Glass structure and ion dynamics of lead–cadmium fluorgermanate glasses C. C. Tambelli, J. P. Donoso, C. J. Magon, L. A. Bueno, Y. Messaddeq, S. J. L. Ribeiro, L. F. C. de Oliveira, and I. Kosacki Citation: The Journal of Chemical Physics 120, 9638 (2004); doi: 10.1063/1.1712905 View online: http://dx.doi.org/10.1063/1.1712905 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/120/20?ver=pdfcov Published by the AIP Publishing This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 186.217.234.225 On: Tue, 14 Jan 2014 13:25:58 http://scitation.aip.org/content/aip/journal/jcp?ver=pdfcov http://oasc12039.247realmedia.com/RealMedia/ads/click_lx.ads/www.aip.org/pt/adcenter/pdfcover_test/L-37/586982248/x01/AIP-PT/JCP_CoverPg_101613/aipToCAlerts_Large.png/5532386d4f314a53757a6b4144615953?x http://scitation.aip.org/search?value1=C.+C.+Tambelli&option1=author http://scitation.aip.org/search?value1=J.+P.+Donoso&option1=author http://scitation.aip.org/search?value1=C.+J.+Magon&option1=author http://scitation.aip.org/search?value1=L.+A.+Bueno&option1=author http://scitation.aip.org/search?value1=Y.+Messaddeq&option1=author http://scitation.aip.org/search?value1=S.+J.+L.+Ribeiro&option1=author http://scitation.aip.org/search?value1=L.+F.+C.+de+Oliveira&option1=author http://scitation.aip.org/search?value1=I.+Kosacki&option1=author http://scitation.aip.org/content/aip/journal/jcp?ver=pdfcov http://dx.doi.org/10.1063/1.1712905 http://scitation.aip.org/content/aip/journal/jcp/120/20?ver=pdfcov http://scitation.aip.org/content/aip?ver=pdfcov Glass structure and ion dynamics of lead–cadmium fluorgermanate glasses C. C. Tambelli, J. P. Donoso,a) and C. J. Magon Institute of Physics, USP, P.O. Box 369, 13560-970 Sa˜o Carlos, SP, Brazil L. A. Bueno, Y. Messaddeq, and S. J. L. Ribeiro Laboratory of Photonic Materials–Institute of Chemistry–UNESP, P.O. Box 355, 14801-970 Araraquara, SP, Brazil L. F. C. de Oliveira Núcleo de Espectroscopia e Estrutura Molecular, Instituto de Cieˆncias Exatas, UFJF, 36036-330, Juiz de Fora, MG, Brazil I. Kosacki Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830 ~Received 23 October 2003; accepted 1 March 2004! Glass structure and fluorine motion dynamics are investigated in lead–cadmium fluorgermanate glasses by means of differential scanning calorimetry, Raman scattering, x-ray absorption~EXAFS!, electrical conductivity~EC!, and19F nuclear magnetic resonance~NMR! techniques. Glasses with composition 60PbGeO3–xPbF2–yCdF2 ~in mol %!, with x1y540 andx510, 20, 30, 40, are studied. Addition of metal fluorides to the base PbGeO3 glass leads to a decrease of the glass transition temperature (Tg) and to an enhancement of the ionic conductivity properties. Raman and EXAFS data analysis suggest that metagermanate chains form the basic structural feature of these glasses. The NMR study leads to the conclusion that the F–F distances are similar to those found in pure crystalline phases. Experimental results suggest the existence of a heterogeneous glass structure at the molecular scale, which can be described by fluorine rich regions permeating the metagermanate chains. The temperature dependence of the NMR line shapes and relaxation times exhibits the qualitative and quantitative features associated with the high fluorine mobility in these systems. ©2004 American Institute of Physics.@DOI: 10.1063/1.1712905# I. INTRODUCTION It is well known by glassmakers that the addition of fluoride ions to oxide based glass batches leads to pro- nounced effects on the properties of the resulting glass. Fluo- rides decrease melting temperatures, contribute to eliminate OH residual groups, decrease refractive index and provide fluorine ion conductivity. From a structural point of view, a typical metal~M! oxide glass network is described by the aperiodic association of basic structural units like the@MO4# tetrahedral, known to exist in silica or germania based sys- tems. Fluoride anions in these mixed systems can be consid- ered mainly as nonbridging, therefore, the addition of fluo- ride ions leads to a decrease in connectivity. Part of the fluoride ions in mixed fluoride/oxide glasses, weakly bonded to the glass network, have been identified as the charge car- riers in conductivity measurements.1–6 In fact, the enhanced conductivity observed in different mixed glasses suggested different electrochemical applications such as halide sensors, solid-state batteries and glass purifiers. Besides, these mixed systems have interesting crystallization properties. The so- called ultratransparent glass ceramics, where metal fluorides nanocrystals are identified in the oxide glass host, can be obtained by controlled crystallization treatment.7–15 These oxifluoride materials have been studied by differ- ent experimental techniques such as optical spectroscopy, transmission electron microscopy, thermal analysis, conduc- tivity measurements, and F(1s) x-ray photoelectron spectra.1–15 Nuclear magnetic resonance~NMR! is a well- known experimental technique to study glass structure and ion dynamics. High resolution and spectral deconvolution NMR techniques have been used to study structural arrange- ments of metal fluoride glasses.16,17 Variable temperature NMR line shape and spin-lattice relaxation provide an effec- tive probe for ion dynamics on the microsecond to second time scale.16–24 This paper reports the study of cadmium–lead fluoro- germanate glasses. These glasses have been proposed before as potential hosts for rare earth containing transparent glass ceramics, but no systematic study of the glass structure was performed.11 We will see hereafter that the studied glasses display interesting conductivity properties. In fact, enhanced electrical conductivity observed with the addition of lead fluoride (PbF2) to different oxide glasses seems to be a very general feature, which does not depend on the nature of the oxide glass host.5 The general purpose of this report is to build up a picture of the base glass structure. The knowledge of such structural features can offer further support for a better comprehension of the enhanced mobility of fluoride ions observed for simi- lar mixed glasses and, also, to understand the structural a!Author to whom correspondence should be addressed. Fax:155 16 273 9876. Electronic mail: donoso@if.sc.usp.br JOURNAL OF CHEMICAL PHYSICS VOLUME 120, NUMBER 20 22 MAY 2004 96380021-9606/2004/120(20)/9638/10/$22.00 © 2004 American Institute of Physics This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 186.217.234.225 On: Tue, 14 Jan 2014 13:25:58 http://dx.doi.org/10.1063/1.1712905 modifications occurring during heat treatments performed at temperatures above the glass transition temperature (Tg), which leads to transparent glass-ceramics. Measurements in- clude differential scanning calorimetry~DSC!, Raman scat- tering, x-ray absorption~EXAFS!, electrical conductivity ~EC!, and19F nuclear magnetic resonance~NMR!. II. EXPERIMENT Glasses with composition 60PbGeO3–xPbF2–yCdF2 ~in mol %!, with x1y540 andx510, 20, 30, 40, were prepared by the classical melting (T51073 K for 30 min in open Pt–Au crucibles! and quenching method~to glass transition temperature,Tg , in brass molds! from vitreous PbGeO3, a-PbF2 ~orthorhombic, Aldrich, 99.99%! and CdF2 ~cubic, Aldrich, 99%!. Vitreous PbGeO3, was obtained from ana- lytical purity PbO and GeO2 well mixed and melted in Pt crucibles at 1273 K, followed by quenching to room tem- perature. The amorphous nature of the glass samples was checked by x-ray diffraction of powdered samples. Raman measurements were performed for powdered samples using a Micro-Raman set-up from Renishaw, with He–Ne laser excitation~6345 Å!. Impedance measurements were carried out by the ac ~two probes! technique, using a Solartron 1260 frequency response analyzer with 1296 interface, which operates in the 0.1– 53106 Hz frequency range and is capable to measure resistance values up to 1010 V. All the measurements were performed under air atmosphere in the temperature range of 293–623 K. From the complex impedance data, taken as a function of the electric field frequency, the relative contribu- tion of the bulk, grain boundaries and electrode resistances could be determined. Typical results are represented as a Cole–Cole diagram, composed of three semicircles attrib- uted to the different relaxation times of each response. With the aid of a parallel connected resistor–capacitor equivalent circuit, the diagrams were fitted and analyzed, being the high- and intermediate-frequency semicircles related to the bulk and grain boundary resistances, while the low- frequency semicircle was attributed to the electrode re- sponse. The bulk resistance was represented by the high- frequency semicircle and its value, as determined from the fitting of the impedance diagram, was used to calculate the bulk conductivity, hereafter denoted bys0 . X-ray absorption~EXAFS! experiments were conducted at the XAFS station of the LNLS~Brazilian National Syn- chrotron Light Laboratory, www.lnls.br! ring, operating at 1.37 GeV and 100 mA of nominal current with the beam monochromatized by a Si~111! double crystal. Spectra were recorded at the GeK edge~11104 eV! in the transmission mode with Ar filled ionization chambers in the detection. Powdered samples~grain size,20mm) were deposited on Milipore membranes~2 mm! with powder quantities adjusted in order to obtain reasonable absorption coefficients. 19F NMR line shapes and spin-lattice relaxation times were measured in the temperature range 100–800 K, using a pulsed NMR spectrometer operating at 36 MHz and equipped with a TECMAG NMR-kit. For measurements, small pieces of the samples were placed inside the 4 mm diam sample tubes and, measurements were performed be- ginning at the lowest temperature and increasing the tem- perature up to aboveTg . For each run, an individual sample was used. NMR spectra were obtained by Fourier transfor- mation of the averaged free induction decay signal~p/2 pulse'2 ms). Spin-lattice relaxation times,T1 , were deter- mined by means of the saturation-recovery pulse sequence. The spin-lattice relaxation time in the rotating frame,T1r , was measured at 36 MHz for a rotating rf field of about 5 G. III. RESULTS AND DISCUSSION Homogeneous and transparent glasses were obtained with no crystallization traces detectable by x-ray diffraction, and exhibiting characteristic temperatures that could be eas- ily identified in the DSC scans~not shown here!. Table I summarizes the relevant parameters obtained from DSC analysis. The glass transition temperature,Tg , is observed at 643 K for the vitreous PbGeO3 precursor. With the addition of 40 mol % of PbF2 , Tg decreases to 500 K. The addition of the same amount of CdF2 to the base glass leads to a less pronounced decrease inTg ~to 594 K!. The decrease inTg salient the modifier activity played by the metal fluorides, consisting of the substitution of nonbridging fluorine atoms TABLE I. Summary of parameters obtained from~a! DSC: Tg is the glass transition temperature,Tx is the onset of the crystallization peak, andTp is the temperature at the exothermic crystallization peak maximum,~b! EXAFS: N is the number of atoms in the coordination shell at average interatomic distance R from the absorbing atom, as determined from fitting analysis in the regionk53.88– 12.62 assuming hexagonal monoclinic PbGeO3, and~c! 19F NMR: M 2 is the second moment of the spectra at 173 K andEA is the activation energy for fluorine motions determined from the 1/T1 data in the temperature regions II and III. r is the material density. PbGeO3 PbF2 CdF2 r (g/cm3) Tg ~K! Tx ~K! Tp ~K! N (60.5) R ~Å! (60.01) M 2 (G2) (60.5) EA ~eV! 100 0 0 6.84 643 693 715 4.1 1.74 ¯ ¯ 60 40 0 7.66 500 543 569 4.1 1.74 4.1 0.28~II ! 0.75~III ! 60 30 10 7.40 529 580 604 4.0 1.74 ¯ 0.30~II ! 0.62~III ! 60 20 20 7.17 552 611 636 4.1 1.74 5.7 0.28~II ! 60 10 30 6.92 574 715 750 4.0 1.74 ¯ ¯ 60 0 40 6.83 594 724 747 4.1 1.74 6.2 0.38~II ! 0.63~III ! 9639J. Chem. Phys., Vol. 120, No. 20, 22 May 2004 Structure and ion dynamics in glasses This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 186.217.234.225 On: Tue, 14 Jan 2014 13:25:58 for bridging oxygen atoms. As shown in Table I,Tg is ob- served in the range 500–594 K for glasses with different amounts of PbF2 and CdF2 . Earlier studies lead to the con- clusion that the network modifier character of PbF2 in the SiO2– PbF2– CdF2 glassy system was much more pro- nounced, emphasizing the differences in the modifying role played by PbF2 and CdF2 in the glass structure.15 Concerning the base PbGeO3, an exothermic feature re- lated to devitrification is observed in the DSC scan, peaking at 715 K. Heat treatments performed at this temperature lead to the monoclinic~space groupP2/n) PbGeO3, isomorphous to the alamosite PbSiO3 , whose structure is described by (GeO3)n chains with twelve@GeO4# tetrahedra linked in a repeated unit.25 With respect to the glass preparation, some additional remarks deserve careful consideration. Starting from GeO2 and PbO mixtures, submitted to heat treatments at the temperatures for which the phase diagrams state the uniqueness of monoclinic PbGeO3, a mixture of lead ger- manates with different stoichiometric Pb/Ge ratios were al- ways obtained, even when long lasting heat treatments of about two to three days were employed. Pure monoclinic PbGeO3 could only be obtained by the crystallization, at 715 K, of a glass prepared with that same composition deter- mined from the phase diagram. Such experimental evidence strongly suggests similarities between the PbGeO3 glass and the crystalline monoclinic structures. It also corroborates the model to be proposed hereafter, in which the structure of the lead–cadmium fluorgermanate glasses has many similarities with that of their PbGeO3 precursor. A. Raman and x-ray absorption Figure 1 shows the Raman spectra obtained for the crys- talline @Fig. 1~a!# and amorphous@Fig. 1~b!# PbGeO3. The main bands, occurring at the same spectral region for both, crystalline and amorphous phases, are inhomogeneously broadened for the glasses. In the high wavenumber region, the bands occurring at 743, 780, and 814 cm21 in Fig. 1~a! could be assigned to the localized Ge–O stretching modes of the polymerized metagermanate structure. The broadband observed for the glass at 794 cm21 @Fig. 1~b!# could also be assigned to the same vibrational modes. The NMR nomen- clature used in connection with the germanate compounds classifies the different germanate species asQn (n50 – 4), wheren denotes the number of bridging oxygen atoms for each@GeO4# basic tetrahedra. With this definition,Q4 relates to the structure containing only bridging oxygen atoms linked to Ge atoms and,Q0 to isolated@GeO4# tetrahedra. In an earlier work we proposed that the bands observed in the Raman spectrum of the vitreous PbGeO3 could be assigned to vibrational modes ofQ2 species,26 meaning that each @GeO4# tetrahedron displays two bridging and two non- bridging oxygen atoms. Recalling the spectra of Fig. 1~a!, we remark that some lines are observed in the medium wave number range at 442, 487, 508, 559, and 575 cm21. The broadband centered at 528 cm21, observed for the glasses in Fig. 1~b!, could be interpreted as the envelope of the crystal- line phase lines. Stretching vibrational modes of Ge–O–Ge bonds are observed in this region. The bands at low wave- number could be assigned either to extended vibrational modes or to Pb–O localized modes. The only observed change in the spectrum obtained for the PbGeO3 glass, upon addition of lead and cadmium fluo- rides, is a slight blueshift ('10 cm21) of the main high wave number band. This increase in band order may be re- lated to depolymerization effects, more easily reflected in the decrease ofTg ~Table I!. As mentioned before, fluoride ad- dition leads to a decrease in the connectivity of the base oxide matrix with nonbridging fluorine atoms substituting for oxygen atoms. Figures 1~c!–1~g! display the Raman spectra obtained for the five glasses studied here, and all spectra display the broadband peaking at 786 cm21. Additional re- sults ~not shown here! exhibit similar Raman spectra for all samples representatives of the vitreous domain of the system PbGeO3– PbF2– CdF2 . X-ray absorption~EXAFS! data obtained at the GeK edge were analyzed according to the procedure given in Refs. 14 and 15. The general procedure of pre-edge, back- ground removal, normalization and extraction of thex(k) EXAFS oscillations was employed. The data were Fourier transformed leading to spectra scaled in distances, and the peaks in the Fourier transforms, corresponding to particular coordination shells, were filtered and back-transformed to k-space. The resulting EXAFS-filtered signal was treated as a sum of sinusoidal wave functions using single scattering approximation.27 Table I shows the obtained results. Four FIG. 1. Raman spectra:~a! PbGeO3–crystal,~b! PbGeO3–glass,~c! 60PbGeO3–40PbF2,~d! 60PbGeO3–30PbF2–10CdF2,~e! 60PbGeO3– 20PbF2–20CdF2,~f! 60PbGeO3–10PbF2–30CdF2, and~g! 60PbGeO3– 40CdF2. 9640 J. Chem. Phys., Vol. 120, No. 20, 22 May 2004 Tambelli et al. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 186.217.234.225 On: Tue, 14 Jan 2014 13:25:58 coordinated oxygen atoms, at a mean distance of 1.74 Å, were determined for Ge atoms in all samples. The fourfold oxygen coordination of Ge atoms, as deter- mined by EXAFS, leads to the conjecture that metager- manate chains, similar to those found in the PbGeO3 crystal- lized glass, constitute an important feature of the lead– cadmium fluorgermanate glass structure. This finding is consistent with the Raman results shown in Fig. 1. EXAFS data obtained here could not distinguish between oxygen and fluorine atoms, but some depolymerization effects due to the substitution of terminal fluorine atoms for bridging oxygen atoms is also clear from Raman and DSC measurements. B. 19F nuclear magnetic resonance 1. Static spectra The temperature dependence behavior of the19F NMR spectra of the samples are similar, and Fig. 2 shows typical results obtained with the glass 60PbGeO3– 20PbF2– 20CdF2 . Fluorine nuclei (I 5 1 2) have a large gyro- magnetic ratio,gn/2p540.055 MHz/T, and 100% natural abundance. The absence of ionic motion at low temperatures ~a temperature region commonly referred as the rigid net- work! causes the19F resonance spectrum to be inhomoge- neously broadened due to dipole–dipole couplings between neighboring spins, resulting in an approximated Gaussian line shape. Considering that the nonzero nuclear spins,207Pb, 111Cd, 113Cd, 73Ge, and17O have small gyromagnetic ratios or low natural abundance, we can assume that the19F–19F dipole–dipole interaction is the main source of the line broadening at low temperatures. The Van Vleck second mo- ment of the Gaussian line shape,M2 , can be used to estimate the strength of the nuclear dipolar coupling, which is in- versely proportional to the sixth power of the internuclear distances.28 The experimental determination of the second moments has been used to estimate average internuclear dis- tances in glasses.19,28,29 The low temperature fluorine second moments estimated from the Gaussian fitting of the NMR spectra~at T 5173 K) are shown in Table I. It is interesting to draw com- parisons between the obtainedM2 values with those reported in the literature for corresponding fluoride crystals. For ex- ample, the valueM254.1 G2, obtained for the glass with composition 60PbGeO3– 40PbF2 compares well with the one reported for crystallineb-PbF2 , where the F–F distance is 2.97 Å andM254 G2.30 A value of 6.260.5 G2 was ob- tained for the glass with composition 60PbGeO3– 40CdF2 and this value compares with the second moment calculated for CdF2 (M256.5 G2) where the F–F distance is 2.7 Å. Finally, the result obtained for 60PbGeO3– 20PbF2– 20CdF2 (M255.760.6 G2) is consistent with the second moment calculated for solid solutions Cd12xPbxF2, whereM2 is in the range 3.8– 6.5 G2. In this last case the lattice constant was found to depend linearly on composition, froma 55.927 Å forx50 to a'5.94 Å for x51.31 From these comparisons it is possible to affirm that the fluorine ions are not uniformly distributed through the entire structure of the material. This conclusion can be corrobo- rated by a simpler argument, as follows. Taking into account the density~Table I! and the nominal composition of the 60PbGeO3– 40PbF2 glass, the number of fluorine atoms per cm3 of the glass isn51.2531022. If we suppose, just for the sake of argument, that these atoms are homogeneously dis- tributed, corresponding to maximized F–F distances of (1/n)1/354.3 Å, the resulting fluorine second moment esti- mated from the Van Vleck method should be 0.42 G2, which is one order of magnitude smaller than the experimental value obtained for this glass (M254.1 G2). Similar conclu- sion can be drawn for the other glass compositions. Taking into account the similarity of the fluorine second moment in both materials, 60PbGeO3– 40PbF2 glass and crystalline b-PbF2 , the average F–F distance in the glass is estimated to be'3 Å. To explain these results, we can recall the description of the glass structure proposed on the basis of Raman and EXAFS measurements, in which the metagermanate chains are forming the basic element of the microscopic glass struc- ture, with some nonbridging fluorine atoms substituting oxy- gen atoms. NMR results provide additional evidence that fluorine rich regions are permeating metagermanate chain structures, in which, F–F distances are comparable to those found in crystals. These arguments imply that fluorine phases are distributed in microdomains at the interface of the amor- phous network formed by the metagermanate chains, with a FIG. 2. Typical19F NMR spectra of the glass 60PbGeO3– 20PbF2– 20CdF2 at indicated temperatures. All spectra were measured at the Larmor fre- quency of 36 MHz. The dashed spectrum corresponds to the Gaussian fitting of the line shape at 173 K. 9641J. Chem. Phys., Vol. 120, No. 20, 22 May 2004 Structure and ion dynamics in glasses This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 186.217.234.225 On: Tue, 14 Jan 2014 13:25:58 local order similar to that of the corresponding crystal. This assumption can explain most of the present experimental data and can well account for the interesting and particular crystallization properties of these oxyfluoride glasses,7,15 in which the nucleation of a fluoride crystal would be energeti- cally favored in those fluorine-rich regions. 2. Motional line narrowing The ionic conduction in these glassy materials is pro- moted mainly by fluorine motion, therefore, the NMR data obtained at higher temperatures can, in theory, provide infor- mation regarding the correlation time scale and activation energy of the relevant microscopic dynamical processes. As can be seen in Fig. 2, the observed narrowing of the NMR line emerges above 240 K and the line shape changes pro- gressively from Gaussian~at T5173 K) towards Lorentzian ~at T5380 K). In the intermediate region, the line shape is more complex and resembles a superposition of a narrow Lorentzian line and a broad Gaussian line~note the 298 K spectrum in Fig. 2!. Such inhomogeneous narrowing process suggests the existence of fluorine species characterized by different mobility, being the narrow line associated to the fraction of mobile nuclei at that temperature. The criterion for motion narrowing is that the rate of fluctuation of the local fluorine dipolar fields, which is generally described in terms of a correlation timets , become much greater than the rigid lattice linewidth expressed in frequency units, i.e., ts 21@(g2M2)1/2.28 Considering the 60PbGeO3– 20PbF2– 20CdF2 glass data we estimatets'1.731025 s at the temperature corresponding to the onset of motional nar- rowing. As will be further discussed later, this value consti- tutes the lower value of the fluorine motional correlation time within the investigated temperature range. Finally, it should be noted that the onset of motional narrowing of the 19F and 7Li NMR line in fluorzirconate glasses is usually observed at higher temperatures; for example, at 300 K in ZrF4– BaF2– LaF3– AlF3– LiF ~ZBLALi ! and at 400 K in ZrF4– BaF2– LaF3– AlF3– NaF ~ZBLAN !.32 Therefore, we may conclude that the fluorine ion mobility in our oxyfluo- ride glass is sufficiently high to average dipolar interactions at a lower temperature compared to fluorzirconate glasses. 3. Spin-lattice relaxation Above room temperature, the19F spin-lattice relaxation rate is strongly influenced by the transport properties due to diffusive movements of F2 ions in the glass network. The relaxation process can be interpreted in terms of the fluctua- tions of the19F–19F dipolar interaction resulting from the fluorine motion. The approach used in the Bloembergen– Purcell–Pound~BPP! model assumes noncorrelated isotropic random motions, yielding to a pair–pair spin correlation function of exponential form,Gs(t)5exp(2t/ts), parameter- ized by the correlation timets , which defines the time scale for changes of the local magnetic field experienced by the resonant nucleus.28 In this context, the spectral density func- tion, J(v,ts), given by the Fourier transform of the related correlation function, results J~v,ts!5 ts 11~vts! 2 . ~1! The experimentally observable spin-lattice relaxation rate can be expressed in terms of the spectral density function evaluated at the NMR Larmor frequency,v0 , and at its first harmonic, 2v0 ,28,33 T1 21}@J~v0 ,ts!14J~2v0 ,ts!#. ~2! In practice, the validity of the BPP model can be tested experimentally by verifying some of its main characteristic features:~i! T1 21 should display a symmetric maximum at a temperature at which the conditionv0ts50.62 is fulfilled ~usually approximated byv0ts'1) and, ~ii ! at the low- temperature side of the maximum (v0ts@1), the relaxation times should depend quadratically on the frequency (T1 }v0 2ts). For thermally activated processes such as ion diffusion in glasses,ts must be related to the individual ionic jump correlation time,t0 , which is usually expressed by Arrhen- ius temperature dependence, t05t0,̀ eEA /kBT. ~3! Here, kB is the Boltzmann constant,EA is the microscopic barrier as seen by the hopping ion~or the activation energy for the process!, and 1/t0,̀ is the attempt frequency of the order of an optical phonon frequency (1012– 1013 s21). For many physical systems, the conditionts5t0 can constitute a fair approximation, leading to an observable behavior with some additional features:~iii ! when ln(T1 21) is plotted against inverse temperature, the activation energy,EA , can be deter- mined from the slopes at either sides of the maximum, and ~iv! if EA is known,t0,̀ can be estimated from the maximum condition ~i! and Eq.~3!. However, deviations from the BPP behavior are fre- quently encountered in disordered systems, where theT1 21 dependence on frequency is weaker thanv0 2 and asymmetric relaxation plots have been observed, with the slope on the high temperature side of theT1 21 maximum being steeper than that on the low temperature side.22,34,35More probably, these observations indicate a nonexponential decay of the correlation functionGs(t). A nonexponential decay may rep- resent an ensemble average of exponential decays corre- sponding to a distribution of jump processes, each one with characteristic activation energy and correlation time.22 Alter- natively, it is also possible that the shape of the correlation function decay be inherently nonexponential, due to intrinsic cooperative interactions~mainly Coulomb interactions! among the mobile charged ions and their interaction with the glassy network.23,36,37 In the case of heavy metal fluoride glasses, the tempera- ture dependence of the19F T1 21 has been interpreted in terms of three main mechanisms:~a! spin relaxation processes at- tributed to low-frequency excitation of disorder modes, usu- ally noticeable at temperatures below 300 K,~b! diffusive ionic motions which become significant in the region 300 K,T,Tg , and ~c! fast diffusive ionic motions, which are responsible for a19F spin-lattice relaxation rate maxi- mum, generally localized at temperatures aboveTg .20,24,38,39 9642 J. Chem. Phys., Vol. 120, No. 20, 22 May 2004 Tambelli et al. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 186.217.234.225 On: Tue, 14 Jan 2014 13:25:58 Before going any deeper in the theoretical foundations of the problem, we address to Fig. 3, where the temperature dependence of the19F spin-lattice relaxation rates (T1 21) of some of our studied glasses is plotted. In order to comment the main features of the relaxation curves shown in Fig. 3, it is useful to define temperature regions in which it is apparent that specific dynamic processes are ruling the spin relaxation. The limits of such temperature regions~as sketched with dashed lines in Fig. 3! are not exactly the same for all samples. By comparison, the characteristic temperatures de- termined by DSC,Tg andTx , and the room temperature are also marked in Fig. 3. For all temperatures in the defined regions I, II, and III, the recoveries of the longitudinal mag- netization towards equilibrium are described by exponential decays of time constantT1 . In the temperature region I, below room temperature, the NMR relaxation rates exhibits weak temperature depen- dence, as seen clearly in Figs. 3~b! and 3~d!. In region II the T1 21 values increase with increasing temperature, closely fol- lowing a straight line in the plots of Fig. 3. Increasing the temperature to inside region III, the data depart from the preceding straight-line behavior exhibiting a larger slope, with the inflection point at a temperature belowTg , denoted hereafter byTm , which depends on the glass composition. Further increase of the temperature, toward the region IV, will cause an abrupt decrease of theT1 21 values, resulting in an apparent discontinuity of theT1 21 versus 1/T plot. The region III in Fig. 3~b! does not exists or seems to be too narrow to be identified. In region IV the magnetization re- covery is, in all cases, nonexponential and well fitted by a weighted sum of two exponential functions with different time constants. Besides, due in part to a lower signal to noise ratio, the T1 data obtained in this region is affected by a larger uncertainty. A brief examination of theT1 21 plots presented in Fig. 3 indicates that they cannot be completely understood within the framework of the BPP model. Starting from room tem- perature,T1 21 increases with increasing temperature, how- ever, a maximum in theT1 21 temperature dependence is not observed. Indeed, it is apparent that before such maximum could be reached at some temperature aboveTg , a sudden change in theT1 21 behavior is observed, leading to nonexpo- nentialT1 decays characterized by longer time constants. A more detailed discussion of the relaxation behavior on each region will be outlined in the following paragraphs. In region I, individual fluorine ions mobility is too small to exert an influence on the nuclear relaxation process. A considerable number of NMR relaxation studies in inorganic glasses have found thatT1 21 increases monotonically with increasing temperature and depends sublinearly on the Lar- mor frequency. The process has been interpreted in the framework of thermally activated low-frequency excitations of disorder modes intrinsic to the glassy state of matter.20,38–40Since the microscopic structure of the disor- dered modes in glasses is unknown, they are commonly de- scribed on the basis of an asymmetric double-well potential configuration. Under these assumptions the spin-lattice relax- ation rate has been expressed as a power law dependence on temperature and frequency,T1 21}Tav2g, with 1