FRACTONS AND THE HOMOGENEOUS LINEWIDTH OF THE 5D0 - 7F0 TRANSITION IN Eu3+-DOPED GLASSES

F l uorescence I i ne narrowing measurements of the5~O-7~0 transit ion in severa I structural 1 y di ss imi l ar Eu-doped g1 asses are presented. The homogeneous I inewidth exhibits a T~ dependence from 30 to 300 K. We show that this behavior can be accounted for by Raman processes with the anomalous vibrational modes of the fractal structure of the glass. I INTRODUCTION By the use of high resol ution lasers, subsets of ions within the inhomogeneous l y broadened spectra 1 prof i l e can be se l ect i ve l y excited in glasses so that their homogeneous linewidth can be measured. Hole-burning in absorption and fluorescence linenarrowing (FLN) in emission make use of this technique. FLN experiments /1/ on E U ~ + ions in a si l icate glass have shown a homogeneous l inewidth at low temperatures substantially larger than seen in crystals and a quadratic temperature dependence that is unexpected for any known linebroadening mechanism in crystals. In this paper we report FLN measurements on E U ~ + in three structural l y di ssimi1 ar g 1 asses at temperatures ranging from 10 to 300 K. A T ' dependence for the homogeneous 1 i new i dth i s observed in each of these l ending support to the notion that this is a uni versa1 property of glasses. To account for these results, a simple model based on the fracton concept of Alexander and Orbach /2/ is developed for Raman and direct process broadening. Both the quadratic dependence and the approximate magnitude of the broadening are consistent with this model. I 1 EXPERIMENTAL Site sel ect ion was achieved with a nitrogen1 aser-pumped tunab 1 e dye 1 aser using coumarin dye. The 10 ns excitation pulse was narrowed to 0.15 cm-' by passing it through an extra-cavity etalon. The samples were mounted on the coldfinger of a c l osed-cyc l e he l ium cryostat permitting measurements between 10 and 300 K. The fluorescence was measured by a I-m monochromator with slits set for 0.08 A. A shutter placed between the sample and the monochromator was opened 0.1 ms after the excitation, eliminating the possibl ity of contamination by scattered 1 ight. It has been shown elsewhere that energy transfer does not broaden the fluorescence on this time sca l e / 3 / . The three europium doped glasses studied here had the following compositions in Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985760 C7-332 JOURNAL D E PHYSIQUE mole percent: l ithium si l icate glass (LS) 57.0 Si02, 27.5 Li20. 10.0 CaO, 2.5 A1 203, 3.0 Eu20j; sodium si l icate glass (NS) 72.0 Si02, 15.0 Na20, 5.0 BaO, 5.0 ZrO, 3.0 Eu203; and potassium germanate glass (KG) 65.3 Ge02. 17.0 K20. 17.0 BaO. 0.7 Eu203. The spectral properties of these glasses have been reported previously /3/ . For each glass excitation spectra were obtained at 577.5 nm and 580 nm on the high and low energy sides of the inhomogeneous prof i le of the 5~0-7~0 transition, respectively. I 1 1 HOMOGENEOUS INHO'MOGENEOUS_ BROADENING OF THE FLN LINEWIOTH The temperature dependence of the FLN linewidth is shown in Fig. I. These data have been reduced using the approximation of Kushida and Takushi /4/ for a resonantly excited transition, where Av is the l inewidth of the transit ion, Avobs is the measured f 1 uorescence 1 inewidth, and Avres is the instrumental resol ution. TEMPERATURE (K) Fig. I FLN l inewidth on the high and low energy sides of the inhomogeneous prof i 1 e. A denotes excitation at 577.5 nm; 0, at 580 nm. The residual broadening at low temperatures is due to imperfect site selection as discussed in the text. At high temperatures each linewidth has an approximately quadratic temperature dependence, but approaches a temperature-independent 1 lmlt at low temperatures. This l imi t i ng va l ue i s about an order of magnitude l arger than our exper irnenta 1 resolution. We interpret it as residual inhomogeneous broadening due to imperfect site selection. We note i n this regard that such a limiting value was not observed by Sel zer, et a 1. / I / using a laser with an order of magnitude smal 1 er 1 inewidth. The reduction in the inhomgeneous linewidth by site selection makes it possible to deconvolute the homogeneous and inhomogeneous contributions by the same techniques used in crystalline hosts. The results of this procedure are displayed in Fig. 2. Fig. 2 Homogeneous 1 inewidth after substraction of the residua1 inhomogeneous broadening. Symbol s are as in Fig. 1. A l 1 data are consistent with a T ' dependence as shown by the I ines. A1 I the homogeneous l inewidths are consistent with a T ' dependence over the entire temperature range. One notes, however, that the homogeneous l inewidth is sma 1 I er on the high energy side of the inhomogeneous profile than on the low energy side in the LS glass. This behavior differs from that seen in the NS and KG glasses and also from the results of Morgan, et al., for a variety of glasses at room temperature /5/. This provides a clear indication that a quadratic temperature dependence may be a universal property of otherwise dissimilar glasses. I V FRACTONS AND THE HOMOGENEOUS LINEWIDTH The idea that systems with fractal structure might have an anoma lous v ibrational density of states was introduced by Stapl eton, et al. /6/ to explain the spin-lattice relaxation time seen in iron-containing proteins. This has led to the e l egant deve l opment of the "f racton" model of l oca l ized v i brat ions on f racta I structures by Alexander and Orbach and co-workers / 2 , 7 / . They have shown that plane waves are a poor representation of the vibrational modes except at long wavelengths. They find a critical length scale L for the Debye approximation, on shorter scales. 1, the vibrations (now cat led fractons) are localized. The density of states for the vibrations is then where IAD and aF are the f~equencies of the Debye phonons and fractons of characteristic length L; d, and d are the Euclidean and fracton dimensionalities. The linewidth due to interaction of the electronic states with the vibrational strain field via direct processes generally has the form C7-334 JOURNAL DE PHYSIQUE and the Ramn broadening is where tv': en: v> is a matrix element of the average local strain, is the electrostatic matrix element for the direct or Raman process and Aj is the splitting to the jth neighboring el ectronic state. These expressions give the conventional resu I ts for crystals when the Debye approximat'ion is used. They may be appl Led to the glass problem using the dispersion relation /2/ for the fracton w = I ~ / ~ on a sel f-simi lar fractal of Hausdorff dimensional ity a and noting that the average local strain from a normal mode with amplitude Q and localization I should scale as Q/1. For a direct process the temperature dependence of the linewidth will be dominated by the thermal population of vibrational quanta with energy Aj as in crystals, but the magnitude will be changed in proportion to the density of states at that energy. For Ramn processes one has where the first integral is over the Debye1 i ke modes and the second is over the fractons. The exponent p = Zd(2/d +I)-4. For fractal structures in a 3 dimensional glass, one has 3>a>2.5, the value for a critically percolating cluster. Alexander and Orbach /2/ conjecture that is uni versa1 l y 4/3; the effective medium approximaFig. 3 Contribution of the fractonsJo the homogeneous I i n~width via Raman processes. Curve A: a=3, d=4/3; curve 8: a=2.5, d=4/3; curve C: a=3, d=l; curve D: a=2.5, d=l. Note that each curve is approximately T~ for T/BL>3. eL is expected to be roughly 10 K. tion /7/ gives ;*I. The specific heat of epoxy can be fit /7/ above I K with d = 1.3, eL=14 K and eD=29 K. Fig. 3 shows numerical results for the fracton contribut ion to the 1 inewidth. A T ' dependence is expected for the broadening throughout the range of our experiment if the 8's for our glasses are simi l ar to those for epoxy. The contribution from the Debye-l i ke modes is negl igibl e at these temperatures. Similarly, the parameter A that governs the magnitude of the Raman broadening can be estimated from the McCumber and Sturge /8/ a parameter for a crystal with the same average density and sound velocity as the glass. This equivalent a is given by where BX is the Debye temperature of this equivalent crystal. In our glasses thehomogeneous 1 inewidth is =Io-~T' cm-l, giving a-10' cm-' which is the same magnitudeseen for rare earth transitions in crysta l s. Thus, the e 1 ectron-fracton Ramanprocess accounts for both the magnitude and temperature dependence of the homo-geneous broadening in glasses. As the glass structure enters the model through a,Fig. 3 suggests on 1 y a weak structural dependence if the A l exander and Orbachconjecture ho l ds.It is also of interest to compare the magnitude ofthe direct process broad-ening in glass tothat seen in crystals. Forthe same equivalent crystal usedtocompare the Rarnan broadening, AvGlass=Avxta for Aj/hfor o for Aj>u~. Assuming the same coup1 ingL Jstrenght ;l in both the glass and the crystal, the fracton contributuon tothe direct process broadening is AvFracton=AvXta (l/3)uD5uL-q(~j/h)q-5 whereq=d(l+Z/a). Since the lowest l eve1 for a direct process is "250 cm-l above theground state in EU~', no observab l e direct process contribution to the l inewidth isexpected at the temperatures of these experiments.This reseach was supported by Rome Air Development Center and the NationalScience Foundation under grant number DMR-82-16551. REFERENCES/1/ P.M. Selzer, D. L. Huber. D. 5. Hamilton. W. M. Yen, and M. J. Weber, Phys.Rev. 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