Mechanics of Advanced Functional Materials

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Author: Biao Wang
Language: English
ISBN/ISSN: 9787308100250
Published on: 2012-09
Hardcover

This book is an attempt to tackle mainly the followingtwo proplems:(1) to analyze the effect of stress and deformation on the functionalproperties of the materials, and (2) to establish the quantitative models relatedwith the microstructural evolution. The general formulation will be developedfrom the detailed analyses of the separated examples.



Introduction
Basic Solutions of Elastic and Electric Fields of Piezoelectric Materials with Inclusions and Defects
2.1 The Coupled Differential Equations of Elastic and Electric Fields in Piezoelectric Solids
2.1.1 Thermodynamic Framework
2.1.2 Linear Constitutive Equations
2.1.3 The Equation of Equlibrium
2.1.4 The Basic Equations of a Static Electric Field
2.1.5 Differential Equations for Piezoelectric Materials
2.2 Boundary Conditions
2.3 Solution Methods for Two-Dimensional Problems
2.3.1 The Stroh Formalism for Piezoelectric Materials
2.3.2 The Lekhnitskii Formalism for Piezoelectric Materials
2.3.3 Conformal Transformation of the Core Function
2.4 Basic Solutions for Two-Dimensional Problems
2.4.1 Elliptical Cylindrical Inclusions in Piezoelectric Materials
2.4.2 Cracks
2.4.3 Dislocations and Line Charges
2.5 Solution Methods for Three-Dimensional Problems
2.5.1 Eigenstrains and Equivalent Inclusion Method
2.5.2 Method of Fourier Integrals
2.5.3 Method of Green's Function
2.6 Basic Solution for Three-Dimensional Problems
2.6.1 Ellipsoidal Inhomogeneous Inclusions
2.6.2 Flat Elliptical Cracks
2.6.3 Ellipsoidal Inhomogeneity Embedded in an Infinite Matrix when both Phases Undergo Eigenstrains
2.6.4 Green's Function
2.7 Remarks
References
3 Micromechanics Models of Piezoelectric and Ferroelectric Composites
3.1 Background
3.2 Some Definitions
3.3 Effective Material Constants of Piezoelectric Composites
3.3.1 The Dilute Model
3.3.2 The Self-Consistent Model
3.3.3 The Mori-Tanaka Mean Field Model
3.3.4 The Differential Model
3.4 Energy Formulation of Ferroelectric Composites
3.4.1 Elastic Strain Energy Density for Ferroelectric Composites
3.4.2 Intrinsic Free Energy Density for Ferroelectric Composites
3.4.3 Total Free Energy for Ferroelectric Composites with Spherical Inclusions
3.5 Phase Diagrams
3.5.1 Total Free Energy for Ferroelectric Composites with Spherical Inclusions and Equiaxed Strains
3.5.2 Phase Diagrams and Total Polarizations
3.6 Remarks
Appendix A: Radon Transform
References
4 Determination of the Smallest Sizes of Ferroelectric Nanodomains
4.1 Introduction
4.2 Electric Fields in Ferroelectric Thin Film
4.2.1 General Expression of Electric Field of Ferroelectric Domain
4.2.2 AFM-Induced Electric Field in Ferroelectric Thin Films
4.3 Energy Expressions
4.3.1 Energy Expression for 180~ Domain in a Ferroelectric Film Covered with Top and Bottom Electrodes
4.3.2 Energy Expression for 180~ Domain in Ferroelectric Film Induced by an AFM Tip without the Top Electrode
4.4 Driving Force and Evolution Equations of Domain Growth
4.5 Stability Analysis
4.6 Remarks
Appendix B: Derivation of the Electric and Magnetic Field for a Growing 180° Domain
References
5 Size and Surface Effects of Phase Transition on Nanoferroelectric Materials
5.1 Introduction and Overview of Ferroelectrics in Nanoscale Dimensions
5.1.1 Ferroelectric Thin Films in Nanoscale Dimensions
5.1.2 Ferroelectric Tunneling Junctions and Capacitors in Nanoscale Dimensions
5.1.3 Ferroelectric Multilayers in Nanoscale
5.1.4 Ferroelectric Nanowires and Nanotubes
5.1.5 Ferroelectric Nanograins or Nanoislands on Substrates
5.2 Thermodynamic Modeling and Stability Analysis of Ferroelectric Systems
5.2.1 Background of the Thermodynamic Modeling for Ferroelectrics
5.2.2 Electrostatics for Ferroelectrics
5.2.3 Thermodynamics of Ferroelectrics
5.2.4 Stability Analysis on Critical Properties of Ferroelectric Systems
5.3 Ferroelectric Thin Films in Nanoscale
5.3. 1 Thermodynamic Model for a Thick Ferroelectric Film
5.3.2 Size and Surface Effects on Ferroelectric Thin Films
5.3.3 The Evolution Equation and Stability of the Stationary States
5.3.4 Curie Temperature and Critical Thickness
5.3.5 Curie-Weiss Law of Ferroelectric Thin Film in Nanoscale
5.4 Critical Properties of Ferroelectric Capacitors or Tunnel Junctions
5.4.1 The Thermodynamic Potential of the Ferroelectric Capacitors or Tunnel Junctions
5.4.2 The Evolution Equation and Stability of the Stationary States
5.4.3 Curie Temperature of the Ferroelectric Capacitors or Tunnel Junctions
5.4.4 Polarization as a Function of Thickness of the Ferroelectric Capacitors or Tunnel Junctions
5.4.5 Critical Thickness of the Ferroelectric Capacitors or Tunnel Junctions
5.4.6 Curie-Weiss Relation of the Ferroelectric Capacitors or Tunnel Junctions
5.5 Ferroelectric Superlattices in Nanoscale
5.5.1 The Free Energy Functional of Ferroelectric Superlattices
5.5.2 The Phase Transition Temperature ofPTO/STO Superlattice
5.5.3 Polarization and Critical Thickness ofPTO/STO Superlattice
5.5.4 The Curie-Weiss-Type Relation ofPTO/STO Superlattice
5.6 Ferroelectric Nanowires and Nanotubes
5.6.1 Surface Tension of Ferroelectric Nanowires and Nanotubes
5.6.2 Size and Surface Effects on Ferroelectric Nanowires
5.6.3 Ferroelectric Nanotubes
5.7 Ferroelectric Nanograins or Nanoislands
5.7.1 Free Energy ofFerroelectric Nanograins or Nanoislands
5.7.2 Stability of the Ferroelectric State and Transition Characteristics
5.7.3 Critical Properties of Nanograins or Nanoislands
5.8 Remarks
References
6 Strain Engineering: Ferroeleetric Films on Compliant Substrates
6.1 Background
6.2 Manipulation of Phase Transition Behavior of Ferroelectric Thin Films on Compliant Substrates
6.2.1 Free Energy Expressions
6.2.2 Evolution Equations
6.2.3 Manipulation of Ferroelectric Transition Temperature and Critical Thickness
6.2.4 Manipulation of the Order of Transition
6.3 Piezoelectric Bending Response and Switching Behavior of Ferroelectric Thin Film with Compliant Paraelectric Substrate
6.3.1 Model of Ferroelectric Thin Film with Compliant Paraelectric Substrate and the Energy Expressions
6.3.2 Solution of the Evolution Equation
6.3.3 The Stationary and Relative Bending Displacements of the Bilayer
6.3.4 Dynamic Piezoelectric and Bending Response of the Bilayer Under a Cyclic Electric Field
6.3.5 Examples and Discussions
6.4 Critical Thickness for Dislocation Generation in Piezoelectric Thin Films on Substrate
6.4.1 Elastic and Electric Fields in a Piezoelectric Semi-Infinite Space with a Dislocation
6.4.2 Critical Thickness for Dislocation Generation
6.4.3 Effect of Piezoelectric Behavior of the Materials on the Critical Thickness for Dislocation Formation
6.5 Critical Thickness of Dislocation Generation in Ferroelectric Thin Film on a Compliant Substrate
6.5.1 Mechanical Properties of the Problem
6.5.2 The Formation Energy and the Critical Thickness of Spontaneous Formation of Misfit Dislocation
6.6 Remarks
References
7 Derivation of the Landau-Ginzburg Expansion Coefficients
7.1 Introduction
7.2 Fundamental of the Landau-Devonshire Theory
……
8 Multiferroic Materials
9 Dielectric Breakdown of Microelectronic and Nanoelectronic Devices
Index 



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