12462
J. Phys. Chem. 1996, 100, 12462-12466
X-ray Diffraction Investigation of Iron in Sodium Phosphate Glasses A. Musinu, G. Piccaluga,* and G. Pinna Dipartimento di Scienze Chimiche, Via Ospedale 72, 09124 Cagliari, Italy ReceiVed: NoVember 29, 1995; In Final Form: March 23, 1996X
The short-range order of a series of sodium-iron phosphate glasses has been studied through X-ray diffraction with the purpose of investigating the structural role of iron ions in these glasses. Fe-O bond lengths and coordination numbers were obtained by simulating the difference radial curves calculated by subtracting the radial distribution function of the proper sodium phosphate glass from those of sodium-iron phosphate glasses. Good fits were obtained by considering the occurrence of about 10% of Fe2+ and two distinct sites for Fe3+; octahedral coordination for all iron ions was demonstrated. The difference radial curves show clearly that well-defined structural arrangements extending to medium-range distances form in all the examined cases around iron, which modifies the properties of glasses, by strengthening the cross-bonding of the phosphate chains.
Introduction The interest for phosphate glasses has grown recently, following the observation that their mechanical properties and resistance to chemical attack are enormously improved by the addition of metal oxides.1 In this connection, Pb(PO3)2 glass doped with Fe2O3 has been thoroughly investigated, and much information about the structural role of iron ions has been acquired.2-5 A number of metal oxides have been studied as possible alternatives to iron oxide (e.g., MgO, Al2O3, CoO, NiO, ZnO, Y2O3, La2O3, CeO2), but none of them were as effective as iron oxide in stabilizing lead phosphate glass.1 However, phosphate glasses other than lead phosphate seldom have been considered.6 Therefore, we decided to study NaPO3 glasses doped with Fe2O3, in order to determine the structural role of iron ions in these samples and to compare the results with those obtained in lead metaphosphate glasses. According to the literature, NaPO3 and Pb(PO3)2 glasses should be very similar as regards the network of phosphate groups which forms the amorphous backbone of the material. In fact, the structure of metaphosphate glasses, like that of the corresponding crystals, is described as consisting of long chains of PO4 tetrahedra interconnected by bridging oxygen atoms.7,8 Proof of this has been provided for the Pb metaphosphate glass by vibrational spectroscopy and liquid chromatography2 and, in the case of Na metaphosphate glass, by MAS-NMR spectra.8,9 In turn, the polyphosphate chains are linked together by the interaction between the metal cations and the nonbridging oxygens of the network. Different cations can give rise to structural differences among the various (glassy or crystalline) metaphosphates. For instance, the polyphosphate chains are differently twisted in various crystals10 and have different repetition frequencies, depending on coordination requirements of the metal ions (coordination numbers, geometries, nature of the Me-O bonds, and so on). Accordingly, Na+ and Pb2+ ions are likely to give rise to differences in the cross bonding of adjacent polyphosphate chains. Although experimental information about Na+ and Pb2+ coordination is poor and discordant, it is plausible that the coordination polyhedra of the two ions are different. In a recent X-ray and neutron diffraction investigation of a sodium metaphosphate glass, Hoppe et al.11 proposed a coordination number * Author to whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, June 1, 1996.
S0022-3654(95)03521-0 CCC: $12.00
of about five oxygens in the environment of the Na+ ions, with a broad but unsplit distribution around the average distance of 2.38 Å. A coordination number of approximately 1.5-2 O atoms around Na+ ions at the average distance of 2.20 Å was instead previously suggested by Suzuki12 on the basis of a highresolution neutron diffraction experiment; it is not clear if this distance is the first component of a split peak analogous to what was observed in silicate11 and borate glasses.13 Similar discrepancies exist in the literature about Pb2+ coordination. By an EXAFS investigation, Greaves et al.4 proposed the coordination of 8 for Pb2+ in a metaphosphate glass, with the site displaying considerable disorder around the average distance of 2.4 Å. This result is consistent with that obtained in an X-ray diffraction study,14 where a total number of ∼9 neighbors was proposed, set at two different coordination distances in a distorted polyhedron. On the contrary, only 5 oxygens at 2.47 Å were detected around Pb2+ in a neutron scattering experiment.15 Although the differences in coordination numbers are not clearly defined, it is beyond doubt that the chemical bonds of Na+ and Pb2+ with the surrounding oxygens have different characteristics. In fact, Na+ is the archetype of the so-called modifier species;6 that is, it breaks the bridging bonds P-OP, generating negatively charged terminal oxygens. Na+ ions interact ionically with surrounding oxygens, setting themselves rather loosely in the holes of the amorphous network. On the other hand, Pb2+ in many oxide glasses is known to play a dual structural role, acting both as network modifier and as network former.17,18 In the latter case, the addition of PbO to a glass leads to formation of [PbO4/2]2- units, which become part of the vitreous network with corner-sharing geometry. The aim of the present work is to verify whether the substitution of Na+ for Pb2+ in the metaphosphate glass affects the structure existing in the proximity of iron ions. Three samples were prepared by adding an increasing amount of Fe2O3 to the NaPO3 glass matrix (M). Both the matrix and the doped samples were examined by X-ray diffraction to obtain information about the structure near the metal ions. The iron-containing samples were also investigated by Mo¨ssbauer spectroscopy; details of this study have been reported in a separate paper.19 Experimental Section Reagent grade Fe2O3 and NaH2PO4‚H2O were used as starting materials. Proper amounts were mixed, melted in platinum © 1996 American Chemical Society
XRD of Iron in Sodium Phosphate Glasses
J. Phys. Chem., Vol. 100, No. 30, 1996 12463
TABLE 1: Nominal and Experimental Compositions (mol % of Oxides) and Densities (g/cm3) of the Glasses Investigateda Na2O
P2O5
Fe2O3
glass
3
d (g/cm )
nom
exptl
nom
exptl
nom
exptl
Fe5 Fe10 Fe15
2.62(1) 2.76(1) 2.84(1)
47.5 45.0 42.5
48.7(2) 47.3(2) 44.3(2)
47.5 45.0 42.5
46.9(2) 43.5(2) 42.6(2)
5 10 15
4.4(1) 9.2(1) 13.1(1)
a Errors are given in parentheses. Sample designations are given in column 1.
crucibles, and kept at 1100 °C for 1 h. The melts were poured into stainless steel molds, cooled by cold water, and then annealed at 300 °C for 1 h. Weight losses during preparation were very close to those expected on the basis of the starting mixture composition. However, chemical analyses of all the doped samples were carried out by standard methods. The experimental compositions are reported in Table 1, together with the nominal compositions, densities, and their errors; sample designations are reported in column 1. Differences between nominal and experimental compositions are small but not negligible (mainly those referring to iron oxide), since their presence can affect the analysis of diffraction data. As unexpected weight loss during melting had not occurred, these differences might reveal inhomogeneities in the melted material. Therefore, chemical analyses were carried out on portions of the powdered samples examined in XRD experiments. X-ray diffraction data were collected using a Siemens D500 θ-2θ diffractometer equipped with a graphite monochromator on the diffracted beam; using Mo KR radiation (λ ) 0.709 Å) and a step scan mode, 80 000-200 000 counts were collected at each preset point in the angular range 2° < θ < 70°, corresponding to the s range 0.6 < s < 16.5 Å-1 (s ) 4π sin θ/λ, where θ is half the scattering angle and λ is the wavelength). The observed intensities were corrected for background, absorption, and polarization.13 As a large portion of incoherent radiation was still present in the diffracted intensities and considering that real peaks at low r were expected in the radial curves due to the shortest P-O distances, the method proposed by Habenschuss and Spedding20 was used for normalization, because it takes the incoherent contribution into account and also minimizes spurious ripples in the low-r region. From the normalized intensities, Ieu, structure functions, i(s), were obtained according to
Figure 1. Experimental (‚‚‚) and simulated (s) radial functions of the three iron-containing glasses and the matrix.
Results The radial functions of the sodium metaphosphate glass and of the three doped samples are reported in Figure 1. The D(r) of the matrix shows two peaks at 1.55 and 2.50 Å. On the basis of the literature information,1-5 the first peak originates from the direct P-O distances and the second from O-O distances in the PO4 tetrahedra. Na+-O interactions too are expected to contribute to the peak at 2.50 Å.11-13 Minor details at r > 3.0 Å are due to longer interaction distances in the polyphosphate chains. The radial functions of the doped samples appear progressively modified, as the percentage of the iron oxide increases: a new peak appears at about 2.0 Å and the peak at about 3.5 Å becomes sharper, with the maximum shifting toward shorter distances. Clearly, these two details are indicative of the first and second coordination shells of iron ions. The quantitative interpretation of diffraction data is based on the Debye scattering equation, which describes the structure function as a sum of contributions from every atom pair distance in the system. Ascribing a Gaussian-type distribution to the interatomic distances, the equation becomes m
m
i(s) ) Ieu - ∑nifi2(s)
(1)
i)1
and radial distribution functions, D(r), were then evaluated by Fourier transform:
D(r) ) 4πr2F0 + (2r/π) ∫s
smax
si(s) M(s) sin(sr) ds
(2)
min
where r is the interatomic distance, F0 is the average electronic number density, ni are the stoichiometric coefficients of the assumed unit containing m types of atoms, fi are the scattering factors of the i species, and M(s) is a modification function of the form
M(s) ) {[∑nifi(0)]2/[∑nifi(s)]2} exp(-ks2) with k ) 0.005. The molecular units were defined in such a way that the same coefficient (arbitrarily chosen equal to 1) was assigned to the P atom in all the samples.
n
i(s) ) ∑∑nififjNij(sin srij/srij) exp(-1/2σij2s2)
(3)
i)1 j)1
Here the first sum is over the number of chemical species; the second, over the number of shells around each i species; rij is the average distance of the jth shell atoms from an origin atom i; σij is the root mean square deviation of the rij distance; and Nij is the average number of j atoms in the shell, that is, the coordination number. This equation can be used to simulate the entire experimental structure function starting from an extended structural model. When the study is limited to the evaluation of the short-range order, it can be used in different ways. To perform the simulation of low-r peaks in real space, the corresponding terms in eq 3 are Fourier transformed into real space, using the same cutoff values as for the experimental curve, and the agreement between experimental and theoretical peaks appearing in the radial functions is optimized by varying the physical parameters rij, σij, and Nij. This procedure subjects both the experimental and simulated curves to the same type of truncation errors (even if the actual error is not necessarily the same).
12464 J. Phys. Chem., Vol. 100, No. 30, 1996
Musinu et al.
TABLE 2: Mean Distances r (Å), Root Mean Square Deviations σ (Å), and Coordination Numbers N Obtained from the Simulation of the P-O Peak in the Radial Functions of the Four Glassesa
a
glass
rP-O
σP-O
NP-O
Fe5 Fe10 Fe15 M
1.547(5) 1.545(5) 1.547(5) 1.545(5)
0.08(1) 0.08(1) 0.07(1) 0.09(1)
3.8(3) 3.8(3) 3.9(3) 3.7(3)
Limit errors are given in parentheses.
Another procedure, quite common in EXAFS spectroscopy,4 is based on a filtering operation: when a peak appears well resolved in the radial function, it can be back-transformed into reciprocal space and the function obtained can then be simulated, introducing only the proper terms in the Debye equation. In the present case, a fitting procedure in real space was used to simulate the P-O intramolecular peak in all four glasses. Although the distances of bridging and nonbridging oxygens from the central P are different, only one term was used in the simulation, because the resolution of the present experiments is not enough to distinguish bond lengths only differing by 0.10.15 Å. The final parameters are reported in Table 2; they are consistent with the expected values.12-15 In the case of the matrix glass, also the second peak of the D(r) was simulated, to obtain indications on Na+ coordination. Since at least two overlapping pair distances (rO-O and rNa+-O) contribute to this peak, the NO-O parameter was not refined but kept fixed to the value expected for the infinite chain model of metaphosphate glasses.7,8 Although this approximation and the uncertainty deriving from the incomplete resolution of the peak cast doubts about the reliability of the final parameters values, the fitting procedure points to an irregular coordination environment. In fact, two average distances with distinct coordination numbers had actually to be taken into account (rINa+-O ) 2.33 Å, NINa+-O ) 2.4; rIINa+-O ) 2.6 Å, NIINa+-O ) 1.4). This description is intermediate between Suzuki’s12 and Hoppe et al.’s11 results mentioned in the introduction and agrees with most of the observations reported for Na+ in oxide glasses.11,13,21 As far as the iron coordination is concerned, the Debye equation was used in combination with a difference method which aims at separating the partial radial distribution DFe-X(r) from the total D(r) of the doped glasses; if the iron atoms do not perturb the structure of the matrix, the difference radial curve ∆D(r) ) D(r) - DM(r) represents the order around Fe. Rigorously, this can never be true; however, it has been demonstrated5,13,14 that, as regards the first coordination shells, the method provides valid results if the accuracy of the experiments is adequate. The three difference radial functions are shown in Figure 2. The peaks at 2.0 and 3.2 Å are now well visible and growing with the iron content. In addition, a small peak is present at about 2.8 Å, which too grows regularly with increasing iron. In addition, the succession of peaks in the medium range is similar in all three cases and points to an ordering effect of the iron ions which goes beyond the shortrange distances. At low r very small spurious ripples appear; it confirms the correctness of the subtraction method and shows that the determination of iron coordination will not be affected by their presence. According to many previous studies of iron in oxide glasses,4,5,22,23 the peak at 2.0 Å is due to Fe-O interactions. As a first attempt,24 this peak was simulated by transforming a single term of eq 3 and refining only one set of parameters (rFe-O, σFe-O, and NFe-O). The best fittings obtained were not completely satisfactory due to oddities in the parameter values and because of the quality of the simulation.
Figure 2. Difference radial functions (‚‚‚) of the three iron-containing glasses; simulation (s) of first and second coordination shells around Fe ions.
Figure 3. Comparison of the back-transforms of the Fe-O peak (‚‚‚) of the ∆D(r)’s with synthetic (s) functions for the three iron-containing glasses.
To understand the reasons for this difficulty, the state of the iron was investigated by Mo¨ssbauer spectroscopy.19 The main conclusions of that study are summarized here: (a) a nonnegligible percentage of FeII (9-13%) is present in all the samples; (b) both isomer shift and quadrupole splitting values are typical of high-spin octahedral Fe2+ and Fe3+ ions; (c) in all the samples ferrous and ferric ions are distributed in two sites, characterized by a markedly different disorder. Following these indications, the simulation of the nearest neighbor environment of iron ions was repeated by introducing in the calculations three different terms: two for two kinds of Fe3+ ions and only one for the less abundant Fe2+ ions. Distances, coordination numbers, and root mean square deviations were independently refined for each contribution, while the percentages of the various species were kept fixed at the values estimated by the Mo¨ssbauer investigation. The best fitting calculations were carried out both in real space and using the back-transform procedure. The very good agreement obtained in all the three cases can be seen in Figure 3, where experimental and synthetic curves are compared in the reciprocal
XRD of Iron in Sodium Phosphate Glasses
J. Phys. Chem., Vol. 100, No. 30, 1996 12465
TABLE 3: Mean Distances r (Å), Root Mean Square Deviations σ (Å), and Coordination Numbers N Obtained in the Final Calculation of the Synthetic Functions of the Three Glassesa rFe3+ord-O σFe3+ord-O NFe3+ord-O rFe3+dis-O σFe3+dis-O NFe3+dis-O rFe2+-O σFe2+-O NFe2+-O rO-O(Fe3+) σO-O(Fe3+) NO-O(Fe3+) rO-O(Fe2+) σO-O(Fe2+) NO-O(Fe2+) rFe-P σFe-P NFe-P rFe-Na σFe-Na NFe-Na a
Fe5
Fe10
Fe15
2.00(1) 0.08(1) 6.7(5) 2.00(1) 0.09(1) 6.7(5) 2.17(2) 0.08(2) 6.1(6) 2.73(3) 0.07(3) 4.7(5) 2.90(3) 0.08(3) 5.0(5) 3.24(3) 0.10(3) 5.2(5) 3.33(3) 0.10(3) 2.0(2)
2.00(1) 0.05(1) 5.6(4) 1.98(1) 0.07(1) 5.5(4) 2.18(2) 0.08(2) 5.8(5) 2.72(3) 0.07(3) 4.2(4) 2.90(3) 0.08(3) 4.2(4) 3.24(3) 0.11(3) 5.3(5) 3.35(3) 0.10(3) 2.2(2)
2.00(1) 0.06(1) 5.5(4) 1.99(1) 0.08(1) 5.5(4) 2.18(2) 0.08(2) 5.4(5) 2.70(3) 0.09(3) 4.1(4) 2.90(3) 0.09(3) 4.2(4) 3.24(3) 0.11(3) 5.0(5) 3.34(3) 0.10(3) 2.0(2)
Limit errors are given in parentheses.
space. The final parameters are reported in Table 3. The meaning of the errors assigned to the parameters has been discussed in detail in previous papers.5,13,14 They represent the limit errors which encompass all the acceptable final values obtained in a complex series of calculations, in which different data ranges are used, or the order of the parameters fitting sequence is changed, or different initial situations are considered. The distance values are fairly close to those expected for octahedral coordination both for Fe2+ and Fe3+ ions. The coordination numbers confirm these indications, within the limits of precision ((10%) ascribed to the N values. The σ values come out slightly but systematically higher for the more disordered Fe3+ site. As mentioned above, the difference method becomes less reliable when applied to features at larger distances. In spite of this, the simulations of the peaks at 2.8 and 3.2 Å gave quite satisfactory results (Figure 2). The first was seen to correspond to the average among O-O distances around Fe3+ and Fe2+ coordination polyhedra; for both oxidation states, distances and coordination numbers are consistent with octahedral arrangement of oxygens around the central iron. As regards the peak at 3.2 Å, good agreements and physically meaningful parameters were obtained only by considering Fe-Na pairs together with Fe-P interactions. Also the final values of these parameters are listed in Table 3. Discussion In spite of some uncertainties in the estimate of coordination numbers, the octahedral coordination of iron in the phosphate glasses examined comes out clearly. This fact is consistent with a lot of new and old literature,1-6,25-30 according to which, while in silicate glasses iron ions can be either tetrahedrically or octahedrically coordinated, they sit in octahedral sites in phosphate glasses. Furthermore, the diffraction results are fully consistent with the Mo¨ssbauer investigation of the same samples.19 In fact, only considering the presence of about 10% of Fe2+ and portioning Fe3+ in two different terms, as suggested by Mo¨ssbauer findings, very good agreement was obtained between experimental and calculated radial functions. These facts agree with literature information. The occurrence of Fe2+
in phosphate glasses doped with Fe2O3 and melted in air has already been documented.6,30 In particular, in Pb(PO3)2 glasses doped with Fe2O3 and melted at 900 °C, at least 99% of the iron was shown to be Fe3+, but in glasses of similar compositions melted at 1000 °C (which is closer to the melting temperature used in the present work) about 10% of iron was Fe2+.3 Also the occurrence of (at least) two nonequivalent Fe3+ species in phosphate glasses has been reported in many cases,1-3,6,30 including NaPO3 and Pb(PO3)2. Although the information regarding long distances cannot be considered quantitatively reliable, the analysis of the peak at about 3.2 Å shows clearly not only that the Fe ions are correlated to the P atoms of the phosphate network via nonbridging oxygens but also that they give rise to nonrandom Fe-Na distributions. This situation recalls the results obtained in Fe2O3-Pb(PO3)2 glasses, where the existence of important FePb correlations was evident.5 In addition, the difference radial functions describing the structuring around the iron in sodium and in lead metaphosphate glasses are very similar even in the medium-range distances.5 This suggests that similar stable structural arrangements have taken place in both glasses, so that a massive improvement of chemical and mechanical stability is expected also for the glasses examined here. This comes true, actually: all the doped samples are very hard (fine powders were obtained only using a steel ball mill) and only soluble in aqua regia, in striking contrast with the sodium phosphate matrix, which dissolves rapidly in cold water. Therefore, at least qualitatively, the same effect already observed in Pb(PO3)21-3 glasses takes place here upon addition of iron oxide. Undoubtedly, iron ions play the key role in modifying the properties of the phosphate glasses, by strengthening the cross bonding of the phosphate chains. Conclusions The structural properties of some sodium-iron phosphate glasses have been studied by X-ray diffraction through comparison with pure sodium metaphosphate glass. Information on Fe-O coordination polyhedra was obtained by simulation of the difference radial curves, calculated by subtracting the radial distribution function of the iron-free glass from those of iron-containing glasses. Good fits were obtained by considering the occurrence of about 10% of Fe2+ and two distinct sites for Fe3+ on the basis of the results of Mo¨ssbauer spectroscopy. The result is consistent with a stable structural arrangement around Fe3+ and Fe2+ ions for which octahedral geometries have been detected. Important features at long-distance values in the difference radial curves indicate situations very similar to those already observed in lead-iron phosphate glasses, where the structural stability was considered to be responsible for the great improvement of the chemical and mechanical characteristics of the phosphate glasses upon addition of iron oxide. Acknowledgment. This work has been supported by CNR and MURST (Rome). References and Notes (1) Sales, B. C.; Boatner, L. A. J. Non-Cryst. Solids 1986, 79, 83. (2) Sales, B. C.; Ramsey, R. S.; Bates, J. B.; Boatner, L. A. J. NonCryst. Solids 1986, 87, 137. (3) Sales, B. C.; Abraham, M. M.; Bates, J. B.; Boatner, L. A. J. NonCryst. Solids 1985, 71, 103. (4) Greaves, G. N.; Gurman, S. J.; Gladden, L. F.; Spence, C. A.; Cox, P.; Sales, B. C.; Boatner, L. A.; Jenkins, R. N. Philos. Mag. B 1988, 58, 271. (5) Musinu, A.; Piccaluga, G.; Pinna, G. J. Non-Cryst. Solids 1990, 122, 52.
12466 J. Phys. Chem., Vol. 100, No. 30, 1996 (6) Brooks, J. S.; Williams, G. L.; Allen, D. W.; de Grave, E. Phys. Chem. Glasses 1992, 33, 167. (7) Van Wazer, J. R. Phosphorous and Its Compounds; Interscience: New York 1951. (8) Martin, S. W. Eur. J. Solid State Inorg. Chem. 1991, 28, 163. (9) Brow, R. K.; Kirkpatric, R. J.; Turner, G. L. J. Non-Cryst. Solids 1990, 116, 39. (10) Jost, K. H. Acta Crystallogr. 1964, 17, 1539. (11) Hoppe, U.; Stachel, D.; Beyer, B. Phys. Scr. 1995, T57, 122. (12) Suzuki, K. J. Non-Cryst. Solids 1987, 95&96, 15. (13) Medda, M. P.; Musinu, A.; Piccaluga, G.; Pinna, G. J. Non-Cryst. Solids 1993, 162, 128. (14) Musinu, A.; Paschina, G.; Piccaluga, G.; Pinna, G. J. Non-Cryst. Solids 1994, 177, 97. (15) Hoppe, U.; Walter, G.; Stachel, D.; Hannon, A. C. Z. Naturforsh. 1995, 50a, 684. (16) Zachariasen, W. H. J. Am. Cer. Soc. 1932, 54, 3841. (17) Rawson, H. Inorganic Glass-Forming Systems; Academic Press: London, New York, 1967. (18) Selvaray, U.; Rao, K. J. J. Non-Cryst. Solids 1988, 103, 300. (19) Concas, G.; Congiu, F.; Muntoni, C.; Pinna, G. J. Phys Chem. Solids 1995, 56, 877.
Musinu et al. (20) Habenshuss, A.; Spedding, F. J. Chem. Phys. 1979, 70, 2797. (21) Corrias, A.; Ennas, G.; Licheri, G.; Magini, M.; Musinu, A.; Paschina, G.; Piccaluga, G.; Pinna, G. Trends Chem. Phys. 1992, 2, 79. (22) Magini, M.; Sedda, A. F.; Licheri, G.; Paschina, G.; Piccaluga, G.; Pinna, G.; Cocco, G. J. Non-Cryst. Solids 1984, 65, 145. (23) Magini, M.; De Moraes, M.; Sedda, F.; Paschina, G.; Piccaluga, G. Phys. Chem. Glasses 1986, 27, 95. (24) Medda, M. P.; Musinu, A.; Piccaluga, G.; Pinna, G. Proceedings of the IV International Conference on Synthesis and Methodologies in Inorganic Chemistry, Bressanone, Italy, 1993. (25) Kurkjian, C. R.; Sigety, E. A. Phys. Chem. Glasses 1968, 9, 73. (26) Lewis, G. K., Jr.; Drickamer, H. G.J. Chem. Phys. 1968, 49, 3785. (27) Maekawa, T.; Yokokawa, T.; Niwa, K. Bull. Chem. Soc. Jpn. 1969, 42, 2102. (28) Coey, J. M. D. J. Phys. C 1974, 35, 89. (29) Dyar, M. D. J. Am. Cer. Soc. 1986, 69, C160. (30) Brooks, J. S.; Williams, G. L.; Allen, D. W. Phys. Chem. Glasses 1992, 33, 171.
JP953521V
