Richard C Powell - Böcker

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...57 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 ...

This graduate-level text presents the fundamental physics of solid-state lasers, including the basis of laser action and the optical and electronic properties of laser materials. Some knowledge of quantum mechanics and solid-state physics is assumed, but the discussion is as self-contained as possible, making the book an excellent reference as well as useful for independent study. After an overview of the topic, the book is divided into two parts. The first begins with a review of the quantum mechanics and solid-state physics, spectroscopy, and crystal field theory; it then treats the quantum theory of radiation, the emission and absorption of radiation, and nonlinear optics; it concludes with discussions of lattice vibrations and ion-ion interactions and of their effects on optical properties and laser action. The second part treats specific solid-state laser materials, the protypical ruby and Nd-YAG systems being treated in greatest detail; it concludes with a discussion of novel and non-standard materials.

This graduate-level text presents the fundamental physics of solid-state lasers, including the basis of laser action and the optical and electronic properties of laser materials. Some knowledge of quantum mechanics and solid-state physics is assumed, but the discussion is as self-contained as possible, making the book an excellent reference as well as useful for independent study. After an overview of the topic, the book is divided into two parts. The first begins with a review of the quantum mechanics and solid-state physics, spectroscopy, and crystal field theory; it then treats the quantum theory of radiation, the emission and absorption of radiation, and nonlinear optics; it concludes with discussions of lattice vibrations and ion-ion interactions and of their effects on optical properties and laser action. The second part treats specific solid-state laser materials, the protypical ruby and Nd-YAG systems being treated in greatest detail; it concludes with a discussion of novel and non-standard materials.

The polar regions (the Arctic and Antarctic) have enjoyed widespread public attention in recent years, as issues of conservation, sustainability, resource speculation and geopolitical manoeuvring have all garnered considerable international media interest. This critical collection of new and original papers - the first of its kind - offers a comprehensive exploration of these and other topics, consolidating the emergent field of polar geopolitics. The expert international contributors to this volume offer a range of insightful comparative, interdisciplinary and global perspectives on polar issues. Key topics discussed include resource extraction, regime formation, knowledge construction, border issues, governance and treaties, and indigenous livelihoods. Contributions from scholars of history, geography, political science, anthropology and international law make this a truly comprehensive take on the current state and future prospects of both the polar regions and polar geopolitics as a distinct discipline. Students and professors of geopolitics, political science and geography - especially those with an interest in the polar regions - will find much of value in this book s concrete expression of a new and fascinating field.

This book covers all of the fundamentals of first-year undergraduate physics, as well as introducing condensed matter, quantum mechanics, relativity, particle physics, and astrophysics. It takes a methodical, visual approach to problem-solving: throughout, the reader is encouraged to draw a picture of the problem, write down the knowns and unknowns, and find the equations that connect them. Each chapter contains an experiment for the student to perform, emphasizing the observational nature of science. The book also contains a wealth of homework problems and end-of-module and -semester tests, making it readily adoptable for introductory physics courses. With its broad topical coverage, calculus-free treatment, and emphasis on problem-solving and experiments, this book will equip students and home learners with the skills and knowledge for further study in physics.