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3.10 j. Centrifuge-assisted falling sphere viscometry (A. Dorfman, K.-U. Hess and D.B. Dingwell)

Complete and accurate viscosity-temperature relationships for silicate melts are of use to geoscientists for several reasons. Due to a number of factors involving the mathematical assumptions and/or mechanical limitations of individual viscometry techniques, the metastability of the liquids or simply the time limits on the duration of well-controlled constant experimental conditions, the measurement of viscosity is often performed on silicate melts in temperature ranges which are different than those where the viscosity data are applied. For the purpose of modelling the physical chemistry of the melts or for parameterizing melt viscosities for the modeling of igneous processes, complete viscosity-temperature relationships are needed. This is because the non-Arrhenian temperature dependence of the viscosity of most melts means that an accurate interpolation or extrapolation of the viscosity beyond the measurement range is a difficult task. This non-Arrhenian temperature dependence remains one of the main hindrances in generating a fully generalizable model of melt viscosities for petrological calculations. The activation energies obtained, for example, by dilatometric versus concentric cylinder viscometry techniques often differ by a factor of two. Linking them requires careful fitting of combined data sets of viscosity for which empirical models (e.g., Tammann-Vogel-Fulcher (TVF), as well as those based on independently-testable models) are employed. Despite the wide range of techniques for the determination of melt viscosity, there often exists, in the geochemical literature, a gap in viscosity determinations between the upper limit of concentric cylinder determinations at 105 Pa s and the lower limit of most dilatometric methods at 109 Pa s. Although the falling sphere method is in principal capable of operating in that gap, the times required for accurately measurable displacements of the falling sphere of appropriate dimensions are too long to make the method practical. Thus previous investigations of the viscosities of silicate melts using the falling sphere method have been restricted to melt viscosities of less than 105 Pa s.

In the present study, a high-temperature furnace built into a centrifuge is used to accelerate the Stokesian settling velocity by up to a factor of 1000-1500. This accelerated falling sphere technique is used to provide data in the viscosity range of 105 - 108 Pa s. The data compare favourably with lower- and higher-temperature viscosity data and improve the constraints on the temperature-dependence of the viscosity.

Pieces of Pt90Rh10 wire are welded into spherical spheres using a contact arc welding device. Due to the surface tension of the melted platinum the cylinders bead into approximately spherical shapes. The final diameters of platinum spheres were 0.2 - 0.7 mm as measured by an micrometer and under an optical microscope. Deviations from the sphericity did not exceed 5 µm.

Cylindrical samples (diameter 5 mm, length 18 mm) of a haplogranitic composition are drilled out from a batch of bubble-free homogenized glass. These are placed into an alumina capsule and rotated at high temperature under an acceleration of 1000 cm/s2 for 1 h in order to remove voids and the gap between capsule walls and the melt. Next a small cavity with a diameter corresponding to the size of the platinum bead is drilled out of the surface of the sample using a diamond coring tool. The Pt-sphere is then placed in the cavity and covered with a pressed powder of haplogranitic glass composition. The sample with the platinum sphere is then centrifuged again for a certain period of time at a desired temperature and then quenched. The alumina capsule is imaged with X-rays and the first position of the Pt-sphere is determined. The capsule is placed again in the furnace, rotated for 600 - 5400 s at a desired temperature, quenched and the new position of the Pt sphere is determined on the X-ray photo.

In order to measure the exact position of the Pt-sphere in the capsule non-destructively, a series of X-ray photos of a quenched sample is obtained using a Rigaku diffractometer. The capsule with the sample together with a sheet of photo-paper placed behind it are attached to the shield at a distance of 0.5 m from the X-ray source. The sample is exposed to the parallel beam of X-rays for 30 s. The alumina capsule and the melt are transparent to X-rays, but the Pt-sphere can be distinctly traced on the photos. By measuring the position of the Pt-sphere on the photos, the displacement of Stokesian sinking spheres have been estimated with a precision of ± 10 µm, thus enabling the velocity to be determined.

The density, the radius of the platinum sphere and the diameter of the alumina capsule have all been corrected for thermal expansion using the linear thermal expansion coefficient of the respective materials. The density of haplogranitic liquid has been calculated from its molar volume and volume thermal expansion coefficients.

The accuracy of the method is comparable to that of the micropenetration method. The usefulness of incorporating results for the falling sphere centrifuge (FSC) determinations in fits to the temperature dependence of viscosity can be demonstrated with the example of a haplogranitic melt series with additions of 5, 10 and 20 wt% Na2O. The combination of high-temperature concentric cylinder and low-temperature micropenetration techniques already demonstrates an increasing degree of non-Arrhenian temperature dependence of the viscosity with increasing Na2O content. The systematics of the variation of the temperature-viscosity relationship towards more non-Arrhenian or fragile behaviour with increasing Na2O are much better defined by the inclusion of the FSC data (Fig. 3.10-8). As a result, the coefficients for the Tamann-Vogel-Fulcher equations in the fits are much more robust. Although the fit quality does not always improve with the addition of the FSC data the systematics of the returned fit coefficients are much better. Such coefficients are required as the input into models for generalizable calculations of the temperature-dependence of silicate melts.

Fig. 3.10-8: The viscosity-temperature relationships for a series of melts based on the addition of Na2O to a haplogranitic melt. Previous work had left a gap in the experimentally accessible viscosity measurement ranges. The present centrifuge assisted falling sphere data fill the viscosity data gap satisfactorily.

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