Optical Properties of Ions in Solids

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Optical Properties of Ions in Solids

Edited by

Baldassare Di Bartolo Department of Physics Boston College Chestnut Hill, Massachusetts

Assistant Editor

Dennis Pacheco Department of PhyricB Borton CoQege Chertnut Hill, MoBStlchUBettB

PLENUM PRESS. NEW YORK AND LONDON Published in cooperation with NATO Scientific Affairs Division

Library of Congress C-ataloging in Publication Data

NATO Advanced Study Institute on Optical Propertills of Ions in Solids, Erice, Italy, 1974. Optical properties of ions in solids.

(NATO advanced study institutes series: Series B, physics; v. 8) Includes bibliographical references and index. 1. Solids-Optical properties-Congresses. 2. Ions-Congresses. 3. Lumines­

cence-Congresses. I. Di Bartolo, Baldassare. II. Title. III. Series. QCI76.8.06N23 1974 541 '.372 75-11910

ISBN-13: 978-1-4684-2789-9 DOl: 10.1007/978-1-4684-2787-5

e-ISBN-13: 978-1-4684-2787-5

Lectures presented at the 1974 NATO Advanced Study Institute on Optical Properties of Ions in Solids, held at Erice, Italy, June 6-21, 1974

©1975 Plenum Press, New York

Softcover reprint of the hardcover 1st edition 1975

A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N.Y. 10011

United Kingdom edition published by Plenum Press, London A Division of Plenum Publishing Company, Ltd. Davis House (4th Floor), 8 Scrubs Lane, Harlesden, London, NWI0 6SE, England

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Preface

These proceedings report the lectures and seminars presented at the NATO Advanced Study Institute on "Optical Properties of Ions in Solids," held at Erice, Italy, June 6-21, 1974. The Institute was the first activity of the International School of Atomic and Molecular Spectroscopy of the "Ettore Majorana" Centre for Scientific Culture.

The Institute consisted of a series of lectures on optical properties of ions in solids that, starting at a fundamental level, finally reached the current level of research. The sequence of lectures and the organization of the material taught were in keeping with a didactical presentation. In essence the Institute had the two-fold purpose of organizing what was known on the subject, and updating the knowledge in the field. Fif'teen series of lectures for a total of 44 hours were given. Five one-hour seminars and five twenty-minute seminars were presented.

A total of 57 participants came from 40 laboratories in the following countries: Belgium, Canada, France, Germany, Ireland, Israel, Italy, Netherlands; Polatid, Romania, Switzerland, the United Ki~gdom, and the United States. The secretaries of the Institute were: D. Pacheco for the scientific aspects and A. La Francesca for the administrative aspects of the meeting.

These proceedings report the lectures, the one-hour seminars (abstracts only) and the twenty-minute- seminars (titles only). The proceedings report also the contributions sent by Prof. K. Rebane and Dr. L. A. Rebane who, unfortunately, were not able to come.

I would like to acknowledge the sponsorship of the Institute by the North Atlantic Treaty Organization, the National Science Foundation, the Italian Ministry of Public Education, the Italian Ministry of Scientific and Technological Research, the Regional Sicilian Government and the Department of Physics of Boston College.

v

vi PREFACE

I would like to thank for their help Prof. A. Zichichi, Director of the "Ettore Majorana" Centre for Scientific Culture, the members of the organizing committee (Professors D. Curie, R. Orbach and F. Williams), Professor R. L. Carovillano, Dr. A. Gabriele, Ms. M. Zaini, Ms. P. Savalli, Prof. V. Adragna, Dr. G. Denaro, Dr. C. La Rosa, and Dr. T. L. Porter of the National Science Foundation.

It was a pleasure to direct this Institute and to edit these lectures.

December 1974, Chestnut Hill, Massachusetts

B. Di Bartolo Editor, and Director

of the Institute

Contents

HISTORICAL SURVEY OF STUDIES OF THE OPTICAL PROPERTIES OF IONS IN SOLIDS, F. Williams . . . . . . . . . . . . . 1

Abstract I. Introduction II. Early Investigations of Optical Transitions III. Quantum Mechanical Considerations IV. Crystal and Ligand Field Theory V. Energy Transfer VI. Ion Pairs VII. Multiphoton Transitions VIII. Concluding Remarks

References

MAGNETIC IONS IN SOLIDS, B. Di Bartolo

Abstract I. Introduction II. Symmetry Concepts

II.A Properties of a Group II.B Example II.C Classes II.D Representations II.E Characters II.F Group Theory and Quantum Mechanics

III. Energy Levels of Atoms III.A Some Groups of Interest

1. Full Rotational Group 2. The Group C aoh

III.B Complete Set of Commuting Operators III.C Atomic States

1. The Hamiltonian 2. The Unperturbed Hamiltonian 3. The Electron-Electron Interaction 4. The Spin-Orbit Interaction 5. The Zeeman Interaction

vii

15

viii CONTENTS

IV. Magnetic Ions in Crystals IV.A Magnetic Ions

1. Transition Metal Ions of the First Series (Iron Group)

2. Transition Metal Ions of the Second Series (Palladium Group)

3. Transition Metal Ions of the Third Series (Platinum Group)

4. Rare Earth Ions (Group of the Lanthanides) 5. Actinide Ions

IV.B The Crystalline Field IV.C The Weak Field Scheme

1. The Hamiltonian of the Free Ion 2. The Crystalline Field Perturbation 3. Examples

IV.D The Intermediate Field Scheme 1. The Hamiltonian of the Free Ion 2. The Crystalline Field Perturbation 3. The Spin-Orbit Interaction 4. Example

IV.E The Strong Field Scheme 1. The Unperturbed Hamiltonian 2. The Crystalline Field Perturbation 3. The Electron-Electron Interaction 4. The Spin-Orbit Interaction 5. Example

IV. F Kramers' Theorem V. Effect of Covalent Bonding

V.A Why Covalent Bonding ? V.B Molecular Orbitals V.C Examples

1. N2 Molecule 2. HF Molecule 3. H20 Molecule 4. NH3 Molecule 5. CH4 Molecule ; HYbridization

V.D Octahedral Complexes V.E Charge Transfer Spectra

1. Ligand to Metal Transfer Spectra 2. Metal Oxidation Spectra 3. Rydberg Spectra 4. Intraligand Spectra

References

CONTENTS ix

FUNDAMENTALS OF RADIATIVE TRANSITIONS OF IONS AND OF ION PAIRS IN SOLIDS, F. Williams . . . . . . . . . . . . . 63 Abstract I. Introduction II. Transitions Induced by Perturbations Periodic in Time III. Transitions Induced by the Electromagnetic Radiation Field IV. Spontaneous Radiative Transitions V. Applications of the Theory to Radiative Transitions of

Ions in Solids References

ABSORPTION AND EMISSION SPECTRA, D. Curie .

Abstract I. The One-Dimensional Configurational Coordinate Model

I.A Introduction I.B The Emission and Absorption Peaks I.C The Shape of Emission and Absorption Spectra I.D A Study of Some Particular Cases

1. The Case of Linear Coupling 2. The Case of Quadratic Coupling

71

I.E Simple Improvement of the Semi-Classical Approximation: H. Payen de la Garanderie's Law of the Rectilinear Diameter

II. The Huang and Rhys Model II.A The Emission Spectrum II.B The Absorption Spectrum II.C A Remark ILD Shape and Asymmetry of Huang's and Rhys' and

Pekarian Curves 1. The Moments 2. A More Detailed Study of the Pekarian Curve

III. A Deeper Insight into the Shape of the Spectra III.A Weak Coupling and Strong Coupling III.B The Case of a Distribution of Phonons Interacting

with the Emitting Center 1. Selection Rules 2. The Coupling Parameter S 3. The Moments of the Shape Function

IV. A Study of Some Experimental Cases IV.A Large Band Spectra of II-VI Compounds

1. ZnS:Cu 2. ZnSe:Cu 3. CdS:Ag 4. ZnS:Ag,Cl 5. Self-Activated Materials

IV.B ZnS:Mn

x

IV.C IV.D IV.E

The R-Lines of Ruby Edge Emissions in II-VI Compounds Stokes versus Anti-Stokes Emission

References

CONTENTS

QUANTUM THEORY OF LATTICE VIBRATIONS, R. Orbach . . . . . . . 107

Abstract I. Lattice Vibrations

I.A Linear Diatomic Chain 1. Equations of Motion 2. One Dimensional Zone Scheme 3. Density of States

I.B Three Dimensional Lattice. Classical Theory 1. Potential Energy 2. Equations of Motion 3. Eigenvalue Spectrum and Eigenvectors 4. Boundary Conditions and the Reciprocal Lattice 5. Brillouin Zones 6. Energy Surface Theorem

I.C Three Dimensional Lattice. Quantum Theory 1. Introduction Coordinates 2. Commutation Relations 3. Energy Matrix 4. Eigenvalue Spectrum

II. Thermodynamic Properties of Lattice Vibrations II.A Construction and Use of the Partition Function

1. Distribution Function 2. Summation of Terms 3. Internal Energy 4. Free Energy 5. Entropy 6. Specific Heat

II.B Density of States 1. Enumeration of States 2. Critical Points, Small Wave Vector Limit.

Debye Approximation 3. Critical Points. Minima 4. Critical Points. Maxima 5. Critical Points. Saddle Points 6. Conditions on Number and Types of Critical

Points II.C Equation of State

ILD

1. Gruneisen Constant 2. Lattice Vibrational Equation of State 3. Relation between Gruneisen Constant and

Compressibility Effect of the Boundary Conditions on the Frequency Distribution References

CONTENTS

THEORY OF VIBRONIC SPECTRA, W. A. Wall

Abstract I. Introduction II. Infrared Absorption

xi

187

II.A Characteristics of Infrared Absorption in Crystals II.B Quantum Mechanical Treatment of Infrared

Processes III. Raman Scattering

III.A Characteristics of Raman Scattering in Crystals

III.B Theoretical Treatment of Raman Scattering IV. Neutron Scattering

IV.A Characteristics of Neutron Scattering from Crystals

!V.B Theory of Neutron Scattering V. Vibronic Spectra

V.A Magnetic Ions in Host Lattices V.B Characteristics of Vibronic Spectra V.C Theory of Vibronic Transitions V.D Vibronic Selection Rules from Group-Theoretical

Analysis V.E. Vibronic Theory: Alternate Approaches and

Numerical Calculations VI. Example: Analysis of 2Eg -4A2g Sideband of MgO :V2+

References

LUMINESCENCE AND SPECTROSCOPY OF SMALL MOLECULAR IONS IN CRYSTALS, K. K. Rebane and L. A. Rebane .• 227

Abstract I. Introduction II. General Description of the Spectra of Molecular Centres

in Crystals

III.

IV.

II.A Structure of Luminescence and Absorption Spectra. Parameters of Potential Curves

II.B Electron-Phonon Interaction. Structure of Phonon Wings

II.C Electron-Phonon Interaction. Anharmonicity Effects. No-Phonon Lines

II.D Radiationless Transitions and Vibrational Relaxation in Molecular Centres

Rotation and Libration of the N02 Ion in Potassium Halide Crystals III.A Hindered Rotation of the Impurity Molecule in

Crystals III.B Rotational Structure of N02 Vibronic Spectra TTT " ..L..L..Le"" Polarization &ld Structure of Raman Scattering

Lines of N02• The Role of Librations Reorientation of S2 in KI References

xii CONTENTS

SOME PROBLEMS OF THE VIBRATIONAL STRUCTURE OF OPTICAL SPECTRA OF IMPURITIES IN SOLIDS, K. K. Rebane . . . . 247

Abstract I. No-Phonon Lines and Phonon Wings (Sidebands)

I.A Vibronic Spectra of Absorption and Luminescence

I.B Infrared Absorption Spectra I.C Light Scattering Spectra I.D Hot Luminescence Spectra I.E Shpolsky Spectra

II. Inhomogeneous Broadening of Luminescence Spectra References

SPECTROSCOPY OF MAGNETIC INSULATORS, D. S. McClure . . . . . 259

Abstract I. Introduction II. Interacting Ions

II.A Two Interacting Electrons 1. Non-Overlapping Wavefunctions 2. Finite Overlap 3. Effect of the Spin 4. Biquadratic Terms

II.B Many-Electron Problems II.C The Heisenberg Hamiltonian II.D Direct Exchange or Superexchange? II.E Transition Probabilities in Coupled Systems

III. Crystalline Systems III.A Frenkel Excitons and Davydov Splitting III.B Effect of Vibration on the Davydov Splitting

and Exciton Dispersion III.C Exciton Dispersion and Davydov Splitting in

a Magnetic Crystal IV. Electronic Structure of Magnetic Crystals

IV.A Spin Waves 1. The Case of a Chain, S = ~, Periodic

Boundary Conditions 2. The Three-Dimensional Case 3. Antiferromagnetic Spin Waves

IV.B Anisotropy Field and Exchange Field IV.C Weiss Theory of Ferromagnetism IV.D Antiferromagnets IV.E Effects of External Magnetic Fields IV.F Group Theory

V. Examples of Spectra of Magnetic Crystals V.A MnF2 V.B Cr203 V.C FeC03 V.D Other Examples References

CONTENTS

ENERGY TRANSFER PHENOMENA, R. K. Watts •• • . . • • • . • • 307

Abstract I. Introduction II. Ion-Ion Interactions III. Statistical Treatment IV. Inhomogeneous Broadening

References

STEPWISE UPCONVERSION AND COOPERATIVE PHENOMENA IN FLUORESCENT SYSTEMS, R. K. Watts . . . . . . . . . • . . . 337

Abstract I. Introduction II. Stepwise Upconversion III. Cooperative Transfer IV. Energy Transfer with Photon Cooperation

References

RELAXATION AND ENERGY TRANSFER, R. Orbach . . . . . . . • . . 355 Abstract I. Introduction II. Non-Radiative Relaxation

II.A Weak Coupling Limit

ILB

II.C ILD

1. Crystal Field Theory 2. Symmetry of Phonon Interaction "Hamiltonian 3. Magnitude of Interaction Constants Strong Coupling Limit 1. Reduction of Operator Matrix Elements 2. Numerical Estimates The One-Phonon Processes MUltiphonon Processes 1. Two-Phonon Processes 2. Many-Phonon Processes

III. Energy Transfer III.A Spatial Transfer (Resonant)

1. Inter-Ion Coupling Mechanisms 2. Range Dependence. Transition Energies

Less than the Debye Energy 3. Range Dependence. Transition Energies

Greater than the Debye Energy 4. Inhomogeneous Broadening. Lack of Transport

for Short-Range Interactions 5. Inhomogeneous Broadening. Critical

Concentration for Energy Transfer 6. Inhomogeneous Broadening. Relation to

Fluorescence Efficiency III.B Phonon-Assisted Energy Transfer

1. Form of Interaction 2. Dependence on Temperature

xiii

xiv CONTENTS

3. Dependence on Energy 4. Range Dependence 5. Effect of Strong Coupling

IV. Summary and Future Prospects References

CHARGE TRANSFER SPECTRA, D. S. McClure . . . . . . . . . . . 401

Abstract I. Introduction II. Elementary Aspects of Charge Transfer III. Relation between Optical and Chemical Charge Transfer IV. Theory of Charge Transfer Spectra

IV.A Change of Energy with Atomic Number IV.B Application of Molecular Orbitals

1. Molecular Orbital Theory 2. The Case of the One Open Shell 3. More than One Open Shell

V. Conclusions References

THE ROLE OF THE JAHN-TELLER EFFECT IN THE OPTICAL SPECTRA OF IONS IN SOLIDS, T. L. Estle . . . . . . . . . . . . . . 419

Abstract I. Introduction II. The Jahn-Teller Theorem III. A Model Illustrating the Jahn-Teller Effect IV. The Hamiltonian for a Magnetic Ion in a Crystal V. Configuration-Coordinate Diagrams

V.A E Electronic States in Cubic Symmetry V.B T Electronic States Coupled to E Modes V.C T Electronic States Coupled to T Modes

VI. Broad Band Optical Spectra VI.A Introduction VI.B Transitions from a Doublet VI.C Transitions to a Doublet VI.D Transitions Involving an Orbital Triplet

Coupled to an E Mode VI.E Other Possibilities

VII. Vibronic Structure in Energy Levels and Optical Spectra VII.A Vibronic Structure of EStates VII.B Optical Evidence of EState Vibronic Structure VII.C Vibronic Structure of T States VII.D Optical Evidence of T State Vibronic Structure

VilI. Concluding Remarks References

CONTENTS

SPECTRA OF ASSOCIATED DONOR-ACCEPTOR PAIRS, D. Curie

Abstract I. Introduction II. The Matrix Element for D-A Transition Probabilities III. Capture Cross-Sections IV. Shape of the Spectrum

References

ZERO-PHONON AND PHONON-ASSISTED RADIATIVE TRANSITIONS OF DONOR-ACCEPTOR PAIRS IN LUMINESCENT SEMICONDUCTORS,

449

L. Mehrkam and F. Williams ..•.•....•••...• 459

Abstract I. Introduction II. Analysis of Experimental Spectra III. Application of the Theory

References

PRESENT TRENDS IN LUMINESCENCE RESEARCH, F. Williams . . . . 469

Abstract I. Introduction II. Unusual Materials III. Recent Phenomena IV. Applied Research on Luminescence

LONG SEMINARS (ABSTRACTS)

APPLICATION OF VIBRONIC SPECTROSCOPY -­STRONTIUM TITANATE AS AN EXAMPLE, R. C. Powell

RADIATIONLESS DECAY OF IMPURITY IONS IN SOLIDS, R. Englman . . . . . . ..•......

LUMINESCENCE FROM YAG: Cr3+, MgO: V2+ and MgO: Cr3+ , G. F. Imbusch • • . . . . . . . • • • . • . • .

SPECTROSCOPY OF 5f-SYSTEMS: ACTINIDES VERSUS LANTHANIDES,

473

475

477

R. G. Pappalardo . • . • . . • • • . . . • • • . . 479

ELECTRONIC AND VIBRATIONAL TRANSITIONS OF LEAD AZIDE AND EFFECTS THEREON OF PHOTODECOMPOSITION, F. Williams ...••. • 483

SHORT SEMINARS (TITLES ONLY) 487

CONTRIBUTORS 489

INDEX. . . . • 491

xv