Thermodynamic Activity of SiO₂ in CaO–SiO₂–Al₂O₃–MnO–MgO System Molten Slags

Abstract

To understand the thermodynamic characteristics of the reaction between Al and SiO₂ during the continuous casting process of the high-aluminum steel, the activity coefficients of SiO₂ and MnO in molten slags of (18–43%) CaO-(33–64%) SiO₂-(9–21%) Al₂O₃-(2–3%) MgO-(<2.4%) MnO were measured at 1400°C, 1450°C and 1500°C by the experiments of the Si and Mn equilibrium between liquid copper and molten slag in the graphite crucible under the mixed gas atmosphere of CO and Ar. The effects of SiO₂, Al₂O₃, the basicity, the radio of CaO/Al₂O₃ and the temperature on the activity coefficients of SiO₂ and MnO in molten slag were discussed. The quadratic regression relationships among the activity coefficient of SiO₂ or MnO, the concentration of component, the basicity and the temperature were investigated by the regression analysis method.

1. Introduction

During the production of high-aluminum steel, SiO₂ in the slag will be reduced by the aluminum in the high-aluminum molten steel, which will have an important impact on the quality of the continuous casting slabs and the molten steel. Therefore, no matter the inclusion control and the slagging in the process of the secondary refining, or the control of the composition and performance of the mold flux during the continuous casting process of the high-aluminum steel, the activity coefficient and the activity of SiO₂ in the CaO–SiO₂–Al₂O₃–MnO–MgO slags are required when the thermodynamics of the reaction at the metal-slag interface are analyzed, especially the data at 1400 to 1500°C.

There have been many researches reports on the activity of SiO₂ in the CaO–SiO₂–Al₂O₃ slag system. According to the equilibrium concentration of SiO₂ in the slag and Si in the molten metal obtained from the equilibrium experiment at 1425°C to 1700°C, the activity of SiO₂ in CaO–SiO₂(30–60%)-Al₂O₃(≤20%) slags was calculated by Fulton and Chipman¹⁾ from the known standard free energy data of the reaction and the activity of Si in the metal. Taylor’s research group^2,3) determined the activity of SiO₂ in the CaO-(32–70%) SiO₂-(0–41%) Al₂O₃ slags based on the measured CO partial pressure of the equilibrium of the reduction reaction of SiO₂ to SiC by carbon. The activities of SiO₂ in CaO-(36–60%) Al₂O₃-(<12%) SiO₂ slags and in CaO-(48–54%) Al₂O₃-(4.5–6.5%) SiO₂ slags were measured by Ozturk and Fruehan,⁴⁾ and Park et al.⁵⁾ used the reaction equilibrium of Si between Fe–C–Si alloy and slag in a graphite crucible at 1600°C under the Ar + CO mixed gas or pure CO for 10 to16 hours, respectively. Kang et al.⁶⁾ changed the reference metal to Cu and studied the activity of SiO₂ in CaO-(36–56%) Al₂O₃-(4–11%) SiO₂ and in CaO-(35–52%) Al₂O₃-(3–9%) SiO₂-10%MgO slags through the reaction equilibrium of Si between the liquid copper and the slag at 1600°C. Kume et al.⁷⁾ used the reaction equilibrium of the reduction of SiO₂ by Ca, Al and Mg to study the activity of SiO₂ in CaO-(0.085–0.562) Al₂O₃-(0.071–0.876) SiO₂ (in mole fractions) slags and in CaO-(0.41–0.64)SiO₂-(0.11–0.51) MgO (in mole fractions) slags. So far, a large amount of data on the thermodynamic properties of SiO₂ in the CaO–Al₂O₃–SiO₂ slags involved in the various processes of the ferrous metallurgy have been accumulated.^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)} In these studies, the temperature was mainly 1550–1600°C,^{1,2,3,4,5,6,7,8,9,11,13,14,15)} but a small number of studies involved the temperatures of 1400–1500°C.^1,10) But the results of the activity of SiO₂ obtained differed as much as two or three orders of magnitude. According to the phase diagram of CaO–SiO₂,¹⁷⁾ there will be the decomposition of 3CaO·2SiO₂ (C₃S₂) (1464°C), the eutectic reaction between CaO·SiO₂ (CS) and 2CaO·SiO₂ (C₂S) (1460°C), and the eutectic reaction between CaO·SiO₂ (CS) and SiO₂ (1436°C) in the range of the temperature of 1400–1500°C when the SiO₂ concentration is 35–80% (%CaO/%SiO₂ = 0.25–2.3). The temperature of 1400–1500°C closes to the melting point of CaO·SiO₂ (CS) (1544°C). What effects will these characteristics have on the thermodynamic properties of SiO₂?

This research is aimed at CaO–SiO₂–Al₂O₃ slags with MgO and MnO of continuous casting mold flux. The activity coefficients of SiO₂ and MnO in molten slag of CaO-SiO₂-Al₂O₃-(<2.4%) MnO-(2–3%) MgO were measured through the reaction equilibrium of Si and Mn between the metal Cu and the slag in the graphite crucible for 30 hours under Ar + CO mixed gas atmosphere at the temperature of 1400°C, 1450°C and 1500°C, respectively. The effects of the components, the basicity and the temperature on the activity coefficients and the activities of SiO₂ and MnO in the slags were investigated. The relationships among the activity coefficient of SiO₂ or MnO, the concentrations of components in the slag, the basicity and the temperature were also studied by the regression analysis method.

2. Experimental

The experimental device and the experimental process used in this research have been reported in detail in the determination of MnO and FeO activity.^18,19) But in order to measure the temperature of the melt in the crucible more accurately, the thermocouple was moved from the bottom of the crucible into the corundum crucible. The number of reaction crucibles in the corundum crucible was increased to six. The blowing flow rate was increased to ensure that the atmosphere above the melt met the experimental requirements.

99.9% copper powder was used as the reference metal in the experiment, and the slag was prepared by the combination of chemical reagents with purity 98% CaO, AR grade SiO₂ and Al₂O₃, 98.5% MgO and 99.5% MnO. The ingredients of the mixed slag are shown in Table 1. The reaction crucible was a graphite crucible with a size of 36 mm inner diameter, 40 mm outer diameter, and 57.5 mm high. During the experiment, six graphite crucibles containing 15 g of copper powder and 25 g of premixed slag material were placed in a corundum crucible. The temperature in the corundum crucible was raised to the preset temperature (1400°C, 1450°C and 1500°C, respectively) under the protection of Ar gas with a flow of 1200 mL·min⁻¹ and a purity of 99.999%. After this status had been stood for 15 min to homogenize the composition and temperature, the Ar gas flow rate was adjusted to 500 mL·min⁻¹, and a 99.995% purity CO gas with the flow rate of 200 mL·min⁻¹ was passed into the corundum crucible above the six graphite crucibles (the partial pressure of CO gas P_CO is 0.286 atm). And then timing started after standing for another 30 minutes. After the counted time had reached 30 h, six crucibles were all taken out from the furnace one by one and were cooled down in an Ar gas stream. A XRF method was used to determine the content of each component in the slag sample. Metal Cu samples were analyzed for the content of Si and Mn by ICP-AES method.

Table 1. Charge compositions, mass%.

No.	Temperature/°C	Al2O3	SiO2	CaO	MnO	MgO
1	1400	11.40	61.75	21.85	3.00	2.00
2	1400	9.50	39.90	45.60	3.00	2.00
3	1400	12.35	39.90	42.75	3.00	2.00
4	1400	13.30	62.70	19.00	3.00	2.00
5	1400	14.25	54.15	26.60	3.00	2.00
6	1400	16.15	39.90	38.95	3.00	2.00
7	1400	19.95	45.60	29.45	3.00	2.00
8	1400	17.10	46.55	31.35	3.00	2.00
9	1400	20.00	35.71	39.29	3.00	2.00
10	1400	20.00	41.67	33.33	3.00	2.00
11	1400	20.00	46.88	28.13	3.00	2.00
12	1400	20.00	37.50	37.50	3.00	2.00
13	1400	20.00	42.86	32.14	3.00	2.00
14	1400	20.00	39.47	35.53	3.00	2.00
15	1400	20.00	44.12	30.88	3.00	2.00
16	1400	20.00	45.45	29.55	3.00	2.00
17	1400	20.00	40.54	34.46	3.00	2.00
18	1400	20.00	50.00	25.00	3.00	2.00
19	1450	19.00	39.90	36.10	3.00	2.00
20	1450	18.05	43.70	33.25	3.00	2.00
21	1450	17.10	46.55	31.35	3.00	2.00
22	1450	13.30	62.70	19.00	3.00	2.00
23	1450	17.10	54.15	23.75	3.00	2.00
24	1450	20.00	39.47	35.53	3.00	2.00
25	1450	20.00	37.50	37.50	3.00	2.00
26	1500	17.10	46.55	31.35	3.00	2.00
27	1500	14.25	54.15	26.60	3.00	2.00
28	1500	11.40	61.75	21.85	3.00	2.00
29	1500	13.30	62.70	19.00	3.00	2.00
30	1500	17.10	54.15	23.75	3.00	2.00
31	1500	19.95	45.60	29.45	3.00	2.00
32	1500	20.00	40.54	34.46	3.00	2.00
33	1500	20.00	39.47	35.53	3.00	2.00
34	1500	20.00	37.50	37.50	3.00	2.00
35	1500	20.00	35.71	39.29	3.00	2.00
36	1500	20.00	34.09	40.91	3.00	2.00
37	1500	20.00	32.61	42.39	3.00	2.00

The equilibrium time of reaction of Si and Mn in the system has been found to be 22 hours through the preliminary experiments, so the equilibrium time in the experiments was taken as 30 hours.

3. Experimental Results

The following reaction equilibrium was determined under the experimental conditions.   

$$\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_2\right)+2\mathrm{C}\left(\mathrm{s}\right)={\left[\mathrm{S}\mathrm{i}\right]}_{\mathrm{i}\mathrm{n}\mathrm{C}\mathrm{u}}+2\mathrm{C}\mathrm{O}\left(\mathrm{g}\right)$$(1)

  

$$K_1=\frac{a_{\text{Si}}{p}_{\text{CO}}^2}{a_{\text{C}}^2{a}_{{\text{SiO}}_{\text{2}}}}=\frac{{\gamma }_{\text{Si}}^{}{x}_{\text{Si}}{p}_{\text{CO}}^2}{{\gamma }_{{\text{SiO}}_{\text{2}}}{x}_{{\text{SiO}}_{\text{2}}}}$$(2)

Where γ_Si and a_Si are the Raoultian activity coefficient and activity of Si in the liquid copper in reference to the pure liquid silicon, respectively; γ_SiO2 and a_SiO2 are the Raoultian activity coefficient and activity of SiO₂ in the molten slag in reference to pure solid silica, respectively; x_Si and x_SiO2 are the mole fractions of Si in the liquid copper and SiO₂ in the molten slag, respectively; a_C is the activity of carbon, and a_C = 1 in the case of using a graphite crucible; p_CO is the partial pressure of CO; K is the equilibrium constant of the reaction (1), which can be calculated from the standard free energy change of the reaction (3) under the selected standard state of activity.   

$$\begin{array}{l}\mathrm{S}\mathrm{i}{\mathrm{O}}_2\left(\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{z}\right)+2\mathrm{C}\left(\mathrm{s}\right)=\mathrm{S}\mathrm{i}\left(\mathrm{l}\right)\mathrm{\hspace{0.17em} }\hspace{0.17em}+2\mathrm{C}\mathrm{O}\left(\mathrm{g}\right)\\ \mathrm{\Delta }G°=728\mathrm{\hspace{0.17em} }853-377.27T\left(\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l}\right)\end{array}$$(3) ²⁰⁾

The Raoultian activity coefficient of Si in the liquid copper is equal to that of an infinite dilute solution of Si in the liquid copper, γ_Si = ${\gamma }_{\mathrm{S}\mathrm{i}(\mathrm{l})\mathrm{\hspace{0.17em} }\mathrm{i}\mathrm{n}\mathrm{\hspace{0.17em} }\mathrm{C}\mathrm{u}}^{\circ }$ at the very low concentration of Si.   

$$ln{\gamma }_{\mathrm{S}\mathrm{i}(\mathrm{l})\mathrm{\hspace{0.17em} }\mathrm{i}\mathrm{n}\mathrm{\hspace{0.17em} }\mathrm{C}\mathrm{u}}^{\circ }=-\frac{7\mathrm{\hspace{0.17em} }549}{T}+0.0143\hspace{0.17em}$$(4) ²¹⁾

Then the activity coefficient of SiO₂ in the slag can be derived from Eq. (2) as follows:   

$${\gamma }_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2(\mathrm{s})}=\frac{p_{\mathrm{C}\mathrm{O}}^2}{K_3}\cdot {\frac{{\gamma }_{\mathrm{S}\mathrm{i}}^{\circ }{x}_{\mathrm{S}\mathrm{i}}}{x_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}}|}_{x_{\mathrm{S}\mathrm{i}}\to 0}$$(5)

Similarly, there is the reaction equilibrium for MnO as follows:   

$$\begin{array}{l}\mathrm{M}\mathrm{n}\mathrm{O}\left(\mathrm{s}\right)+\mathrm{C}\left(\mathrm{s}\right)=\mathrm{M}\mathrm{n}\left(\mathrm{l}\right)+\mathrm{C}\mathrm{O}\mathrm{\hspace{0.17em} }\left(\mathrm{g}\right)\\ \mathrm{\Delta }G°=286\mathrm{\hspace{0.17em} }604-170T\left(\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l}\right)\end{array}$$(6) ²⁰⁾

The activity coefficient of MnO in molten slag can be obtained by Eq. (7).¹⁸⁾   

$${\gamma }_{\mathrm{M}\mathrm{n}\mathrm{O}(\mathrm{s})}=\frac{p_{\mathrm{C}\mathrm{O}}^{}}{K_6}\cdot {\frac{{\gamma }_{\mathrm{M}\mathrm{n}}^{\circ }{x}_{\mathrm{M}\mathrm{n}}}{x_{\mathrm{M}\mathrm{n}\mathrm{O}}}|}_{x_{\mathrm{M}\mathrm{n}}\to 0}$$(7)

Where γ_MnO is the Raoultian activity coefficient of MnO in the molten slag in reference to pure solid manganese oxide, ${\gamma }_{\mathrm{M}\mathrm{n}}^{\circ }$ is the Raoultian activity coefficient of Mn in an infinite dilute solution of Mn in the liquid copper in reference to the pure liquid manganese.   

$$ln{\gamma }_{\mathrm{M}\mathrm{n}(\mathrm{l})\mathrm{\hspace{0.17em} }\mathrm{i}\mathrm{n}\mathrm{\hspace{0.17em} }\mathrm{C}\mathrm{u}}^{\circ }=-\frac{981}{T}+0.0159\hspace{0.17em}$$(8) ²¹⁾

The activity coefficients and the activities of SiO₂ and MnO in the experimental slags are shown in Table 2, respectively.

Table 2. Equilibrium concentrations in metal and slag, and the activity coefficient and the activity of SiO₂ and MnO.

No.	Temperature /°C	Metal (mass%)		Molten slag (mass%)					Activity coefficient		Activity (×10−3)
		Si	Mn	Al2O3	SiO2	CaO	MgO	MnO	γSiO2(s) (×10−3)	γMnO(s)	aSiO2	aMnO
1	1400	0.20	0.73	9.50	51.82	34.50	2.00	1.74	8.686	0.105	4.554	1.569
2	1400	0.022	1.21	9.78	40.60	45.41	2.54	1.37	1.243	0.226	0.505	2.621
3	1400	0.066	1.32	12.76	41.06	42.16	2.51	1.17	3.635	0.284	1.515	2.861
4	1400	0.10	0.48	12.97	63.35	18.59	2.11	2.39	3.519	0.050	2.320	1.051
5	1400	0.11	0.58	14.28	54.25	26.40	2.29	2.30	4.489	0.062	2.528	1.258
6	1400	0.032	1.11	16.34	40.70	38.57	2.43	1.56	1.740	0.175	0.733	2.400
7	1400	0.13	0.64	16.81	54.74	23.39	2.30	2.20	5.209	0.071	3.002	1.395
8	1400	0.14	0.96	17.40	46.74	31.46	2.36	1.79	6.571	0.131	3.208	2.076
9	1400	0.017	1.08	19.75	36.53	39.27	2.45	1.63	0.053	0.162	0.020	2.348
10	1400	0.069	1.06	19.71	42.53	33.34	2.36	1.60	0.184	0.161	0.083	2.301
11	1400	0.048	0.65	19.72	47.15	28.19	2.24	2.20	0.115	0.072	0.058	1.417
12	1400	0.027	1.18	19.91	38.34	37.48	2.40	1.46	0.080	0.196	0.032	2.550
13	1400	0.045	0.88	19.83	43.77	31.77	2.30	1.89	0.117	0.113	0.054	1.917
14	1400	0.089	1.29	19.95	40.23	35.62	2.49	1.30	0.250	0.240	0.106	2.787
15	1400	0.036	0.71	19.85	44.69	30.59	2.29	2.06	0.092	0.084	0.043	1.553
16	1400	0.092	0.89	19.92	46.21	29.21	2.33	1.87	0.224	0.115	0.110	1.928
17	1400	0.081	1.16	20.15	41.22	34.31	2.43	1.46	0.222	0.192	0.097	2.512
18	1400	0.13	0.74	19.99	50.55	24.71	2.19	2.05	0.290	0.087	0.156	1.612
19	1450	1.70	1.59	20.28	39.47	37.00	2.49	0.34	22.958	0.624	9.532	1.889
20	1450	0.52	1.42	19.29	41.99	34.90	2.44	0.86	6.776	0.226	2.991	1.731
21	1450	0.92	1.26	17.60	47.10	31.59	2.33	0.97	10.564	0.176	5.204	1.510
22	1450	0.68	0.70	13.32	63.04	19.10	2.23	1.69	5.950	0.057	3.902	0.851
23	1450	0.85	1.00	17.66	54.56	23.33	2.29	1.56	8.337	0.086	4.803	1.197
24	1450	0.43	1.46	20.05	41.14	35.34	2.39	0.82	5.688	0.242	2.461	1.771
25	1450	1.60	1.60	20.65	37.60	38.66	2.48	0.25	22.453	0.845	8.877	1.881
26	1500	0.28	1.02	17.13	47.38	30.98	2.43	1.62	0.860	0.049	0.426	0.705
27	1500	0.66	0.96	14.46	54.44	26.62	2.27	1.75	1.786	0.043	1.009	0.667
28	1500	1.40	1.21	10.11	50.77	35.29	2.11	1.12	4.091	0.086	2.106	0.827
29	1500	0.52	0.74	13.02	63.03	18.72	2.32	2.02	1.233	0.029	0.810	0.524
30	1500	0.50	0.88	17.26	54.63	23.47	2.27	1.85	1.333	0.037	0.767	0.614
31	1500	0.23	0.99	20.01	46.41	29.28	2.24	1.64	0.722	0.047	0.355	0.695
32	1500	0.36	1.39	20.28	41.34	34.59	2.41	0.98	1.263	0.110	0.551	0.967
33	1500	0.59	1.60	20.30	40.29	36.01	2.45	0.59	2.123	0.211	0.901	1.110
34	1500	0.39	1.55	20.15	38.66	37.85	2.39	0.60	1.479	0.203	0.601	1.086
35	1500	0.28	1.63	20.18	36.97	39.57	2.42	0.49	1.111	0.262	0.431	1.141
36	1500	0.31	1.72	20.21	34.88	41.78	2.48	0.40	1.305	0.339	0.476	1.201
37	1500	0.23	1.74	20.26	33.40	43.18	2.43	0.35	1.014	0.393	0.354	1.219

4. Discussions

4.1. About the Structure of the Molten Slag

It can be known from textbooks that when the temperature is not too high from the melting point, the pressure is not too low, and the gasification temperature is much higher than the research temperature, the short-range order theory of silicate melt believes that the melt structure is close-range order. The arrangement and spacing of neighbors are similar to those in solid crystals. When the crystal is heated to the melting point and melted into a melt, there are still a certain number of relatively regularly arranged particles around the particles. Only when it is far away from the center particles, the regular arrangement is gradually disappeared. The structural feature of the melt is short-range order and long-range disorder.

According to the polymer structure theory of silicate melts, the high temperature still does not completely destroy the covalent bonds in the original solid state when a considerable number of strong covalent bonds are in the structure. The remaining covalent bonds combine the melt component atoms into a large number of “polymers” with different polymerization degrees, which are highly dispersed and coexist with each other. There are $\mathrm{S}\mathrm{i}{\mathrm{O}}_4^{4-}$ (monomers), $\mathrm{S}{\mathrm{i}}_2{\mathrm{O}}_7^{6-}$ (dimers), $\mathrm{S}{\mathrm{i}}_3{\mathrm{O}}_{10}^{8-}$ (trimers), $\mathrm{S}{\mathrm{i}}_n{\mathrm{O}}_{3n+1}^{2n+2-}$ (n-mers) and three-dimensional fragments [SiO₂]_n and other anions, and the free metal cations in the silicate melt. The type and quantity of polymers in the silicate melt are mainly related to the composition and temperature of the melt.

Based on the above two theories, it is believed that even if the compound molecules in the molten slag do not exist in the solid state, they will exist in the molten slag in the form of “clusters” related to the compound in the solid state. The types of compounds that may exist in the molten slag can obviously be obtained from the phase diagrams of the relevant slag series. The components that do not generate complex compounds with other oxides are called free components, such as free CaO. Obviously, when a component in the slag exists in a free form, the activity of the free component must be higher than that of the component in the form of a certain complex compound type “cluster”. The higher the stability of the complex compound, the lower the activity of the oxide component in this compound type “cluster”. However, according to polymer structure theory of silicate melts, free CaO can be ionized into Ca²⁺ and O²⁻ ions, so as to exist in the molten slag in the form of ions.

The following will explain the experimental results based on the above viewpoint.

4.2. Effects of SiO₂

Figures 1 and 2 show the effects of SiO₂ in the slag on the activity coefficients of SiO₂ and MnO at 1400°C and 1500°C, respectively. The reported results^{4,5,6,18,22,23,25,26)} are also illustrated in the figures for comparison. It can be seen from Fig. 1 that when SiO₂<52%, the activity coefficient of SiO₂ in the slag at 1500°C is higher than the value of 1400°C. At 1400°C and when SiO₂<52%, the activity coefficient of SiO₂ increase with the increase of SiO₂. At 1400°C and when SiO₂>54%, the activity coefficient of SiO₂ decreases with the increase of SiO₂ and its value is far higher than the value when SiO₂<52%. The transition point of concentration of the changes for the activity coefficient of SiO₂ is about 52–54% SiO₂ at 1400°C. At 1400°C and when SiO₂>54%, the activity coefficient of SiO₂ is also higher than the value at 1500°C. The activity coefficient of SiO₂ increases with the increase of SiO₂ at 1500°C. It can be seen that the interaction between temperature and basicity has an effect on the activity coefficient of SiO₂.

Fig. 1.

The effect of SiO₂ on the activity coefficient of SiO₂ at 1400°C and 1500°C.

Fig. 2.

The effect of SiO₂ on the activity coefficient of MnO at 1400°C and 1500°C.

The composition points of the equilibrium slag with CaO/SiO₂<0.65 at 1500°C in Fig. 1 (the points with “▲” in Fig. 1) are located in the CaO·SiO₂ (CS) + SiO₂ phase zone in the CaO–SiO₂ binary phase diagram and in the concentration triangle of the CS–SiO₂–CaO·Al₂O₃·2SiO₂ (CAS₂) in the CaO–SiO₂–Al₂O₃ ternary phase diagram.¹⁷⁾ The experimental temperature (1500°C) is near the melting temperature of CS (1544°C) and the decomposition temperature of C₃S₂ (1475°C). The change of the activity coefficient and the activity of SiO₂ in the slag should be related to these factors. With the increase of SiO₂, the molar ratio of CaO:SiO₂:Al₂O₃ in the slag change from 1:1.48:0.52 to 1:3.14:0.33, as shown in Table 3. The formation of CAS₂ type clusters in every 100 grams of molten slag consumes 0.26 to 0.39 mol of SiO₂ calculated based on the Al₂O₃ content in the molten slag. The generation of CS type clusters in every 100 grams of molten slag will consume 0.33 to 0.55 mol of SiO₂ calculated based on the CaO content in the molten slag. Because the concentrations of MnO and MgO in the molten slag are very low and are basically the same, and the composition points fall in the concentration triangle of the CS–SiO₂–CAS2 in the CaO–SiO₂–Al₂O₃ ternary phase diagram, the consumption of SiO₂ combined with MnO and MgO is temporarily ignored. Since CaO may exists in complex compounds such as CS and CAS2 at the same time, the CaO consumed to generate CAS2 can no longer exist in CS. Therefore, the number of moles of SiO₂ in molten slag is first subtracted the SiO₂ consumed to generate CAS2. Then the SiO₂ consumed to generated CS (formed by the remaining CaO combining with SiO₂) is subtracted. If C2AS or C3S2 is also generated, it continues to subtract the SiO₂ consumed to generate C2AS or C3S2. The number of moles of the SiO₂ that remains in the molten slag is finally gotten. It is represented by “n_SiO2 remained” and is listed in the last column of Table 3. SiO₂ remained in the molten slag increase from 0.05 to 0.59 mol with the increase of SiO₂. Therefore, the activity coefficient of SiO₂ in the molten slag increases with the increase of SiO₂, just like the results of many researchers.^{1,2,3,5,9,11)}

Table 3. The phase zone in the CaO–SiO₂–Al₂O₃ phase diagram where the experimental point in Fig. 1 is located, the n_i/n_CaO ratio and the n_SiO2 consumed by the formation of complex compounds.

No.	Temp./°C	symbol	Concentration triangle	nAl2O3/nCaO	nSiO2/nCaO	nSiO2 for CS	nSiO2 for CAS2	nSiO2 remained
5	1400	■	CS-SiO2-CAS2	0.30	1.92	0.47	0.28	0.29
7	1400	■	CS-SiO2-CAS2	0.40	2.18	0.42	0.33	0.33
4	1400	■	CS-SiO2-CAS2	0.38	3.18	0.33	0.25	0.60
9	1400	●	CS-CAS2-C2AS	0.28	0.87	0.70	0.39	−0.29
12	1400	●	CS-CAS2-C2AS	0.29	0.95	0.67	0.39	−0.23
14	1400	●	CS-CAS2-C2AS	0.31	1.05	0.64	0.39	−0.16
17	1400	●	CS-CAS2-C2AS	0.32	1.12	0.61	0.40	−0.12
10	1400	●	CS-CAS2-C2AS	0.33	1.19	0.59	0.39	−0.08
13	1400	●	CS-CAS2-C2AS	0.34	1.29	0.57	0.39	−0.03
15	1400	●	CS-SiO2-CAS2	0.36	1.36	0.55	0.39	0.00
16	1400	●	CS-SiO2-CAS2	0.38	1.48	0.52	0.39	0.05
11	1400	●	CS-SiO2-CAS2	0.38	1.56	0.50	0.39	0.09
18	1400	●	CS-SiO2-CAS2	0.44	1.91	0.44	0.39	0.20
31	1500	▲	CS-SiO2-CAS2	0.38	1.48	0.52	0.39	0.05
26	1500	▲	CS-SiO2-CAS2	0.30	1.43	0.55	0.34	0.07
27	1500	▲	CS-SiO2-CAS2	0.30	1.91	0.47	0.28	0.29
30	1500	▲	CS-SiO2-CAS2	0.40	2.17	0.42	0.34	0.32
29	1500	▲	CS-SiO2-CAS2	0.38	3.14	0.33	0.26	0.59
37	1500	▼	C3S2-CS-C2AS	0.26	0.72	0.77	0.40	−0.41
36	1500	▼	CS-CAS2-C2AS	0.27	0.78	0.75	0.40	−0.36
35	1500	▼	CS-CAS2-C2AS	0.28	0.87	0.71	0.40	−0.29
34	1500	▼	CS-CAS2-C2AS	0.29	0.95	0.67	0.40	−0.23
33	1500	▼	CS-CAS2-C2AS	0.31	1.04	0.64	0.40	−0.17
32	1500	▼	CS-CAS2-C2AS	0.32	1.12	0.62	0.40	−0.13

Note: “n_SiO2 for CS “ refers to the number of moles of SiO₂ consumed when CaO·SiO₂ is produced, and is calculated based on the number of moles of CaO; “n_SiO2 for CAS2” refers to the number of moles of SiO₂ consumed when CaO·Al₂O₃·SiO₂ is produced, and is calculated based on the twice the number of moles of Al₂O₃ because the number of moles of Al₂O₃ is lower than that of CaO. “n_SiO2 Remained” refers to the number of moles of SiO₂ remained SiO₂ without combination with other oxides, which is calculated by the n_SiO2 in slag subtracting the SiO₂ consumed to generate CS and CAS2, without repeating the calculation of the amount of CaO in these two compounds.

When CaO/SiO₂>0.84 at 1500°C (the points with “▼” in Fig. 1), except for one slag sample falling on the concentration triangle of the C3S2-CS-C2AS, the other composition points all fall within the concentration triangle of the CS-CAS2-C2AS. At this time, SiO₂ in the slag may form CS (CaO·SiO₂) type, CAS2 (CaO·Al₂O₃·2SiO₂) type and/or C2AS (2CaO·Al₂O₃·SiO₂) type, and/or C3S2 (3CaO·2SiO₂) type clusters with other oxides. There is no the SiO₂ which formed the compound with other oxides. However, it can be seen from Table 3 that the negative value of the “n_SiO2 remained” gradually decreases with the increase of SiO₂. So, the activity coefficient of SiO₂ increases.

The composition points of the equilibrium slag with CaO/SiO₂<0.49 at 1400°C in Fig. 1 (the point with “■”) are located in the CaO·SiO₂ (CS) + SiO₂ phase zone in the CaO–SiO₂ binary phase diagram and in the concentration triangle of the CS–SiO₂–CAS₂ in the CaO–SiO₂–Al₂O₃ ternary phase diagram.¹⁷⁾ The experimental temperature (1400°C) is slightly lower than the eutectic temperature (1436°C) of this two-phase zone. As shown in Table 3, with the increase of SiO₂ concentration, SiO₂ remained in the molten slag in every 100 grams of molten slag increases from 0.29 to 0.60 mol. Therefore, the activity coefficient of SiO₂ in the slag should increase with the increase of SiO₂ concentration, just like the results when CaO/SiO₂<0.65 at 1500°C and the results of many researchers.^{1,2,3,5,9,11)} The result that the SiO₂ activity coefficient decreases with the increase of SiO₂ concentration when CaO/SiO₂<0.49 at 1400°C in Fig. 1, whether can be explained as: with the increase of SiO₂, the SiO₂ that is not formed the complex compounds will continue to generate some silicon-oxygen anions with more complex structure, so the activity coefficient of SiO₂ decreases. At 1500°C and %CaO/%SiO₂<0.65, the high temperature causes the silicon-oxygen anions with a complex structure to disintegrate, and the structure of silicon-oxygen anions is simplified. Therefore, the SiO₂ activity coefficient increases with the increase of SiO₂ concentration.

When CaO/SiO₂>0.49 and the temperature is 1400°C, the composition points all fall within the CS-CAS2-C2AS concentration triangle (the point with “●” in Fig. 1). It can be seen from Table 3 that the “n_SiO2 remained” keeps increasing as the increases of SiO₂, but the concentration of the remaining SiO₂ in the slag is not high enough. The generated Si–O anions are not much enough to form complex ion clusters with a very complex structure. So, the SiO₂ activity coefficient increases with the increase of the SiO₂ concentration. At 1400°C, the transition point of concentration of the changes for the activity coefficient of SiO₂ is about 52–54% SiO₂. The maximum n_SiO2 remained for this concentration is 0.29, and the molar ratio of n_SiO2:n_CaO is 1.92 at mass%Al₂O₃ = 20. It is speculated that at this concentration ratio at 1400°C, the structure of SiO₂ in the molten slag will have a relatively large change.

The MnO combines with SiO₂ to form not only MnO·SiO₂ type clusters easily, but also more stable CaO·MnO·2SiO₂ type clusters. The activity coefficient of MnO in the slag reduces with the increase of SiO₂, as shown in Fig. 2. But when CaO/SiO₂ = 0.98–1.27 at 1400°C, SiO₂ forms CS type clusters with CaO, and even CAS₂ type clusters with CaO and Al₂O₃. The number of SiO₂ which used to form MnO–SiO₂ type clusters with MnO is relatively reduced. So, the activity coefficient of MnO increases as SiO₂ increases. This is different from the change of the activity coefficient of MnO when CaO/SiO₂ = 0.84–1.29 at 1500°C. Because the high temperature of 1500°C makes CAS₂ clusters unstable and even it is difficult for the CAS₂ clusters to be formed. SiO₂ is more inclined to form MnO–SiO₂ clusters with MnO. Hence, the activity coefficient of MnO decreases still with the increase of SiO₂.

4.3. Effects of Al₂O₃

When SiO₂ = 33.27–54.74% and basicity CaO/SiO₂ = 0.42–1.27, the activity coefficient of SiO₂ in the slag decreases with the increase of Al₂O₃ at 1400°C and 1500°C, as shown in Fig. 3. Because the Al₂O₃ concentration in the equilibrium slag in Fig. 3 is lower than that of the molar ratio of Al₂O₃ to SiO₂ in CaO·Al₂O₃·2SiO₂ (CAS₂) and in 2CaO·Al₂O₃·SiO₂(C₂AS), the SiO₂ is continuously consumed to form the stable CAS₂ and C₂AS type clusters as Al₂O₃ increases. Hence, the activity coefficient of SiO₂ decreases with the increase of Al₂O₃. When the basicity and the SiO₂ are the same, the activity coefficient of SiO₂ at 1400°C is slightly higher than the value at 1500°C (the points with “■●” in Fig. 3 is higher than the point with “◆”). It can also be seen that the interaction between temperature and basicity has an effect on the activity coefficient of SiO₂.

Fig. 3.

The effect of Al₂O₃ on the activity coefficient of SiO₂ at 1400°C and 1500°C.

The activity coefficients of MnO at 1400°C and 1500°C decrease both slightly with the increase of Al₂O₃, as shown in Fig. 4. Al₂O₃ is easy to form MnO·Al₂O₃ type clusters with MnO as Al₂O₃ increases, and even forms 2MnO·Al₂O₃·5SiO₂ type clusters with MnO and SiO₂ easily. Therefore, the activity coefficient of MnO at 1500°C decreases slightly with the increase of Al₂O₃. At 1400°C, the effect of Al₂O₃ on the activity coefficient of MnO is related to the basicity and SiO₂ content. Hence, the interaction of Al₂O₃ with basicity and SiO₂ complicates the change of the activity coefficient of MnO.

Fig. 4.

The effect of Al₂O₃ on the activity coefficient of MnO at 1400°C and 1500°C.

4.4. Effects of Basicity

The activity coefficient of SiO₂ in the slag decreases with the increase of basicity (R = %CaO/%SiO₂) at 1400°C and 1500°C, as shown in Fig. 5. As the basicity increases, SiO₂ in the molten slag forms CaO·SiO₂ (CS) type clusters with CaO, even CAS₂ type clusters with CaO and Al₂O₃. So, the activity coefficient and the activity of SiO₂ in the slag decreases, as shown in Fig. 5.

Fig. 5.

The effect of the basicity on the activity coefficient of SiO₂ at 1400°C and 1500°C.

The activity coefficient of MnO in the slag increases with the increase of basicity at 1500°C, as shown in Fig. 6, but there is a transition point around the basicity of 0.6 to 0.7. When the basicity is greater than 0.7, the slope of the change in the activity coefficient of MnO increases. At 1400°C, the increasing of the activity coefficient of MnO with the increase of the basicity is the overall trend. However, when Al₂O₃ = 19.69–20.15% and SiO₂ = 33.27–50.55%, the change of activity coefficient of MnO has a maximum point when the basicity is around 0.9–1.0.

Fig. 6.

The effect of the basicity on the activity coefficient of MnO at 1400°C and 1500°C.

At 1500°C, as the basicity increases, SiO₂ forms CS type clusters with CaO, and even forms CAS₂ and C₂AS type clusters with CaO and Al₂O₃. The MnO, which is used to form MnO·SiO₂ (MS) type clusters with SiO₂, is decrease. So, the activity coefficient of MnO in the slag increases. In addition, from the viewpoint of ionic of the molten slag structure, as the basicity increases, the O²⁻ concentration in the molten slag increases, which also increases the activity coefficient of MnO in the slag. It can be seen from Fig. 6 that when the basicity is higher than the transition point of 0.7, the SiO₂ in the equilibrium slags in the experiments is lower, but the Al₂O₃ is higher. After SiO₂ has formed CS, CAS₂ and C₂AS type clusters, there is less SiO₂ and more MnO in the slag, so the activity coefficient of MnO increases faster with the increase of the basicity.

4.5. Effects of the Ratio of CaO/Al₂O₃

At 1400°C, the activity coefficient of SiO₂ decreases with the increase of the ratio of CaO/Al₂O₃, as shown in Fig. 7. At 1500°C, when the basicity CaO/SiO₂ = 0.29–0.67, the activity coefficient of SiO₂ increases with the increase of the CaO/Al₂O₃ ratio. At 1500°C, when the basicity CaO/SiO₂ = 0.67–1.29, the activity coefficient of SiO₂ decreases with the increase of the CaO/Al₂O₃ ratio.

Fig. 7.

The effect of the ratio of CaO/Al₂O₃ on the activity coefficient of SiO₂.

At high basicity, it can be seen from Fig. 7 that Al₂O₃ in the slag is almost unchanged. As the ratio of CaO/Al₂O₃ increases, CaO increases. Then SiO₂ forms CS-type clusters with CaO, even CAS₂ and C₂AS-type clusters. Therefore, the activity coefficient of SiO₂ decreases with the increase of the ratio of CaO/Al₂O₃. When the basicity is low, the strong acid slag has high SiO₂. Although SiO₂ forms Al₂O₃·SiO₂ type clusters with Al₂O₃, even CAS₂ type or C₂AS type clusters, the number of the clusters containing Al₂O₃ decreases with the increase of CaO/Al₂O₃. The activity coefficient of SiO₂ increases with the increase of the CaO/Al₂O₃ ratio.

As the ratio of CaO/Al₂O₃ increases, SiO₂ forms CS type clusters with CaO, and even forms CAS₂ type or C₂AS type clusters, and then the number of MnO-SiO₂ type clusters which has been formed decreases. Hence, the activity coefficient and the activity of MnO increase, as shown in Fig. 8. In addition, the O^2– concentration in the slag increases with the increase of CaO/Al₂O₃ ratio, which also increases the activity coefficient and the activity of MnO. Corresponding to the change of the activity coefficient of SiO₂, at low basicity (%CaO/%SiO₂ = 0.29–0.67) at 1500°C, it can be seen from Fig. 8 that at this time Al₂O₃ is lower and SiO₂ is higher. As the ratio of CaO/Al₂O₃ increases, the Al₂O₃ decreases, and the number of the more stable clusters of Al₂O₃-containing type decreases. And then the SiO₂ combined with MnO increases, so the activity coefficient and the activity of MnO increase little. When the basicity is high (%CaO/%SiO₂ = 0.67–1.29), Al₂O₃ is higher and SiO₂ is lower. As the ratio of CaO/Al₂O₃ increases, SiO₂ forms CS, CAS₂ and C₂AS type clusters with CaO, and the rest SiO₂ is combined with MnO. The remained number of SiO₂ which is used to form the clusters with MnO is small, so the slope of the increase of the activity coefficient and the activity of MnO is relatively large.

Fig. 8.

The effect of the ratio of CaO/Al₂O₃ on the activity coefficient of MnO.

4.6. Effects of the Temperature

The effects of temperature on the activity coefficient of SiO₂ are related to the basicity (R = %CaO/%SiO₂) of the slag, as shown in Fig. 9. When the basicity is lower (R≤0.67, acidic slag), the activity coefficient of SiO₂ is lower at 1500°C than at 1400°C. When the basicity is higher (R>0.8), the activity coefficient of SiO₂ is higher at 1500°C than at 1400°C.

Fig. 9.

The effect of temperature on the activity coefficient of SiO₂ in the slag.

It can be seen from the Fig. 9 that the activity coefficient of SiO₂ is higher at 1450°C than at 1400°C or 1500°C when SiO₂, Al₂O₃ and basicity are basically the same. This may be related to the fact that the eutectic temperatures of the two-phase zones of C₃S₂ + CS and of SiO₂ + CS are just around 1450°C.

The effect of temperature on depolymerization is greater at higher silica contents because such melts are in a state of high level of polymerization.²⁰⁾ As the temperature rises, the polymer of Si–O anions in molten slag ($\mathrm{S}{\mathrm{i}}_{n+1}{\mathrm{O}}_{3n+4}^{2(n+2)-}$) disintegrate as follows:³⁷⁾   

$$\mathrm{S}{\mathrm{i}}_{n+1}{\mathrm{O}}_{3n+4}^{2(n+2)-}+{\mathrm{O}}^{2-}=\mathrm{S}\mathrm{i}{\mathrm{O}}_4^{4-}+\mathrm{S}{\mathrm{i}}_n{\mathrm{O}}_{3n+1}^{2(n+2)-}$$(9)

The concentration of O^2- ions in the slag is reduced. The activity coefficient of MnO decreases when CaO/SiO₂<0.88, as shown in Fig. 10. When CaO/SiO₂>0.96, the disintegration of Si–O complex anions in the molten slag is small, and the O²⁻ concentration increases as the increases of the basicity. Hence, the activity of MnO increases.

Fig. 10.

The effect of temperature on the activity coefficient of MnO in the slag.

4.7. The Relationship between the Activity Coefficient and Concentration

According to the above discussion, the activity coefficients of SiO₂ and MnO in the slag are related to the concentration, basicity and temperature. The interactions between the composition & the basicity and between the basicity & the temperature also affect the activity of SiO₂ and MnO greatly. To obtain the relationship between the activity coefficient of SiO₂ and MnO in the slag and the concentration, all the data in Table 2 are used to obtain the quadratic regression relationship, as shown in Eqs. (10), (11), (12), (13).

At 1673 K, when SiO₂ = 36–64%, Al₂O₃ = 9–20%, MgO = 2–3% and MnO <2.4%,   

$$\begin{array}{l}log{\gamma }_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}=-239.216+1.643(\%\mathrm{C}\mathrm{a}\mathrm{O})+3.491(\%\mathrm{S}\mathrm{i}{\mathrm{O}}_2)\\ +2.419(\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)+0.827(\%\mathrm{M}\mathrm{n}\mathrm{O})+2.156(\%\mathrm{M}\mathrm{g}\mathrm{O})\\ +0.00426{(\%\mathrm{C}\mathrm{a}\mathrm{O})}^2-0.0129{(\%\mathrm{S}\mathrm{i}{\mathrm{O}}_2)}^2-0.0253{(\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)}^2\\ +0.385\mathrm{B}\times (\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)\pm 0.168\\ (\alpha =0.05,\mathrm{\hspace{0.17em} }\mathrm{R}=0.99,\mathrm{\hspace{0.17em} }\mathrm{A}\mathrm{d}\mathrm{j}.{\mathrm{R}}^2=0.95)\end{array}$$(10)

  

$$\begin{array}{l}log{\gamma }_{\mathrm{M}\mathrm{n}\mathrm{O}}=-14.062+0.131(\%\mathrm{C}\mathrm{a}\mathrm{O})\\ +0.137(\%\mathrm{S}\mathrm{i}{\mathrm{O}}_2)+0.164(\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)-0.396(\%\mathrm{M}\mathrm{n}\mathrm{O})\\ +0.250(\%\mathrm{M}\mathrm{g}\mathrm{O})+1.544\times {10}^{-4}{(\%\mathrm{C}\mathrm{a}\mathrm{O})}^2\\ +5.180\times {10}^{-6}{(\%\mathrm{S}\mathrm{i}{\mathrm{O}}_2)}^2-5.469\times {10}^{-4}{(\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)}^2\\ -0.00450\mathrm{B}\times (\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)\pm 0.00877\\ (\alpha =0.05,\mathrm{\hspace{0.17em} }\mathrm{R}=1.000,\mathrm{\hspace{0.17em} }\mathrm{A}\mathrm{d}\mathrm{j}.{\mathrm{R}}^2=0.998)\end{array}$$(11)

At 1773 K, when SiO₂ = 33–63%, Al₂O₃ = 9–20%, MgO = 2–3% and MnO <2%,   

$$\begin{array}{l}log{\gamma }_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}=-59.053+0.0670(\%\mathrm{C}\mathrm{a}\mathrm{O})+1.497(\%\mathrm{S}\mathrm{i}{\mathrm{O}}_2)\\ -0.319(\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)-0.580(\%\mathrm{M}\mathrm{n}\mathrm{O})+0.919(\%\mathrm{M}\mathrm{g}\mathrm{O})\\ +0.00220{(\%\mathrm{C}\mathrm{a}\mathrm{O})}^2-0.0103{(\%\mathrm{S}\mathrm{i}{\mathrm{O}}_2)}^2+0.0123{(\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)}^2\\ +0.355\mathrm{B}\times (\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)\pm 0.0489\\ (\alpha =0.05,\mathrm{\hspace{0.17em} }\mathrm{R}=0.99,\mathrm{\hspace{0.17em} }\mathrm{A}\mathrm{d}\mathrm{j}.{\mathrm{R}}^2=0.94)\end{array}$$(12)

  

$$\begin{array}{l}log{\gamma }_{\mathrm{M}\mathrm{n}\mathrm{O}}=-11.444-0.557(\%\mathrm{C}\mathrm{a}\mathrm{O})+0.321(\%\mathrm{S}\mathrm{i}{\mathrm{O}}_2)\\ -0.0214(\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)-0.557(\%\mathrm{M}\mathrm{n}\mathrm{O})+0.0971(\%\mathrm{M}\mathrm{g}\mathrm{O})\\ +9.936\times {10}^{-4}{(\%\mathrm{C}\mathrm{a}\mathrm{O})}^2-0.00235{(\%\mathrm{S}\mathrm{i}{\mathrm{O}}_2)}^2\\ +2.919\times {10}^{-4}{(\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)}^2-0.105\mathrm{B}\times (\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)\pm 0.0233\\ (\alpha =0.05,\mathrm{\hspace{0.17em} }\mathrm{R}=1.000,\mathrm{\hspace{0.17em} }\mathrm{A}\mathrm{d}\mathrm{j}.{\mathrm{R}}^2=0.997)\end{array}$$(13)

When the effect of the temperature is considered, the regression relationship can be obtained as follows at 1673 K–1773 K when SiO₂ = 33–64%, Al₂O₃ = 9–21%, MgO = 2–3% and MnO <2.4%:   

$$\begin{array}{l}log{\gamma }_{\mathrm{S}\mathrm{i}{\mathrm{O}}_2}=-187.984+3.679\times {10}^4\times \frac{1}{T}\\ +0.825(\%\mathrm{C}\mathrm{a}\mathrm{O})+2.795(\%\mathrm{S}\mathrm{i}{\mathrm{O}}_2)+1.442(\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)\\ -0.0917(\%\mathrm{M}\mathrm{n}\mathrm{O})+2.518(\%\mathrm{M}\mathrm{g}\mathrm{O})+0.0115{(\%\mathrm{C}\mathrm{a}\mathrm{O})}^2\\ -0.0130{(\%\mathrm{S}\mathrm{i}{\mathrm{O}}_2)}^2-0.0153{(\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)}^2+0.596\mathrm{B}\\ \times (\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)-2.255\times {10}^4\mathrm{B}\times \frac{1}{T}\pm 0.294\\ (\alpha =0.05,\mathrm{\hspace{0.17em} }\mathrm{R}=0.93,\mathrm{\hspace{0.17em} }\mathrm{A}\mathrm{d}\mathrm{j}.{\mathrm{R}}^2=0.82)\end{array}$$(14)

  

$$\begin{array}{l}log{\gamma }_{\mathrm{M}\mathrm{n}\mathrm{O}}=-14.728+1.573\times {10}^4\times \frac{1}{T}\\ -0.143(\%\mathrm{C}\mathrm{a}\mathrm{O})+0.309(\%\mathrm{S}\mathrm{i}{\mathrm{O}}_2)\\ -0.140(\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)-0.585(\%\mathrm{M}\mathrm{n}\mathrm{O})\\ +0.323(\%\mathrm{M}\mathrm{g}\mathrm{O})+0.00196{(\%\mathrm{C}\mathrm{a}\mathrm{O})}^2\\ -0.00292{(\%\mathrm{S}\mathrm{i}{\mathrm{O}}_2)}^2+0.00197{(\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)}^2\\ +0.117\mathrm{B}\times (\%\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)-1.169\times {10}^3\mathrm{B}\times \frac{1}{T}\pm 0.0401\\ (\alpha =0.05,\mathrm{\hspace{0.17em} }\mathrm{R}=0.99,\mathrm{\hspace{0.17em} }\mathrm{A}\mathrm{d}\mathrm{j}.{\mathrm{R}}^2=0.99)\end{array}$$(15)

where B = (mass%CaO + mass%MnO + mass%MgO)/mass%SiO₂. From the |t Stat| or the P-value of regression analysis, the order of the effect of various factors on the activity coefficient of SiO₂ is: 1/T, SiO₂, the interaction of basicity B and Al₂O₃ (B × Al₂O₃), CaO², SiO₂², Al₂O₃, MgO, the interaction of basicity B and the reciprocal of temperature, Al₂O₃², CaO, MnO. 1/T has a very significant effect on the activity coefficient of SiO₂. SiO₂, the interaction of basicity B and Al₂O₃ (B × Al₂O₃), CaO², SiO₂² have a significant effect on the activity coefficient of SiO₂. The order of the effect of various factor on the activity coefficient of MnO is as follows: 1/T, MnO, SiO₂², the interaction of basicity B and Al₂O₃ (B × Al₂O₃), CaO², SiO₂, MgO, Al₂O₃², Al₂O₃, CaO, the interaction of basicity B and the reciprocal of temperature. 1/T, MnO, SiO₂², the interaction of basicity B and Al₂O₃ (B × Al₂O₃), CaO² has a very significant effect on the activity coefficient of MnO. SiO₂ has a significant effect on the activity coefficient of MnO.

Therefore, in the study of the calculation model of the activity of the components in the slag, the quadratic terms of the concentration of each component^27,28,29) or even a more complex terms^{30,31,32,33,34,35,36)} are often included. It is also necessary to consider the interaction between the components. Regarding the calculation models of the activities of the components in the slag, the most famous are the ionic solution model (Temkin model), the regular solution model (Lumsden Model^27,28,29,36)), the molecular ion coexistence model,^30,31,32) and the modified quasi-chemical solution model.^33,34,35) Both in the Temkin model and in the Lumsden model, the presence of Si–O complex anions in the molten slag and its influence on the activity are not considered, and both models are generally suitable for high-basicity slags. The various structure forms of the Si–O complex anion of silicate molten slag are considered in the Masson model, but the Masson model can only be applied to binary system slag generally. The existence of complex compound molecules and simple ions in the molten slag is considered in the molecular ion coexistence model, but the existence and influence of complex anions such as Si–O is not considered. The influence of the more complex Si–O complex anions in the low-basicity slag is not considered in the quasi-chemical solution model also. From the mathematical expression point of view, Eqs. (10), (11), (12), (13), (14), (15) are similar to the regular solution model, and both include the first and quadratic terms of the component concentration in the slag. But the quadratic term in the regression formula (Eqs. (10), (11), (12), (13), (14), (15)) contains the interaction of the components themselves, the interaction between basicity and components, and the interaction between basicity and temperature. In order to reduce the number of interactions between components, the interaction between basicity and components is used to reflect the interaction between components and to simplify the regression formula. Figure 11 shows the comparison between the calculated values of the molecular ion coexistence model (MIC Model), of the quasi-chemical model (calculated by FactSage software), and that of the Eqs. (10), (12) and (14) and the experimental values. It can be seen from the Fig. 11 that the calculated values of Eqs. (10) and (12) are in good agreement with the experimental values. The calculated values of the molecular ion coexistence model and the quasi-chemical model are much larger than the experimental values, even up to 1 to 2 orders of magnitude. Therefore, the existing models need to be further improved for strong acid slag.

Fig. 11.

Comparison of the measured activity of SiO₂, calculated activity of SiO₂ by the regression equation and by the models.

5. Conclusions

The activity coefficients of SiO₂ and MnO in (18–43%) CaO-(33–64%) SiO₂-(9–21%) Al₂O₃-(2–3%) MgO-(<2.4%) MnO slags were determined through the chemical equilibrium experiments of Si and Mn in the liquid copper and the molten slag in a mixed gas atmosphere of CO and Ar at temperatures of 1400°C, 1450°C and 1500°C, respectively. The effects of SiO₂, Al₂O₃, basicity, the ratio of CaO/Al₂O₃ and temperature on the activity coefficients of SiO₂ and MnO were discussed. The quadratic regression relationships between the activity coefficients of SiO₂ or MnO, the concentration, the basicity in the slag and the temperature were obtained by the regression analysis method. The results show:

(a) At 1400°C and 1500°C, the change of the activity coefficient of SiO₂ with the increase of SiO₂ is complicated, and it is related to the concentration of the component, the basicity and the temperature. When SiO₂>40%, the activity coefficient of MnO in the slag at 1400°C and 1500°C decrease with the decrease of SiO₂.

(b) When SiO₂ = 33.27–54.74%, basicity CaO/SiO₂ = 0.42–1.27, the activity coefficient of SiO₂ in the slag decreases with the increase of Al₂O₃ at 1400°C and 1500°C. The activity coefficients of MnO decrease slightly with the increase of Al₂O₃ at 1500°C.

(c) When Al₂O₃ = 12.76–20.3%, as the basicity increases, the activity coefficient of SiO₂ in the slag decreases at 1400 and 1500°C.

(d) When SiO₂, Al₂O₃ and basicity are basically the same, the activity coefficient of SiO₂ and MnO at 1450°C is higher than that of 1400 and 1500°C.

Acknowledgements

The author expresses his gratitude to the funding support by National Natural Science Foundation of China (No. 51874198).

References

• 1)   J. C.  Fulton and  J.  Chipman: JOM, 6 (1954), 1136. https://doi.org/10.1007/BF03398049
• 2)   J. D.  Baird and  J.  Taylor: Trans. Faraday Soc., 54 (1958), 526. https://doi.org/10.1039/TF9585400526
• 3)   D. A. R.  Kay and  J.  Taylor: Trans. Faraday Soc., 56 (1960), 1372. https://doi.org/10.1039/TF9605601372
• 4)   B.  Ozturk and  R. J.  Fruehan: Metall. Trans. B, 18 (1987), 746. https://doi.org/10.1007/BF02672895
• 5)   J.  Park,  S.  Sridhar and  R. J.  Fruehan: Metall. Mater. Trans. B, 44 (2013), 13. https://doi.org/10.1007/s11663-012-9786-4
• 6)   Y. J.  Kang,  D.  Sichen and  K.  Morita: ISIJ Int., 47 (2007), 805. https://doi.org/10.2355/isijinternational.47.805
• 7)   K.  Kume,  K.  Morita,  T.  Miki and  N.  Sano: ISIJ Int., 40 (2000), 561. https://doi.org/10.2355/isijinternational.40.561
• 8)   H.  Ohta and  H.  Suito: Metall. Mater. Trans. B, 29 (1998), 119. https://doi.org/10.1007/s11663-998-0014-1
• 9)   H.  Ohta and  H.  Suito: Metall. Mater. Trans. B, 27 (1996), 943. https://doi.org/10.1007/s11663-996-0008-9
• 10)   M.  Sakamoto,  Y.  Yanaba,  H.  Yamamura and  K.  Morita: ISIJ Int., 53 (2013), 1143. https://doi.org/10.2355/isijinternational.53.1143
• 11)   T.  Fujisawa and  H.  Sakao: Tetsu-to-Hagané, 63 (1977), 1504 (in Japanese). https://doi.org/10.2355/tetsutohagane1955.63.9_1504
• 12)   M.  Meraikib: Ironmaking Steelmaking, 33 (2006), 120. https://doi.org/10.1179/174328106X80055
• 13)   S. W.  Cho and  H.  Suito: ISIJ Int., 34 (1994), 177. https://doi.org/10.2355/isijinternational.34.177
• 14)   E. T.  Turkdogan: Ironmaking Steelmaking, 27 (2000), 32. https://doi.org/10.1179/030192300677354
• 15)   E. T.  Turkdogan: ISIJ Int., 41 (2001), 930. https://doi.org/10.2355/isijinternational.41.930
• 16)   F. D.  Richardson: Trans. Faraday Soc., 52 (1956), 1312. https://doi.org/10.1039/TF9565201312
• 17)   M.  Kowalski,  P. J.  Spencer and  D.  Neuschütz: Slag Atlas, 2nd ed., Verlag Stahleisen GmbH, Düsseldorf, (1995), 63.
• 18)   J. B.  Chen,  H. H.  Huang,  R.  Chu and  Y. Q.  Sun: ISIJ Int., 61 (2021), 1842. https://doi.org/10.2355/isijinternational.ISIJINT-2020-730
• 19)   J. B.  Chen,  J. G.  Li,  R.  Chu and  Y. Q.  Sun: Ironmaking Steelmaking, 48 (2021), 1239. https://doi.org/10.1080/03019233.2021.1958632
• 20)   E. T.  Turkdogan: Physical Chemistry of High Temperature Technology, Academic Press, New York, (1980), 7.
• 21)   G. K.  Sigworth and  J. F.  Elliott: Can. Metall. Q., 13 (1974), 455. https://doi.org/10.1179/cmq.1974.13.3.455
• 22)   D. H.  Woo,  Y. B.  Kang and  H. G.  Lee: Metall. Mater. Trans. B, 33 (2002), 915. https://doi.org/10.1007/s11663-002-0075-5
• 23)   B. J.  Yan,  X. X.  Chen and  J.  Tao: Metall. Mater. Trans. B, 48 (2017), 1100. https://doi.org/10.1007/s11663-016-0859-7
• 24)   S. M.  Jung,  C. H.  Rhee and  D. J.  Min: ISIJ Int., 42 (2002), 63. https://doi.org/10.2355/isijinternational.42.63
• 25)   S. J.  Kim,  J.  Takekawa,  H.  Shibata,  S. Y.  Kitamura,  K.  Yamaguchi and  Y. B.  Kang: ISIJ Int., 53 (2013), 1325. https://doi.org/10.2355/isijinternational.53.1325
• 26)   C. H.  Eom,  S. H.  Lee,  J. G.  Park,  J. H.  Park and  D. J.  Min: ISIJ Int., 56 (2016), 37. https://doi.org/10.2355/isijinternational.ISIJINT-2015-243
• 27)   J.  Lumsden: Physical Chemistry of Process Metallurgy, Part I, Interscience Publishers, New York, (1961), 165.
• 28)   S.  Ban-Ya: ISIJ Int., 33 (1993), 2. https://doi.org/10.2355/isijinternational.33.2
• 29)   L. S.  Darken: Trans. Metall. Soc. AIME, 239 (1967), 80.
• 30)   X. M.  Yang,  C. B.  Shi,  M.  Zhang and  J.  Zhang: Steel Res. Int., 83 (2012), 244. https://doi.org/10.1002/srin.201100233
• 31)   X. M.  Yang,  J. P.  Duan,  C. B.  Shi,  M.  Zhang,  Y. L.  Zhang and  J. C.  Wang: Metall. Mater. Trans. B, 42 (2011), 738. https://doi.org/10.1007/s11663-011-9491-8
• 32)   X. M.  Yang,  C. B.  Shi,  M.  Zhang,  G. M.  Chai and  F.  Wang: Metall. Mater. Trans. B, 42 (2011), 1150. https://doi.org/10.1007/s11663-011-9547-9
• 33)   A. D.  Pelton and  M.  Blander: Metall. Trans. B, 17 (1986), 805. https://doi.org/10.1007/BF02657144
• 34)   G.  Eriksson and  A. D.  Pelton: Metall. Trans. B, 24 (1993), 807. https://doi.org/10.1007/BF02663141
• 35)   H.  Gaye and  J.  Welfringer: Proc. 2nd Int. Symp. on Metallurgical Slags and Fluxes, (Lake Tahoe, NV), The Metallurgical Society of AIME, Lake Tahoe, Nevada, (1984), 357.
• 36)   D. B.  Hyun and  J. B.  Shim: Trans. Iron Steel Inst. Jpn., 28 (1988), 736. https://doi.org/10.2355/isijinternational1966.28.736
• 37)   F.  Oeters: Metallurgy of Steelmaking, Verlag Stahleisen mbH, Düsseldorf, (1994), 10.