Tensor properties of solids : phenomenological development of the tensor properties of crystals / Richard F. Tinder.

Format:

Book

Author/Creator:

Tinder, Richard F. (Richard Franchere), 1930-2011.

Series:

Synthesis lectures on engineering.

Synthesis lectures on engineering

Language:

English

Subjects (All):

Crystallography, Mathematical.

Calculus of tensors.

Thermodynamics.

Transport theory.

Physical Description:

1 online resource (250 p.)

Place of Publication:

[San Rafael] : Morgan & Claypool Publishers, c2007.

Language Note:

English

Summary:

Tensor Properties of Solids presents the phenomenological development of solid state properties represented as matter tensors in two parts: Part I on equilibrium tensor properties and Part II on transport tensor properties.Part I begins with an introduction to tensor notation, transformations, algebra, and calculus together with the matrix representations. Crystallography, as it relates to tensor properties of crystals, completes the background treatment. A generalized treatment of solid-state equilibrium thermodynamics leads to the systematic correlation of equilibrium tensor properties. This

Contents:

Tensor Properties of Solids: Phenomenological Development of the Tensor Properties of Crystals; ABSTRACT; Keywords; Preface; Acknowledgments; Contents; PART I - Equilibrium Tensor Properties of Solids; Chapter 1 Introduction; 1.1 DEFINITION OF A TENSOR PROPERTY; 1.2 CONCEPTS OF EQUILIBRIUM AND REVERSIBILITY; 1.3 INTERACTION DIAGRAMS AND FIRST-ORDER EQUILIBRIUM PROPERTY NOMENCLATURE AND REPRESENTATION; 1.4 INTERACTION DIAGRAM FOR THE FIRST-ORDER NONEQUILIBRIUM TENSOR PROPERTIES; Chapter 2-Introduction to Tensor Notation, Tensor Transformations, Tensor Calculus...

2.1 INTRODUCTION TO TENSOR AND MATRIX NOTATION2.2 TRANSFORMATION OF TENSORS; 2.2.1 Transformation of Scalars; 2.2.2 Transformation of Vectors; 2.2.3 Transformation of Second-Rank Tensors; 2.2.4 Symmetrical and Antisymmetrical Second-Rank Tensors; 2.2.5 Quadratic Transformation Forms; 2.2.6 Transformation of Third-Rank Tensors; 2.2.7 Transformation of Fourth-Rank Tensors; 2.2.8 Summary of Tensor Transformation Laws; 2.3 INTRODUCTION TO TENSOR ALGEBRA; 2.3.1 Tensor Addition; 2.3.2 Tensor Multiplication; 2.3.3 Outer Product; 2.3.4 Tensor Contraction; 2.4 AXIAL TENSORS

2.6 TENSOR FIELDS AND TENSOR OPERATORS2.6.1 Gradient of a Tensor Field; 2.6.2 Divergence of a Tensor Field; 2.6.3 Kronecker Delta, Permutation Tensor, Vector Cross Product, and Tensorial Contraction; Chapter 3-Crystal Systems, Symmetry Elements, and Symmetry Transformations; 3.1 INTRODUCTION; 3.2 MACROSCOPIC CRYSTAL SYMMETRY AND SYMMETRY TRANSFORMATIONS; 3.2.1 Permissible Rotations; 3.2.2 Center of Symmetry; 3.3 SPACE LATTICES, UNIT CELLS, CRYSTALLOGRAPHIC PLANES, AND DIRECTIONS-MILLER INDICES; 3.4 THE MACROSCOPIC SYMMETRY OF CRYSTALS AND THE 32 CONVENTIONAL POINT GROUPS

3.8 LONGITUDINAL AND TRANSVERSE EFFECTS FOR SYMMETRICAL SECOND-RANK PROPERTY TENSORSChapter 4-Generalized Thermostatics and the Systematic Correlation of Physical Properties; 4.1 Energy Representations and the Criteria for Thermodynamic Equilibrium; 4.1.1 Energy Density Representation; 4.2 Thermodynamic Definition of Parameters; 4.3 Generalized Compliance and Rigidity Matrices; 4.4 Symmetry of the General Compliance and Rigidity Matrices; 4.5 Systematic Enumeration and Correlation of First-Order Tensor Properties- Generalized Maxwell Rel; 4.5.1 Principal Effects

4.5.2 Independent Coupled Effects4.6 Effect of Measurement Conditions on the First-Order Tensor Properties; Chapter 5 -The Dependent Coupled Effects and the Interrelationships Between First-Order Tensor Pro; 5.1 THE DEPENDENT COUPLED EFFECTS; 5.2 INTERRELATIONSHIP BETWEEN FIRST-ORDER PROPERTIES-USE OF INTERACTION DIAGRAMS; Chapter 6 - Third- and Fourth-Rank Tensor Properties-Symmetry Considerations; 6.1 DIRECT AND CONVERSE PIEZOELECTRIC EFFECTS; 6.1.1 Direct Piezoelectric Effect; 6.1.2 Converse Piezoelectric Effect; 6.1.3 Crystal Symmetry Considerations

6.1.4 Brute-Force Method for the Trigonal and Hexagonal Classes- The Piezoelectric Moduli

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 201-204) and index.

OCLC:

794328574