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: |