Technische Universität Graz. Institute of Solid State Physics. 22. Crystal Physics
|
|
- Lorena Gibson
- 5 years ago
- Views:
Transcription
1 Technische Universität Graz Institute of Solid State Physics 22. Crystal Physics Jan. 7, 2018
2 Hall effect / Nerst effect
3 Technische Universität Graz Institute of Solid State Physics Crystal Physics Crystal physics explains what effects the symmetries of the crystal have on observable quantities. An Introduction to Crystal Physics Ervin Hartmann International Tables for Crystallography Kittel chapter 3: elastic strain
4 Strain A distortion of a material is described by the strain matrix x (1 ) xˆ yˆ zˆ xx xy xz y xˆ(1 ) yˆ zˆ yx yy yz z xˆ yˆ(1 ) zˆ zx zy zz ẑ ẑ ŷ ŷ ˆx ˆx
5 Stress z 9 forces describe the stress Xx, Xy, Xz, Yx, Yy, Yz, Zx, Zy, Zz Xz y x Xx Xy Xx is a force applied in the x-direction to the plane normal to x Xy is a sheer force applied in the x-direction to the plane normal to y stress tensor: Stress is force/m 2 X x X y X A A A x y z Yx Yy Y A A A x y z Z x Z y Z A A A x y z z z z
6 Stress and Strain s ij ijkl kl The stress - strain relationship is described by a rank 4 stiffness tensor. The inverse of the stiffness tensor is the compliance tensor. c ij ijkl kl Einstein convention: sum over repeated indices. s s s s s xx xxxx xx xxxy xy xxxz xz xxyx yx xxyy yy s s s s xxyz yz xxzx zx xxzy zy xxzz zz
7 Statistical Physics Microcannonical Ensemble: Internal energy is expressed in terms of extrinsic quantities U(S, M, P,, N). U U U U du ds d dp dm S P M ij K l ij k l du TdS d E dp H dm ij ij k K l l The normal modes must be solved for in the presence of electric and magnetic fields.
8 Internal energy in an electric field In an electric field, if the dipole moment is changed, the change of the energy is, Using Einstein notation U EP du E dp k k This is part of the total derivative of U E k U P k du TdS d E dp H dm ij ij k K l l
9 Statistical Physics Microcannonical Ensemble: Internal energy is expressed in terms of extrinsic quantities U(S, M, P,, N). V U U U U du ds d dp dm S P M ij K l ij k l du TdS d E dp H dm ij ij ij k K l l ij Cannonical ensemble: At constant temperature, make a Legendre transformation to the Helmholtz free energy. F = U - TS F(V, T, N, M, P, ) Make a Legendre transformation to the Gibbs potential G(T, H, E, ) GUTS E P HM ij ij k K l l
10 Helmholtz free energy Cannonical ensemble: At constant temperature, make a Legendre transformation to the Helmholtz free energy. F = U - TS F(T, N, M, P, ) F F F F F df dt dn d dp dm T N P M i ij k l i ij K l df = du - TdS - SdT df SdT dn d E dp H dm i i ij ij k k l l S F T F F ij ij,,, i NMP,,, Ni TMP,,,, Nji NMPT E k F F l Pk NMT,,, M l NTP,,, H
11 Gibbs free energy G(T,, H, E, ) G U TS N E P H M i i ij ij k K l l du TdS dn d E dp H dm i i ij ij k K l l dg SdT N d d P de M dh i i ij ij k k l l G G G G G dg dt d d de dh T E H i ij k l i ij k l S G T, E, H, N i G i T, E, H, ij G ij T, E, H, P k G G M l Ek T,, H, l T,, E, H
12
13 Direct and reciprocal effects (Maxwell relations) Useful to check for errors in experiments or calculations
14 Multiferroics simultaneously ferroelectric and ferromagnetic BiFeO 3 If two magnetic sublattices have different charge, changing the magnetic field can change the polarization and changing the electric field can change the magnetization.
15 Maxwell relations Useful to check for errors in experiments or calculations
16 Replace P and V with and
17 edition available through TU Graz library
18 The properties of solids H Ze e ZZe A A B i A i 2me A 2mA i, A 40riA ij 40rij AB40rAB electronic band structure E vs. k structure bond potentials phonon band structure vs. k density of states Boltzmann transport optical absorption density of states equilibrium properties c v, free energies, bulk modulus,... optical properties
19 Calculating free energies Electronic component Phonon component
20 Groups Crystals can have symmetries: translation, rotation, reflection, inversion,... x x y 0 cos sin y z 0 sin cosz Symmetries can be represented by matrices. All such matrices that bring the crystal into itself form the group of the crystal. A, B G AB G 32 point groups (one point remains fixed during transformation) 230 space groups
21 Cyclic groups C 2 C 4
22 Pyroelectricity i 2 G E T i Pyroelectricity is described by a rank 1 tensor Pi i T x x x y y y z z x x y y z z 0
23 Pyroelectricity Quartz, ZnO, LaTaO 3 example Turmalin: point group 3m for T = 1 C, E ~ V/m Pyroelectrics have a spontaneous polarization. If it can be reversed by an electric field they are called Ferroelectrics (BaTiO 3 ) Pyroelectrics are at Joanneum research to make infrared detectors (to detect humans). 10 Pyroelectric crystal classes: 1, 2, m, mm2, 3, 3m, 4, 4mm, 6, 6mm
24 Rank 2 Tensors Electric susceptibility Dielectric constant Magnetic susceptibility Thermal expansion Electrical conductivity Thermal conductivity Seebeck effect Peltier effect
25 UP Electric susceptibility Px xx xy xz Ex P E y yx yy yz y P z zx zy zz E z P E i ij j Transforming P and E by a crystal symmetry must leave the susceptibility tensor unchanged UE 1 1 U UP U UE ij 2 G EiE = U -1 U j If rotation by 180 about the z axis is a symmetry, U U U U xz = yz = zx = zy = 0 1 xx xy xz U yx yy yz zx zy zz
26
27 Cubic crystals All second rank tensors of cubic crystals reduce to constants 216: ZnS, GaAs, GaP, InAs 221: CsCl, cubic perovskite 225: Al, Cu, Ni, Ag, Pt, Au, Pb, NaCl 227: C, Si, Ge, spinel 229: Na, K, Cr, Fe, Nb, Mo, Ta
28
29
30 Rank 3 Tensors Piezoelectricity Piezomagnetism Hall effect Nerst effect Ettingshausen effect Nonlinear electrical susceptibility
31 Tensor notation We need a way to represent 3rd and 4th rank tensors in 2-d g rank 3 rank 4 36 g g g
32 Piezoelectricity average position + is average position - P k G E k average position + not average position - 2 P k G ij Ek ij d ijk
33 Piezoelectricity (rank 3 tensor) AFM's, STM's Quartz crystal oscillators Surface acoustic wave generators Pressure sensors - Epcos Fuel injectors - Bosch Inkjet printers No inversion symmetry lead zirconate titanate (Pb[Zr x Ti 1 x ]O 3 0<x<1) more commonly known as PZT barium titanate (BaTiO 3 ) lead titanate (PbTiO 3 ) potassium niobate (KNbO 3 ) lithium niobate (LiNbO 3 ) lithium tantalate (LiTaO 3 ) sodium tungstate (Na 2 WO 3 ) Ba 2 NaNb 5 O 5 Pb 2 KNb 5 O 15 Piezoelectric crystal classes: 1, 2, m, 222, mm2, 4, -4, 422, 4mm, -42m, 3, 32, 3m, 6, -6, 622, 6mm, -62m, 23, -43m
34 Nonlinear optics Period doubling crystals no inversion symmetry P E E E G 1 G Pi Ej EjEk EE 2 EE E i j i j k t t cos 1 cos(2 ) nm light : lithium iodate (LiIO 3 ) 860 nm light : potassium niobate (KNbO 3 ) 980 nm light : KNbO nm light : monopotassium phosphate (KH 2 PO 4, KDP), lithium triborate (LBO) nm light : gallium selenide (GaSe) 1319 nm light : KNbO 3, BBO, KDP, lithium niobate (LiNbO 3 ), LiIO 3
35 Birefringence (Doppelbrechung) Calcite Two indices of refraction k
Solid State Theory Physics 545
olid tate Theory hysics 545 Mechanical properties of materials. Basics. tress and strain. Basic definitions. Normal and hear stresses. Elastic constants. tress tensor. Young modulus. rystal symmetry and
More informationClassification of Dielectrics & Applications
Classification of Dielectrics & Applications DIELECTRICS Non-Centro- Symmetric Piezoelectric Centro- Symmetric Pyroelectric Non- Pyroelectric Ferroelectrics Non-Ferroelectric Piezoelectric Effect When
More informationPiezoelectric materials for MEMS applications Hiroshi Funakubo Tokyo Institute of Technology
Piezoelectric materials for MEMS applications Hiroshi Funakubo Tokyo Institute of Technology MEMS Engineer Forum 2016/5/11 11:50-12:15 Content 1. Introduction 2. Processing 3. Materials Matter Content
More informationAPPENDIX A Landau Free-Energy Coefficients
APPENDIX A Landau Free-Energy Coefficients Long-Qing Chen Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 180 USA The thermodynamics of
More informationELECTRONICS DEVICES AND MATERIALS
2-2-2 ELECTRONICS DEVICES AND MATERIALS Atsunori KAMEGAWA SYLLABUS! Introduction to materials structure and dielectric physics (04/27)! Ferroelectricity involved in structural phase transitions (05/25)
More informationPrinciples of Active Vibration Control: Piezoelectric materials
Principles of Active Vibration Control: Piezoelectric materials Introduction: Piezoelectric materials are materials that produce a voltage when stress is applied. Since, this effect also applies in the
More informationFerroelectricity. Phase transition. Material properties. 4/12/2011 Physics 403 Spring
Ferroelectricity. Phase transition. Material properties 4/12/211 Physics 43 Spring 211 1 Ferroelectricity. outline Ferroelectricity. Definition Discovery Main properties Phenomenological theory Some materials
More informationFerroelectric Materials and Their Applications
Ferroelectric Materials and Their Applications Yuhuan Xu University of California Los Angeles, CA, USA J» m 1991 NORTH-HOLLAND AMSTERDAM LONDON NEW YORK TOKYO Foreword by L.E. Cross Foreword by S.B. Lang
More informationLecture 05 Structure of Ceramics 2 Ref: Barsoum, Fundamentals of Ceramics, Ch03, McGraw-Hill, 2000.
MME 467 Ceramics for Advanced Applications Lecture 05 Structure of Ceramics 2 Ref: Barsoum, Fundamentals of Ceramics, Ch03, McGraw-Hill, 2000. Prof. A. K. M. Bazlur Rashid Department of MME, BUET, Dhaka
More informationIntroduction to Condensed Matter Physics
Introduction to Condensed Matter Physics Elasticity M.P. Vaughan Overview Overview of elasticity Classical description of elasticity Speed of sound Strain Stress Young s modulus Shear modulus Poisson ratio
More informationTransduction Based on Changes in the Energy Stored in an Electrical Field
Lecture 7-1 Transduction Based on Changes in the Energy Stored in an Electrical Field - Electrostriction The electrostrictive effect is a quadratic dependence of strain or stress on the polarization P
More informationElectrical Properties
Electrical Properties Electrical Conduction R Ohm s law V = IR I l Area, A V where I is current (Ampere), V is voltage (Volts) and R is the resistance (Ohms or ) of the conductor Resistivity Resistivity,
More informationThe electronic structure of materials 1
Quantum mechanics 2 - Lecture 9 December 18, 2013 1 An overview 2 Literature Contents 1 An overview 2 Literature Electronic ground state Ground state cohesive energy equilibrium crystal structure phase
More informationLecture 7. Properties of Materials
MIT 3.00 Fall 2002 c W.C Carter 55 Lecture 7 Properties of Materials Last Time Types of Systems and Types of Processes Division of Total Energy into Kinetic, Potential, and Internal Types of Work: Polarization
More informationFerroelectricity. Phase transition. Material properties
Ferroelectricity. Phase transition. Material properties BaTiO 3 DKDP KDP PZN-PT(9%) PMN-PT(30%) PMN-PT(40%) 4/1/2016 Physics 403 Spring 2016 1 Ferroelectricity. outline Ferroelectricity. Definition Discovery
More informationPEAT SEISMOLOGY Lecture 2: Continuum mechanics
PEAT8002 - SEISMOLOGY Lecture 2: Continuum mechanics Nick Rawlinson Research School of Earth Sciences Australian National University Strain Strain is the formal description of the change in shape of a
More informationElectromagnetic Properties of Materials Part 2
ECE 5322 21 st Century Electromagnetics Instructor: Office: Phone: E Mail: Dr. Raymond C. Rumpf A 337 (915) 747 6958 rcrumpf@utep.edu Lecture #3 Electromagnetic Properties of Materials Part 2 Nonlinear
More informationElasticité de surface. P. Muller and A. Saul Surf. Sci Rep. 54, 157 (2004).
Elasticité de surface P. Muller and A. Saul Surf. Sci Rep. 54, 157 (2004). The concept I Physical origin Definition Applications Surface stress and crystallographic parameter of small crystals Surface
More informationESO 205 Nature and Properties of Materials
Dielectric Materials Topics to discuss Principles of dielectrics Dielectrics Loss and Breakdown Polarizations Frequency dependence Ferro-, Piezo- and Pyro- electrics ESO 205 Nature and Properties of Materials
More informationChapter 4: Partial differentiation
Chapter 4: Partial differentiation It is generally the case that derivatives are introduced in terms of functions of a single variable. For example, y = f (x), then dy dx = df dx = f. However, most of
More information18. Active polarization control
18. Active polarization control Ways to actively control polarization Pockels' Effect inducing birefringence Kerr Effect Optical Activity Principal axes are circular, not linear Faraday Effect inducing
More informationMECH 5312 Solid Mechanics II. Dr. Calvin M. Stewart Department of Mechanical Engineering The University of Texas at El Paso
MECH 5312 Solid Mechanics II Dr. Calvin M. Stewart Department of Mechanical Engineering The University of Texas at El Paso Table of Contents Thermodynamics Derivation Hooke s Law: Anisotropic Elasticity
More informationMaterials 218/UCSB: Phase transitions and polar materials
Materials 218/UCSB: Phase transitions and polar materials Ram Seshadri (seshadri@mrl.ucsb.edu) Background: Intrinsic stability of thermodynamic systems (after H. B. Callen, Thermodynamics and an introduction
More informationOrientation of Piezoelectric Crystals and Acoustic Wave Propagation
Orientation of Piezoelectric Crystals and Acoustic Wave Propagation Guigen Zhang Department of Bioengineering Department of Electrical and Computer Engineering Institute for Biological Interfaces of Engineering
More informationPHYSICAL PROPERTIES OF CRYSTALS
PHYSICAL PROPERTIES OF CRYSTALS THEIR REPRESENTATION TENSORS AND MATRICES BY By J. F. NYE, F.R.S. CLARENDON PRESS OXFORD NOTATION INTRODUCTION xiii xv PART 1. GENERAL PRINCIPLES I. THE GROUNDWORK OF CRYSTAL
More informationInnovation and Development of Study Field. nano.tul.cz
Innovation and Development of Study Field Nanomaterials at the Technical University of Liberec nano.tul.cz These materials have been developed within the ESF project: Innovation and development of study
More informationPiezoelectricity: Basics and applications. Friday Morning Meeting, Technical Talk Petar Jurcevic
Piezoelectricity: Basics and applications Friday Morning Meeting, 30.07.2010 Technical Talk Petar Jurcevic 1 Overview -A simple molecular model -Mathematical modelling -Some general notes -Overview Motors
More informationA DARK GREY P O N T, with a Switch Tail, and a small Star on the Forehead. Any
Y Y Y X X «/ YY Y Y ««Y x ) & \ & & } # Y \#$& / Y Y X» \\ / X X X x & Y Y X «q «z \x» = q Y # % \ & [ & Z \ & { + % ) / / «q zy» / & / / / & x x X / % % ) Y x X Y $ Z % Y Y x x } / % «] «] # z» & Y X»
More informationMSE 201A Thermodynamics and Phase Transformations Fall, 2008 Problem Set No. 7
MSE 21A Thermodynamics and Phase Transformations Fall, 28 Problem Set No. 7 Problem 1: (a) Show that if the point group of a material contains 2 perpendicular 2-fold axes then a second-order tensor property
More informationFerroelectric materials contain one or more polar axes along which a spontaneous
Chapter 3 Ferroelectrics 3.1 Definition and properties Ferroelectric materials contain one or more polar axes along which a spontaneous polarization can be developed below the material s Curie temperature.
More informationFerroelectrics. Disordered Ferroelectrics Relaxors.
Ferroelectrics. Disordered Ferroelectrics Relaxors. 1 Ferroelctricity Main properties History. Discovery. Materials Relaxors Applications 2 Ferroelectric Materials. A ferroelectric material is a material
More informationFerroelectric Materials
Ferroelectric Materials The permanent electric dipole moment possessed by all pyroelectric [polar] materials may, in certain cases, be reoriented by the application of an electric field. Such crystals
More informationDIPOLES III. q const. The voltage produced by such a charge distribution is given by. r r'
DIPOLES III We now consider a particularly important charge configuration a dipole. This consists of two equal but opposite charges separated by a small distance. We define the dipole moment as p lim q
More informationFerroelectrics and ferroelectric domains
Ferroelectrics and ferroelectric domains MatjažPanjan mentor: dr. Peter Prelovšek. April 003 Abstract This seminar gives introduction to ferroelectricity, ferroelectric domains and domain walls. There
More informationIntroduction. Statistical physics: microscopic foundation of thermodynamics degrees of freedom 2 3 state variables!
Introduction Thermodynamics: phenomenological description of equilibrium bulk properties of matter in terms of only a few state variables and thermodynamical laws. Statistical physics: microscopic foundation
More informationPhys 412 Solid State Physics. Lecturer: Réka Albert
Phys 412 Solid State Physics Lecturer: Réka Albert What is a solid? A material that keeps its shape Can be deformed by stress Returns to original shape if it is not strained too much Solid structure
More informationPiezoelectric transducers
Piezoelectric transducers are beased on the property to accumulate charges if stressed (direct effect)and to strain in case of an electric signal is applied across their electrods(inverse effect) 1 basics..
More informationComplex Electric-Field Induced Phenomena in Ferroelectric/Antiferroelectric Nanowires
University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 4-7-2017 Complex Electric-Field Induced Phenomena in Ferroelectric/Antiferroelectric Nanowires Ryan Christopher
More informationRoger Johnson Structure and Dynamics: Displacive phase transition Lecture 9
9.1. Summary In this Lecture we will consider structural phase transitions characterised by atomic displacements, which result in a low temperature structure that is distorted compared to a higher temperature,
More information16.20 HANDOUT #2 Fall, 2002 Review of General Elasticity
6.20 HANDOUT #2 Fall, 2002 Review of General Elasticity NOTATION REVIEW (e.g., for strain) Engineering Contracted Engineering Tensor Tensor ε x = ε = ε xx = ε ε y = ε 2 = ε yy = ε 22 ε z = ε 3 = ε zz =
More informationRaman and IR spectroscopy in materials science. Symmetry analysis of normal phonon modes Boriana Mihailova
University of Hamburg, Institute of Mineralogy and Petrology Raman and IR spectroscopy in materials science. Symmetry analysis of normal phonon modes Boriana Mihailova Outline. The dynamics of atoms in
More informationLecture 21 Reminder/Introduction to Wave Optics
Lecture 1 Reminder/Introduction to Wave Optics Program: 1. Maxwell s Equations.. Magnetic induction and electric displacement. 3. Origins of the electric permittivity and magnetic permeability. 4. Wave
More informationFerroelectric Ceramic Technology for Sensors. Jim McIntosh Ceramic Operations Manager PCB Piezotronics
Ferroelectric Ceramic Technology for Sensors Jim McIntosh Ceramic Operations Manager PCB Piezotronics Overview Ferroelectricity versus Piezoelectricity Historical Background Ferroelectric Ceramic Composition
More information3.032 Problem Set 4 Fall 2007 Due: Start of Lecture,
3.032 Problem Set 4 Fall 2007 Due: Start of Lecture, 10.19.07 1. A microelectronic sensor is to be made of conductive wires deposited on a thin Si wafer. During design considerations, it was decided that
More informationCOURSE OUTLINE. Introduction Signals and Noise Filtering Sensors: Piezoelectric Force Sensors. Sensors, Signals and Noise 1
Sensors, Signals and Noise 1 COURSE OUTLINE Introduction Signals and Noise Filtering Sensors: Piezoelectric Force Sensors Piezoelectric Force Sensors 2 Piezoelectric Effect and Materials Piezoelectric
More informationChapter 1 Fluid Characteristics
Chapter 1 Fluid Characteristics 1.1 Introduction 1.1.1 Phases Solid increasing increasing spacing and intermolecular liquid latitude of cohesive Fluid gas (vapor) molecular force plasma motion 1.1.2 Fluidity
More information4: birefringence and phase matching
/3/7 4: birefringence and phase matching Polarization states in EM Linear anisotropic response χ () tensor and its symmetry properties Working with the index ellipsoid: angle tuning Phase matching in crystals
More informationLecture 6 - Bonding in Crystals
Lecture 6 onding in Crystals inding in Crystals (Kittel Ch. 3) inding of atoms to form crystals A crystal is a repeated array of atoms Why do they form? What are characteristic bonding mechanisms? How
More informationPiezo materials. Actuators Sensors Generators Transducers. Piezoelectric materials may be used to produce e.g.: Piezo materials Ver1404
Noliac Group develops and manufactures piezoelectric materials based on modified lead zirconate titanate (PZT) of high quality and tailored for custom specifications. Piezoelectric materials may be used
More informationLecture 4: Anisotropic Media. Dichroism. Optical Activity. Faraday Effect in Transparent Media. Stress Birefringence. Form Birefringence
Lecture 4: Anisotropic Media Outline Dichroism Optical Activity 3 Faraday Effect in Transparent Media 4 Stress Birefringence 5 Form Birefringence 6 Electro-Optics Dichroism some materials exhibit different
More informationChapter 3. Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc.
Chapter 3 Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc. Concepts Energy functions F and G Chemical potential, µ Partial Molar properties
More informationmaterials and their properties
materials and their properties macroscopic properties phase state strength / stiffness electrical conductivity chemical properties color / transparence spectroscopical properties surface properties density
More informationG. Ravichandran Aeronautics & Mechanical Engineering Graduate Aeronautical Laboratories California Institute of Technology
Multi-Disciplinary University Initiative Army Research Office Engineering Microstructural Complexity in Ferroelectric Devices Mechanical Characterization G. Ravichandran Aeronautics & Mechanical Engineering
More informationEffective mass: from Newton s law. Effective mass. I.2. Bandgap of semiconductors: the «Physicist s approach» - k.p method
Lecture 4 1/10/011 Effectie mass I.. Bandgap of semiconductors: the «Physicist s approach» - k.p method I.3. Effectie mass approximation - Electrons - Holes I.4. train effect on band structure - Introduction:
More informationACII-Part II: Structure of solids; Structure-properties relationship
ACII-Part II: Structure of solids; Structure-properties relationship Dr. Liliana Viciu ACII: Prof. Reinhard Nesper and Dr. Liliana Viciu 1 Liliana Viciu B. Sc. and M.Sc. at University of Bucharest, Romania
More informationContinuum mechanism: Stress and strain
Continuum mechanics deals with the relation between forces (stress, σ) and deformation (strain, ε), or deformation rate (strain rate, ε). Solid materials, rigid, usually deform elastically, that is the
More informationContinuum Mechanics. Continuum Mechanics and Constitutive Equations
Continuum Mechanics Continuum Mechanics and Constitutive Equations Continuum mechanics pertains to the description of mechanical behavior of materials under the assumption that the material is a uniform
More informationPhysics of Continuous media
Physics of Continuous media Sourendu Gupta TIFR, Mumbai, India Classical Mechanics 2012 October 26, 2012 Deformations of continuous media If a body is deformed, we say that the point which originally had
More informationSome properties of the Helmholtz free energy
Some properties of the Helmholtz free energy Energy slope is T U(S, ) From the properties of U vs S, it is clear that the Helmholtz free energy is always algebraically less than the internal energy U.
More informationTUTORIAL 6: PHONONS, LATTICE EXPANSION, AND BAND-GAP RENORMALIZATION
Hands-On Tutorial Workshop, July 29 th 2014 TUTORIAL 6: PHONONS, LATTICE EXPANSION, AND BAND-GAP RENORMALIZATION Christian Carbogno & Manuel Schöttler Fritz-Haber-Institut der Max-Planck-Gesellschaft,
More informationEvaluation and comparison of estimated wave elastic modulus of concrete, using embedded and surface bonded PZT sensor/actuator systems
Evaluation and comparison of estimated wave elastic modulus of concrete, using embedded and surface bonded PZT sensor/actuator systems Presented by: Ayumi Manawadu, Ph.D. student Zhidong Zhou, Ph.D. student
More informationPHYSICAL REVIEW B 71,
Coupling of electromagnetic waves and superlattice vibrations in a piezomagnetic superlattice: Creation of a polariton through the piezomagnetic effect H. Liu, S. N. Zhu, Z. G. Dong, Y. Y. Zhu, Y. F. Chen,
More informationMaxwell s Equations:
Course Instructor Dr. Raymond C. Rumpf Office: A-337 Phone: (915) 747-6958 E-Mail: rcrumpf@utep.edu Maxwell s Equations: Physical Interpretation EE-3321 Electromagnetic Field Theory Outline Maxwell s Equations
More informationNDT&E Methods: UT. VJ Technologies CAVITY INSPECTION. Nondestructive Testing & Evaluation TPU Lecture Course 2015/16.
CAVITY INSPECTION NDT&E Methods: UT VJ Technologies NDT&E Methods: UT 6. NDT&E: Introduction to Methods 6.1. Ultrasonic Testing: Basics of Elasto-Dynamics 6.2. Principles of Measurement 6.3. The Pulse-Echo
More informationCreation of DIPOLE (two poles) (distortion of crystal structure by the small displacement of the ion in direction of electric field)
Dielectricity Dielectric materials: Materials which is generally insulators. Under applied electric field, there is a tiny movement of charge inside the material. Electric field Creation of DIPOLE (two
More informationIntroduction, Basic Mechanics 2
Computational Biomechanics 18 Lecture : Introduction, Basic Mechanics Ulli Simon, Lucas Engelhardt, Martin Pietsch Scientific Computing Centre Ulm, UZWR Ulm University Contents Mechanical Basics Moment
More information8. Propagation in Nonlinear Media
8. Propagation in Nonlinear Media 8.. Microscopic Description of Nonlinearity. 8... Anharmonic Oscillator. Use Lorentz model (electrons on a spring) but with nonlinear response, or anharmonic spring d
More informationFinite Element Method in Geotechnical Engineering
Finite Element Method in Geotechnical Engineering Short Course on + Dynamics Boulder, Colorado January 5-8, 2004 Stein Sture Professor of Civil Engineering University of Colorado at Boulder Contents Steps
More informationNENG 301 Week 8 Unary Heterogeneous Systems (DeHoff, Chap. 7, Chap )
NENG 301 Week 8 Unary Heterogeneous Systems (DeHoff, Chap. 7, Chap. 5.3-5.4) Learning objectives for Chapter 7 At the end of this chapter you will be able to: Understand the general features of a unary
More information12. Stresses and Strains
12. Stresses and Strains Finite Element Method Differential Equation Weak Formulation Approximating Functions Weighted Residuals FEM - Formulation Classification of Problems Scalar Vector 1-D T(x) u(x)
More informationPIEZOELECTRIC TECHNOLOGY PRIMER
PIEZOELECTRIC TECHNOLOGY PRIMER James R. Phillips Sr. Member of Technical Staff CTS Wireless Components 4800 Alameda Blvd. N.E. Albuquerque, New Mexico 87113 Piezoelectricity The piezoelectric effect is
More informationSolid State Physics (condensed matter): FERROELECTRICS
Solid State Physics (condensed matter): FERROELECTRICS Prof. Igor Ostrovskii The University of Mississippi Department of Physics and Astronomy Oxford, UM: May, 2012 1 People: Solid State Physics Condensed
More informationCrystals Statics. Structural Properties. Geometry of lattices. Aug 23, 2018
Crystals Statics. Structural Properties. Geometry of lattices Aug 23, 2018 Crystals Why (among all condensed phases - liquids, gases) look at crystals? We can take advantage of the translational symmetry,
More informationLecture10: Plasma Physics 1. APPH E6101x Columbia University
Lecture10: Plasma Physics 1 APPH E6101x Columbia University Last Lecture - Conservation principles in magnetized plasma frozen-in and conservation of particles/flux tubes) - Alfvén waves without plasma
More informationProblem Set 2 Due Thursday, October 1, & & & & # % (b) Construct a representation using five d orbitals that sit on the origin as a basis:
Problem Set 2 Due Thursday, October 1, 29 Problems from Cotton: Chapter 4: 4.6, 4.7; Chapter 6: 6.2, 6.4, 6.5 Additional problems: (1) Consider the D 3h point group and use a coordinate system wherein
More informationUnit IV State of stress in Three Dimensions
Unit IV State of stress in Three Dimensions State of stress in Three Dimensions References Punmia B.C.,"Theory of Structures" (SMTS) Vol II, Laxmi Publishing Pvt Ltd, New Delhi 2004. Rattan.S.S., "Strength
More informationME 515 Mechatronics. Overview of Computer based Control System
ME 515 Mechatronics Introduction to Sensors I Asanga Ratnaweera Department of Faculty of Engineering University of Peradeniya Tel: 081239 (3627) Email: asangar@pdn.ac.lk Overview of Computer based Control
More information3 Constitutive Relations: Macroscopic Properties of Matter
EECS 53 Lecture 3 c Kamal Sarabandi Fall 21 All rights reserved 3 Constitutive Relations: Macroscopic Properties of Matter As shown previously, out of the four Maxwell s equations only the Faraday s and
More informationFerromagnetism. Iron, nickel, and cobalt are ferromagnetic.
Ferromagnetism Technische Universität Graz Institute of Solid State Physics Ferromagnetism elow a critical temperature (called the Curie temperature) a magnetization spontaneously appears in a ferromagnet
More informationBrief introduction to groups and group theory
Brief introduction to groups and group theory In physics, we often can learn a lot about a system based on its symmetries, even when we do not know how to make a quantitative calculation Relevant in particle
More informationHolcomb Group Capabilities
Holcomb Group Capabilities Synchrotron Radiation & Ultrafast Optics West Virginia University mikel.holcomb@mail.wvu.edu The Physicists New Playground The interface is the device. - Herbert Kroemer, beginning
More informationHong Zhou, Guang-Xiang Liu,* Xiao-Feng Wang and Yan Wang * Supporting Information
Three cobalt(ii) coordination polymers based on V-shaped aromatic polycarboxylates and rigid bis(imidazole) ligand: Syntheses, crystal structures, physical properties and theoretical studies Hong Zhou,
More information36. Nonlinear optics: (2) processes
36. Nonlinear optics: () processes The wave equation with nonlinearity Second-harmonic generation: making blue light from red light approximations: SVEA, zero pump depletion phase matching quasi-phase
More informationProblem Set 2 Due Tuesday, September 27, ; p : 0. (b) Construct a representation using five d orbitals that sit on the origin as a basis: 1
Problem Set 2 Due Tuesday, September 27, 211 Problems from Carter: Chapter 2: 2a-d,g,h,j 2.6, 2.9; Chapter 3: 1a-d,f,g 3.3, 3.6, 3.7 Additional problems: (1) Consider the D 4 point group and use a coordinate
More informationAB-267 DYNAMICS & CONTROL OF FLEXIBLE AIRCRAFT
FLÁIO SILESTRE DYNAMICS & CONTROL OF FLEXIBLE AIRCRAFT LECTURE NOTES LAGRANGIAN MECHANICS APPLIED TO RIGID-BODY DYNAMICS IMAGE CREDITS: BOEING FLÁIO SILESTRE Introduction Lagrangian Mechanics shall be
More informationAdvanced. piezoelectric. materials. Science and technology. Edited by. Kenji Uchino WOODHEAD PUBLISHING. Oxford Cambridge Philadelphia New Delhi
Advanced piezoelectric materials Science and technology Edited by Kenji Uchino WOODHEAD PUBLISHING Oxford Cambridge Philadelphia New Delhi Woodhead Publishing Limited, 2010 Contents Contributor contact
More informationJournal. Three-Dimensional Computer Simulation of Ferroelectric Domain Formation. Theory and Modeling of Glasses and Ceramics
Journal Theory and Modeling of Glasses and Ceramics J. Am. Ceram. Soc., 81 [3] 492 5 (1998) Three-Dimensional Computer Simulation of Ferroelectric Domain Formation Three-dimensional (3-D) computer simulations
More informationElectrical material properties
Electrical material properties U = I R Ohm s law R = ρ (l/a) ρ resistivity l length σ = 1/ρ σ conductivity A area σ = n q μ n conc. of charge carriers q their charge μ their mobility μ depends on T, defects,
More informationFIELD MODELS OF POWER BAW RESONATORS
FIELD MODELS OF POWER BAW RESONATORS MIHAI MARICARU 1, FLORIN CONSTANTINESCU 1, ALEXANDRE REINHARDT 2, MIRUNA NIŢESCU 1, AURELIAN FLOREA 1 Key words: Power BAW resonators, 3D models. A simplified 3 D model,
More informationNONLINEAR CONTINUUM FORMULATIONS CONTENTS
NONLINEAR CONTINUUM FORMULATIONS CONTENTS Introduction to nonlinear continuum mechanics Descriptions of motion Measures of stresses and strains Updated and Total Lagrangian formulations Continuum shell
More informationBasic Equations of Elasticity
A Basic Equations of Elasticity A.1 STRESS The state of stress at any point in a loaded bo is defined completely in terms of the nine components of stress: σ xx,σ yy,σ zz,σ xy,σ yx,σ yz,σ zy,σ zx,andσ
More informationSENSORS and TRANSDUCERS
SENSORS and TRANSDUCERS Tadeusz Stepinski, Signaler och system The Mechanical Energy Domain Physics Surface acoustic waves Silicon microresonators Variable resistance sensors Piezoelectric sensors Capacitive
More informationlectures accompanying the book: Solid State Physics: An Introduction, by Philip ofmann (2nd edition 2015, ISBN-10: 3527412824, ISBN-13: 978-3527412822, Wiley-VC Berlin. www.philiphofmann.net 1 Bonds between
More information535.37(075.8) : /, ISBN (075.8) ISBN , 2008, 2008
.. 2008 535.37(075.8) 22.34573 66.. 66 : /... : -, 2008. 131. ISBN 5-98298-312-8 -,, -,,, -, -., 200203 «-».,,, -. 535.37(075.8) 22.34573 -,.. ISBN 5-98298-312-8.., 2008, 2008., 2008 2 , -. :,, - ;,, ;
More informationinduced _ electric _ field = = = = σ V
The Figure shows that the open-circuit voltage V (an hence the fiel strength ) is proportional to compressive stress T up to a maximum of 5 kv, which occurs at a stress of 50 MPa. Inuce electrical fiel
More informationGiant Piezocaloric Effect in PZT Ceramic Film
Ferroelectrics, 483: 102 107, 2015 Copyright Taylor & Francis Group, LLC ISSN: 0015-0193 print / 1563-5112 online DOI: 10.1080/00150193.2015.1059147 Giant Piezocaloric Effect in PZT Ceramic Film ALEXANDER
More informationIntroduction to Seismology Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 12.510 Introduction to Seismology Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Stress and Strain
More informationThe mathematical description of the motion of Atoms, Molecules & Other Particles. University of Rome La Sapienza - SAER - Mauro Valorani (2007)
The mathematical description of the motion of Atoms, Molecules Other Particles Particle Dynamics Mixture of gases are made of different entities: atoms, molecules, ions, electrons. In principle, the knowledge
More informationMechanics of Earthquakes and Faulting
Mechanics of Earthquakes and Faulting www.geosc.psu.edu/courses/geosc508 Overview Milestones in continuum mechanics Concepts of modulus and stiffness. Stress-strain relations Elasticity Surface and body
More informationIntroduction to solid state physics
PHYS 342/555 Introduction to solid state physics Instructor: Dr. Pengcheng Dai Professor of Physics The University of Tennessee (Room 407A, Nielsen, 974-1509) Chapter 13: Dielectrics and ferroelectrics
More information