Symmetry, group theory, and the physical properties of crystals
著者
書誌事項
Symmetry, group theory, and the physical properties of crystals
（Lecture notes in physics, 824）
Springer, c2010
大学図書館所蔵 全14件
注記
Includes bibliographical references and index
内容説明・目次
内容説明
Whydowelookatsomethingsandthinktheyarebeautifulwhileotherthingsdo 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 ...
目次
Symmetry in Solids.- Group Theory.- Tensor Properties of Crystals.- Symmetry Properties of Point Defects in Solids.- Symmetry and the Optical Properties of Crystals.- Nonlinear Optics.- Symmetry and Lattice Vibrations.- Symmetry and Electron Energy Levels.
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