SpringerSeriesin materials science 129 SpringerSeriesin materials science Editors: R.Hull C.Jagadish R.M.Osgood,Jr. J.Parisi Z.Wang H.Warlimont The Springer Series in Materials Science covers the complete spectrum of materials physics, includingfundamentalprinciples,physicalproperties,materialstheoryanddesign.Recognizing theincreasingimportanceofmaterialsscienceinfuturedevicetechnologies,thebooktitlesinthis seriesreflectthestate-of-the-artinunderstandingandcontrollingthestructureandproperties ofallimportantclassesofmaterials. PleaseviewavailabletitlesinSpringerSeriesinMaterialsScience onserieshomepagehttp://www.springer.com/series/856 Ulrich Messerschmidt Dislocation Dynamics During Plastic Deformation With291 Figures and 56 Video Sequences 123 ProfessorDr.UlrichMesserschmidt GuestScientistatMaxPlanckInstituteofMicrostructurePhysics Weinberg2,06120Halle(Saale),Germany E-mail:[email protected] SeriesEditors: ProfessorRobertHull ProfessorJu¨rgenParisi UniversityofVirginia Universita¨tOldenburg,FachbereichPhysik Dept.ofMaterialsScienceandEngineering Abt.Energie-undHalbleiterforschung ThorntonHall Carl-von-Ossietzky-Straße9–11 Charlottesville,VA22903-2442,USA 26129Oldenburg,Germany ProfessorChennupatiJagadish Dr.ZhimingWang AustralianNationalUniversity UniversityofArkansas ResearchSchoolofPhysicsandEngineering DepartmentofPhysics J4-22,CarverBuilding 835W.DicknsonSt. CanberraACT0200,Australia Fayetteville,AR72701,USA ProfessorR.M.Osgood,Jr. ProfessorHansWarlimont MicroelectronicsScienceLaboratory DSLDresdenMaterial-InnovationGmbH DepartmentofElectricalEngineering PirnaerLandstr.176 ColumbiaUniversity 01257Dresden,Germany SeeleyW.MuddBuilding NewYork,NY10027,USA Additional materialto thisbook (video clips of dislocation motion) canbe downloaded from h ttp://extras.springer.com/2010/978-3-642-03176-2 SpringerSeriesinMaterialsScience ISSN0933-033X ISBN978-3-642-03176-2 e-ISBN978-3-642-03177-9 DOI10.1007/978-3-642-03177-9 SpringerHeidelbergDordrechtLondonNewYork LibraryofCongressControl Number: 2009938024 ©Springer-VerlagBerlinHeidelberg2010 This work is subject to copyright. 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Cover design:eStudio Calamar Steinen Printedonacid-freepaper SpringerisapartofSpringerScience+BusinessMedia(www.springer.com) Preface Very many structural materials like metals and ceramics are of crystalline nature.Undermostoftheconditions,theyundergoplasticdeformationbefore they fail under load. The plastic deformation is mediated by the genera- tionandmotionofone-dimensionalcrystaldefects,the so-calleddislocations. Thus, the density and dynamic properties of the dislocations determine the plastic behavior of the respective materials and frequently also their failure. Thedislocationdynamics,thatis,theresponseofthedislocationstoanexter- nal load, is controlled by the interaction between the moving dislocations with the periodic crystal lattice structure, other crystal defects from point defectsoversmallclusterstolargerprecipitates,withotherdislocationsform- ing a microstructure through which the mobile dislocations have to move, and finally the grain and phase structure of the material. Considering these different interactions,the dislocation motion turns out to be quite a complex process. In situ straining experiments in a transmission electron microscope are a powerful means for studying the microprocesses controlling the dislocation mobility.Withthismethod,dislocationscandirectlybeobservedduringtheir motionunderload.Thetechniqueadvancedwhenhigh-voltageelectronmicro- scopes became commercially available at the end of the 1960s, first in Japan and later on also in other countries. These microscopes enable the transmis- sion of thicker specimens, which have properties similar to macroscopic bulk specimens.Besides,theyoffersufficientroomforelaboratedeformationstages in the specimen chamber. In the last 30 years, in situ straining experiments were performed on many materials, both in conventional and in high-voltage electron microscopes. The present author and his coworkers performed such experiments over about 30 years, yielding many hours of video recordings of dislocation motion. This book gives an introduction into the processes controlling the dislo- cation dynamics and its role in crystal plasticity. It is divided into two parts. PartIdescribesthegeneralpropertiesofdislocationmotioninanintroductory waysuitedalsoforstudentswithoutpriorknowledgeindislocationproperties. VI Preface “Dislocations” in a mowed lawn (solarized) It is based on lectures given in the Physics Department of the Martin Luther University in Halle (Saale). For easy understanding, the mathe- matical treatment is presented on a simple level. In Part II, particular materialsarediscussedcoveringsemiconductors,ceramicsinglecrystals,met- als, and alloys including intermetallic alloys and quasicrystals. The whole text is, whenever possible, illustrated by electron micrographs, partly of dislocations under load taken during in situ straining experiments in a high- voltage electron microscope. Besides, video files can be downloaded from http://extras.springer.com/2010/978-3-642-03176-2 presenting characteristic video sequences of moving dislocations. The videos are commented in the chapters of Part II but are referred to also in Part I. The presentation of the differentmaterialsisnotexhaustivebutintendedto explaintheprocesses showninthevideos.Itisamainaimofthisworktomakethevideosequences available to a greater number of scientists and lecturers. The experimental work frequently referred to in this book and exploited for the video clips was carried out in the Institute of Solid State Physics and ElectronMicroscopyof the Academy of Sciences of the GDR in Halle (Saale) and since 1992 in the Max Planck Institute of Microstructure Physics at the same place. The author is very grateful to all responsible directors, that is, thelateHeinzBethge,VolkerSchmidt,andJu¨rgenKirschner,forcreatingthe experimentalandcollaborativeenvironmentforthesestudies.Thecontinuous high-quality performance of the high-voltage electron microscope was essen- tially due to Christian Dietzsch. The author acknowledges the contributions Preface VII of many scientists to the experiments and interpretations; first of all to Fritz Appel for the work on NaCl, MgO, and some metals, and Martin Bartsch for the studies on all other materials. He had an essential influence on the experiments and the instruction of the PhD students and post-doctoral fel- lowswho workedin projectsfunded by the Deutsche Forschungsgemeinschaft and the Volkswagenstiftung. He also saved the original video recordings in digitalformandhelped tocollectdataforthe book,andhe discussedits con- tents.Manyotherscientistswereinvolvedintheexperiments.Theirnamesare listed below.1 Ju¨rgen Kirschner supported the preparation of the book after myretirement.Hans-RainerTrebin,BorisV.Petukhov,WolfgangBlum,Hart- mut Leipner, and Ichiro Yonenaga discussed special topics or helped finding suitable references. Video clips were made available by Daniel Caillard and Volker Mohles. The author is very grateful for all these contributions. The English of the text was kindly revised by Heike Messerschmidt. Halle (Saale) Ulrich Messerschmidt December 2009 1 Part of the experimental work was carried out by the PhD students and post- doctoral fellows Susanne Guder, Anna Wasilkowska, Dietmar Baither, Bernd Baufeld, Ralf Hausha¨lter, Dietrich Ha¨ussler, Bert Geyer, Ludwig Junker, Lars Ledig, and Aleksander Tikhonovski. Several studies were performed in close collaboration with other laboratories. In this respect, I thank the late Peter Haasen, Manfred Ru¨hle, Knut Urban, Toru Imura, Masaharu Yamaguchi, Eck- hardNembach,BerndReppich,GerhardSauthoff,EduardM.Nadgornyi,PeterJ. Wilbrandt,MarkusWollgarten,MichaelFeuerbacher,PeterSchall,MarkAindow, Ian Jones, Hiro Saka, Yoichi Nishino, Christina Scheu, Easo P. George, Witold Zielinski, and Michael Mills. Furthernames will be found in thereferences. Contents Part I General Properties of Dislocation Motion 1 Introduction............................................... 3 1.1 Theoretical Yield Strength................................ 4 1.2 Plastic Shear by the Motion of Dislocations................. 5 2 Experimental Methods .................................... 11 2.1 Macroscopic Deformation Tests ........................... 11 2.2 Stress Pulse Double Etching Technique..................... 16 2.3 Transmission Electron Microscopy ......................... 18 2.4 In Situ Straining Experiments in the Transmission Electron Microscope ............................................. 20 2.5 Other Methods.......................................... 26 2.5.1 X-Ray Topography In Situ Deformation Experiments .. 27 2.5.2 Surface Studies of Slip Lines ........................ 27 2.5.3 Internal Friction................................... 29 2.5.4 Nuclear Magnetic Resonance........................ 33 3 Properties of Dislocations ................................. 35 3.1 Geometric Properties .................................... 35 3.1.1 Burgers Vector.................................... 35 3.1.2 Glide and Climb Motion of a Dislocation ............. 37 3.1.3 Relation Between Dislocation Motion and Plastic Strain and Strain Rate .................. 39 3.2 Elastic Properties of Dislocations.......................... 40 3.2.1 Stress Fields of Straight Dislocations................. 41 3.2.2 Dislocation Energy ................................ 43 3.2.3 Forces on Dislocations ............................. 47 3.2.4 Interaction Between ParallelDislocations............. 50 3.2.5 Interaction Between Nonparallel Dislocations ......... 52 X Contents 3.2.6 Elastic Interaction Between Dislocations and Elastic Inclusions.............................. 54 3.2.7 Bowed-Out Dislocations............................ 57 3.3 Dislocations in Crystals .................................. 65 3.3.1 Selection of Burgers Vectors ........................ 66 3.3.2 Stacking Faults and Partial Dislocations.............. 66 3.3.3 Twins............................................ 70 3.3.4 Antiphase Boundaries.............................. 71 4 Dislocation Motion ........................................ 73 4.1 Thermally Activated Overcoming of Barriers................ 74 4.2 Lattice Friction ......................................... 78 4.2.1 Peierls–NabarroModel............................. 79 4.2.2 Double-Kink Model................................ 83 4.2.3 Characteristics and Experimental Evidence of the Double-Kink Model .......................... 92 4.3 Slip and Cross Slip ...................................... 93 4.4 The Locking–Unlocking Mechanism........................ 99 4.5 Overcoming of Localized Obstacles ........................101 4.5.1 Friedel Statistics ..................................103 4.5.2 Mott Statistics....................................110 4.6 Transition from the Double-Kink Mechanism to the Overcoming of Localized Obstacles ..................113 4.7 Overcoming of Extended Obstacles ........................116 4.8 Dislocation Intersections .................................126 4.9 Dislocation Motion at High Velocities and Low Temperatures...................................129 4.10 Dislocation Climb .......................................132 4.10.1 Point Defect Equilibrium Concentrations .............132 4.10.2 Climb Forces .....................................134 4.10.3 Emission- or Absorption-controlledClimb ............137 4.10.4 Diffusion-controlled Climb..........................140 4.10.5 Jog Dragging .....................................141 4.11 Drag Forces due to Point Defect Atmospheres...............143 4.12 Dynamic Laws of Dislocation Mobility .....................150 5 Dislocation Kinetics, Work-Hardening, and Recovery ......155 5.1 Dislocation Kinetics .....................................155 5.1.1 Models of Dislocation Generation....................156 5.1.2 Experimental Evidence of Dislocation Generation......162 5.1.3 Dislocation Immobilization and Annihilation..........166 5.2 Work-Hardening and Recovery ............................171 5.2.1 Work-Hardening Models............................172 5.2.2 Thermal and Athermal Components of the Flow Stress .................................180