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ARTICLES Role of Ag2S Nanoparticles on the Dynamics of Silver Ions in Silver-Ultraphosphate Glass Nanocomposites D. Dutta† and A. Ghosh* Department of Solid State Physics, Indian Association for the CultiVation of Science, JadaVpur, Kolkata 700032, West Bengal, India ReceiVed: December 10, 2008; ReVised Manuscript ReceiVed: April 17, 2009
Glass nanocomposites in the system xAg2S - (1 - x)(40Ag2O - 60P2O5) have been prepared by mixing the reagent grade Ag2S, AgNO3, and NH4H2PO4, preheating at 400 °C for 1 h, melting at 900-960 °C, and finally pressing the melts between aluminum plates to form transparent discs of 1 mm thickness. High resolution transmission electron micrographs (HR-TEM) help to find the constitution and composition of the glass nanocomposites. Ag2S nanoparticles of typically 10 nm in diameter dispersed in the nanocomposite matrices have been identified. The dynamics of silver ions in these nanocomposites has been studied in a wide frequency range and in a wide temperature range. It has been observed that as x increases from 0.05 to 0.2, the electrical conductivity increases by 1 to 2 orders of magnitude. The activation energy for the electrical conductivity is 0.6-0.5 eV. There is evidence for the involvement of some silver ions in the building up of nanophases. Evaluation of the Ag+-ion concentration from the electrical conductivity using the Nernst-Einstein relation shows that typically 1021 cm-3 ions participate in the conduction, which is 10-20% of the Ag+-ion concentration, as evaluated from the chemical composition of the material prepared. The ac electrical conductivity data suggest many interesting properties for the nanocomposites from the point of view of its applications. Ag2S nanocrystals have also left a signature on the frequency exponent and the crossover frequency. Scaling of the conductivity spectra is observed to be independent of temperature but dependent on Ag2S content at high frequencies. I. Introduction Nanophase material particles have captured a great deal of attention during the past decade.1-4 The synthesis of ultrafine particles is nowadays one of the most important challenges of new technologies. These materials have properties that are often significantly different from and considerably improved relative to those of their coarser grain counterparts.3,4 Recently, phosphate ceramics have received great attention due to a variety of applications in electrical, optical, prosthetics, structural, and other fields.5 In particular, phosphate ceramics are important since they are used as inorganic and biomaterials finding application as catalysts, ion exchangers, and low thermal expansion ceramic materials.6 It has been shown that phosphate ceramics are more advantageous compared to silicate and some other systems that are used as hosts of impurity doped optical materials.7,8 Cutroni et al.9,10 have studied the ionic conduction and dielectric behavior of silver phosphate glassy materials. Nowinski et al.11,12 have shown that the excess of the dopant salt AgI precipitating in a AgI-Ag2O-P2O5 glassy matrix caused a conductivity decrease of the material. On the contrary, Adams et al.13,14 have observed that the crystallization of silver iodide-silver oxysalt glasses might lead to a substantial increase of their conductivity. In those studies the increase of the conductivity was correlated with the variation of the interfacial * E-mail:
[email protected]. † Present address: Department of Physics, St. Xavier’s College (Autonomous), 30 Park Street, Kolkata-700016, West Bengal, India.
area between crystalline inclusions and a glassy matrix in glassceramics. The details of structural studies of phosphate glasses have been reported in some review articles.15,16 It is noteworthy that there is no general agreement about the fraction of silver ions participating in the transport process, which is one of the most critical parameters to explore the transport mechanism in these systems. Dielectric measurements on ionic materials give useful information about dynamical processes involving ionic motion.17 It is known that the conductivity of glassy materials is frequency dependent so that the diffusivity of the mobile ions is not entirely characterized by the single steady state parameter σdc, quantifying the dc conductivity. As observed in several ion conducting glasses, the dielectric response expressed in terms of frequencydependent conductivity exhibits a dispersive behavior usually described by a power law with exponent n < 1,18 while a further contribution with exponent n > 1 is eventually observed at higher frequencies.9 Silver ion dynamics in phosphate glasses has also been studied in detail using NMR.19 The objective of this article is to study the ion dynamics at various temperatures and frequencies for Ag2S-doped ultraphosphate (40Ag2O - 60P2O5) glass nanocomposites. II. Experiment Glass nanocomposite samples of compositions xAg2S (1 - x)(40Ag2O - 60P2O5), where x ) 0.0-0.2, were prepared from the reagent grade chemicals Ag2S, NH4H2PO4,
10.1021/jp8108539 CCC: $40.75 2009 American Chemical Society Published on Web 05/04/2009
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and AgNO3 (Aldrich Chemical Co.). The appropriate amounts of Ag2S, AgNO3, and NH4H2PO4 powders were thoroughly mixed and preheated in an alumina crucible at 400 °C for 1 h for calcination and then were melted in the temperature range from 900 to 960 °C depending upon composition. After homogenization for 30 min, the melts were finally quenched between two aluminum plates. Transparent samples of thickness ∼1 mm were obtained for all the above-mentioned compositions. The samples were annealed at 100 °C for 2 h. The densities of the compositions were measured using Archimedes’ principle. Formation of nanocomposites was confirmed from the high-resolution transmission electron microscopic (HR-TEM) studies of the samples taken in a transmission electron microscope (JEOL,JEM2010). For electrical measurements, gold electrodes were deposited on both surfaces of the polished samples of diameter ∼10 mm. The dielectric measurements of the samples were carried out in the frequency range from 10 Hz to 2 MHz in an impedance meter (QuadTech, model 7600). Also measurements were taken in the frequency range from 10 MHz to 1.82 GHz in a network analyzer (Agilent, model 4396B) interfaced with a computer. The measurements were taken in the temperature range from 128 to 298 K in a liquid nitrogen cryostat (Quatro Cryosystems, Novocontrol GmBH). III. Results and Discussion Figure 1a shows a transmission electron micrograph of the sample with x ) 0.2 at room temperature. In the micrograph we observe a distribution of nanoparticles of size in the range from 3 to 30 nm embedded in the glassy matrix. Figure 1b shows an HR-TEM image of the same sample showing nanoparticles of size 15 nm in diameter. We have calculated the interplanar spacing (d) between two successive lattice planes from the selected area electron diffraction pattern shown in the inset of Figure 1b. The values of d thus obtained and shown in Table 1 for different compositions are found to agree well with the values of d obtained from the ASTM data sheets,20 mainly for the acanthite (monoclinic) for the crystalline Ag2S, tabulated also in Table 1. The histogram of the diameters obtained from Figure 1a is shown in Figure 1c. It is observed that the particle distribution obeys a log-normal distribution function described elsewhere.21 A similar distribution of nanoparticles was also observed in other compositions. The dc conductivity at different temperatures for different compositions was computed from the complex impedance plots. An Arrhenius temperature dependence of the dc conductivity, shown in Figure 2, has been observed for all compositions. The activation energy was obtained from the least-squares straight line fits of the data. The variation of the dc conductivity and the activation energy with the Ag2S content in the compositions is shown in parts a and b, respectively, of Figure 3. It is observed that the dc conductivity increases by 2 orders of magnitude when x ) 0.05 is added to a 40Ag2O - 60P2O5 glass. The conductivity tends to decrease for x ) 0.10 and then it again shows a slight increment up to x ) 0.15, after which the conductivity almost saturates. The activation energy shows a decreasing trend, on insertion of Ag2S up to x ) 0.10, after which it increases again for x ) 0.15, and then it shows a decrease for x ) 0.20. This type of behavior of the conductivity and the activation energy is due to inclusion of Ag2S nanocrystals in a 40Ag2O - 60P2O5 glass. The variation of the ac conductivity at different frequencies is also shown in Figure 3a. It is clearly observed that the ac conductivity also exhibits the same behavior as the dc conductivity with the Ag2S doping content.
Figure 1. (a) Transmission electron micrograph showing the particle distribution for the sample 0.20Ag2S - 0.80(40Ag2O - 60P2O5). (b) HR-TEM image for the same composition. The inset shows the selected area electron diffraction pattern from which the lattice spacings for the β-Ag2S crystals have been calculated. (c) Histogram of particle diameters fitted to a log-normal distribution function (solid line).21
TABLE 1: Comparison of the Lattice Spacing (d) of Ag2S Obtained from the TEM Micrograph of the 0.20Ag2S 0.80(40Ag2O - 60P2O5) Nanocomposite and the Lattice Spacing (d) of the Acanthite (Monoclinic) Phase for the Crystalline Ag2S Obtained from the ASTM Datasheet d(0A) from TEM micrograph
|
d(0A) from the ASTM data sheet (ref 20)
2.093 2.400 2.840 3.400
| | | |
2.093 2.440 2.836 3.460
It is found that the variation of the average particle size increases to its maximum value of 20 nm for x ) 0.10 and then decreases to an average size of 9 and 15 nm for x ) 0.15 and 0.20 respectively with the Ag2S content in the composites. It was also found that the dc conductivity reaches its minimum value as the average particle size of the Ag2S nanoparticle reaches its maximum value of 20 nm at x ) 0.10. The optimum value of the average particle size for which the conductivity
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increases to its highest value for this xAg2S - (1 - x)(40Ag2O - 60P2O5) composites lies between 9 and 15 nm, corresponding to x ) 0.15 and 0.20 respectively. The conductivity did not change significantly in going from x ) 0.15 to 0.20. Thus, the particle size appears to play a major role on the change in the dc conductivity. The ac conductivity isotherms for different temperatures for a composition are shown in Figure 4a. The conductivity isotherms exhibit frequency independence at low frequencies and a wide dispersion in the high frequency range. The conductivity data, σ(ω), in the frequency range from 10 Hz to 2 MHz have been described by22,23
σ(ω) ) σdc[1 + (ω/ωc)n]
(1)
which is the sum of the dc conductivity, σdc, and a fractional power-law-dependent dispersive conductivity with exponent n < 1, and ωc is a characteristic crossover frequency from the dc to the dispersive conductivity.22,23 Figure 4b shows full spectra of the conductivity isotherms for a composition, while the inset shows the spectra with the dc conductivity removed from them for selected temperatures. We observe from the figure that each isotherm has two slopes: one corresponds to the low frequency region below 2 MHz following the Jonscher power law22 and the other corresponds to the higher frequency region, which has a slope more than 1.7, thus showing a deviation from the Jonscher power law. The conductivity spectra in the high frequency region (10 MHz to 1.8 GHz) have been explained on the basis of the concept of the mismatch and relaxation (CMR) model.24,25 The central idea behind CMR is that each hop of an ion (central ion) creates mismatch between its own position and the positions of its mobile neighbors. There are two competing ways to reduce this mismatch. One possibility is that the “forward” hop of the regarded ion is canceled by a “correlated backward jump”. This route of relaxation, which restores the starting situation, is called the “single-particle route”. The other possibility is that the neighboring mobile ions rearrange, while the central ion stays at its new position. This is the so-called “many-particle” route. All the other compositions demonstrated
Figure 2. Arrhenius temperature dependency of the conductivity for xAg2S - (1 - x)(40Ag2O - 60P2O5) glass nanocomposites.
Figure 3. (a) Variation of the dc conductivity (0) and the ac conductivity at 100 kHz (O) and 1 MHz (∆) at 303 K with Ag2S content for xAg2S - (1 - x)(40Ag2O - 60P2O5) glass nanocomposites. (b) Variation of the activation energy with Ag2S content. Error bars are shown in the figures.
the same nature in their conductivity isotherms. Recentl,y Funke and Banhtti26 have shown that the CMR model does not yield the proper low-frequency behavior of the permitivitty. They have modified the CMR model to the MIGRATION model, which is sufficient to produce the correct very low frequency behavior, while the dynamics at high frequencies remains unchanged. In this MIGRATION concept, the hopping motion of the mobile ions is described in terms of three coupled rate equations (instead of two in CMR). But the differences between the CMR and the MIGRATION concept can be seen at very low frequencies (below 1 Hz) only. For the higher frequencies, as in the present case, the results produced using the MIGRATION model and the CMR model are found to be the same. The low frequency isotherms in the range (10 Hz to 2 MHz) were fitted to eq 1, using σdc, n, and ωc as variable parameters. The variation of the power law exponent n in the low frequency region with Ag2S content is shown in Figure 5 for several compositions. We have noted that values of n are almost independent of temperature and lie between 0.69 and 0.77 for different compositions and correspond to three-dimensional conduction.27 Similar results were also obtained for AgI doped silver phosphate glasses.28 The slope of the conductivity isotherms in the high frequency region for the same glass composition is found to be
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Figure 5. Variation of the frequency exponent n with composition for xAg2S - (1 - x)(40Ag2O - 60P2O5) nanocomposites.
Figure 4. (a) Measured conductivity isotherms at different temperatures are shown as a function of frequency for the 0.15Ag2S - 0.85(40Ag2O - 60P2O5) nanocomposite in the low frequency (10 Hz to 2 MHz) region. (b) Measured ac conductivity at different temperatures is shown as a function of frequency for the same composition as in part a in the complete frequency window (10 Hz to 1.82 GHz). The inset shows the variation of the ac conductivity obtained by subtracting the dc conductivity from the measured ac conductivity over the entire frequency window.
∼1.7, which shows an almost temperature independent nature, as predicted by the CMR model. The crossover frequency ωc obtained from the fits is shown in Figure 6a as a function of reciprocal temperature. We observe that ωc shows Arrhenius behavior. We have observed that the activation energies for ωc and σdc are very close. Figure 6b shows the variation of crossover frequency ωc with varying content of Ag2S (see also Table 2). It is observed that the variation of the crossover frequency is very similar to the dc conductivity. The mobile Ag+ ion concentrations for different compositions have been calculated from the values of σdc for different temperatures obtained from the Nernst-Einstein relation:27
σdc ) q2ξ2ncωh /12πkT
(2)
where nc and ξ are the charge carrier concentration and the jump distance, respectively, and ωh is the hopping frequency. Here
we have assumed that the characteristic relaxation frequency in eq 1 is equal to the hopping frequency ωh in eq 2. This assumption has been verified for different glass systems.29,30 It has been found that nc is almost independent of temperature for all nanocomposites. It is observed that the mobile Ag+ ion concentration obtained from the analysis is 10-20% of the total Ag+ ion concentration obtained from glass composition and density. The variation of dc conductivity and the activation energy as presented in Figure 3 can now be explained. It is clear from the above calculation of mobile Ag+ ion concentration that the ratio of the change in the mobile Ag+ ion concentration is the same as the ratio of the change in the conductivity in going from x ) 0.05 to x ) 0.10. This is due to the fact that the Ag+ ions which contribute to the dc conduction start to agglomerate to form the Ag2S nanocrystals, thereby reducing the available mobile ions and hence the dc conductivity of the nanocomposite system, as shown in Figure 3a. The slight increase in the dc conductivity, when x ) 0.15 is added to 40Ag2O - 60P2O5 glass, is due to the fact that the agglomeration of the Ag+ ions becomes its highest in these composites, as evidenced from HRTEM studies, thereby creating more open channels for the conduction of Ag+ ions in the glassy matrix. The agglomeration saturates and so does the dc conductivity, when more Ag2S is added to 40Ag2O - 60P2O5 glass. Thus, the introduction of Ag2S in the 40Ag2O - 60P2O5 glass initiates and controls agglomeration of Ag+ ions to form nanocomposites. As the power law exponent is independent of temperature for the xAg2S - (1 - x)(40Ag2O - 60P2O5) glass, this leads to the temperature independence of the scaling of the conductivity spectra. The scaling of the conductivity isotherms, by which different conductivity isotherms merge to a common curve, indicates that the relaxation process is governed by a single mechanism modified only by temperature scales.27,30,31 An attempt has been made to scale the conductivity spectra for the present systems. Several other workers,30,31 depending upon the type and composition range of glasses, have chosen appropriate scaling parameters in different forms. Here we have considered
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Figure 6. (a) Reciprocal temperature dependence of the crossover frequency ωc for different compositions of xAg2S - (1 - x)(40Ag2O - 60P2O5) nanocomposites. (b) Variation of the crossover frequency ωc at 303 K with Ag2S content for the same system.
TABLE 2: Logarithmic dc Conductivity at 303 K, dc Activation Energy (Eσ), Logarithmic Crossover Frequency at 300 K, Activation Energy (Ec) of the Crossover Frequency (ωc), and the Frequency Exponent (n) for the xAg2S - (1 x)(40Ag2O - 60P2O5) Glass Composites
x 0.0 0.05 0.10 0.15 0.20
log10(σdc) (Ω-1 cm-1) log10(ωc) (rad s-1) n (T ) 300 K) Eσ (eV) (T ) 300 K) Ec (eV) ((0.01) ((0.01) ((0.03) ((0.01) ((0.01) -7.15 -5.72 -5.98 -5.29 -5.27
0.62 0.60 0.51 0.57 0.52
5.68 6.68 6.68 7.07 7.23
0.60 0.62 0.54 0.60 0.54
0.77 0.73 0.69 0.69 0.70
the crossover frequency ωc and the dc conductivity σdc as the scaling parameters.30 Figure 7a shows the scaling spectra of several conductivity isotherms for a typical composition of xAg2S - (1 - x)(40Ag2O - 60P2O5) nanocomposites. The figure shows that the conductivity isotherms have merged on a common curve following the time-temperature superposition principle, thereby indicating the temperature independence of the relaxation mechanism. The conductivity isotherms for different Ag2S concentrations of the system are scaled using the same procedure for a particular temperature, and the scaling is shown in Figure 7b. The figure shows a good overlap of the
Figure 7. (a) Scaling of the conductivity spectra for different temperatures for the 0.15Ag2S - 0.85(40Ag2O - 60P2O5) nanocomposite. (b) Scaling of conductivity spectra for different nanocomposites shown for a fixed temperature of 263 K.
isotherms except for the higher frequency region. The deviation in the high frequency region is due to the fact that the frequency exponent n controls the higher frequency region of the conductivity spectra. As has already been settled by Hodge, Ngai, and Moynihan,32,33 the electric modulus representation of data provides useful information on the ionic relaxation. The electric modulus32 is defined as M* ) 1/*(ω), where *(ω) is the complex permittivity. The real and imaginary parts of the modulus spectra are shown in parts a and b, respectively, of Figure 8, for a typical composite sample. It can be seen from Figure 8a that the real part of the modulus M′ spectrum shows a frequency dispersion after showing a frequency independent part at the lower frequency region and tends to saturate to M∞′ at higher
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Figure 9. Variation of log10(ωτ) with varying Ag2S content for the xAg2S - (1 - x)(40Ag2O - 60P2O5) nanocomposites at T ) 263 K. Error bars are shown in the figure.
mismatch and relaxation. The Ag+ ion concentration obtained from the low frequency part of the conductivity data is temperature independent and the conductivity is primarily determined by the mobility. The mobile Ag+ ion concentration is 10-20% of the total Ag+ ion concentration. A composition dependence of the conductivity relaxation frequency is similar to the variation of average particle size with composition. The perfect overlap of the scaled conductivity spectra obtained for different temperatures indicates that the nature of ion dynamics for these composites is independent of temperature. But the slight deviation in the high frequency region shows that the ion dynamics is dependent on the Ag2S doping content. Figure 8. (a) Real and (b) imaginary parts of the electric modulus at different temperatures for the 0.15Ag2S - 0.85(40Ag2O - 60P2O5) nanocomposite. The solid lines in the figures are drawn to guide the eye.
frequencies. The imaginary modulus M′′, which is related to ′′ , centered at the the dielectric loss, exhibits a maximum, Mmax dispersion region of M′. Mmax ′′ shifts to higher frequencies with increasing temperature. The conductivity relaxation frequency ′′ , which is related to the conductivity ωτ corresponding to Mmax relaxation time τσ by the relation ωττσ ) 1 (ref 32), has been shown in Figure 9 for all the composites at a particular temperature. It is noted that the conductivity relaxation frequency exhibits the same behavior as the dc conductivity with the change in compositions. This type of behavior in ωτ is attributed to the variation of the average particle size. IV. Conclusions We have reported the influence of Ag2S nanoparticles on the Ag+ ion dynamics in ultraphosphate glass nanocomposites. The variation of the dc conductivity and activation energy of these composites has been explained on the basis of the formation of Ag2S nanocrystals in glassy matrices, which was confirmed by HR-TEM. From the conductivity spectra we have obtained the power law exponents for both high and low frequency regions. It has been observed that the conductivity relaxation obeys Jonscher’s power law in the low frequency region and the high frequency region is separately controlled by the concept of
Acknowledgment. The financial support for the work by the CSIR, Government of India (via Grant No. 03(1095)/07/EMRII), is gratefully acknowledged. The support for the work by the DST, Government of India, under its nano initiative is also gratefully acknowledged. The authors thank Prof. D. Chakravorty for his valuable suggestions. References and Notes (1) Gleiter, H. Acta Mater. 2000, 48, 1. (2) Suryanarayana, C. Bull. Mater. Sci. 1994, 17, 307. (3) Bros, L. J. Phys. Chem. Solids 1998, 59, 459. (4) Lopez-Quintela, M. A. J. Colloid Interface Sci. 1993, 158, 446. (5) Cao, Z.; Lee, B. I.; Samuels, W. D.; Exarhos, G. J. J. Phys. Chem. Solids 2000, 61, 1677. (6) Dinamani, M.; Vishnu Kamath, P. Mater. Res. Bull. 2001, 36, 2043. (7) Crichton, S.; Yamanaka, H.; Matsuoka J.; Wakabayashi, E. In Ceramic Trans. Solid State Optical Mater.; Bruce, A. J., Hiremath, B.V., Eds.; American Ceramic Society: Westerville, OH, 1992; Vol. 28, p493. (8) Marion, J. E.; Weber, M. J. Eur. J. Solid State Inorg. Chem. 1991, 28, 271. (9) Cutroni, M.; Mandanici, A.; Piccolo, A.; Fanggao, C.; Saunders, G. A.; Mustarelli, P. Philos. Mag. B 1996, 73, 349. (10) Cutroni, M.; Mandanici, A. Solid State Ionics 1998, 105, 145. (11) Nowin, J. L.; Wnetrzewski, B.; Jakubowski, W. 1988, 28-30, 804. (12) Wnetrzewski, B.; Nowinski, J. L.; Jakubowski, W. Solid State Ionics 1989, 36, 209. (13) Adams, St.; Hariharan, K.; Maier, J. Solid State Ionics 1995, 75, 193. (14) Adams, St.; Hariharan, K.; Maier, J. Solid State Ionics 1996, 8688, 503. (15) Greaves, G. N.; Sen, S. AdV. Phys. 2007, 56, 1. (16) Ray, N. H. Br. Polym. J. 1979, 11, 163. (17) Funke, K. Prog. Solid State Chem. 1993, 22, 111.
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(18) Jonscher, A. K. Dielectric Relaxation in Solids; Chelsea Dielectrics Press: London, 1996. (19) Vogel, M.; Brinkmann, C.; Eckert, H.; Heuer, A. Phys. Chem. Chem. Phys. 2002, 4, 3237. (20) X-Ray Powder Data File Sets 1-5 (Revised); ASTM Spcl. Tech. Pub. (48-J); p 29; PCPDF File Number 140072. (21) Roy, B.; Chakravorty, D. J. Phys.: Condens. Matter 1990, 2, 9323. (22) Jonscher, A. K. Nature (London) 1977, 267, 673. Almond, D. P.; West, A. R. Nature (London) 1983, 306, 156. (23) Hairetdinov, E. F.; Uvarov, N. F.; Patel, H. K.; Martin, S. W. Phys. ReV. B 1994, 50, 13259. (24) Funke, K.; Rolling, B.; Lange, M. Solid State Ionics 1997, 105, 195. (25) Funke, K.; Wilmer, D. Solid State Ionics 2000, 136 and 137, 1329. (26) Funke, K.; Banhatti, R. D. Solid State Ionics 2004, 169, 1. (27) Sidebottom, D. L. Phys. ReV. Lett. 1999, 82, 3653.
Dutta and Ghosh (28) Cutroni, M.; Mandanici, A.; Raimondo, A. Phys. Chem. Glasses 2006, 47, 388. Cutroni, M.; Mandanici, A.; Mustarelli, P. J. Non Cryst. Solids 2002, 307, 963. (29) Ahmad, M. M.; Yamada, K.; Okuda, T. Solid State Ionics 2004, 167, 285. (30) Ghosh, A.; Pan, A. Phys. ReV. Lett., 2000, 84, 2188. (31) Roling, B.; Happe, A.; Funke, K.; Ingram, M. D. Phys. ReV. Lett. 1997, 78, 2160. (32) Macedo, P. B.; Moynihan, C. T.; Bose, R. Phys. Chem. Glasses 1972, 13, 171. Moynihan, C. T.; Boesch, L. P.; Laberge, N. L. Phys. Chem. Glasses 1973, 14, 122. (33) Hodge, I. M.; Ngai, K. L.; Moynihan, C. T. J. Non-Cryst. Solids 2005, 351, 104. Ngai, K. L.; Moynihan, C. T. Mater. Res. Bull. 1998, 23, 51.
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