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## Über dieses Buch

There are both a remote and a proximate history in the development of this book. We would like to acknowledge first the perceptiveness of the technical administrators at RCA Laboratories, Inc. during the 1970s, and in particular Dr. P. N. Yocom. Buoyed up by the financial importance of yttrium oxysulfide: europium as the red phosphor of color television tubes, they allowed us almost a decade of close cooperation aimed at understanding the performance of this phosphor. It is significant that we shared an approach to research in an industrial laboratory which allowed us to avoid the lure of "first-principles" approaches (which would have been severely premature) and freed us to formulate and to study the important issues directly. We searched for a semiquantitative understanding of the properties observed in luminescence, i. e. , where energy absorption occurs, where emission occurs, and with what efficiency this conversion process takes place. We were aware that the nonradi­ ative transition rates found in practice vary enormously with temperature and, for a given activator, with small changes in its environment. We traced the source of this enormous variation to the magnitude of the vibrational overlap integrals, which have strong dependences on the rearrangements occurring during optical transitions and on the vibrational number of the initial electronic state. We were willing to excise from the problem the electronic aspects - the electronic wavefunctions' and their transition integrals -by treating them as parameters to be obtained from the experimental data.

## Inhaltsverzeichnis

### 1. Introduction

Abstract
A luminescence center is a construct aimed at understanding similarities in the absorption and emission performances found among luminescent materials. The word “center” implies that the most important observed properties can be understood while restricting one’s attention to a particular lattice site and its immediate surroundings. Free excitonic absorption and emission, for example, are beyond the scope of a model of a luminescence “center”, because the nature of these optical processes involves the whole lattice. But for the large majority of observed luminescent materials, the “center” is a useful concept.
Charles W. Struck, William H. Fonger

### 2. Harmonic Oscillator Wavefunctions

Abstract
The study of vibrations naturally leads to the harmonic oscillator. We will later obtain the harmonic oscillator wavefunctions in dimensionless variables. Our starting point is familiarity with Hermite polynomials, though we will derive the relation of these polynomials to the study of vibrations by demonstrating the solution of the Schrödinger equation.
Charles W. Struck, William H. Fonger

### 3. The Manneback Recursion Formulas

Abstract
Manneback [32] first expounded the value of recursion formulas for studying harmonic oscillator wavefunctions. We give in this section his derivation, in our notation, for the recursion formulas for the overlap integrals involved in the optical transitions and, in our model, in the nonradiative transitions also.
Charles W. Struck, William H. Fonger

### 4. The Luminescence Center: The Single-Configurational-Coordinate Model

Abstract
We now tie these A nm to a model of a luminescence center. The model of Fig. 1 need not have equal force constants. Figure 15 is drawn accurately for θ = 42°, α uv = 5.886. This set of parameters, seemingly over-particularized, is related to an equal-force-constants case with simple parameters and has roughly the largest deviation from equal force constants that we have found necessary to consider. The case involving this set of parameters will be taken up again in Sect. 9.1, where the two curves of Fig. 15 are seen again as the dotted curves of Fig. 21. In Sect. 9.1, related equal- and unequal-force constants cases are compared.
Charles W. Struck, William H. Fonger

### 5. Multiple Coordinate Models of a Luminescence Center

Abstract
We approach the multiple coordinate models by considering the convolution (reproductive, multiplicative, combinative) properties of the W p distribution. We assert that two W p distributions having the same <m>, i.e., the same phonon energy ħω, combine according to:
$$\sum\limits_{{p_1} = - \infty }^\infty {{W_{{p_1}}}({S_1},\, < m > )} \,{W_{p - {p_1}}}({S_2},\, < m > ) = {W_p}({S_1} + {S_2},\, < m > )$$
(5.1)
Charles W. Struck, William H. Fonger

### 6. Energy Transfer

Abstract
The theories of energy transfer in the literature are concerned with the distance between the energy donor and acceptor, distributions for these distances as controlled by concentration, averaging over these distances, etc. These concerns enter the electronic factor of the transition rate. Our concern is with the nuclear factor, i.e., with the energy mismatch dependence and with the temperature dependence of these rates. We shall see in Chap. 8 that insofar as the previous authors treat specifically these two dependences they have come to approximate forms of the W p , W p, d/dz , or M p, d/dz rates. In these treatments, and in ours also, the energy donor and the energy acceptor are treated as having vibrational modes totally independent of each other.
Charles W. Struck, William H. Fonger

### 7. Compendium of Useful Equations

Abstract
The harmonic oscillator wavefunctions are defined in terms of Hermite polynomials, Eq. (2.11),
$${v_m} = \;{H_m}({z_v}){e^{ - {z^2}/2}}{(m!{2^m}{\pi ^{1/2}}{X_v})^{ - 1/2}}$$
(7.1)
which are given by their recursion formula, Eq. (2.7), initiated with the first two values, Eqs. (2.3) and (2.4):
$$\begin{array}{*{20}{c}} { - 2k{H_{k - 1}} + 2{z_v}{H_k} - {H_{k + 1}} = 0} \\ {{H_0} = 1} \\ {{H_1} = 2{z_v}} \end{array}$$
(7.2)
Charles W. Struck, William H. Fonger

### 8. Contact with the Theoretical Literature

Abstract
We have already cited the explicit formulas of Hutchisson [33] for the A nm for unequal force constants. These explicit formulas have not proved as useful as the Manneback [32] recursion formulas for computational ease.
Charles W. Struck, William H. Fonger

### 9. Representative Luminescence Centers

Abstract
As one searches for the most perceptive fit of these model functions to all experimental data, one often wishes to describe the same absorption and emission spectra both with equal and with unequal force constants. Such descriptions might keep the sum of the first moments and the product of the second moments constant, i.e., using the first two of Eqs. (4.109) and (4.112) truncated to only their first terms and evaluated at 0 K, would have
$$\begin{array}{*{20}{c}} {{S_v}\hbar \omega + {S_u}\hbar {\omega _u} = 2S\hbar \omega } \\ {\left[ {\frac{{{\omega _v}}}{{{\omega _u}}}S{{(\hbar {\omega _v})}^2}} \right]\left[ {\frac{{{\omega _u}}}{{{\omega _v}}}{S_u}{{(\hbar {\omega _u})}^2}} \right] = {{[S{{(\hbar \omega )}^2}]}^2}} \end{array}$$
(9.1)
Charles W. Struck, William H. Fonger

### 10. Experimental Studies

Abstract
Figure 25 shows the single-configurational-coordinate (SCC) energy level diagram appropriate for Eu3+ in La2O2S, Y2O2S, and LaOCl. The 7F 4f6 states are not shown. They are split into seven J states spanning about 6 000 cm−1 with J between 0 and 6. They would be placed with the zero of energy at the minimum of the 7F0 parabola and with only minor offsets, with Sħω < 100 cm−1. The first set of excited 4f6 states are the 5D states, split into five J states between 0 and 4. These also have only minor offsets. The first four of these states have been identified; the J = 4 state and the other 4f6 states will be referenced only by their absorption energies in nanometers.
Charles W. Struck, William H. Fonger

### 11. Effects Beyond the Model: Oxysulfide: Eu Storage and Loss Processes

Abstract
In this chapter, we shall describe storage and loss performances which are clearly beyond any of the models considered thus far. Figure 57 shows the phosphorescence seen in (Y0.999 Eu0.001)2O2S. While not one transition in Fig. 25 has a time constant greater than a few milliseconds, 5D07F phosphorescence is seen lasting for five minutes. The ordinate is the ratio of the phosphorescence to the steady-state emission intensity as percent.
Charles W. Struck, William H. Fonger

### 12. The Exponential Energy-Gap “Law” for Small-Offset Cases

Abstract
Riseberg, Moos, and coworkers [27] have studied 4f → 4f nonradiative transitions of 3+ rare-earth ions in several hosts.
Charles W. Struck, William H. Fonger

### 13. Conclusions

Abstract
The W p function is the distribution describing the optical band shapes, whether broad or nearly confined to the zero-phonon line, in two models: the single-configurational-coordinate model and the Einstein-Huang-Rhys-Pekar single-frequency multiple-coordinate model.
Charles W. Struck, William H. Fonger

### 14. References

Without Abstract
Charles W. Struck, William H. Fonger

### Backmatter

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