2~/' (CvK~)
R. MARCHAND
6. Conclusion
92 R. MARCHAND
The tetragonal (P42/mnm) «-Gd416CN structure, which is also that of La4IöCN and Gd4Br6CN, contains R6 octahedra centered by C~- anionic groups and double tetrahedra centered by N atoms (N3-). The units are alternately connected via common edges to form linear chains [R2tLI/2C2] [R2/2R2/2N]2. In the hexagonal (P6) ~-Gd416CN, which is obtained at 1300 K from the « form, the chains are more densely packed.
The same units, C2-centered octahedra and N-centered double tetrahedra are found in the two isotypic triclinic (P1) compounds Y7It2C2N and Ho7112CN. They exhibit a semiconducting behavior.
Lastly, the structure of Y6IgC2N is composed of chains of pairs of Y-octahedra and Y-tetrahedra, respectively. The octahedra are centered by C2 groups, the tetrahedra by N atoms.
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Handbook on the Physics and Chemistry o f Rare Earths Vol. 25
edited by K.A. Gschneidner, Jl: and L. Eyring
© 1998 Elsevier Science B.V. All rights reserved
Chapter 167
S P E C T R A L INTENSITIES OF f - f T R A N S I T I O N S Christiane GORLLER-WALRAND and Koen BINNEMANS
K.U. Leuven, Department of Chemistry, Coordination Chemistry Division, Celestijnenlaan 200E 3001 Heverlee, Belgium
Contents
List of symbols and abbreviations 102
1. Introduction 104
2. Transition mechanisms for lanthanide ions 105 2.l. Interaction between light and matter 105 2.2. Intraconfigurational f - f transitions 107 2.2.1. Magnetic dipole transitions 107 2.2.2. Induced electric dipole transitions 107 2.2.3. Electric quadrupole transitions 108 2.3. Determination of the induced electric
dipole or magnetic dipole character of a
transition 108
3. Definition of terms employed in intensity
theory 109
3.1. Introductory remarks on dimensions and
units 109
3.2. MoIar absorptivity 109
3.3. Dipole strength (D') and oscillator strength (P') of a single spectral line in
an oriented system l 11
3.4. Dipole strength (D) and oscillator strength (P) of a transition in a
randomly-oriented system 114
3.5. Effect of the dielectric medium 117 3.6. Experimental dipole strength and
oscillator strength 119
3.7. Mixed ED-MD transitions 120 3.8. Fractional thermal population 120 4. Magnetic dipole (MD) transitions 121
4.1. Magnetic dipole matrix element for a single spectral line in an oriented system 121 4.2. Selection rules for magnetic dipole
transitions 123
4.3. Sum rule 125
5. Judd-Ofelt theory for induced electric
dipole (ED) transitions 126
5.1. Preiiminary remarks 126
5.2. Induced electric dipole matrix element for a single spectral line in an oriented
system 126
5.3. Description of the states ~ and tpf 128 5.4. Crystal-field Hamiltonian 129 5.5. First-order perturbation 130 5.6. Matrix elements in the transition operator 130
5.7. Approximations I31
5.7.1. First approximation: J" and M"
are degenerate 132
5.7.2. Second approximation: q/' and J "
are degenerate 136
5.7.3. Third approximation: n', l', ~p"
and J " are degenerate 140 5.7.4. Fourth approximation: lN-~(n'l ')
far above l N 140
5.8. Judd's final expression for the matrix in
the transition operator 14I
5.9. Calculation of the reduced matrix
elements 142
5.10. Matrix element of the electric dipole operator of a single line in an oriented
system 143
5.11. Dipole strength of an induced electric dipole transition (single line and oriented
system) 144
5.12. Oscillator strength of an induced electric dipole transition (single line and oriented
system) 144
101
102 C. GORLLER-WALRAND AND K. BINNEMANS 5.13. Selection rules for induced electric
dipole transitions 144
6. Intensity parametrization of transitions between crystal-field levels 147 6.1. Static-coupling model for line transitions 147 6.2. Reid- Richardson intensity model 149 7. Intensity parametrization of transitions
between J-multiplets 154
7.1. Judd's parametrization scheme 154 7.1.1. Solutions of rare-earth ions 154 7.1.2. Effect of random orientation on
the crystal-field operator 156 7.1.3. Effect of random orientation on
the transition operator 159 7.1.4. Summation over all components
of the ground state and the excited state and over all p's 159 7.1.5. Dipole strength and oscillator
strength for randomly-oriented systems in Judd's parametrization
scheme 160
7.2. Carnall's 34 intensity parameters 162 7.3. g2~ intensity parameters 163
7.3.1. Definition 163
7.3.2. Determination of f2;~ intensity
parameters 164
7.3.2.1. Standard least-squares
method 165
7.3.2.2. Chi-square method 167 7.3.3. Additivity of intensity parameters 168 7.3.4. Mixed ED-MD transitions 168 7.4. Successes and failures of the Judd-Ofelt
theory 168
7.5. Ab initio calculation of intensity
parameters 212
7.6. Simulation of absorption spectra 216
7.7. Luminescence spectra 218
8. Hypersensitivity 220
8.1. Definition and experimental evidence 220 8.2. Theoretical models for hypersensitivity 224 8.3. Application of hypersensitivity 229 9. Compositional dependence of the intensity
parameters 229
10. Two-photon spectra 233
11. Vibronic transitions 236
12. Color of lanthanide ions 239
13. Intensities of transitions in actinide ions 247
14. Conclusions 250
Acknowledgments 251
References 252
List of symbols and abbreviations
A absorbance D'
A ( ~ J , tp,j,) probability for spontaneous D~p emission (Einstein coefficient) D0p Akq crystal-field coefficient
A~, intensity parameter
A~.,~ intensity parameter for vibronic D
transitions DBM
AjK M intensity parameter DC
t~kq crystal field coefficient (or dim.
parameter) DPA
B~.kq intensity parameter
c speed of light DTPA
C concentration e
CDA chelidamate E
CDO chelidonate E
Cp cyclopentadiene Ec T
d optical pathlength ED
D dipole strength (randomly-oriented EDTA system)
exp
dipole strength (oriented system) experimental dipole strength experimental dipole strength for ED transition, corrected for the MD contribution
Debye
1,3 -diphenyl- 1,3-propanedione dynamic coupling
dimension dipicolinate
(2,6-pyridinedicarboxylate) diethylenetriaminepentaacetate elementary charge
electric field energy
charge-transfer energy
(induced) electric dipole transition ethylenediaminetetraacetate experimental