Predicting Liquidus Temperature

8.2.1 Comparing Liquidus Calculations and Quenching Experiments

The liquidus temperature indicates the formation of minerals. Below this temperature, the onset of a non-Newtonian flow was verified, chapter 7.5. The liquidus temperature was computed by the Slag Viscosity Predictor (SVP), chapter 3.1. To calculate the thermochemical equilibrium, the software FactSageTM _{was applied. First, SlagA was} selected. Later, SlagH was chosen to cover thermochemical equilibrium calculations with fluorine containing slags. The influence on predicted liquidus temperatures by different databases must be taken into account. Temperature differences were calculated by Eq. (42) where Tliq,SlagH and Tliq,SlagA are the liquidus temperature calculated on SlagH and SlagA, respectively.

∆𝑇 = 𝑇𝑙𝑖𝑞,𝑆𝑙𝑎𝑔𝐻− 𝑇𝑙𝑖𝑞,𝑆𝑙𝑎𝑔𝐴 (42)

As given in Figure 77, liquidus temperatures calculated by SlagA can vary between - 40 and +30 K to SlagH. For oxidizing conditions, the disagreement fluctuates for the B/A<1. For B/A≥1, the disagreement becomes close to 0 K. A trend can be found for reducing atmospheres. The deviation increases by an increasing B/A-ratio. The liquidus temperatures calculated by SlagA were up to 40 K higher than calculated by SlagH at a B/A-ratio of 2.126. The high amount of iron is responsible for the discovered behavior at

8. Advanced Viscosity Modelling Approach 104 elevated B/A-ratios. While predictions at oxidizing conditions show an abundance of Fe3+ in liquid slag, reducing conditions are forming more Fe2+_{. This results in deviations.}

In conclusion, there is no dramatic difference in calculated liquidus temperatures in comparison with the investigated temperature ranges. A deviation of less than 50 K is acceptable at temperatures up to 1700 °C. Furthermore, the opportunity to calculate fluorine containing slags is available with SlagH. Finally, it is more important to compare the predicted liquidus temperatures to experimentally found ones. This is done in the following section.

Figure 77: Differences of liquidus temperatures calculated by SlagH and SlagA solution species.

XRD-analysis on quenched samples were carried out to determine the temperature range of initial crystallization, chapter 7.3. These results were superimposed with liquidus temperatures computed by the Slag Viscosity Prediction Tool (SVP), Figure 78. The experimentally obtained temperature range is pictured by double-T symbols. Some double-T symbols overlapping the maximum or minimum temperature of the plot. This indicates two properties. First, the overlapping of the maximum temperature means an insufficient temperature during sample quenching due to the limited temperature of the quench furnace, ca. 1575 °C. Second, the overlapping of the minimum temperature means no detection of minerals at the lowest quenching temperature. Slag is glassy.

The accordance between calculated and experimentally obtained temperatures fluctuates over the B/A-ratio.

Three groups of liquidus prediction exist:

o _{The first group of liquidus temperatures is predicted within or close to the} measured liquidus temperatures; these are S31, S36, S39, and S42. Samples S4, S13, and S14 contained small mineral contents due to the limitation of attainable maximum quench furnace temperature. The calculated liquidus temperature seems to be valid. If these samples would be completely molten, supercooling would be expected due to the elevated amount of network modifiers. 0.0 0.5 1.0 1.5 2.0 2.5 -50 -40 -30 -20 -10 0 10 20 30 40 S4 S6 S13 S14 S16 S20 S29 S32 S36 S40 S42 S7 S19 S30 S31 S35 S39 S41 oxydizing reducing T Sl agH -S la gA in K B/A on mass

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8. Advanced Viscosity Modelling Approach 106 liquidus temperature calculations are an opportunity to estimate the onset of mineral formation.

Figure 79: Calculated liquidus temperatures of selected slags.

Thermochemical equilibrium calculations cannot represent the influence of cooling rates. To overcome this problem, the temperature difference in Kelvins between predictions and measurements is calculated by Eq. (43) where 𝑇𝑐𝑎𝑙𝑐 and 𝑇𝐷𝑇𝐴 are

calculated liquidus temperature and experimentally obtained onset temperatures, respectively.

∆𝑇 = 𝑇𝑐𝑎𝑙𝑐− 𝑇𝐷𝑇𝐴 (43)

The temperature difference obtained under oxidizing and reducing conditions is given in Figure 80 a) and b), respectively. No DTA signal was obtained for sample S14. Nevertheless, S14 was taken over to Figure 79 for completeness. Due to the lack of any DTA signal, no temperature difference was calculated for S14.

Two parameters are influencing the disagreement between calculations and measurements.

First, temperature differences decrease with an increasing B/A-ratio. This observation is explained by the improved crystallization. As pointed out in chapters 7.3 and 8.2.1, mineral formation was detected on all samples with B/A-ratios above 0.8. Crystallization unsteadily occurred below B/A=0.8, e.g. samples S6 and S7; S30 and S31.

Second, the temperature difference increases with an increasing cooling rate. This effect results in temperature differences up to 775 °C for cooling rates of -60 K/min and B/A-ratios below 0.5. The low B/A-ratio represents elevated amounts of network formers. Supercooling occurs and crystallization is suppressed. In reverse, low cooling rates result in temperatures close to calculated ones. The slag has more time to equilibrate. Crystallization is enhanced, e.g. by increased seed formation or improved material transport to growing minerals.

Almost all slags show a positive temperature difference. This implies the calculated liquidus temperature is above the experimentally obtained one. Only slags S30, S31 and

S6 S7 S13 S14 S16 S19 S20 S29 S30 S31 S32 S35 S36 S39 S40 S41 S42 0.0 0.5 1.0 1.5 2.0 2.5 1100 1200 1300 1400 1500 1600

1700 Calculated liquidus temperatures

B/A on mass

Tl

iq

in

8. Advanced Viscosity Modelling Approach 107 S32 exhibit negative differences. In other words, calculated temperatures are below the measured onset temperatures. A clear explanation cannot be given, but the crystallization mechanism seems to be part of the effect. Slag S30 exhibit no mineral formation for quenching experiments obtained under a cooling rate of -2 K/min. An exothermal event was detected by DTA at equal and lower cooling rates. Sample S31 belongs to the only pair of slags, where liquidus temperature calculation was above the liquidus temperature range estimated by quenching at -2 K/min. Sample S32 has high amounts of minerals in the range of 70 vol.-%, Figure 59.

There are no significant influences of atmospheric conditions. Temperature calculations for oxidizing conditions are slightly closer to measurements than for reducing atmospheres. An extensive investigation could not be carried out, because not all cooling rates could be repeated at reducing conditions.

Figure 80: Temperature differences of calculated liquidus temperatures and onset temperatures obtained by DTA under a) oxidizing and b) reducing conditions.

8.2.3 Summary of Last Chapter

o Three groups of slags were found when the calculated liquidus temperature is compared with temperature ranges obtained by quenching experiments

o The first group is in accordance with calculations and crystallization ranges over wide B/A-ratio range.

o _{The second group overpredicts liquidus temperature. Supercooling due to} elevated contents of network formers seems to be the reason. This effect is mostly observed on B/A< 0.9.

o The third group underestimate the liquidus temperature due to highly improved crystallization. The effect is especially observed on slags with elevated amounts of network modifiers and B/A>1.0.

o Thermochemical equilibrium calculations are not covering cooling rate effects. o Crystallization is supported by elevated B/A-ratios. Consequently, DTA

measurements and thermochemical equilibrium calculations are in agreement.

0.0 0.5 1.0 1.5 2.0 2.5 -200 0 200 400 600 800 S29 S13 S16 S6 S20 S32 S36 _S40 S42 T in K B/A on mass a) 0.0 0.5 1.0 1.5 2.0 2.5 -200 0 200 400 600 800 S30 S7 S19 S31 S35 _S39 S41 T in K B/A on mass b) 0.0 0.5 1.0 1.5 2.0 2.5 -200 0 200 400 600 800

a= -1K/min a= -2 K/min a= -10 K/min a= -20 K/min a= -60 K/min

T in K

B/A on mass

8. Advanced Viscosity Modelling Approach 108 o The atmospheric conditions seem not to significantly influence the obtained

results.