Before comparing the results with our model, we note from figure 4, that two of the samples investigated (samples 2 and 3) follow curves which appear to be shifted from the others. In the case of sample 3, there may be a high temperature residual width responsible for the shift. Since we are only interested in analyzing the broadening attributed to the change in structure resulting from the composition fluctuations, we subtract this width, and consider only the fractional change in width. A lack of high temperature data prevents a similar analysis of the data from sample 2, therefore, we will assume that it also has a residual width. The data in the form:

{ak7 [2.15(1000)-0.627

J = ((A In 7)2) { αóknT [ 2.15

1

(29)

is plotted in figure 7 for all four samples. The individual deviations from the composite curve are of the order of the experimental uncertainty, as can be seen from the error bars on the data. At this point, the equation proposed above can be fitted to the data, with a, and Ro as undetermined variables. The results are shown in figure 7. The proposed function describes the three regions in the curve. Of particular interest are the large increase in width and the saturation of the width near Te. Using the value of 11 Å for 1, the range of interaction for structural relaxation, ro, is calculated to be 41 A. In a previous paper, using the OZD function, we calculated ro to be 56 A [25]. This shows that while the form of the pair-correlation function influences the value obtained, its order of magnitude is well established by the data in relation to the three regions measured in ((A ln 7)2). Such a large value for ro indicates that shear viscous flow is truly a wide ranging process!

5. Summary and Conclusion

5.1. Treatment of Supercritical Relaxation Experiments by the Environmental Relaxation Model

A model is proposed which indicates that systems with a broad continuous distribution of mobilities will exhibit large supercritical effects. The model predicts that the supercritical effect will manifest itself in the width of the distribution of relaxation times. The relaxation mechanism is assumed to be characterized by a distance, ro, which represents a finite range for the interactions which lead to relaxation. This range is characteristic of the material and independent of critical point phenomena. The dependence of width on reduced temperature, e, consists of three regions characterized by the relative sizes of A, the range of fluctuations, and ro the range of structural influence, as shown in figure 8 where we have represented the

distribution of mobilities by two distinct phases for simplicity. Region I, in which A(e) <ro, represents high temperatures, far above Te, and shows that due. to space averaging within Vo=4/3 r3, all relaxing species interact with similar neighborhoods and the distribution of relaxation times is narrow, and in simple liquids is single. The distribution is temperature independent and Arrhenian viscosity behavior is observed. In Region II, as one approaches the critical temperature, A approaches ro. Now, large differences in environment appear as relaxing species begin to be surrounded by different local environments. The

FIGURE 7. Comparison of the critical increase in width, with the proposed model, (solid line).

width of the relaxation time spectrum increases as the temperature approaches the critical point and the viscosity no longer follows Arrhenian behavior. An anomalous excess viscosity appears. In Region III, A(e) > ro, the temperature is close to the critical point, and the fluctuations are large. Relaxing species are well imbeded within the fluctuations so that further changes in A(e) have little effect on the local compositions. The width of the relaxation time spectrum saturates, changing little as one approaches Te. This is reflected in a saturation of the anomalous excess viscosity despite a divergence of the correlation length A. The viscosity appears to revert to Arrhenian behavior because, although a broad distribution of relaxation times remains at temperatures near Te, the character of the distribution ceases the change with temperature that gave rise to the non-Arrhenian behavior. Actual Arrhenian behavior is however only observed if the most probable relaxation time, 7', is also Arrhenian. The Gaussian function proposed fits all three regions well and has the proper asymptotic behavior near and far from Te. The range of structural influence, ro, is quite large with a value of 41 to 56 Å, and spans over many molecular diameters. This explains why, in some oxide glasses, the addition of small amounts of impurities changes the relaxation properties: an addition of 5 ppm of Na2O to pure SiO2 changes the viscosity by a factor of two [28].

5.2. Generalization to Other Materials The work presented herein has been concerned with explaining the origin of distributions of relaxation times observed above the critical points of a series of immiscible oxide mixtures. For this reason, we have been primarily concerned with describing the microstructure in the environment in terms of supercritical composition fluctuations. Microstructure in the environment may, however, arise from other causes: association, density and various other ordering phenomena. The analysis presented here would also apply in such cases in qualitative terms. The three regions described previously would be expected to occur in an analysis of the spectral width as the order parameter varies in size relative to the range of structural influence, ro.

Boron trioxide glass, for example, has a log-Gaussian shear distribution of relaxation times [8] but has no composition fluctuations. Yet its relaxation time spectrum and its distribution of activation energies broaden as the temperature is lowered, exhibiting not only higher activation energy values as expected, but also lower ones as well. This apparent paradox is easily explained by the present relaxation model, as we attribute the appearance of lower and higher activation energies to the formation of a distribution of regions in the melt with varying degrees of association, some low and some high (low E and high E). A temperature dependent spectrum of relaxation times also occurs in GeO2 glass at temperatures near its transformation region [13]. According to the model, this would indicate that there is a degree of microheterogeneity whose size is of the order of ro at the transformation region in this glass. Since ro is a property of the material, it is likely to vary little among simple oxide glassformers so that the model suggests a value of 50 A to the size of the

microstructure in GeO2 in the transformation region. Electron micrographs on GeO2 [29] have revealed that, indeed, there is microheterogeneity in GeO2 in the transformation region of the order of 25 to 50 Å.

Although, the environmental relaxation model can give a qualitative description of the behavior of the width of the relaxation time spectrum in terms of the size of the order parameter (i.e., Regions I, II, and III). a description in terms of temperatures is not possible for normal glasses. An analysis of the temperature dependence of the order parameter, and the form of the pair correlation function are needed before a treatment similar to the immiscible melts can be carried out on normal or single component molten oxides.

[1] Fulcher, G. S., J. Am. Ceram. Soc. 8, 339 (1925).

[2] Gibbs, J. H., Modern Aspects of the Vitreous State, Vol. 1, J. D. Mackenzie, Ed. (Butterworths, London, 1960). [3] Turnbull, D., and Cohen, M. H., J. Chem. Phys. 34, 120 (1961). [4] Goldstein, M., J. Chem. Phys. 51, 3728 (1969).

[5] Litovitz, T. A., Non-Crystalline Solids, V. D. Frechette, Ed. (John Wiley, New York, 1960).

[6] Montrose, C. J., and Litovitz, T. A., J. Acous. Soc. Am. 47, 1250 (1970).

[7] Isakovich, M. A., and Chaban, I. A., Soviet Phys. Doklady 10, 1053 (1966); Sov. Phys. JETP 23, 893 (1966).

[8] Tauke, J. Litovitz, T. A., and Macedo, P. B., J. Am. Ceram. Soc. 51, 158 (1968).

[9] Macedo, P. B., and Napolitano, A., J. Chem. Phys. 49, 1887 (1968).

[10] Herzfeld, K. F., and Litovitz, T. A., Absorption and Dispersion of Ultrasonic Waves (Academic Press, New York, N.Y., 1959).

[11]

[12]

[13]

Goldstein, M., Modern Aspects of the Vitreous State, Vol. 3,
J. D. Mackenzie, Ed. (Butterworth, Washington, 1964).
Macedo, P. B., and Napolitano, A., J. Res. NBS 71A, 231 (1967).
Napolitano, A., and Macedo, P. B., J. Res. NBS 72A, 425 (1968);
Boesch, L., Napolitano, A., and Macedo, P. B., J. Am. Ceram.
Soc. 53, 148 (1970).

[14] Fröhlich, H., Theory of Dielectrics (Clarendon Press, Oxford, 1949).

[15] Chu, B., J. Am. Chem. Soc. 86, 3557 (1964); Fisher, M., J. Math. Phys. 5, 944 (1964).

[24] Landau, L. D., and Lifshitz, E. M., Statistical Physics (AddisonWesley Publishing Co., Reading, Mass. 1958).

[25] Simmons, J. H., and Macedo, P. B., J. Chem. Phys. 54, 1325 (1971).

[26] Munster, A., Small Angle X-Ray Scattering, (Gordon and Breach, 1967) p. 401.

[27] Riebling, E. F., J. Am. Ceram. Soc. 47, 478 (1964). [28] Hagy, H., private communication.

[29] Zarzycki, J., and Mezard, R., Phys. Chem. Glasses 3, 163 (1962).

(Paper 75A3-661)

1. Introduction

The present study is part of a program [1, 2, 3]1 to btain a better understanding of the behavior of varius Pt-group metals and metal oxides when heated ogether in an oxidizing environment. Considering the act that several of these metals are used as secondary standards on the International Practical Temperature Scale (IPTS 1968) [4] as well as for container maerials for high temperature applications, knowledge of the phase relations between these metals and other materials becomes important. This work presents the results of an investigation of the equilibrium relationships between the condensed phases in the system STO-IrO-Ir in air.

=

Strontium oxide (SrO) has a cubic, sodium chloridetype structure with a 5.1602 A [5]. The melting point of SrO has been reported to be 2424 °C [6].

Iridium (Ir) has a face-centered cubic, copper-type structure with a 3.8394 Å [7]. Its freezing point, 2447 °C, is listed as a secondary reference point on the IPTS (1968).

Iridium has a strong tendency to form iridium dioxide (IrO2) when heated in air at moderate temperatures. The unit cell dimensions of IrO2 are reported as (tetragonal) a = 4.4983 Å and c=3.1544 A [8]. However, above 1021 °C [2] Ir metal is the only solid phase that exists in equilibrium with air.

Even though Ir oxidizes to IrO2 when heated in air, complete oxidation of the entire sample is often difficult to obtain. By utilizing IrO2 rather than Ir as starting material, an approach to equilibrium could be achieved

Figures in brackets indicate the literature references at the end of this paper. This scale (IPTS 1968) applies to all temperatures listed in this paper.

Specimens were prepared from 0.4 g batches of various combinations of strontium carbonate (SrCO3) and IrO2, each having a purity of at least 99.8 percent. Calculated amounts of these end members, corrected for ignition loss, were weighed to the nearest milligram. Each batch was thoroughly hand mixed and calcined in a muffle furnace at a minimum temperature of 800 °C or heated directly at the temperature of interest. Specimen containers employed in this study were open or sealed gold tubes, open or sealed platinum tubes, and open fused silica tubes. Portions of each calcined batch were refired in a platinum alloy wire-wound quench furnace at various temperatures for different periods of time. The specimens were quenched in air, ice water, or liquid nitrogen. Temperatures in the quench furnace were measured with a Pt versus 90 percent Pt-10 percent Rh calibrated thermocouple. All reported temperatures pertaining to quench furnace data are considered accurate to within ±5 °C. The precision of the measurements was estimated to be ± 2 °C.

Equilibrium was assumed to have been achieved when the x-ray pattern showed no change after successive heat treatments of the specimen or when the data were consistent with the results from a previous set of experiments. An attempt was made on various compositions to obtain equilibrium by increasing the oxygen pressure of the environment exposed to the specimen. The specimen was placed in an open gold tube and heated at moderate temperatures to decom

sonic spectroscopy provided the material is fluid enough to relax in a time scale comparable to the period of the ultrasonic waves, and one is equipped with instruments sensitive enough to detect the highly damped shear waves.

The evidence conflicting with the thermodynamic approaches first came from ultrasonic measurements [8]. Log-Gaussian distributions of relaxation times were found to represent the data well for vitreous B2O3. At high temperatures, when the static viscosity followed an Arrhenian behavior, it was seen that attributing a single relaxation time to the flow units was sufficient to account for the frequency dependence of the modulus. As the temperature was reduced, however, the shear viscosity departed from the Arrhenius curve, and a broadening distribution of relaxation times was required to fit the data. It was seen that the broadening occurred concurrently with the departure of the viscosity from Arrhenian behavior. Use of the Eyring Rate-Equation led to an analysis of the distribution of activation energies. The latter was found to be Gaussian and to broaden with decreasing temperature as did the distribution of relaxation times. The mean activation energy, however, did not change with temperature over the range of measurements. In conclusion, contrary to the assumption implicit in most phenomenological equations of the thermodynamic approaches, the non-Arrhenian behavior of the viscosity was not associated with an increase in the average activation energy with decreasing temperature, but rather with the appearance of a distribution of energies; some indeed higher, but others lower than the average. These lower activation energies could not be explained within the framework of existing viscosity theories.

Further support for these conclusions came from measurements of the viscosity of B2O3 in the range 1010 to 1014 P [9], in which the viscosity appeared to revert to Arrhenian behavior at low temperatures. The authors could find no reasonable fits of this extended data by any of the viscosity theories, as the parameter [ In ns/o (1/T)] = Eapp representing apparent activation energy, approached a temperatureindependent behavior near T, while all existing theories predicted a continued increase with decreasing temperature. In this case, a temperatureindependent apparent activation energy implies Arrhenian viscosity behavior. They thus concluded that the temperature dependence of the viscosity was not controlled by structural effects, such as free volume, and configurational entropy, but rather by some activation energy effects, represented [ở In ŋs/0 (1/T)]. A successful theory would have to lead to a constant parameter [ In n/a (1/T)], or activation energy spectrum near Tg. It became apparent that a microscopic model was needed which could explain the appearance of a symmetric distribution of activation energies, and give physical significance to both the distribution of relaxation times and the temperature dependence of the viscosity.

In analyzing the origin of a spectrum of relaxation times, one cannot differentiate between the occurrence

of the same nonexponential relaxation for all flow units. and the weighted sum of varying but exponential relaxation effects caused by a varying environment [11]. This problem was considered in the analysis of annealing experiments on several inorganic glasses [12, 13]. In the case of a borosilicate crown glass [12] both volume relaxation and ionic conduction were measured. Of the various models present in the literature, only a modified version of Fröhlich's model [14] attributing the existence of a distribution of activation energies to a distribution of environments, could fit both sets of data consistently. In these measurements, it was found that if the distribution were represented by two relaxation times, the fast volume relaxation could be related to the fast electrical conductivity relaxation. The results implied that there are definite regions in these materials which are associated with the different relaxations.

The connection between a distribution of activation energies and a distribution of environments was postulated long ago by Fröhlich, but until recently, due to a lack of sufficiently detailed electron micrographs and high temperature x-ray instrumentation, no structure was observed in molten oxide glasses with known distributions of relaxation times. The model presented in the annealing investigations ruled out the pos sibility of nonexponential decays, but only indicated the possibility of applying some environmental model to the analysis of structural relaxation in inorganic oxide glasses. The problem in interpreting ultrasonic and other relaxation experiments arises from the fact that a distribution of relaxation times does not necessarily indicate any particular molecular relaxation process. As Goldstein [11] clearly suggested, calculation of a distribution of relaxation times in the analysis of a response function is only a mathematical transform and cannot carry physical significance by itself. One must first begin with a model for the molecular mechanisms for structural relaxation and then derive a resulting set or distribution of relaxation times. For this reason, we have chosen to investigate the viscous relaxation process in a series of inorganic oxide glasses with predictable distributions of environments and to attempt to analyze the results in terms of the related microstructure.

Microstructure in molten oxides can best be controlled by selective doping, or by approaching the critical point of an immiscible system. Since x-ray data or electron micrographs describing the structure of normal glasses are lacking, immiscible systems offer the best solution due to the possibility of specifying the temperature dependence of the structure from analysis of the supercritical composition fluctuations.

The immiscibility phase transition is quite widespread in oxide glasses. Liquid-liquid phase separations occur in such systems by changes in composition associated with phases of widely different viscosities. Phase separation at the concentration which has the highest transition temperature, Te (top of the immiscibility dome), occurs by means of a pseudo secondorder phase transition which is characterized by the continuity of the free energy and its first derivatives

150 A

These

supercritical

composition fluctuations drastically change the environment of the flow species as the temperature is varied. Consequently, the presence of these fluctuations in composition is expected to have large effects on the viscous flow processes of the materials. Recently, light scattering and x-ray diffraction experiments have observed such fluctuations above the critical point [15, 16]. The effect is usually referred to as critical opalescence.

Theoretical analyses first derived to describe gasliquid critical point phenomena, were applied to liquid-liquid phase transitions by replacing density fluctuations with fluctuations in composition [15].

Equations are thus available to describe the wavelengths, A, and lifetimes, 7, of the existent fluctuations. as a function of temperature for T> Te. The wavelength, or range of fluctuations varies from very small values far from the critical point, to macroscopic extent near Te. The range of fluctuations, A(T/Te), is expressed as:

The classical exponent of 1/2 is shown here, but there has been strong evidence that a larger value such as 0.6 may be more appropriate for some liquids. Such a small difference has little effect on our model, so we will follow the classical equation. The parameter is a constant of the material, and has been shown to vary little among liquid-liquid nonpolymeric systems (see table 4 of ref. [17]). Taking the average value of 11 Å, which also coincides with results from low angle x-ray scattering measurements on PbO-B2O3-Al2O3, we may plot the most probable fluctuation wavelength as a function of reduced temperature in figure 1, and thus predict the size of the microstructure present in such critical systems above the solution temperature. It is now possible to investigate the effect of environmental microstructure on viscous flow by conducting structural relaxation measurements above the critical point of some immiscible oxide mixtures, and analyzing the resulting parameters in terms of reduced temperatures.

We have recently reported results from an experimental investigation of the behavior of the viscosity [18] and the frequency-dependent modulus [19] above the critical temperature of a series of immiscible oxide glasses. We will review, here, the salient features of these results and then proceed to analyze the observed supercritical effects in terms of a proposed mechanism for the interaction between the viscous

RANGE OF FLUCTUATIONS, A

100 Å

The samples chosen for this study are four sodiumborosilicate oxides with similar high-temperature structures but widely varying critical temperatures. These characteristics were chosen to allow separation of effects due to the presence of supercritical composi tion fluctuations from the noncritical material behavior. Sample 1, with a composition of 70.5 percent SiO2, 22.7 percent B2O3, and 6.8 percent Na2O by mole is the critical composition (top of the dome) of its system [20], and has a critical temperature of 752 °C. Samples 2, 3, and 4 were made by adding 2.1 mol percent CaO; 1.8 mol percent Al2O3; and 1.05 mol percent CaO+ 0.9 mol percent Al2O3 respectively to the concentrations of sample 1. Samples 2, 3, and 4 have resulting transition temperatures of 830, 643, and 741 °C respectively. These samples clearly provide many advantages. First, the viscosities of the separated phases differ by several orders of magnitude, so that the composition fluctuations can be expected to induce effects of large magnitude on the shear viscous relaxation samples occur at such high viscosities as to allow parameters. Then, the critical temperatures of the investigation of the distribution of shear relaxation times by ultrasonic relaxation spectroscopy.

The shear viscosity was measured by a rotation viscometer [21]. The results [18] were found to vary somewhat, between the samples, at high temperatures, reflecting the effect of doping (log viscosities of 2.41, 2.32, 2.71, and 2.46 at 1300 °C for samples 1, 2, 3, and 4 respectively). The viscosity curves were therefore normalized by the values at 1300 °C, in order to study only the critical point effects. This normalized viscosity: