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©2009 Old City Publishing, Inc. Published by license under the OCP Science imprint, a member of the Old City Publishing Group High Temperatures-High Pressures, Vol. 38, pp. 245–257 Reprints available directly from the publisher Photocopying permitted by license only Density and surface tension of liquid iron oxides* F. Millot1,**, J.C. Rifflet1, G. Wille2 and V. Sarou-Kanian1 CEMHTI/CNRS Orleans Université Orléans 2 BRGM Orleans 1 Received: October 1, 2008. Accepted: December 17, 2008. New data are presented for the density ρ and the surface tension σ of the liquid oxides FeOX in the range of x between 1.05 and 1.35 and temperatures T from 1865 to 2155 K. The results obtained with contactless techniques indicate that ρ. and σ are almost constant with T and x within uncertainties. Practical values are ρ = 4.35 ± 0.1g/cm3 and σ = 0.59 ± 0.02 N/m. Keywords: Iron oxide, melt, surface tension, density, levitation. 1 INTRODUCTION The density of liquid iron oxides is not accurately known. There are only few sources of data obtained with the Archimedean method [1–3]. Reported density values range from 4500 Kg/m3 [1,2] to 3800–4300 Kg/m3 [3] in small domains of temperature (1680K<T<1880 K) and composition (1.05<[O]/[Fe]<1.2). In this paper we report values of the density and surface tension of liquid iron oxides obtained with containerless experimental techniques which have been developed by our group during the last ten years [4–6]. 2 EXPERIMENTAL Figure 1 is a scheme of the aerodynamic levitation furnace. 2–3 mm diameter drops are maintained stable on a gas flowing through a convergent-divergent copper nozzle. Its convergent and divergent parts act also as a concentrating *Paper presented at the 18th European Conference on Thermophysical Properties, Pau, 2008. **Corresponding author: [email protected] 245 245-257 pp HTHP_1036.indd 245 12/9/2009 2:59:24 PM 246 F. Millot et al. optical pyrometer λ=0.85µm CO2 Laser Fast CCD Camera Chamber Droplet Nozzle Motion Analyzer Water cooling Levitation gas Oxygen analyzer CO2 Laser optical pyrometer λ=0.85µm Figure 1 Experimental set up. optics for the 8 mm diameter 10.6 µm laser rays that heat the top and the bottom of the sample. 240 Watt effective heating are available allowing heating up to 3300 K in favourable cases. Liquid drop can be maintained pollution free and stable during very long time (hours) with movements of the gravity centre of a few microns only although convection movements are expected from the shear of the flowing gas and the surface deposition of the laser energy. The gas for levitation is a mixture of argon and oxygen obtained from electronic flow-regulators. The oxygen partial pressure of the gas (10–5 – 105 Pa) is also measured with a ZrO2/Y2O3 solid oxide electrolytic cell having a Pd/PdO reference electrode and working at T = 907 K. Thermophysical measurements of the properties of a liquid levitating sample are performed with contactless methods: The temperature is estimated from two optical pyrometers aiming at the top and bottom of the drop. This supposes knowledge of the emissivity of the sample at the wavelength (0.85 µm) of the pyrometers. In general, emissivity is not accurately known and temperature uncertainties of 20–50 K are reasonable. In practice, temperatures are obtained from a calibration of pyrometers at the solidification of liquid alumina drops cooling freely under argon atmosphere. This corresponds to an emissivity of approximately 0.9 and temperature of 2327 K [8]. The initial product is Fe2O3 powder (Specpure from Johnson Matthey). It is compacted with an uniaxial press. Small pieces of the compact are introduced in the levitation nozzle and quickly melted to obtain drops. 245-257 pp HTHP_1036.indd 246 12/9/2009 2:59:25 PM Density and Surface Tension of Liquid Iron Oxides 247 Fe2O3 is melted in the levitation furnace with an Ar/O2 gas. The partial pressure of the gas is measured with the electrolytic cell and the power of the two lasers is adjusted in order to have only small differences of temperature between the top and the bottom of the drop. After these settings, the levitating drop is left in the gas during 15 minutes. Finally, 1250 images are recorded with exposure times of 1ms in order to determine density and surface tension. Just after this, lasers are shut off allowing the free cooling and crystallization of the drop. During this last period, the signal of the two pyrometers is recorded as shown on various examples on figure 2. The cold drop is then weighed with a precision of 10–5 g. We have also characterized the cold drops in order to determine the ratio [O]/[Fe]. The drops have been heat treated in air in an alumina single crystalline crucible which was obtained by machining a plate of a Verneuil single crystal in order to manage small cavities to receive drops. After a treatment of 2 days at 1000ºC and 1 day at 1200ºC we obtain a drop constituted of Fe2O3. No pollution of the alumina single crystal by iron oxide can be detected (see figure 3b) contrary to the common observation of a pollution leading to the darkening of alumina polycrystalline crucibles. The change of the weight of the drop before and after the thermal treatment is a direct measurement of [O]/[Fe] with the formula: [O]/[Fe] = 1.5–4.99*(1–mi/mf) 2400 Temperature (K) 2200 2000 3 1800 1600 2 1 1400 1200 1000 0 2 4 6 8 time (s) Figure 2 Cooling curves and solidification: 1-in argon, 2- in Ar/3*10-2O2, 3-Ar/0.3O2. 245-257 pp HTHP_1036.indd 247 12/9/2009 2:59:26 PM 248 F. Millot et al. Figure 3 Drop picture immediately after laser processing (up) and after re-oxidation to Fe2O3 (down). where mi and mf are the initial and final weight of the drop after the heat tre atment. Weight changes mf-mi are between 1 to 5 mg depending on samples. 3 RESULTS In this experimental study, we have to define and measure various quantities: –– –– –– –– The temperature of the experiment. The composition of the sample. The surface tension of the sample. The density of the sample. 3.1 Temperature T Figure 2 presents the recordings of the two pyrometers aiming at the top and the bottom of three samples that have approximately the same weight (≈ 40 mg) denoted as 1, 2 and 3. The three recordings represent the free cooling of drops after the shut down of lasers at time t = 1s. The first part of the curves (from 1 to 3 s) is the 245-257 pp HTHP_1036.indd 248 12/9/2009 2:59:27 PM Density and Surface Tension of Liquid Iron Oxides 249 cooling of the liquid. The jump at t ≈ 3s corresponds to the beginning of solidification of the undercooled liquid. The right side of curves are the solidification and finally the cooling of solids. The main difference between the three samples is the nature of the flowing Ar/O2 gas mixture. 1 is almost pure argon (Po2 ≈ 10–5 atm.), 2 contains 3*10–2 parts of O2 and 3 contains 0.3 parts of O2. There are, however, striking differences between the three curves of figure 2: –– The cooling rate of the liquid is different for the three curves, being much smaller in Ar/0.3 O2 than in pure argon. –– The two pyrometers indicate the same temperature of the liquid for the sample flown in argon (1) but different curves for the argon containing oxygen curves 2 and 3, the temperature of the bottom of the drop being higher than that of the top. These differences could be satisfactorily explained if an exothermic absorption of oxygen happens during the cooling of the drop (which is what we expect from thermodynamics). They have the consequence that the composition of the drop which is measured after its cooling is certainly representative of its composition at the moment of the solidification but it may have changed during the cooling period of the liquid and may present composition gradients in the temperature gradients when the lasers are heating. The figure 4 has been obtained by comparing the classical phase diagram obtained by Muan [9] and Darken and Gurry [10] with the temperature at the beginning of solidification (see figure 2). We observe a 20 K systematic dif- 1900 M+L L Temperature (K) 1800 M L+M 1700 M+H 1600 W+Fe W+M W 1500 1,0 1,1 1,2 1,3 1,4 1,5 composition x in FeOX Figure 4 Liquidus temperature versus measured composition x compared to the phase diagram of the Fe/O system. 245-257 pp HTHP_1036.indd 249 12/9/2009 2:59:28 PM 250 F. Millot et al. ference between the phase diagram liquidus temperature and the points corresponding to almost congruent solidification (wustite between 1.05 and 1.2 and magnetite between 1.33 and 1.35). The agreement is then correct since it reproduces the essential features of the phase diagram and it confirms the fact that the composition of drops is representative of their state at the moment of the solidification. These data also confirm that our temperature measurements are representative of the temperature of the drops. We have also examined (not reported in detail) that there is only slight differences between the emissivity of the solid and liquid iron oxides by performing solidifications without or few undercooling of the liquid. 3.2 Composition [O]/[Fe] As early explained, the composition of the drops have been obtained after the experiment by their weight change after oxidation to Fe2O3. We have also anticipated the fact that oxygen is able to react very quickly with the liquid during its cooling making the final measurement of the composition different from that of the liquid of interest. In order to examine this point we have compared the compositions that we have determined after experiment with the composition that we should have expected from the oxygen pressure above the drop at the temperature T of the liquid. However, we have already remarked that the drop should present temperature gradients, particularly when the lasers are heating it. This point is easily revealed if we transform the beginning of the cooling curve of the liquid as shown in figure 2 to a new curve expressing the variations of the inverse of the cube of the temperature 1/T3 vs time t (see an example in figure 5). The transition from the steady state of the drop with the lasers impinging the surface to their free cooling having an approximate linear relation between time and 1/T3 is characterized by a short unsteady period of time (between points A and B) when the temperature gradients that were produced by the deposition of energy of the lasers on the surface of the drop almost vanish. The point A and B correspond to a temperature difference of approximately 80 K and point B is the temperature that we should use to guess at the mean temperature of the liquid instead of point A which represents the laser overheated surface of the drop. In order to calculate the liquid compositions from the values of the temperature and the partial pressure of oxygen of the Ar/O2 mixture flowing the liquid sample, we have used the data of Darken and Gurry [10]: From the partial molal heat of solution of oxygen in liquid of composition x = [O]/[Fe] and temperature T(K) in the gas at pO2 (atm), we deduce: 245-257 pp HTHP_1036.indd 250 R ∂log(p O2 ) = -145660 + 69500x 2 ∂(1/T) x 12/9/2009 2:59:28 PM Density and Surface Tension of Liquid Iron Oxides 251 -10 2,0x10 -10 1,8x10 -10 1/T3 (K-3) 1,6x10 -10 1,4x10 B -10 1,2x10 -10 1,0x10 A -11 8,0x10 0 1 2 time t (s) Figure 5 1/T3 versus time cooling curve showing the unsteady period A to B. And the approximate linear relationship between x and log (pO2) at 1873K is: log(p ) O2 1873K = 21.8x - 30.19 By combination, we obtain: x= log(p O2 ) + 30.19 + 63662* (1/T -1/1873) 21.8 + 30376* (1/T -1/1873) The calculation of the composition x has been performed at the point B of figure 5 which represents the mean temperature of the liquid under study. We have also calculated the composition x of the liquid for an infinitely fast exchange of oxygen between the gas and the liquid leading to an equilibrium value immediately before the beginning of the solidification (see figure 2). These values have been plotted vs the composition x that we have determined experimentally after the experiment and appear on figure 6 with a straight line which represents the perfect agreement between measured and calculated values. We observe from figure 6 that the composition of the liquid was correctly measured for compositions in the range 1.10–1.30 which corresponds to oxygen poor Ar/O2 mixtures (PO2 ≤ 10−2 atm.). On the contrary, the oxygen rich Ar/O2 mixtures (PO2 ≥ 10−1 atm.) corresponding to x > 1.35 can equilibrate very fast with the drops since the final composition represents approxi- 245-257 pp HTHP_1036.indd 251 12/9/2009 2:59:29 PM 252 F. Millot et al. 1,45 x calculated from PO2 and T 1,40 1,35 1,30 1,25 1,20 1,15 1,10 1,05 1,00 1,00 1,05 1,10 1,15 1,20 1,25 1,30 1,35 1,40 1,45 x of FeOX measured after experiment Figure 6 Composition [O]/[Fe] calculated from T, pO [10] versus composition measured after the cooling 2 of the sample. # mean temperature of the liquid during experiments, +temperature of the liquid sample just before the solidification. mately that of the liquid just before the solidification (some additional oxidation of the solid during the cooling cannot be completely excluded which is consistent with the slight deviations of the “cross” points with the straight line of figure 6). The apparent diffusion coefficient is of the order of 10-2 cm2/s which is at least two order of magnitude higher than classical values in quiet liquids. This comparison again points the importance of the movements of the liquid in the levitated drops. Finally, these comparisons between measured and calculated values of the composition show that we should use the calculated composition of the liquid at the temperature of interest. 3.3 Surface tension σ The surface tension acts as a spring counteracting the temporal deformations of the drop induced by external forces (gas shear, laser interaction etc…). This makes characteristic frequencies νi of drops of known weight m to be directly related to surface tension σ. In case of a drop with no external force on it, 3π ⋅ m ⋅ ν 22 there is only one characteristic frequency ν2 and the result is: σ = 8 [11]. In other cases, deformation, rotation and precession play a direct role on the frequency spectrum of the drop [6]. However, for moderate deviation from 245-257 pp HTHP_1036.indd 252 12/9/2009 2:59:29 PM Density and Surface Tension of Liquid Iron Oxides 253 the spherical drop and observation nearly along the rotation axis, five characteristic frequencies can be identified and related to surface tension: 2 2 (ν2-1 + ν2+1 ) (ν2-2 + ν2+2 ) 1 ν 22 = ν 220 + + 5 2 2 A typical result of the treatment of images is shown on figure 7. It was obtained on a 51.33 mg drop at t = 1862 K under argon. The relative amplitude of vibration of the surface is approximately 4*10–3. The Fourier transform of the surface and orientation of the drop is interpreted with the five peak frequency spectrum which is characteristic of a rotating and slightly deformed drop [6]. The precession of the rotation axis is also responsible for the comb shape of the peaks. This example illustrates the fact that it is difficult to assess the exact position of the various frequencies. Selection rules are helpful to do that since ν0 can only be found in the surface spectrum, ν±2 appears only in the orientation spectrum and finally ν±1 is appearing in the two spectra. We have also ν 2 - ν-2 = 2*(ν1 - ν-1 ) . The final result is shown on figure 8. We observe almost the same value of the surface tension (σ = 0.59 ± 0.02 N/m) whatever the temperature or the composition. The comparison with literature indicates similar trends with the results of Kidd and Gaskell [12] and those of Bhattacharyya and Gaskell [13]. ν -2 ν -1 ν0 ν1 ν2 amplitude (a.u.) 40 orientation 20 surface 0 85 90 95 100 105 110 115 120 125 Frequency (Hz) Figure 7 Fourier transform of the oscillations of the surface and the orientation of a liquid sample and determination of the characteristic frequencies νi. 245-257 pp HTHP_1036.indd 253 12/9/2009 2:59:30 PM 254 F. Millot et al. 0,65 Maurakh (T=1873K) Kozakevitch (T=1673K) Okunev (T=1673K) Kawaï (T=1650-1700K) Kidd et Gaskell t=1733K Kidd T=1683K Bhattacharyya (T=1708K) This work (T=2112-2155K) This work (T=1862K) This work (T=2017-2054K) This work (T=1916-1956K) surface tension (N/m) 0,60 0,55 0,50 0,45 0,40 0,35 1,0 1,1 1,2 1,3 1,4 1,5 1,6 composition X of FeO X Figure 8 Surface tension obtained in this study at different temperatures versus the calculated composition of the liquid at T, pO2 are compared with Kidd and Gaskell [12], Bhattacharyya and Gaskell [13], Kozakevitch [15], Okunev and Galimov [16], Kawai et al [17], Maurakh et al [18], data. Another interesting result comes from the relative position of the three characteristic frequencies ν0*, ν1* and ν2* of the non rotating drop. These are easily obtained by taking the average position of the 0, ±1 and ±2 frequencies of the rotating drop. These frequencies are directly related to the two permanent distortions ε2 and ε4 that describe the deviation from sphericity [14]: ν 0 * = ν * (1 - 0.6758 ε2 - 2.176 ε 4) ν1 * = ν * (1 - 0.3379 ε2 + 1.4507 ε 4) ν 2 * = ν * (1 + 0.6758 ε2 - 0.3627 ε 4) where ν* is the arithmetic mean value of the five characteristic frequencies. The calculation of ε2 and ε4 from our data indicate that ε4 is always smaller than 1.5% whereas ε2 is between 2 and 10%. These large deformations which concern mainly the flattening of the drop along the vertical axis are in part produced by the rotation force on the drop. They will influence our methodology for the determination of density. 3.4 Density ρ The density is the ratio of the weight to the liquid volume. Weight is measured immediately after the cooling of the drop which lasts a few seconds 245-257 pp HTHP_1036.indd 254 12/9/2009 2:59:31 PM Density and Surface Tension of Liquid Iron Oxides 255 after an experiment. Volume V is obtained indirectly from the measurement of the surface S of the images of the drop. For small enough mass and not too high rotation rates, the deformation from sphere of the drop is less than 1% inducing only small uncertainty in the simplified formula of the sphere: V = S3/2 / 36π . In case of deviation from spherical shape, corrections must be done. For instance, with a static deformation ε2 corresponding to the flat2 ness of the drop the volume becomes V = (1 - ε2 ) (1 + ε2 )S3/2 36π . Various calibrations have been used in order to measure the size of image pixels (calibrated drops and calibrated arrays of micrometric lines) with an absolute uncertainty of 1/1000. The density of the liquid iron oxides is represented for four different temperature ranges on figure 9 and it covers the domain of compositions x going from 1.05 to 1.35. The weights of samples are between 40–70 mg and 3 extra samples between 90–115 mg. Glorieux [19] have proposed a limit for the non-dimensional parameter mg/σr = 0.7 (σ = surface tension and r = radius of the drop) in order to have negligible deviations (<1%) from the spherical shape of a drop in order to evaluate the density of a levitated liquid. In the case of liquid iron oxides this means that drop weight should be lower than 150 mg. We have, however, 6,0 5,8 3 density (g/cm ) 5,6 5,4 5,2 5,0 4,8 4,6 4,4 This work (T=2112-2155K) This work (T=1862K) This work (T=2017-2054K) This work (T=1916-1956K) Hara (T=1743-1881K) Mori (T=1723K) Mori (T=1748K) Mori (T=1773K) Mori (T=1798K) Lee (T=1773K) 4,2 4,0 3,8 3,6 1,05 1,10 1,15 1,20 1,25 1,30 1,35 1,40 1,45 composition X of FeO X Figure 9 Experimental densities corrected for the deformations of the drop (see text). Comparison with literature data: Lee and Gaskell [1], Hara et al [2], Mori and Suzuki [3]. 245-257 pp HTHP_1036.indd 255 12/9/2009 2:59:32 PM 256 F. Millot et al. deduced in paragraph 3.2 from the frequency spectrum of the liquid iron oxides that the weight of the drop is not the only parameter that can change the spherical shape. For this reason we have applied corrections with ε2 distortions deduced from characteristic frequency measurements. The precision on the density data is calculated from the ratio of the number of pixels of the perimeter to the number of pixels of the surface of the images recorded with the high speed camera. Characteristic values for our samples are ∆ρ/ρ = 3%. The error coming from the weight of the drop is much smaller (1/1000). Figure 9 clearly shows that the density of liquid oxides are only weakly dep endent on the composition [O]/[Fe]. A practical value is: ρ = 4.35 ± 0.1 g/cm3. It is also observed that the relatively bad precision (3%) of the density values do not permit to seriously predict its temperature dependence. Comparison with the conflictive previous results of Mori and Suzuki [3] and Hara et al [2] which include in their analysis the results of Lee and Gaskell [1] indicate agreement with Hara on the fact that the comparable densities should not change significantly with the composition of the liquid and also on the fact that the temperature coefficient of the density should be sufficiently small in order to not be detected in our data. This means that it should be less than (∆ρ/ρ)∆T = 1.2*10-4K-1, where ∆ρ/ρ = 0.1/4.35 is the total scatter of the density values and ∆T = 200 K is the domain of temperature of our study (the values of this temperature coefficient are 7*10-5K-1 for Hara et al [2] and between 2.5*10-4K-1 and 4.8*10-4K-1 for Mori and Suzuki from their data). CONCLUSION The surface tension and density of the liquid oxides have been measured with contactless methods in the temperature domain 1865–2155 K and composition [O]/[Fe] ranging from 1.05 to 1.35. The temperature and composition has been carefully evaluated by comparing our measurements with the thermodynamic properties of the iron/oxygen system previously reported in the literature. The experimental data obtained for density as well as for surface tension is particularly simple since it reduces to ρ = 4.35 ± 0.1 g/cm3 and σ = 0.59 ± 0.02 N/m with almost no change with temperature and composition. These data permit to choose density values between conflictive results [2,3]. REFERENCES [1] Lee Y. E., Gaskell D. R . Met. Trans. 5 (1974) 853. [2] Hara S., Hirie K., Gaskell D. R., Ogino K. Trans Japan Inst. Met. 12 (1988) 977. [3] Mori K., Suzuki K. Trans. ISIJ 8 (1968) 382. 245-257 pp HTHP_1036.indd 256 12/9/2009 2:59:32 PM Density and Surface Tension of Liquid Iron Oxides 257 [4] Glorieux B., Millot F., Rifflet J.C., Coutures J. P. Int. J. Thermophys. 20 (1999) 1085. [5] Glorieux B., Millot F., Rifflet J. C. Int. J. Thermophys. 23 (2002) 1249. [6] F. Millot, J. C. Rifflet, G. Wille, V. Sarou-Kanian and B. Glorieux, J. Am. Ceram. Soc. 85 (2002) 187–92. [7] Millot F., Paradis P. F., Rifflet J. C., Ishikawa T. Int. J. Mat. Prod. Technol. 26 (2006) 274. [8] Sarou-Kanian V., Rifflet J. C., Millot F. Int. J. Thermophys. 26 (2005) 1263. [9] Muan A.. Am. J. Sci. 256 (1958) 171. [10] Darken L. S., Gurry R. W. J. Am. Chem. Soc. 68 (1946) 798. [11] Lord Rayleigh, Proc. R. Soc. London 29 (1879) 71. [12] Kidd M. and Gaskell D.R. Metall. Trans. B 17 (1986) 771. [13] Bhattacharyya P. K., Gaskell D. R. Metall. And Mater. Trans B 27 (1996) 139. [14] Cummings D.L. and Blackburn D.A. J. Fluid Mech. 224 (1991) 395. [15] Kozakevitch P. Revue de Métallurgie 46 (1949) 505. [16] Okunev A. I., Galimov M. D. Oxydation of iron and sulphur in oxide sulphite systems Nauka, Moscow 1983. [17] Kawai Y., Mori K., Shiraishi H., Yamada N. Tetsu-To-Hagané 62 (1976) 53. [18] Maurakh M. A., Mitin B.C., Roitberg M. B., Zadovskaya Laroratoiya 33 (1967) 1160. [19] Glorieux B. Thèse University of Orléans, (France) 2000. 245-257 pp HTHP_1036.indd 257 12/9/2009 2:59:32 PM