Continuum models for phase transitions and twinning in crystals. (©2003)

• Record Type: Book
• Further Information: Note: Mario Pitteri, Giovanni Zanzotto.
• Other Names: Pitteri, Mario; Zanzotto, Giovanni
• Contents: 1. Introduction. 1.1. Outline of chapter contents. 1.2. Some experimental observations -- 2. Preliminaries. 2.1. Basic notation. 2.2. Some notions of elementary group theory. 2.3. Linear and orthogonal transformations. 2.4. Affine transformations. 2.5. Continuum mechanics -- 3. Simple lattices. 3.1. Definitions and global symmetry. 3.2. Geometric symmetry and crystal systems. 3.3. Arithmetic symmetry and Bravais lattice types. 3.4. The fourteen Bravais lattices. 3.5. Fixed sets of lattice groups. 3.6. Symmetry-preserving stretches for simple lattices. 3.7. Lattice subspaces, packings and indices. 3.8. Lattice groups and fixed sets for planar lattices -- 4. Weak-transformation neighborhoods and variants. 4.1. Reconciliation of global and local symmetries. 4.2. Symmetry-breaking stretches for simple lattices. 4.3. Small deformations and weak phase transformations. 4.4. Constructing the small symmetry-breaking stretches. 4.5. Variant structures (local orbits) in the wt-nbhds -- 5. Explicit variant structures. 5.1. Variant structures in cubic wt-nbhds. 5.2. Variant structures in hexagonal wt-nbhds. 5.3. Kinematics of weak phase transformations. 5.4. Irreducible invariant subspaces for the holohedries -- 6. Energetics. 6.1. Invariance of simple-lattice energies. 6.2. The Cauchy-Born hypothesis. 6.3. Thermoelastic constitutive equations for crystals. 6.4. Energy minimizers and their general properties. 6.5. Constitutive functions for weak phase transitions. 6.6. In the vicinity of an energy well. 6.7. Anisotropic elasticity -- 7. Bifurcation patterns. 7.1. Introduction. 7.2. Isolated critical points and bifurcation points. 7.3. Reduced bifurcation problems; order parameters. 7.4. Analysis of the reduced bifurcation problems. 7.5. Behavior of the moduli along the transitions. 7.6. Examples of energy functions for simple lattices. 7.7. Relation with the Landau theory. 7.8. General references -- 8. Mechanical twinning. 8.1. Coherence and rank-1 connections. 8.2. The twinning equation. 8.3. Solutions of the twinning equation. 8.4. Short remarks -- 9. Transformation twins. 9.1. General properties. 9.2. Rk-1 connections in a cubic wt-nbhd. 9.3. Rk-1 connections in a hexagonal wt-nbhd. 9.4. The Mallard law -- 10. Microstructures. 10.1. Piecewise homogeneous equilibria. 10.2. Generalized solutions. 10.3. Examples of microstructures that are not laminates. 10.4. Habit planes in martensite -- 11. Kinematics of multilattices. 11.1. Crystals as multilattices. 11.2. The global symmetry of multilattices. 11.3. The affine symmetry of multilattices. 11.4. The arithmetic symmetry of multilattices. 11.5. Examples. 11.6. Weak-transformation neighborhoods. 11.7. The energy of a multilattice and its invariance. 11.8. Twinning in multilattices.
• Publisher Details: Boca Raton, FL : Chapman & Hall/CRC
• Publication Date: 2003
• Copyright Date: 2003
• Extent: 1 online resource (385 pages), illustrations
• Subjects: 548/.8; Twinning (Crystallography); Continuum mechanics; Phase transformations (Statistical physics); SCIENCE -- Physics -- Crystallography; Continuum mechanics; Phase transformations (Statistical physics); Twinning (Crystallography); Electronic books
• Languages: English
• ISBNs: 0849303273; 9780849303272; 1420036149; 9781420036145
• Notes: Note: Includes bibliographical references (pages 351-370) and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.