Ferroic Functional Materials: Experiment, Modeling and Simulation PDF
Preview Ferroic Functional Materials: Experiment, Modeling and Simulation
CISM International Centre for Mechanical Sciences 581 Courses and Lectures Jörg Schröder Doru C. Lupascu Editors Ferroic Functional Materials Experiment, Modeling and Simulation International Centre for Mechanical Sciences CISM International Centre for Mechanical Sciences Courses and Lectures Volume 581 Series editors The Rectors Elisabeth Guazzelli, Marseille, France Franz G. Rammerstorfer, Vienna, Austria Wolfgang. A. Wall, Munich, Germany The Secretary General Bernhard Schrefler, Padua, Italy Executive Editor Paolo Serafini, Udine, Italy Theseriespresentslecturenotes,monographs,editedworksandproceedingsinthe field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences. More information about this series at http://www.springer.com/series/76 ö ö J rg Schr der Doru C. Lupascu (cid:129) Editors Ferroic Functional Materials Experiment, Modeling and Simulation 123 Editors Jörg Schröder Doru C.Lupascu Institute of Mechanics Instiute forMaterials Science University of Duisburg-Essen University of Duisburg-Essen Essen Essen Germany Germany ISSN 0254-1971 ISSN 2309-3706 (electronic) CISMInternational Centre for MechanicalSciences ISBN978-3-319-68881-7 ISBN978-3-319-68883-1 (eBook) https://doi.org/10.1007/978-3-319-68883-1 LibraryofCongressControlNumber:2017955266 ©CISMInternationalCentreforMechanicalSciences2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Functional materials play a key role in many modern technical devices ranging fromconsumermarketitemstoapplicationsinhigh-endequipmentforautomotive, aircraft and spacecraft, medical, and information technologies. Among functional materials, smart materials represent a class that transforms one basic physical propertyintoanother.Thedevelopmentofdevicesutilizingsmartmaterials,aswell astheirtesting,isgenerallyveryexpensive.Therefore,considerableefforthasbeen made to develop modeling tools that allow bypassing many of the experimental steps previously required in design. Important smart materials are ferroelectrics (couplingbetweenelectricpolarizationandstrain),ferromagnets(couplingbetween magnetizationandstrain),shape-memoryalloys(couplingbetweentemperatureand strain), and magnetoelectric multiferroics (coupling between electric polarization andmagnetization).Thelatteronescombinethemutualcontrollabilityofmagnetic and electric state variables. They are of great interest in the development of mul- tifunctionaldevices.Insingle-phasemultiferroics,themagnetoelectricinteractionis generally very weak and mostly occurs at cryogenic temperatures. Therefore, the experimental preparation and characterization of composite materials, as well as their constitutive description based on homogenization strategies, are key chal- lenges for the optimization of such magnetoelectric composites. The development of such composites made from two different ferroics is based on a comprehensive understanding of both the experimental and theoretical details of these materials. Thus, this CISM course covers the modeling of ferroelectric materials, ferromag- netic materials and shape-memory alloys, the formation offerroic microstructures and their continuum-mechanical modeling, the experimental preparation and characterization of magnetoelectric multiferroics, computational homogenization, and the algorithmic treatment in the framework of numerical solution strategies. TheCISMcourseon“FerroicFunctionalMaterials:Experiment,Modeling,and Simulation,”heldinUdinefromSeptember8to12,2014,wasaddressingdoctoral studentsandpostdoctoralresearchersincivilandmechanicalengineering,materials science,physicsandappliedmathematics,andindustrialresearcherswhowishedto broaden their knowledge in experiments and theory offerroic materials. The main focus was on the state-of-the-art experimental methods and advanced modeling v vi Preface techniques,whichareessentialtoqualifyyoungscientistsforhigh-qualityresearch, and the development of innovative products and applications. It is our pleasure to thank the lecturers of the CISM course Kaushik Bhattacharya (Pasadena, USA), Manfred Fiebig (Zurich,Switzerland), JohnHuber (Oxford, UK), Christopher Lynch (Los Angeles, USA), Marc-André Keip (Stuttgart, Germany) as well as the additional contributors to these CISM lecture notes Dorinamaria Carka (Old Westbury, USA), Irina Anusca (Essen, Germany), Morad Etier (Essen, Germany), Yanling Gao (Essen, Germany), Gerhard Lackner (Essen, Germany), Ahmadshah Nazrabi (Essen, Germany), Mehmet Sanlialp (Essen, Germany), Harshkumar Trivedi (Essen, Germany), Matthias Labusch (Essen, Germany), and Naveed Ul-Haq (Essen, Germany). We furthermore thank theparticipantswhomadethecourseasuccess.Finally,weextendourthankstothe Rectors, the Board, and the staff of CISM for the excellent support and kind help. Essen, Germany Jörg Schröder Doru C. Lupascu Contents FundamentalsofMagneto-Electro-MechanicalCouplings:Continuum Formulations and Invariant Requirements. . . . . . . . . . . . . . . . . . . . . . . 1 Jörg Schröder Ferroelectric and Ferromagnetic Phase Field Modeling . . . . . . . . . . . . . 55 Dorinamaria Carka and Christopher S. Lynch Semiconductor Effects in Ferroelectrics . . . . . . . . . . . . . . . . . . . . . . . . . 97 Doru C. Lupascu, Irina Anusca, Morad Etier, Yanling Gao, Gerhard Lackner, Ahmadshah Nazrabi, Mehmet Sanlialp, Harshkumar Trivedi, Naveed Ul-Haq and Jörg Schröder Electromechanical Models of Ferroelectric Materials. . . . . . . . . . . . . . . 179 J. E. Huber An FE2-Scheme for Magneto-Electro-Mechanically Coupled Boundary Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Matthias Labusch, Jörg Schröder and Marc-André Keip Multiscale Modeling of Electroactive Polymer Composites. . . . . . . . . . . 263 Marc-André Keip and Jörg Schröder vii Fundamentals of Magneto-Electro-Mechanical Couplings: Continuum Formulations and Invariant Requirements JörgSchröder Abstract Couplings of magnetic and electric fields in materials could allow for promising applications in medical and information technology. In this contribu- tion,werecapitulatewell-knownaspectsofmagneto-electro-mechanicalproperties and their couplings. At first, we echo basic aspects of electricity and magnetism and Maxwell’s equations. Secondly, we summarize the governing equations for electrostatics and magnetostatics, point out the properties of physical fields across internalsurfaces,anddiscussthework-energytheoremofelectrodynamics,theso- calledPoynting‘stheorem.Thirdly,wewilldiscusssomefundamentalconceptsof magneto-electro-mechanical couplings in matter. Here, we will formulate thermo- dynamic potentials depending on different basic variables in order to be flexible withaviewtodifferentmodelingaspects.Afterwards,wediscussaspectsofform- invariance of physical laws under coordinate transformations: Lorentz invariance, Galileantransformationandtimereversal.Here,wefocusonpiezoelectricaswellas onmagneticsymmetrygroupsandgiveremarksonclassicalinvarianttheorysuitable forcoordinate-invariantmodelingofthermodynamicalpotentials. Partsofworkpresentedinthiscontributionaretakenfromcommonworkstogetherwithmy former co-workers Holger Romanowski, Ingo Kurzhöfer, Marc-André Keip, and Matthias Labusch.Theauthorgreatlyappreciatesthe“DeutscheForschungsgemeinschaft”(DFG)for thefinancialsupportundertheresearchgrantSCHR570/12-1withintheresearchgroupFOR 1509 on “Ferroische Funktionsmaterialien—Mehrskalige Modellierung und experimentelle Charakterisierung”. B J.Schröder ( ) FacultyofEngineering,DepartmentCivilEngineering,InstituteofMechanics, UniversityofDuisburg-Essen,Essen,Germany e-mail:[email protected] ©CISMInternationalCentreforMechanicalSciences2018 1 J.SchröderandDoruC.Lupascu(eds.),FerroicFunctionalMaterials, CISMInternationalCentreforMechanicalSciences581, https://doi.org/10.1007/978-3-319-68883-1_1 2 J.Schröder 1 Introduction In this course, we are interested in the continuum modeling of ferroic functional materials. Of particular interest are materials which allow for couplings between differentphysicalquantitiesasforinstancecouplingbetweenelectricandmechanical (ferroelectrics),mechanicalandmagnetic(ferromagnetics),ormagneticandelectric fields(multiferroics),whicharedefinedas • ferroelectricmaterialshaveaspontaneouselectricpolarization,wheretheinternal electric dipoles are coupled to the material lattice, that can be switched by an appliedelectricfield, • ferromagnetic materials, governed by their crystalline structure and microstruc- ture,haveaspontaneousmagneticpolarizationthatcanbereversedbyamagnetic field,and • multiferroicmaterialsexhibittwoormoreferroicproperties,likeferroelectricity, ferromagnetism,andferroelasticity,inthesamephase. However, the coexistence of magnetic and electric orderings in the same phase isratherdifficult.Basedontheoreticalstudies,ithasbeenshownthatusualatomic- levelmechanismswhicharedrivingferromagnetismandferroelectricityaremutually exclusive.Forexample,ferromagnetismrequirespartiallyfilledorbitals(“d”-shells) andferroelectricityemptyorbitalsintheatomicstructure.Ingeneral,theproperties offunctionalmaterialsemergeondifferentscales.Someexistontheatomicscale,as forexamplethemagnetization.Others,ase.g.theelectricpolarization,arepresent ontheunitcelllevelofacrystal.Furthermore,somematerialsobtaintheirfunctional properties only when the above quantities couple over a larger length scale, as for instanceincaseofmultiferroiccomposites. In this course, we will recapitulate well known basic properties, balance equa- tions and some formulations of thermodynamics. Furthermore, we will focus on sometransformationproperties:Physicallaws,validinaframeofreference,satisfy specificsymmetryconditions.Forexample,thesymmetrywhichreflectstheform- invarianceofphysicallawsundercoordinatetransformations.Invariancemeans,that somephysicalquantitiesremainunchangedunderspecifictransformations.Inorder togetadeeperinsightintothemathematicalmodelingofelectro-mechanicallycou- pledmaterials,wediscussthepropertiesoftheassociatedphysicalquantitiesunder thecoordinate-transformations:rotations,spatialreflections,andtime-reversal. AnoverviewofelectromagnetictheoriesisgiveninLandauandLifschitz(1985), FabrizioandMorro(2003),Tipler(1999),Jackson(2002),Griffiths(2008),Bobbio (2000), Fließbach (1999), Fließbach (2000), Grehn and Krause (2007), and Zohdi (2012). For a detailed discussion of Maxwell Equations see Maugin et al. (1991), EringenandMaugin(1989),EringenandMaugin(1990)orWeileetal.(2014).
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