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DrorSarid Exploring Scanning Probe Microscopy with MATHEMATICA Second, Completely Revised and Enlarged Edition WILEY-VCH Verlag GmbH & Co. KGaA DrorSarid ExploringScanningProbeMicroscopy withMATHEMATICA 1807–2007 Knowledge for Generations Each generation has its unique needs and aspirations. When Charles Wiley first openedhis small printing shop in lower Manhattan in 1807, it was a generation of boundless potential searching for an identity. And we were there, helping to define a new American literary tradition. Over half a century later, in the midst of the Second Industrial Revolution, it was a generation focused on building the future. Onceagain, we werethere, supplying the criticalscientific,technical, and engineering knowledge that helped frame the world. Throughout the 20th Century, and into the new millennium, nations began to reach out beyond their own bordersand a new international community was born.Wiley was there, ex- panding its operations around the world to enable a global exchange of ideas, opinions,and know-how. For 200 years, Wiley has been an integral part of each generation’s journey, enabling the flow of information and understanding necessary to meet their needs and fulfill their aspirations. Today, bold new technologies are changing the way we live and learn. Wiley will be there, providing you the must-have knowledge you need to imagine new worlds, new possibilities, and new oppor- tunities. Generations come and go, but you can always count on Wiley to provide you the knowledge you need,when and whereyou need it! WilliamJ. Pesce PeterBooth Wiley Presidentand Chief ExecutiveOfficer Chairman of the Board DrorSarid Exploring Scanning Probe Microscopy with MATHEMATICA Second, Completely Revised and Enlarged Edition WILEY-VCH Verlag GmbH & Co. KGaA TheAuthor AllbookspublishedbyWiley-VCHarecarefully produced.Nevertheless,authors,editors,and publisherdonotwarranttheinformation Prof.DrorSarid containedinthesebooks,includingthisbook,to CollegeofOpticalScience befreeoferrors.Readersareadvisedtokeepin UniversityofArizona mindthatstatements,data,illustrations, Tucson,Arizona85721 proceduraldetailsorotheritemsmay USA inadvertentlybeinaccurate. [email protected] LibraryofCongressCardNo.: Cover: appliedfor Threebuckyballsadsorbedonthe surfaceofSi(100),obtainedusing BritishLibraryCataloguing-in-PublicationData ultrahighvacuumSTM. Acataloguerecordforthisbookisavailablefrom theBritishLibrary Bibliographicinformationpublishedby theDeutscheNationalbibliothek TheDeutscheNationalbibliothekliststhis publicationintheDeutscheNationalbibliografie; detailedbibliographicdataareavailableinthe Internetat<http://dnb.d-nb.de>. ©2007WILEY-VCHVerlagGmbH&Co.KGaA, Weinheim Allrightsreserved(includingthoseoftranslation intootherlanguages).Nopartofthisbookmaybe reproducedinanyform–photoprinting,microfilm, oranyothermeans–transmittedortranslatedinto amachinelanguagewithoutwrittenpermission fromthepublishers.Registerednames, trademarks,etc.usedinthisbook,evenwhennot specificallymarkedassuch,arenottobe consideredunprotectedbylaw. Typesetting Da-TeXGerdBlumenstein,Leipzig Printing StraussGmbH,Mörlenbach Binding Litges&DopfBuchbindereiGmbH, Heppenheim PrintedintheFederalRepublicofGermany Printedonacid-freepaper ISBN: 978-3-527-40617-3 ToLea,Rami,Uri,Karen,andDanieli 7 Contents Preface 17 1 Introduction 22 1.1 Style 22 1.2 MathematicaPreparation 23 1.2.1 General 23 1.2.2 Example 24 1.3 RecommendedBooks 25 1.3.1 MathematicaProgrammingLanguage 25 1.3.2 ScanningProbeMicroscopies 26 2 UniformCantilevers 27 2.1 Introduction 27 2.2 BendingDuetoFz 30 2.2.1 GeneralEquations 30 2.2.2 Slope 31 2.2.3 AngularSpringConstant 31 2.2.4 Displacement 32 2.2.5 LinearSpringConstant 32 2.2.6 NumericalExample:Si 33 2.2.7 NumericalExample:PtIr 33 2.3 BucklingDuetoFx 36 2.3.1 GeneralEquations 36 2.3.2 Slope 36 2.3.3 AngularSpringConstant 36 2.3.4 Displacement 37 2.3.5 LinearSpringConstant 37 2.3.6 NumericalExample:Si 37 2.3.7 NumericalExample:PtIr 39 2.4 TwistingDuetoFy 40