The F Center

Exposure of transparent solids, both glasses and crystals, to high-energy radiation frequently makes them colored. The defects responsible for this are known as color centers. The first of these defects to be characterized was the F center, a term derived from the German Farbzentrum (color center). 

These defects were first produced by exposing alkali halide crystals to high-energy radiation such as X rays. This causes the crystals to become brightly colored with fairly simple bell-shaped absorption spectra. The peak of the absorption curve, rn lx, moves to higher wavelengths as both the alkali metal ion size and halide ion 

Compound Absorption Wavelength max/nm Color3 Lattice Parameter/nm 

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In this case, we use 6 as a small fraction since the actual number of defects is small in relation to the overall number of ions actually present. For the F-Center, the brackets enclose the complex consisting of an electron captured at an anion vacancy. Note that these equations encompass all of the mechanisms that we have postulated for each of the individual reactions. That is, we show the presence of vacancies in the Schottlqr case and interstitial cations for the Frenkel case involving either the cation or anion. The latter, involving an interstitlcd anion is called, by convention, the "Anti-Frenkel" case. The defect reaction involving the "F-Center" is also given. 

These equations illustrate how the crystal responds to the presence of sodium vapor, i.e.- excess Na- -, by forming anion vacaneies, to form the F-center. 

They are usually joined along the 110 plane of the lattice of the face-centered salt crystal, although we have not shown them this way (The 100 plane is illustrated in the diagram). Note that each vacancy has captured an electron in response to the charge-compensation mechanism which is operative for all defect reactions. In this case, it is the anion which is affected whereas in the "F-center", it was the cation which was affected (see equation 3.2.8. given above). These associated, negatively-charged, vacancies have quite different absorption properties than that of the F-center. 

In alkali halide crystals containing color-centers (F-centers) illumination with light of appropriate energy causes transient changes of hardness (Nadeau, 1964). This effect apparently results from changes in the effective sizes of the F-centers when they become excited. 

Subsequent to the advent of the dye laser, tunable lasers based upon other lasing media were developed which operate over various wavelength ranges. Nobable among these are the f-center lasers and diode lasers which are tunable in the infrared. 

The F center is an electron excess center and arises because the crystal contains a small excess of metal. Similar metal excess F centers exist in compounds other than... 

The F center absorption maximum for KC1 is at 565 nm and that for KF is 460 nm (Table 9.1). (a) What is the composition of a natural crystal with color centers showing an absorption peak at 500 nm (b) If the absorption peak for KF corresponds to the promotion of an electron from the F center to the conduction band, determine the energy of the color center with respect to the conduction band. (The band gap in KF is 10.7 eV.) If the relative position of the color center energy level remains the same throughout the KF-KC1 solid solution range, estimate (c) the band gap of KC1 and (d) the band gap for the natural crystal. 

EXAMPLE 5.4 Figure 5.8 shows the absorption spectrum of a NaCl crystal containing color centers generated by irradiation. The band peaking at 443 nm is related to the so-called F centers, for which the oscillator strength isf= 0.6. From this absorption band, determine the density of the F centers that have been produced by the irradiation process. Assume a refractive index of n = L6 for NaCl. 

Figure 5.8 The absorption spectrum at 77 K of an irradiated NaCl crystal. The absorption band at 443 nm is due to the F centers generated after irradiation. The fuU width at half maximum of this band is indicated on the figure.

Because of their importance as basic primary centers, we will now discuss the optical bands associated with the F centers in alkali halide crystals. The simplest approximation is to consider the F center - that is, an electron trapped in a vacancy (see Figure 6.12) - as an electron confined inside a rigid cubic box of dimension 2a, where a is the anion-cation distance (the Cr -Na+ distance in NaCl). Solving for the energy levels of such an electron is a common problem in quantum mechanics. The energy levels are given by... 

As shown in Example 6.5, the previous simple model for the F center overestimates its transition energy somewhat. In fact, the experimentally measured values... 

The anion-cation distance in potassium chloride (KCl) is 0.315 nm. (a) Using the simple model of an electron in a rigid box, estimate the wavelength peaks of the two lowest energy transitions for the F centers in KCl. (b) Now determine the wavelength peak of the lowest energy transition from the experimental tit to expression (6.5) and comment on the differences relative to the result obtained in (a). 

The F center in sodium fluoride (NaF) shows a broad absorption band that peaks at 335 nm (77 K). The shape of this absorption band fits a Huang-Rhys parameter of 28 and coupling with a phonon mode of 0.0369 eV. Estimate the peak position of the F center emission in NaF. 

F centers may act as adsorption centers not only in the alkali halides, but in any other crystals as well. Take, for example, a crystal of ZnO, in which the F center is an oxygen valency with two (not one ) electrons localized near it, as depicted in Fig. 30. From the chemical point of view such a center represents two adjacent localized free valencies of like sign which on an ideal surface could never meet because of Coulomb repulsion between them. (This should be especially stressed.) As a result of this property, such an F center may play a specific role in catalysis acting as an active center for a number of reactions. 

Figure 11.13. Alternate ways of choosing a unit cell for the centered monoclinic lattice, a, fi, c, define the body-centered (/) cell a, b c define the A-centered cell a, fi, c define the F-centered cell.

COLOR CENTERS. Certain crystals, such as the alkali halides, can be colored by the introduction of excess alkali metal into the lattice, or by irradiation with x-rays, energetic electrons, etc. Thus sodium chloride acquires a yellow color and potassium chloride a blue-violet color. The absorption spectra of such crystals have definite absorption bands throughout the ultraviolet, visible and near-infrared regions. The term color center is applied to special electronic configurations in the solid. The simplest and best understood of these color centers is the F center. Color centers are basically lattice defects that absorb light. 

Figure 15. Schematic (two dimensional) representation of the F-center formed in -irradiated alkali hydroxide ice at 77°K. (the striations represent the ice matrix).

In Table 2 we summarize the results of the DDCI calculations on the lowest excitation energies for terrace, step and comer F and F+ centers. As expected, for a given transition the excitation energy decreases as the coordination of the defect decreases. For F centers, the allowed singlet to singlet lowest transition occurs at 3.4 eV for the surface, 2.9 eV for the step and 2.6 eV for the comer. The same trend is found for the F+ centers, where the first doublet to doublet transition, goes from 3.6 eV for the surface, to 2.6 eV for the step and 2.4 eV for the comer. As observed previously for the bulk calculations, excitations for the F+ centers appear around 0.2 eV below the excitations due to F centers. The excitations at the step and comer sites are shifted about 0.5-1.2 eV compared to... 

The DDCI results for the F centers in MgO at different sites ofthe (IOO) surface show a decrease of the excitation energy with the decrease in the coordination of the vacancy. Assuming an error in the calculated transition energies of 15%, similar to the error observed for the transitions in bulk F centers, we can assign the peaks observed around 3 eV to regular surface F centers, the band observed around 2.4 eV to step sites and the band around 2.2 eV can be assigned to comer sites. 

The variation of bulk Zr3+ and surface related F-center concentration as a function of S (specific surface area) was studied in [50]. The intensity of F-center signal increased and the intensity of Zr3+ markedly decreased with the increase of S. At S < 16 m2/g (2R > 24.5 nm) the Zr3+ signal increased sharply ([Zr3+] > 1017 spin/g), while the F-center signal practically vanished [50]. 

Quantitative experiments have indicated that the F-center EPR signal intensity increased and the Zr3+ signal intensity decreased with the increase in S [50]. Fig. 8.6 shows some graphs constructed from the data published in [50]. 

Several models based on the electronic properties of mixtures of metals and molten salts have been proposed, i.e., the localized electron model, the free electron model and the band model. A model which gives a good description of the properties of alkali metal-alkali halide mixtures at low metal concentrations is the model of trapped electrons or the so-called model of F-centers [76,77], An F-center may be regarded as a localized state, and the electron is then trapped in a cavity with octahedral coordination with the neighboring cations. On average, the F-center may be considered as an M65+ species. 

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