A literature review and interpretation of the properties of high-TiO2 slags

Synopsis The properties of high-TiO2 slags are markedly different from those of many other metallurgical slags. The objective of this paper is twofold: firstly, to assemble in one document the TiO2 slag properties, including Ti3+/Ti4+ ratio, liquidus temperatures, heat capacity, density, viscosity, thermal conductivity, and electrical conductivity: all expressed in terms of temperature and composition dependency. Secondly, this paper attempts to correlate published experimentally measured data with theoretically based parameters, which will enable the application of the measured properties to wider slag compositions within the pseudobrookite-TiO2 slag system.


Introduction
Slag properties are an essential tool in problem solving, both in equipment design and metallurgical process control. Experimental work on high-TiO 2 slags is particularly difficult because of their chemically corrosive nature and compositional sensitivity to oxygen partial pressure. While ample publications are available and are still being produced for silicate-based slags, comparatively few results are available for high-TiO 2 slags. The objective of this work is firstly to summarize the essential properties for liquid TiO 2 slags. Secondly, an attempt is made to derive correlations from the published experimental work which are based on a theoretical concept. In this way, it is believed that the experimental data can be cautiously extrapolated to other high-TiO 2 slags. To this end, a set of typical high-TiO 2 slags based on a data-set published in earlier work (Kotze and Pistorius, 2010) is used throughout this paper. The chemical composition of this set is given in Table I. Although 94%TiO 2 is not considered 'typical', it was included in the example slags because many producers migrate to higher TiO 2 slags.
The experimental data cited in this work is by no means claimed to be all-inclusive. Glimmers of work done in Eastern European countries are present, though not easily interpreted by Englishspeaking researchers. On occasion experimental data was not used because of a discrepancy in the data or experimental method.

Ti 3+ /Ti 4+ ratio
Titania slag compositions are typically expressed as TiO 2 because analytical methods measuring the total titanium are fast and less cumbersome than the wet chemistry titration method required to measure Ti 3+ (Tranell, Ostrovski, and Jahanshahi, 2002). When appreciable amounts of Ti 2 O 3 are included in the TiO 2 value, titania is expressed as the equivalent TiO 2 . In these instances, slag assays exceed 100 because the oxygen is overestimated. The assay total is therefore an indication of the level of reduction. Previous attempts by the author to correlate measured Ti 3+ values with assay totals yielded unsatisfactory results.
The balance between Ti 4+ and Ti 3+ follows Reaction [1] and like other transition elements, it is governed by a redox reaction such as the O-type behavior of Reaction [2] (Tranell, Ostrovski, and Jahanshahi, 2002). The Ti 3+ /Ti 4+ ratio is therefore expected to be dependent on the oxygen partial pressure and the oxygen activity in the slag bath. Tranell and co-workers Jahanshahi, 1997, 2002) investigated these relationships in TiO 2 -Ti 2 O 3 -SiO 2 -CaO slags and found the Ti 3+ /Ti 4+ ratio to depend on the oxygen partial pressure raised to the power of 0.21 (Tranell, Ostrovski, and Jahanshahi, 1997) and 0.23 (Tranel, Ostrovski, and Jahanshahi, 2002). Using optical basicity to represent oxygen activity, they derived a correlation using temperature, oxygen partial pressure, and optical basicity to calculate the Ti 3+ /Ti 4+ ratio. This correlation yielded good results with all the slags they investigated, but not with those of other researchers. [1] [2] In this work, electronic polarizability was investigated as an alternative measure to predict the activity of oxygen. Electronic polarizability is described as the 'ability of oxygen to transfer electron density to surrounding cations' (Dimitrov and Komatsu, 2010). It is a measure of the propensity of compounds to donate charge from oxygen ions to the surrounding electron cloud (Duffy and Ingram, 1976). In this context, Ca 2+ with a cation polarizability of 1.57Å 3 is 'generous' while Si 4+ at 0.284 Å 3 is comparatively 'stingy.' A few mutually exclusive data-sets exist to calculate electronic polarizability. The data used in this work is based on the large data-set of dynamic polarizabilities published by Shannon and Fischer (2016) which includes a value for the cation polarizability of Ti 3+ . The Ti 3+ /Ti 4+ ratios of the CaO-SiO 2 -TiO x slags from Tranell were found to correlate well with the ratio of the polarizabilities of Ca 2+ and Si 2+ , (polarizability Å 3 ; mole fraction X).This result corroborates the polarizability ratio of Ca 2+ and Si 4+ as a measure of the oxygen activity in the bath. The Ti 3+ /Ti 4+ ratios of the slags Tranell studied were subsequently calculated using a correlation with two parameters: the experimental oxygen partial pressure and the polarizability ratio Ra. Figure 1 shows the results of this correlation to compare well with the experimental Ti 3+ /Ti 4+ ratios.
The validity of the correlation between oxygen partial pressure, electronic polarizability, and Ti valency was tested against industrial TiO 2 slags using measurements reported by Geldenhuys and Pistorius (1999). These workers measured the oxygen partial pressure in pilot plant TiO 2 slags and reported the TiO 2 and Ti 2 O 3 values of the slags at the time of measurement. Their measured oxygen partial pressures in the slags are plotted as the circles in Figure 2. Since the full assays of the slags used in the Geldenhuys study were not given, their results are compared with the calculated TiO 2 and Ti 2 O 3 values of the example slags in Table I using the correlation derived from the work by Tranell. This is not ideal, but a reasonable replacement, as the impurity levels of the ilmenites used in the Geldenhuys study and those used in the Kotze (Kotze and Pistorius, 2010) study -on which the example slags were based were similar. The calculated results shown with the solid and broken lines in Figure 2 compare well with the experimental data. It is worthwhile to note that several studies found the same Ti 3+ / Ti 4+ ratios in industrial slags as were found in the Geldenhuys pilot plant study. Few of these results are published such as the industrial slag data points given in Figures 4 to 6, but many are unpublished due to intellectual property rights.
The dependency of the Ti 3+ /Ti 4+ ratio on the oxygen partial pressure and CaO/SiO 2 ratio (based on the work by Tranell) is summarized in Figure 3. Lower oxygen partial pressures lead to greater reduction and hence higher Ti 3+ /Ti 4+ ratios. Higher CaO/ SiO 2 ratios create higher oxygen activity, which in turn decreases the Ti 3+ /Ti 4+ ratio. In a given smelting process the oxygen partial pressure is largely governed by the Fe FeO equilibrium in the slag (Pistorius, 2007), while the CaO/SiO 2 ratio is determined by the raw material quality.
In an earlier paper Tranell also reports MgO to affect the Ti 3+ /Ti 4+ ratio (Tranell, Ostrovski, and Jahanshahi, 1997). A correlation including the polarizability of Mg 2+ did not fit the industrial data. The industrial data was a small set, though, and it does not exclude the potential of MgO (as possibly Al 2 O 3 ) tosimilarly to CaO and SiO 2 influence the Ti 3+ /Ti 4+ ratio. Future work will investigate this possibility.  The Journal of the Southern African Institute of Mining and Metallurgy VOLUME 120 FEBRUARY 2020 Pesl and Eriç (1999) conducted experimental work on slags of the TiO 2 -Ti 2 O 3 -FeO system, controlling the oxygen partial pressure with CO-H 2 gas mixtures, and calibrating slag samples at 1500°C and 1600°C in platinum or molybdenum crucibles for 6 to 8 hours before rapidly quenching them to capture the high-temperature phases. Their predicted liquidus isotherms for 1500°C and 1600°C are reproduced for axes in mass% and given in Figure 4 and Figure 5 as dotted lines. No accuracy or error prediction was reported. Seim melted slags in an induction furnace with a slag freeze-lining to protect the crucible walls (Seim, 2011;Seim and Kolbensen, 2010). Experiments were conducted in an Ar atmosphere, using titanium metal and haematite additions to control the level of reduction. Liquidus temperatures were determined from cooling curves captured by a spectropyrometer looking down onto the upper surface of the slag. The tolerances for individual measurements on the iron-saturated samples are given as 4.9°C to 33.3°C. Seim modelled a liquidus surface for the FeTiO 3 -Ti 2 O 3 -TiO 2 system using the measured liquidus temperatures of the iron-saturated slags and expanding the thermodynamic data-set with two optimized ternary parameters. The model is considered to accurately predict the measured liquidus temperatures of the iron-saturated slags. The liquidus temperature measurements on the iron-unsaturated samples were unexpectedly and unexplainably lower and not used in the modelling exercise. Despite this, the measured liquidus temperatures of the iron-unsaturated slags plot on average 108°C below the modelled liquidus and 59°C above the modelled solidus temperatures. The model isotherms for 1500°C, 1600°C, and 1700°C were reproduced to have TiO 2 , Ti 2 O 3 , and FeO as corners of the ternary and are shown in Figure   Thermodynamic data for the binary systems TiO 2 -FeO and Ti 2 O 3 -TiO 2 were published by Eriksson and Pelton (1993) and they illustrated the validity of using this data to calculate the solid phase relationships in the ternary system below 1400°C. They did not publish liquidus predictions (Eriksson and Pelton, 1996). The maximum inaccuracy of the data was given as ±20°C.

Liquidus temperatures
In the present work the thermodynamic data from Eriksson were used in the Modified Quasichemical Approach (Pelton and Blander, 1986) to calculate the liquidus temperatures in the TiO 2 -Ti 2 O 3 -FeO system. A temperature, dependent activity coefficient was calculated for the pseudobrookite M 3 O 5 phase from the experimental data by Pesl (Pesl and Eric, 1999). The calculated liquidus isotherms for 1550°C, 1600°C, and 1700°C are shown Figure 4, Figure 5, and Figure 6 as solid lines. The low-temperature trough these isotherms along approximately 55%TiO 2 is in line with the experimentally measured low melting point measured in argon by Brauer and Littke (1960) for the TiO 2 Ti 2 O 3 binary: 1660°C between TiO 1.70 and TiO 1.75 (43% to 53% TiO 2 ).
All three isotherm sets show a liquid slag field with (i) an upper phase boundary with the liquid slag + TiO x phase field, (ii) a lower phase boundary with the liquid slag + liquid iron phase   (Pistorius, 2002) are shown as dark squares on the ternaries. For the high-FeO slags the dotted 1500°C and 1600°C upper boundary isotherms by Pesl imply a 100°C drop in liquidus with a ±1% change in FeO (approximately 19% to 18%). This seems an unlikely discontinuity in the known FeO-liquidus temperature relationship of the system. The more likely case is a more gradual temperature gradient as shown by the calculated 50°C spaced isotherms in Figure 7. These are also in agreement with the isotherms by Seim -at least up to 20%Ti 2 O 3 .
According to the calculated isotherms the industrial slag series have liquidus temperatures ranging from 1550°C for 20%FeO eq up to 1700°C for ±9%FeO eq , while the broken line isotherms (Seim model) indicate a liquidus range starting somewhere above 1600°C to just over 1700°C. Given the stated tolerances and inaccuracies, the different sets of isotherms are regarded to give similar results, especially in the area of concern for typical industrial TiO 2 slags. It will be worthwhile, though, to clarify the discrepancy in the size of the liquid slag phase fields as predicted by the different sets of isotherms. Figure 7 shows how the liquidus increases with decreasing %FeO: higher reduction yields a higher slag liquidus. However, for a given FeO content, e.g. 10mass%, higher reduction will increase the Ti 3+ /Ti 4+ ratio, which will decrease the liquidus, until the Ti 3+ /Ti 4+ ratio crosses the low liquidus trough between TiO 2 and Ti 2 O 3 . On the lower TiO 2 and higher Ti 2 O 3 side of this trough, the liquidus will increase again with increasing Ti 3+ /Ti 4+ . In practice, where a process receives a stable ilmenite quality, higher reduction will lead to a simultaneous decrease in FeO and an increase in Ti 2 O 3 , and the net effect will be an increase in liquidus, though smaller in size than what would have resulted from a decrease in FeO only.
To apply phase temperature behaviour from the ternary FeO-TiO x (Figure 7) (Borowiec, 2009;Pistorius, 2002). There are indications that MnO does not fully partition to the M 3 O 5 phase but that a potentially significant portion thereof separates to the silicate phase (Seim, 2011;Pesl and Eric, 2002). Without quantitative data on the behaviour of MnO though, the correlation showed by Pistorius is followed. The liquidus isotherms in Figure 7 can therefore applied to industrial slags when the FeO and Ti 2 O 3 are expressed in their equivalent forms. The FeO eq and Ti 2 O 3 eq of the example slags (Table I), together with their calculated liquidus temperatures, are listed in Table II. [4] High-TiO 2 slags have a narrow gap between liquidus and solidus temperatures. Seim measured the liquidus and solidus temperatures on synthetic slags using differential thermal analysis/thermal gravity analysis (Seim, 2011). For a TiO 2 -Ti 2 O 3 -5.6%FeO slag the liquidus and solidus were 1696°C and 1682°C respectively, and for a TiO 2 -Ti 2 O 3 -16.9%FeO slag, 1664°C and 1644°C respectively. These results imply a narrow temperature gap of 14°C to 20°C between liquidus and solidus. Borowiec (2009) measured solidus and liquidus temperatures on slags with 11-12%, 6-7%, and 2% gangue impurities (the publication gives the impurities for the first and third slag, while impurities for the second slags were deduced from other publications using the same slag). The temperature differences were 136°C, 83°C, and 66°C respectively (Borowiec, 2009). Provided the SiO 2 content in the gangue impurities is low (i.e. <5% in >10% total gangue, and <3% in <7% total gangue), these differences are indications of the solidus temperatures of high-TiO 2 slags.

Heat capacity
The heat capacities of liquid TiO 2 slags were reported by Kotze and Pistorius (2010) and are repeated here, Equation [5] (C p in J/ kg.K). The heat capacity values for the example slags in Table I  are listed in Table III. [5]

Density
With most liquid slag systems, a density calculation needs to incorporate the enthalpy of mixing. For slags with only a small deviation from ideality, such as high-TiO 2 slags (Eriksson and Pelton, 1993;Gaskell, 2008, p. 247), a weighted average of the densities of the pure liquids suffices. The density of liquid TiO 2 was taken as 3.3 g/cm 3 at 1600°C from the measurements by Dingwell (1991). The density of liquid Ti 2 O 3 was measured by Ikemiya et al. under an Ar-H 2 gas mixture (1993); extrapolated to 1600°C, Ti 2 O 3 has a density of 4.0 g/cm 3 . Finally, the density of liquid FeO was taken as 4.4 g/cm 3 at 1600°C based on the measurements done by Xin et al. (2019). The resultant calculated densities for the example slags (Table I) are given in Figure 8. It is concuded that typical high-TiO 2 slags have a density range of 3.5 g/cm 3 to 3.7 g/cm 3 . This is lower than the temperatureindependent value of 3.8 g/cm 3 often cited in literature (Kotze and Pistorius, 2010;Zietsman and Pistorius, 2006). Figure  8 shows that the slag densities decrease with increasing temperature, as well as with increasing total TiO 2 .
Since electrical conductivity is the movement of electron charges, the concept of electronic polarizability was tested against the experimental electrical conductivity measurements. By using the polarizability of the oxide components (Table IV), it was possible to reproduce the electrical conductivities of the high-gangue TiO 2 slags using a correlation of the form given in Equation [6] (electrical conductivity s [Ω -1 cm -1 ]; electronic polarizability of the slag a slag [Å 3 ] calculated with Equation [7] and the oxide polarizabilities given in Table IV; a a constant; and n a temperature-dependent constant). The calculated electrical conductivities for the high-gangue group (lower TiO 2 eq ) are given by the broken lines in Figure 9: these calculated values correspond remarkably well with the measured data from Desrosiers.
[6]  Table I   [8] Applying Equation [6] to the low-gangue group (high-TiO 2 eq ) yielded fair, but not, good results. The addition of a temperaturedependent valency ratio R valency , Equation [8], improved the calculation significantly: the results are shown by the solid lines in Figure 9.
The electrical conductivities calculated for the example slags (Table I) are shown in Figure 10. The results of the 82%, 85%, and 88%TiO 2 eq slags correspond with the measured values of similar slags shown in Figure 9. The predicted electrical conductivities for the 91% and 95% TiO 2 slags cannot be verified against experimental data, but since the calculation is based on parameters which supports the theory of electrical conductivity in slags, the prediction carries some level of confidence. Judging from the intervals between the lines of the five example slags, the increase in electrical conductivity accelerates with increasing TiO 2 eq . A similar phenomenon is shown for high-FeO slags up to 100% FeO (Jiao and Themelis, 1988).

Viscosity
The viscosity of slags is known to be structure-dependent and high-TiO 2 slags are no different: above their liquidus temperatures TiO 2 slags dissociate into Ti 4+ , Ti 3+ , and Fe 2+ ; these have no structure such as SiO 2 networks provide for silicate slags. Consequently, fully liquid TiO 2 slags have very low viscosities. The measured data for 'low-FeO' Sorel slag (Handfield and Charette, 1971) and 95%QMM slag (Borowiec, 2009) are reproduced in Figure 11: above their liquidus temperatures these slags measured 0.3 dPa.s and 0.15 dPa.s. A recent study reports 0.6 dPa.s for fully liquid slags (Hu et al., 2018). Though these numbers are different, they are all very low and not sensitive to composition or temperature. A second point of importance is that the critical temperature where viscosity increases sharply is only slightly below the slags' liquidus temperatures (Borowiec, 2009;Hu et al., 2018).
Considering these results, the viscosities of the example slags (Table I) are estimated as shown in Figure 12. The dominant feature in these viscosity curves is the sharp upwards turn, the estimated positioning of which, was based on the calculated liquidus temperatures of the example slags given in Table II. In industrial smelting the slag bath is likely to contain some unreacted reagent. The Einstein-Roscoe equation was used to quantify the impact thereof on the viscosity of the liquid bath (Equation [9]: viscosity of the liquid with solids, η [Pa.s]; viscosity of fully liquid phase η0 [Pa.s]; f volume fraction of the solids; assumed density for reductant 0.9 g/cm 3 ). This is an approximation because the Einstein-Roscoe equation was derived for solid spheres and reductants are often angular. The calculated    A literature review and interpretation of the properties of high-TiO 2 slags ▶ 128 FEBRUARY 2020 VOLUME 120 The Journal of the Southern African Institute of Mining and Metallurgy viscosities for 0%, 5%, and 10mass% reductant in the 88%TiO 2 fully liquid slag are shown in Figure 13. At 10mass% reductant the viscosity of the slag bath increases from around 0.4 dPa.s to 1.5 dPa.s. This is similar to a change from olive oil at 35°C to maple syrup at 25°C (Nierat, Musameh, and Abdel-Raziq, 2014;Ngadi and Yu, 2004): not unmanageable -as Handfield points out: blast furnace slags are still tappable at 5 dPa.s, but also not insignificant considering the foaming tendency of TiO 2 slag baths. [9]

Thermal conductivity
The thermal conductivity of solid TiO 2 slags was reported as 0.00175T + 0.3 W/m°C, which gives a thermal conductivity range of 1.0 to 2.9 W/m°C from 400°C to 1500°C (Kotze and Pistorius, 2010). Thermal conductivity measurements on solid TiO 2 slags from room temperature to 1050°C varied from just above 1 W/mK to approximately 2.5 W/mK with mostly, but not always, a positive relationship with temperature (Heimo, 2018). A single measurement in the same study gave 5 W/m°C at 1400°C. In the absence of data for liquid slag, 1 W/m°C is sometimes used in modelling (Zietsman and Pistorius, 2006). In the following paragraphs an attempt is made to approximate the thermal conductivity of high-TiO 2 slags based on the structure of these slags and their optical properties. The thermal conductivity of slags is a combination of lattice k latt , radiation k rad , and electronic conduction k e (Mills and Susa, 1992). Lattice conduction is structure-dependent because it relies on the velocity of phonons v through the slag, and the mean free path of phonons L through the slag, (Equation [10]; heat capacity at constant pressure C p ). In solids the crystal lattice provides the structure along which phonons travel; in silicate slags, the SiO 2 network provides the means. Thermal conductivity values measured with the transient hot wire method, a technique which isolates lattice conductivity, range from 0.03 to 1 W/mK for silicate slags (Glaser and Sichen, 2013;Kang et al., 2012). Lattice thermal conductivities decrease with increasing temperature, reflecting the diminishing slag structure with increasing temperature. In TiO 2 slags -judging from the low viscosities above liquidus temperatures -no significant structure exists. Lattice thermal conductivities in high-TiO 2 slags are therefore expected to be small. Nevertheless, the lattice conductivity where estimated from a correlation between reported transient hot wire thermal conductivities and calculated viscosities of silicate slags. The model used for viscosity calculations is based on the work by Zang , a little-known model for SiO 2 -Al 2 O 3 -CaO-MgO-FeO-MnO-K 2 O slags, but with good reproducibility of experimental data, and with potential to be expanded to more oxide components (Kotze, 2017). [10] The radiative component of thermal conductivity k rad is calculated with Equation [11] (Mills and Susa, 1992) (Stefan Boltzmann constant s = 5.67x10-8 W/m 2 K 4 ; refractive index of the slag n [dimensionless]; temperature T [K]; absorption coefficient β [cm -1 ] usually denoted as a in the literature but changed here to avoid confusion with the earlier mentioned electronic polarizability). The refractive indexes of the transition metal oxides are generally higher: 2 and more, compared to 1.535 for SiO 2 , 1.805 for CaO, 1.715 for MgO, and 1.79 for Al 2 O 3 . Based on this the radiative component in the TiO 2 slags could be expected to be higher than for silicate slags. However, the absorption coefficient for FeO is two orders of a magnitude higher (Susa, Nagata, and Mills, 1993), and that of Ti 2 O 3 three orders of a magnitude higher (Li, 2016) than those of SiO 2 , CaO, MgO and Al 2 O 3 . Consequently, the radiative component of high-TiO 2 slags is low compared to low FeO silicate slags. [11] The electronic thermal conductivity k e was calculated with the Wiedemann-Franz formula (Ok et al., 2018) (Equation [12], electrical conductivity s [Ω -1 m -1 ]; Lorenz number L = 2.44x10 -8 WΩ/K 2 ; temperature T [K]). Due to the high electrical conductivity of TiO 2 slags, electronic conductivity, which is negligible in silicate slags, can be significant for TiO 2 slags. [12] The etimated lattice, and calculated radiative and electronic conductivities of example slags 1, 3, and 5 (94%, 88%, and 82% TiO 2 eq ) are shown in Figure 14. Total thermal conductivities are shown with the thicker solid lines. The total thermal conductivity for liquid high-TiO 2 slags is estimated to range from 0.4 W/mK to close to 1 W/mK over the liquid temperature range. The thermal conductivity is predicted to increase non-linearily with increasing TiO 2 eq (Figure 15) which is attributed to the increase in electronic conduction with increasing TiO 2 eq .

Summary
Experimentally measured properties of high-TiO 2 slags were investigated and correlated with theoretically based parameters. Based on these correlations, the properties for five typical high-TiO 2 slags were calculated.
➤ The Ti 3+ /Ti 4+ ratio of the liquid slags depends on the oxygen partial pressure and the oxygen activity in the bath. The polarizability ratio between Ca 2+ and Si 4+ cations was found to be a good parameter to quantify the oxygen activity. Future work will endeavor to investigate this concept against more TiO 2 slag data and other slag systems. ➤ Liquidus temperatures increase with decreasing FeO, but can increase or decrease with increasing Ti 2 O 3 depending on the ratio between Ti 3+ and Ti 4+ . Following on from the Ti 3+ /Ti 4+ correlations, liquidus temperatures depend therefore on FeO, oxygen partial pressure, and the CaO and SiO 2 impurities. Other impurities such as MgO, MnO, Al 2 O 3 , Cr 2 O 3 , and V 2 O 5 also affect liquidus values when they stabilize the M 3 O 5 pseudobrookite phase. The partitioning of MnO between the M 3 O 5 and silicate phases needs to be reviewed.
➤ The heat capacity of liquid high-TiO 2 slags cover a narrow range from 1000 to 1020 J/kgK. ➤ Liquid slag densities range from 3.5 to 3.7 g/cm 3 , with the lower range applying at higher temperatures and to higher TiO 2 eq slags. ➤ The electrical conductivities of liquid high-TiO 2 slags are one to two order of magnitudes higher than those of silicate slags and increase with increasing temperature. This is an important point for both AC and DC furnace design. The electrical conductivity of high-gangue TiO 2 slags correlates with the slags' electronic polarizability, while for lowgangue TiO 2 slags (high-TiO 2 eq ), the electrical conductivity was reproduced by using the slags' electronic polarizability and the valency ratio between Fe and Ti cations. ➤ The viscosities of high-TiO 2 slags above liquidus temperatures are very low but increase sharply just below liquidus temperatures. Though the viscosities of fully liquid slags are low, the presence of unreacted reductant in the bath will increase its viscosity. ➤ The thermal conductivities of liquid high-TiO 2 slags were derived from their viscosities and optical properties. For the example slags the thermal conductivities are estimated to range from 0.5 to 1 W/mK. Electronic thermal conduction is dominant and contributes to most to the total thermal conductivity.
Though the intention of this paper is to create a basis for extrapolation to TiO 2 slags not covered in the specific set of experimental work, the correlations derived here are still only applicable to the typical TiO 2 , pseudobrookite M 3 O 5 slags.
Slag properties are evasive: the need to estimate the thermal conductivity of the TiO 2 slags from theoretical considerations is a point in case. It is a complex field but our understanding of slag properties has expanded over the last approximate two decades. It is the author's hope that many a publication on the properties of TiO 2 slags is still to see the light.