Continuum models for phase transitions and twinning in crystals

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Continuum models for phase transitions and twinning in crystals / Mario Pitteri, G. Zanzotto

資料種別:

図書

出版情報:

Boca Raton, Fla. : Chapman & Hall/CRC, c2002

形態:

385 p. ; 24 cm

シリーズ名:

Applied mathematics / ed. R.J. Knops ; 19 <BA48104086>

著者名:

ISBN:

9780849303272 [0849303273]

書誌ID:

BA57995089

子書誌情報

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他の版・巻

書誌詳細

注記:

Includes bibliographical references and index

主題:

Continuum mechanics; Phase transitons (Statistical physocs); Twinning (Crystallography)

言語:

英語

目次情報:

List of figures

List of tables

Foreword

Introduction / 1：

Outline of chapter contents / 1.1：

Some experimental observations / 1.2：

Preliminaries / 2：

Basic notation / 2.1：

Some notions of elementary group theory / 2.2：

Basic definitions / 2.2.1：

Conjugacy / 2.2.2：

Group actions and symmetry / 2.2.3：

Linear and orthogonal transformations / 2.3：

Tensors with period two / 2.3.1：

Simple shears / 2.3.2：

Finite groups of tensors or matrices / 2.3.3：

Affine transformations / 2.4：

Continuum mechanics / 2.5：

Deformation / 2.5.1：

Thermodynamic potentials and their invariance / 2.5.2：

Stability of equilibrium / 2.5.3：

Simple lattices / 3：

Definitions and global symmetry / 3.1：

Geometric symmetry and crystal systems / 3.2：

Crystallographic point groups and holohedries / 3.2.1：

Crystal classes and crystal systems / 3.2.2：

Laue groups / 3.2.3：

Arithmetic symmetry and Bravais lattice types / 3.3：

Lattice groups / 3.3.1：

Conjugacy in O (crystal systems) and in GL(3, Z) (Bravais lattice types) / 3.3.2：

Centerings / 3.3.3：

The fourteen Bravais lattices / 3.4：

Fixed sets of lattice groups / 3.5：

An example / 3.5.1：

Symmetry-preserving stretches for simple lattices / 3.6：

Commutation relations / 3.6.1：

Structure of the fixed sets / 3.6.2：

The Bain stretch in the centered cubic lattices / 3.6.3：

Lattice subspaces, packings and indices / 3.7：

Lattice rows and lattice planes / 3.7.1：

Close-packed structures / 3.7.2：

Miller indices and crystallographic equivalence / 3.7.3：

Miller-Bravais indices for hexagonal lattices / 3.7.4：

Lattice groups and fixed sets for planar lattices / 3.8：

Weak-transformation neighborhoods and variants / 4：

Reconciliatio of global and local symmetries / 4.1：

Symmetry-breaking stretches for simple lattices / 4.2：

Small deformations and weak phase transformations / 4.3：

Small symmetry-preserving stretches / 4.3.1：

Small symmetry-breaking stretches / 4.3.2：

Constructing the small symmetry-breaking stretches / 4.4：

Variant structures (local orbits) in the wt-nbhds / 4.5：

General definitions / 4.5.1：

Variants and cosets / 4.5.3：

Variant structures and conjugacy classes / 4.5.4：

Explicit variant structures / 5：

Variant structures in cubic wt-nbhds / 5.1：

Tetragonal conjugacy class and variant structure / 5.1.1：

Rhombohedral conjugacy class and variant structure / 5.1.2：

Orthorhombic conjugacy classes and variant structures / 5.1.3：

Orthorhombic 'cubic edges' variants / 5.1.3.1：

Orthorhombic 'mixed axes' variants / 5.1.3.2：

Monoclinic conjugacy classes / 5.1.4：

Monoclinic 'cubic edges' variants / 5.1.4.1：

Monoclinic 'face-diagonals' variants / 5.1.4.2：

Triclinic conjugacy class and variant structure / 5.1.5：

Variant structures in hexagonal wt-nbhds / 5.2：

Orthorhombic conjugacy class and variant structure / 5.2.1：

Monoclinic conjugacy classes and variant structures / 5.2.2：

Monoclinic 'basal diagonals' variants / 5.2.2.1：

Monoclinic 'basal side-axes' variants / 5.2.2.2：

Monoclinic 'optic axis' variants / 5.2.2.3：

Kinematics of weak phase transformations / 5.2.3：

Irreducible invariant subspaces for the holohedries / 5.4：

General properties / 5.4.1：

Reduced actions and reduced symmetry groups on the i.i. subspaces / 5.4.2：

Decompositions of Sym under the action of the holohedries / 5.4.3：

Triclinic decompositions / 5.4.3.1：

Monoclinic decompositions / 5.4.3.2：

Orthorhombic decompositions / 5.4.3.3：

Rhombohedral decompositions / 5.4.3.4：

Tetragonal decompositions / 5.4.3.5：

Hexagonal decompositions / 5.4.3.6：

Cubic decompositions / 5.4.3.7：

Energetics / 6：

Invariance of simple-lattice energies / 6.1：

The Cauchy-Born hypothesis / 6.2：

The Born rule / 6.2.1：

Failures of the Born rule / 6.2.2：

Thermoelastic constitutive equations for crystals / 6.3：

Invariance of the response functions of elastic crystals / 6.3.1：

Energy minimizers and their general properties / 6.4：

Multiplicity of the symmetry-related minimizers / 6.4.1：

Multiphase crystals: minimizers that are not symmetry-related / 6.4.2：

Lack of convexity and symmetry-induced instabilities / 6.4.3：

Constitutive functions for weak phase transitions / 6.5：

Weak and symmetry-breaking transformations / 6.5.1：

Domain restrictions for the constitutive functions / 6.5.2：

Energy wells in the wt-nbhds / 6.5.3：

In the vicinity of an energy well / 6.6：

Thermal expansion and compressibility of a crystal / 6.6.1：

The elasticity tensor / 6.6.2：

Temperature-dependence of the elastic moduli / 6.6.3：

Anisotropic elasticity / 6.7：

Bifurcation patterns / 7：

The Landau theory / 7.1：

Isolated critical points and bifurcation points / 7.2：

Neighborhoods of bifurcation points / 7.2.1：

Genericity / 7.2.2：

Reduced bifurcation problems; order parameters / 7.3：

Analysis of the reduced bifurcation problems / 7.4：

Reduced problem (1) / 7.4.1：

Reduced problem (2) / 7.4.2：

Reduced problem (3) / 7.4.3：

Reduced problem (4) / 7.4.4：

Reduced problem (5) / 7.4.5：

Reduced problem (6) / 7.4.6：

Comparison with the kinematic transitions of [section]5.3 / 7.4.7：

Behavior of the moduli along the transitions / 7.5：

Examples of energy functions for simple lattices / 7.6：

A schematic 1-dimensional example / 7.6.1：

Energies for cubic-to-tetragonal and for tetragonal-to-monoclinic transitions / 7.6.2：

Orientation relationships and lattice correspondence / 7.6.3：

Relation with the Landau theory / 7.7：

General references / 7.8：

Mechanical twinning / 8：

Coherence and rank-1 connections / 8.1：

The twinning equation / 8.2：

Solutions of the twinning equation / 8.3：

Different descriptions of the same twin and cosets / 8.3.1：

Crystallographically equivalent twins / 8.3.2：

Reciprocal twins / 8.3.3：

Generic twins / 8.3.4：

Type-1 and Type-2 (conventional) twins / 8.3.5：

Compound twins / 8.3.6：

Conventional twins and rationality conditions / 8.3.7：

Short remarks / 8.4：

Experimental data / 8.4.1：

Mechanical twinning and the Born rule / 8.4.2：

Growth twins / 8.4.3：

Transformation twins / 9：

Procedure to determine the transformation twins / 9.1：

Rk-1 connections in a cubic wt-nbhd / 9.2：

Tetragonal variant structure / 9.2.1：

Rhombohedral variant structure / 9.2.2：

Orthorhombic variant structures / 9.2.3：

Orthorhombic 'cubic edges' wells / 9.2.3.1：

Orthorhombic 'mixed axes' wells / 9.2.3.2：

Monoclinic variant structures / 9.2.4：

Monoclinic 'cubic edges' wells / 9.2.4.1：

Monoclinic 'face-diagonals' wells / 9.2.4.2：

Triclinic variant structure / 9.2.5：

Rk-1 connections in a hexagonal wt-nbhd / 9.3：

Orthorhombic variant structure / 9.3.1：

Monoclinic 'basal diagonals' wells / 9.3.2：

Monoclinic 'basal side-axes' wells / 9.3.2.2：

Monoclinic 'optic axis' wells / 9.3.2.3：

The Mallard law / 9.3.3：

Microstructures / 10：

Piecewise homogeneous equilibria / 10.1：

Generalized solutions / 10.2：

The minors relations / 10.2.1：

The N-well problem / 10.2.2：

Examples of microstructures that are not laminates / 10.3：

Habit planes in martensite / 10.4：

Geometrically nonlinear theory / 10.4.1：

Self-accommodation in shape memory alloys / 10.4.2：

Wedges and other microstructures / 10.4.3：

Kinematics of multilattices / 11：

Crystals as multilattices / 11.1：

Descriptors and configuration spaces for deformable multilattices / 11.1.1：

Essential descriptions of multilattices / 11.1.2：

The global symmetry of multilattices / 11.2：

Indeterminateness of the descriptors (P[subscript 0,...], P[subscript n-1], e[subscript a]) / 11.2.1：

Indeterminateness of the descriptors (P[subscript 0], [varepsilon subscript [sigma]) / 11.2.2：

Nonessential descriptors of multilattices / 11.2.3：

The affine symmetry of multilattices / 11.3：

Space groups; crystal class and crystal system of a multilattice / 11.3.1：

The arithmetic symmetry of multilattices / 11.4：

Lattice groups of multilattices / 11.4.1：

Relation between the arithmetic and the space-group symmetries / 11.4.2：

Examples / 11.5：

Three-dimensional 2-lattices and hexagonal close-packed structures / 11.5.1：

The structure of quartz as a 3-lattice / 11.5.2：

Weak-transformation neighborhoods / 11.6：

The energy of a multilattice and its invariance / 11.7：

Minimizing out the internal variables of complex crystals / 11.7.1：

Local invariance of multilattice energies; the example of quartz / 11.7.2：

Twinning in multilattices / 11.8：

A proposal for a class of twins / 11.8.1：

Two examples / 11.8.2：

A model for stress relaxation / 11.8.3：

References

Index

List of figures

List of tables

Foreword

Introduction / 1：

Outline of chapter contents / 1.1：

Some experimental observations / 1.2：

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