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OverviewWhydowelookatsomethingsandthinktheyarebeautifulwhileotherthingsdo notappearestheticallypleasingtous?Thisisaquestionthathasalwaysinterested mankind. Oneanswerisgivenbythefollowingquotationfromanearlypresidentof theCollegeofNewJersey(nowPrincetonUniversity): ""Beautyisfoundinimmaterialthingslikeproportionoruniformity...calledbyvariousnamesofregularity,order,uniformity,symmetry, 1 proportion,harmony,etc. ""...JonathanEdwards Symmetrynotonlyprovidesthenaturalharmonythatmakessomethingappear beautifultous,butalsoisofgreatvaluetosciencebecauseitdictatesthephysical traitsofmanyobjects. Natureitselfseemstolovebeautysinceatomstendtoself? assemble into shapes with speci?c symmetry and crystals grow in geometric lattices. Inmanycases,ifweknowthesymmetryofsomethingwecanpredict someofitsimportantpropertieswithouthavingtoresorttoexperimentationor complicatedcalculations. One area where the concept of symmetry plays an important role is that of crystalline solids. Crystals, by their very nature, exhibit speci?c symmetries. Crystallinematerialshavemanyimportantapplicationsindevicesbasedontheir electronic,optical,thermal,magnetic,andmechanicalproperties. Solidstatep- sicistsandchemists,aswellasmaterialscientistsandengineers,havedeveloped rigorousquantumtheoreticalmodelstodescribethesepropertiesandsophisticated measurementtechniquestoverifythesemodels. Manytimes,however,inscreeningmaterialsforanewapplicationitisuseful to be able to quickly and easily determine if a speci?c material will have the appropriatepropertieswithoutmakingdetailedcalculationsorexperiments. This canbedonebyanalyzingthesymmetrypropertiesofthematerial. Themathema- calformalismthathasbeendevelopedtoaccomplishthisiscalledgrouptheory. Thesymmetrypropertiesofacrystalcanbedescribedbyagroupofmathematical 1 J. Edwards,WorksofJonathanEdwards(BannerofTruthTrust,Edinburgh,1979) v vi Preface operations. Thenusingsimplegrouptheoryprocedures,thephysicalpropertiesof thecrystalcanbedetermined. Duringthe45yearsIhavebeeninvolvedinteachingandresearchinvarious areasofsolidstatephysics,Ihavemadeextensiveuseoftheconceptsofgroup theory. YetIhavebeensurprisedathowlittleemphasisthistopicreceivesinany formaleducationalcurriculum. Generally,astudentstudyingsolidstatephysicsor chemistrywillbeexposedtocrystalstructuresearlyinthesemesterandthenhave nofurtherexposuretocrystalsymmetryuntilsomespecialtopicsuchasnonlinear opticsisdiscussed. Thisbookfocusesonthesymmetryofcrystalsandthedescr- tionofthissymmetrythroughtheuseofgrouptheory. Althoughspeci?cexamples are provided of using this formalism to determine both the microscopic and macroscopicpropertiesofmaterials,theemphasisisonthecomprehensive,per- sivenatureofsymmetryinallareasofsolidstatescience. Theintentofthebookistobeareferencesourceforthosedoingresearchor teachinginsolidstatescienceandengineering,oratextforaspecialtycoursein grouptheoryappliedtothepropertiesofcrystals. Tucson,AZ RichardC. Powell June2010 Contents 1 SymmetryinSolids...1 1. 1 Symmetry...1 1. 2 CrystalStructures...4 1. 3 SymmetryinReciprocalSpace...15 1. 4 Problems...24 References...24 2 GroupTheory...25 2. 1 BasicConceptsofGroupTheory...27 2. 2 CharacterTables...31 2. 3 GroupTheoryExamples...40 2. 3. 1 C PointGroup...40 3v 2. 3. 2 O PointGroup...45 h 2. 4 GroupTheoryinQuantumMechanics...47 2. 5 Problems...52 References...53 3 TensorPropertiesofCrystals...55 3. 1 First-RankMatterTensors...5 7 3. 2 Second-RankMatterTensors...62 3. 3 Third-RankMatterTensors...68 3. 4 Fourth-RankMatterTensors...73 3. 5 Problems...77 References...77 4 SymmetryPropertiesofPointDefectsinSolids...79 4. 1 EnergyLevelsofFreeIons...79 4. 2 CrystalFieldSymmetry...85 4. 3 EnergyLevelsofIonsinCrystals...87 vii viii Contents 4. 4 Example:d?Electrons...95 4. 5 Example:f-Electrons...100 4. 6 Problems...104 References...104 5 SymmetryandtheOpticalPropertiesofCrystals ... Full Product DetailsAuthor: Richard C PowellPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 2010 Volume: 824 Dimensions: Width: 15.50cm , Height: 1.20cm , Length: 23.50cm Weight: 0.760kg ISBN: 9781441975973ISBN 10: 1441975977 Pages: 230 Publication Date: 10 December 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationI. Symmetry in Solids II. Group Theory III. Tensor Properties of Crystals IV. Symmetry Properties of Point Defects in Solids V. Symmetry and the Optical Properties of Solids VI. Nonlinear Optics VII. Symmetry and Lattice Vibrations VIII. Symmetry and Electron Energy Levels Tab Content 6Author Website:Countries AvailableAll regions |