Understanding Luminescence Spectra and Efficiency Using Wp and Related Functions: 13 - Brossura

Struck, Charles W. W.; Fonger, William H.

Brossura

ISBN 10: 3642486312 ISBN 13: 9783642486319

Casa editrice: Springer, 2012

Riassunto

This book gives a semiquantitative understanding of the properties observed in luminescence, i.e., where energy absorption and emission occur, and with what efficiency these conversion processes take place. The authors give a correct treatment of the offset dependence and the temperature dependence of nonradiative rates. The Wp function is defined as the sum of thermally weighted Franck-Condon factors. It is obtained in one dimension in several forms, and a useful recursion relation is derived between Wp's with nearby p indices.

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Contenuti

1 Introduction.- 1.1 Luminescence Centers and Models of Them.- 1.2 The Simplest Model: One Coordinate and Equal Force Constants.- 1.2.1 The Optical Band Shapes.- 1.2.2 The Nonradiative Rate.- 1.2.3 Six Typical Thermal Quenching Behaviors.- 1.2.3.1 Fast Bottom Crossover.- 1.2.3.2 Outside Crossover.- 1.2.3.3 Small-Offset Multiphonon Emission.- 1.2.3.4 Two-Step Quenching With a Fast Second Step.- 1.2.3.5 Two-Step Quenching with a Slow Second Step.- 1.2.3.6 Low-temperature Tunnelling Crossover.- 1.3 The Franck-Condon Principle for Nonradiative Rates.- 2 Harmonic Oscillator Wavefunctions.- 2.1 Hermite Polynomials.- 2.2 Generating Function for the Harmonic Oscillator Wavefunctions.- 3 The Manneback Recursion Formulas.- 3.1 Introduction.- 3.2 The Overlap Integral.- 3.3 The Generating Function for the Overlap Integral.- 3.4 The Recursion Formulas for the Overlap Integrals.- 3.5 Familiarity.- 3.6 The Orthonormality of the ANM Matrix.- 3.7 Additional Equal-Force-Constants Recursion Relations.- 4 The Luminescence Center: the Single-Configurational-Coordinate Model.- 4.1 The Model for the Radiative Rate.- 4.2 The Equal-Force-Constants Radiative Rate.- 4.3 The Unequal-Force-Constants Radiative Rate.- 4.4 The Model for the Nonradiative Rate.- 4.5 The Wp Recursion Formula.- 4.6 Explicit Series Expression for the Wp Function.- 4.7 Ip Modified Bessel Function Form for Wp.- 4.8 Limiting and Approximate Forms of Wp.- 4.9 The 5-Wp Formula for Wp,z.- 4.10 The p Formula.- 4.11 The Wp,d/dz Expression.- 4.12 The W-p/Wp and Related Ratios.- 4.13 Equal-Force-Constants Moments.- 4.14 Unequal-Force-Constants Moments.- 4.14.1 The Moments.- 4.14.2 Preliminaries I: The (?, m, ?).- 4.14.3 Preliminaries II: The Thermal Averages ?m?? v.- 4.14.4 Preliminaries III: The ?n?m?? uv.- 4.14.5 The Derivation of the Moment Expressions (4.109).- 5 Multiple Coordinate Models of a Luminescence Center.- 5.1 The Einstein-Huang-Rhys-Pekar Single-Frequency Multiple-Coordinate Model.- 5.2 The z and d/dz Multiple-Coordinate Nuclear Factors.- 5.2.1 Preliminaries I: the Yp Function.- 5.2.2 Preliminaries II: Xp, O±.- 5.2.3 Preliminaries III: XX Sums.- 5.2.4 Preliminaries IV: Wp, O±Wp Sums.- 5.2.5 Proof of Eq. (5.6) for Two Coordinates.- 5.3 Multiple-Frequency Models of a Luminescence Center.- 5.3.1 The Selected Model.- 5.3.2 Definition of the 1, z, and d/dz Operator Rates.- 5.3.3 The Condon-Operator Distribution.- 5.3.4 The Recursion Algebra for the z and d/dz Operators.- 5.3.4.1 The ? Functions.- 5.3.4.2 The ? Recursion Algebras.- 5.3.4.3 The ? Functions.- 5.3.4.4 The ? Recursion Algebras in terms of ? Functions.- 5.3.5 The Discretized Debye Equal S and A Model.- 6 Energy Transfer.- 6.1 The Model.- 7 Compendium of Useful Equations.- 7.1 The Wavefunctions.- 7.2 The Manneback Recursion Formulas.- 7.3 The Equal-Force-Constants Wp and Related Functions in One Dimension.- 7.4 The Unequal-Force-Constants Expressions.- 7.5 The Moments.- 7.6 Multiple Coordinate Models of a Luminescence Center.- 7.7 Energy Transfer.- 8 Contact with the Theoretical Literature.- 8.1 Unequal-Force-Constants Anm.- 8.2 Equal-Force-Constants Anm.- 8.2.1 Explicit Formulas.- 8.2.2 Laguerre Polynomial Expressions.- 8.2.3 Citations.- 8.3 The Wp Formula.- 8.4 The Wp,d/dz Formula.- 8.5 The Equal-Force-Constants Moments.- 8.6 The Unequal-Force-Constants Moments.- 8.7 The Single-Frequency-Multiple-Coordinate Derivative Operator Expressions.- 8.7.1 Huang and Rhys.- 8.7.2 Perlin.- 8.7.3 Miyakawa and Dexter.- 8.8 Multiple-Frequency Rates.- 8.8.1 Perlin’s Condon-Operator Distribution.- 8.8.1.1 The Distribution.- 8.8.1.2 Cauchy’s Integral Theorem and its Consequences.- 8.8.1.3 The Saddle Point Approximation.- 8.8.1.4 The Use of the Saddle Point Approximation Here.- 8.8.1.5 The integral of dz/z.- 8.8.1.6 Expansion of vm for Small Offset.- 8.8.1.7 Perlin’s Derivation.- 8.8.2 The Correspondence between Perlin’s and Our Multiple Frequency Expression.- 8.8.3 Perlin’s Multiple-Coordinate Derivative Operator Expression.- 8.8.4 The Correspondence between Perlin’s and Our Multiple Frequency Derivative Expression.- 8.8.5 Mostoller, Ganguly, and Wood.- 8.9 Energy Transfer.- 8.9.1 Förster and Dexter.- 8.9.2 Miyakawa and Dexter.- 9 Representative Luminescence Centers.- 9.1 Equal- and Unequal-Force-Constants Bandshapes and Nonradiative Transitions.- 9.1.1 Bandshapes.- 9.1.2 Nonradiative Rates.- 9.2 One-and NAv-Dimensional Bandshapes.- 9.3 Vibrationally-Enhanced Radiative Transitions.- 9.4 Comparisons of Nonradiative Rate Expressions.- 10 Experimental Studies.- 10.1 Eu in Oxysulfides and in Oxyhalides.- 10.1.1 The Energy Level Diagram and Qualitative Behavior.- 10.1.2 Feeding Fractions.- 10.1.3 Efficiencies under Quenching Conditions.- 10.1.4 Absorption Spectra at T > 0K.- 10.1.5 The Fit of the Absorption Data.- 10.1.5.1 LaOCl.- 10.1.5.2 Oxysulfides.- 10.1.6 Fitting the Quenching Data.- 10.1.6.1 LaOCl.- 10.1.6.2 Oxysulfides.- 10.1.6.3 Fitting the (?i)i.- 10.1.7 Fitting The Feeding Fractions.- 10.1.7.1 LaOCl.- 10.1.7.2 Oxysulfides.- 10.2 Oxysulfides: Other Rare Earths.- 10.2.1 La2O2S: Tm3+.- 10.2.1.1 The Experimental Behavior.- 10.2.1.2 Fitting with Wp Functions.- 10.2.2 Y2O2S: Yb3+.- 10.2.2.1 The Experimental Behavior.- 10.2.2.2 Fitting the Optical Spectra with SCC Model Functions.- 10.2.2.3 Fitting the Quenchings with SCC Model Functions.- 10.3 Alkali and Alkaline Earth Halides: Sm.- 10.3.1 The Model and Expectations.- 10.3.2 The Fitting Parameters.- 10.4 Ruby.- 11 Effects Beyond the Model: Oxysulfide: Eu Storage and Loss Processes.- 11.1 The Need for Enhancement of the Model.- 11.2 Synopsis of the Experiments to Probe the Model.- 11.3 The Model Equations: Notation.- 11.4 CTS Dissociation: The B0/G Behavior.- 11.5 The SCC Model for Understanding Storage-Loss Processes in Oxysulfide: Eu Phosphors.- 11.6 The Steady-State Efficiency and its Dependence on Excitation Intensity: B?/G.- 11.6.1 The Observed Behavior.- 11.6.2 The Equation for B?/G.- 11.6.3 Derivation of Nonlinear Efficiency Expression.- 11.7 The n0? Achieved.- 11.8 The Rise Time.- 11.9 The Assymetry Between Phosphorescence and Build-Up.- 11.10 An Expression for Phosphorescence.- 12 The Exponential Energy-Gap “Law” for Small-Offset Cases.- 13 Conclusions.- 14 References.- Source Code.- Source of Illustrations.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 3642486312
• ISBN 13: 9783642486319
• Rilegatura: Copertina flessibile
• Numero di pagine: 272
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania