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Landau Theory Of Phase Transitions, The.

Author: Pierre Toledano; Jean-claude Toledano
Publisher: Singapore : World Scientific Publishing Company, 1987.
Series: World Scientific lecture notes in physics.
Edition/Format:   eBook : Document : English
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Toledano, Pierre.
Landau Theory Of Phase Transitions, The: Application To Structural, Incommensurate, Magnetic And Liquid Crystal Systems.
Singapore : World Scientific Publishing Company, ©1987
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Pierre Toledano; Jean-claude Toledano
ISBN: 9789812799395 9812799397
OCLC Number: 1020688668
Description: 1 online resource (471 pages).
Contents: Intro; TABLE OF CONTENTS; FOREWORD; Chapter I INTUITIVE APPROACH TO THE BASIC IDEAS OF LANDAU'S THEORY; 1 --
INTRODUCTION; 2 --
MODEL EXAMPLE OF PHASE TRANSITION IN A CRYSTAL; 2.1 --
The system and its degrees of freedom; 2.2 --
Symmetry of the two phases; 2.3 --
Variational free-energy associated to the system; 2.4 --
Symmetry properties of F and form of its 2nd degree Taylor expansion; 2.5 --
Decoupling of the (Px Py) and Pz degrees of freedom. Order-parameter; 2.6 --
Need for an expansion of degree higher than 2 below Tc. 2.7 --
Simple physical consequences of the 4th degree order-parameter expansion2.8 --
Symmetry considerations; 2.9 --
Secondary order-parameters; 3 --
CONCLUSIONS; Chapter II : FORMULATION OF LANDAU'S THEORY; 1 --
INTRODUCTION; 2 --
BASIC CONCEPTS OF GROUP REPRESENTATIONS; 2.1 --
Irreducible representations of a group Go; 2.2 --
Group theoretical properties used in the formulation of Landau's theory; 3 --
LANDAU'S THEORY; 3.1 --
Variational and equilibrium particle density and free-energy; 3.2 --
Decomposition of the density increment into irreducible parts; 3.3 --
Scalar variational degrees of freedom. 3.4 --
Second degree Taylor expansion of F(nkr)3.5 --
Definition of the order-parameter; 3.6 --
Order-parameter expansion and nature of the symmetry change; 4 --
TECHNICAL GROUP THEORETICAL ASPECTS OF LANDAU'S THEORY; 4.1 --
Reduction of an invariant space into irreducible spaces; 4.2 --
Tensorial products of invariant spaces nth power of a representation; 4.3 --
Symmetrized nth power of a representation; 4.4 --
The Landau Condition; 4.5 --
Invariant polynomials and image of Go in the OP-representation; 4.6 --
Minimization of the free-energy and symmetry breaking; 5 --
SECONDARY ORDER-PARAMETER. 5.1 --
Coupling between secondary and primary OP5.2 --
Possible symmetries of secondary OP and form of o(Ss nr); 5.3 --
Equilibrium value of the secondary OP nearby Tc; 5.4 --
Irrelevance of the secondary OP to the symmetry below Tc; 6 --
CONCLUSIONS; Chapter III CONTINUOUS STRUCTURAL TRANSITIONS BETWEEN PERIODIC PHASES; 1 --
INTRODUCTION; 2 --
CRYSTALLOGRAPHIC SPACE-GROUPS AND THEIR REPRESENTATIONS; 2.1 --
Crystallographic space-groups; 2.2 --
Irreducible representations of the space-groups; 3 --
THE LIFSCHITZ CRITERION; 3.1 --
Derivation of the Lifschitz criterion. 3.2 --
Procedure of application of the Lifschitz criterion3.3 --
Selection of ko-vectors resulting from the Litschitz criterion; 3.4 --
Lifschitz criterion and periodicity of the low-symmetry phases; 4 --
IMAGES AND FREE-ENERGIES FOR ACTIVE REPRESENTATIONS; 4.1 --
Active representations of a space-group; 4.2 --
Images of Go for active representations; 4.3 --
Free-energies for active representations; 5 --
DETERMINATION OF THE LOW-SYMMETRY SPACE GROUP G; 6 --
FERROIC CLASSIFICATION OF STRUCTURAL PHASE TRANSITIONS; 6.1 --
Ferroicity and point-symmetry change at Tc; 6.2 --
Proper and improper ferroics. 6.3 --
Pseudo proper ferroics.
Series Title: World Scientific lecture notes in physics.

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