space) lattice? In crystallography, only the geometrical properties of the crystal are of interest, therefore
Decagonal quasicrystals
Decagonal quasicrystals higher dimensional description & structure determination Hiroyuki Takakura Division of Applied Physics, Faculty of Engineering, Hokkaido University 1 Disclaimer and copyright notice
5 Topological defects and textures in ordered media
5 Topological defects and textures in ordered media In this chapter we consider how to classify topological defects and textures in ordered media. We give here only a very short account of the method following
NANO/MICROSCALE HEAT TRANSFER
NANO/MICROSCALE HEAT TRANSFER Zhuomin M. Zhang Georgia Institute of Technology Atlanta, Georgia New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore
The Physics of Ferromagnetism
Terunobu Miyazaki Hanmin Jin The Physics of Ferromagnetism Springer Contents Part I Foundation of Magnetism 1 Basis of Magnetism 3 1.1 Basic Magnetic Laws and Magnetic Quantities 3 1.1.1 Basic Laws of
MASTER OF SCIENCE IN PHYSICS
MASTER OF SCIENCE IN PHYSICS The Master of Science in Physics program aims to develop competent manpower to fill the demands of industry and academe. At the end of the program, the students should have
An Introduction to Stochastic Modeling
F An Introduction to Stochastic Modeling Fourth Edition Mark A. Pinsky Department of Mathematics Northwestern University Evanston, Illinois Samuel Karlin Department of Mathematics Stanford University Stanford,
Linear Differential Transformations of the Second Order
Linear Differential Transformations of the Second Order In: Otakar Borůvka (author); Felix M. Arscott (translator): Linear Differential Transformations of the Second Order. (English). London: The English
Harald Ibach Hans Lüth SOLID-STATE PHYSICS. An Introduction to Theory and Experiment
Harald Ibach Hans Lüth SOLID-STATE PHYSICS An Introduction to Theory and Experiment With 230 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest Contents
Complexes of Differential Operators
Complexes of Differential Operators by Nikolai N. Tarkhanov Institute of Physics, Siberian Academy of Sciences, Krasnoyarsk, Russia KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON Contents Preface
Introduction to the Electronic Properties of Materials
Introduction to the Electronic Properties of Materials David Jiles Ames Laboratory US Department of Energy and Department of Materials Science and Engineering and Department of Electrical and Computer
II KLUWER ACADEMIC PUBLISHERS. Abstract Convexity and Global Optimization. Alexander Rubinov
Abstract Convexity and Global Optimization by Alexander Rubinov School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria, Australia II KLUWER ACADEMIC PUBLISHERS DORDRECHT
Collective behavior, from particles to fields
978-0-51-87341-3 - Statistical Physics of Fields 1 Collective behavior, from particles to fields 1.1 Introduction One of the most successful aspects of physics in the twentieth century was revealing the
Introduction to Magnetism and Magnetic Materials
Introduction to Magnetism and Magnetic Materials Second edition David Jiles Ames Laboratory, US Department of Energy Department of Materials Science and Engineering and Department of Electrical and Computer
Structure Analysis by Small-Angle X-Ray and Neutron Scattering
Structure Analysis by Small-Angle X-Ray and Neutron Scattering L. A. Feigin and D. I. Svergun Institute of Crystallography Academy of Sciences of the USSR Moscow, USSR Edited by George W. Taylor Princeton
Symmetry considerations in structural phase transitions
EPJ Web of Conferences 22, 00008 (2012) DOI: 10.1051/epjconf/20122200008 C Owned by the authors, published by EDP Sciences, 2012 Symmetry considerations in structural phase transitions J.M. Perez-Mato,
Cavity Expansion Methods in Geomechanics
Cavity Expansion Methods in Geomechanics by Hai-Sui Yu School of Civil Engineering, University of Nottingham, U. K. KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON TABLE OF CONTENTS Foreword Preface
Contents. 1 Introduction and guide for this text 1. 2 Equilibrium and entropy 6. 3 Energy and how the microscopic world works 21
Preface Reference tables Table A Counting and combinatorics formulae Table B Useful integrals, expansions, and approximations Table C Extensive thermodynamic potentials Table D Intensive per-particle thermodynamic
Representation of Lie Groups and Special Functions
Representation of Lie Groups and Special Functions Recent Advances by N. Ja. Vilenkint formerly of The Correspondence Pedagogical Institute, Moscow, Russia and A.U. Klimyk Institute for Theoretical Physics,
East Penn School District Secondary Curriculum
East Penn School District Secondary Curriculum A Planned Course Statement For Algebra I C.P. Course # 306 Grade(s) 9-12 Department: Mathematics Length of Period (mins.) 41 Total Clock Hours: 123 Periods
GEOPHYSICAL INVERSE THEORY AND REGULARIZATION PROBLEMS
Methods in Geochemistry and Geophysics, 36 GEOPHYSICAL INVERSE THEORY AND REGULARIZATION PROBLEMS Michael S. ZHDANOV University of Utah Salt Lake City UTAH, U.S.A. 2OO2 ELSEVIER Amsterdam - Boston - London