Prediction Model for SiO2 Activity in the CaO-Al2O3-SiO2-MgO Quaternary Slag System
Abstract
:1. Introduction
2. Thermodynamic Activity Model of the CaO-SiO2-Al2O3-MgO System
2.1. Structural Units and Mass Action Concentrations in the CaO-SiO2-Al2O3-MgO System
2.2. Thermodynamic Data and Chemical Equilibrium Equation
2.3. Mass Balance Equation Construction
+ 2N15 + N16 + 3N17 + N18 + 3N19 + N20 + 2N21) = 0
N22) = 0
2N19 + 2N20 + 2N21) = 0
2.4. CaO-Al2O3-SiO2-MgO Quaternary Slag System Activity Model Verification
2.5. Slag Sample Configuration
3. Results and Discussion
3.1. Influence of SiO2 Content on SiO2 Activity
3.2. Influence of CaO Content on SiO2 Activity
3.3. Influence of w(CaO)/w(Al2O3) on SiO2 Activity
3.4. Influence of R(w(CaO)/w(SiO2)) on SiO2 Activity
4. Conclusions
- (1)
- According to the degree of coincidence between the theoretical prediction value and the literature value, the activity prediction model based on the molecule-ion coexistence theory is feasible, using simple model calculations to generate reasonable and high-precision predictions.
- (2)
- When w(CaO) = 60% and w(MgO)/w(Al2O3) = 0.25, an increased w(SiO2) caused the SiO2 activity to increase initially and then decrease gradually, with SiO2 activity reaching a maximum value of 0.1359 when w(SiO2) was 17.5%.
- (3)
- When w(SiO2) = 15% and w(MgO)/w(Al2O3) = 0.25, the w(CaO) in slag was negatively correlated with SiO2 activity. With increasing w(CaO), SiO2 activity gradually decreased, reaching a maximum value of 0.1268 when the w(CaO) was 55%.
- (4)
- SiO2 activity can be maintained at a high level by controlling w(CaO)/w(Al2O3) and w(CaO)/w(SiO2). When w(SiO2) was 15%, it was found that controlling the w(CaO)/w(Al2O3) to ≤3 can effectively improve SiO2 activity. In addition, when w(MgO) was 2%, w(Al2O3) was 8%, and w(CaO)/w(SiO2) was 3, the highest level of SiO2 activity was obtained, while further increases in w(CaO)/w(SiO2) from 3 to 4 caused the activity of SiO2 to decrease from 0.1326 to 0.1063.
Author Contributions
Funding
Data availability Statement
Acknowledgments
Conflicts of Interest
References
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Slag System | Structural Units |
---|---|
Ca2+, O2−, Mg2+, Al2O3, SiO2 | |
CaO-SiO2 | CaO·SiO2, 2CaO·SiO2, 3CaO·SiO2 |
MgO-SiO2 | MgO·SiO2, 2MgO·SiO2 |
CaO-Al2O3 | 3CaO·Al2O3, 12CaO·7Al2O3, CaO·Al2O3, CaO·2Al2O3, CaO·6Al2O3 |
MgO-Al2O3 | MgO·Al2O3 |
Al2O3-SiO2 | 3Al2O3·2SiO2 |
CaO-MgO-SiO2 | CaO·MgO·2SiO2, CaO·MgO·SiO2, 2CaO·MgO·2SiO2, 3CaO·MgO·2SiO2 |
CaO-Al2O3-SiO2 | 2CaO·Al2O3·SiO2, CaO·Al2O3·2SiO2 |
Number | Formula or Reaction Equation | ΔGθ/(J·mol−1) | ||
---|---|---|---|---|
1 | Ca2+ + O2− = CaO | N1 = NCa2+ + NO2− = 2X1/ | 2X1 = N1 | |
2 | Mg2+ + O2− = MgO | N4 = NMg2+ + NO2− = 2X4/ | 2X4 = N4 | |
3 | SiO2 | N3 = X3/ | X3 = N3 | |
4 | Al2O3 | N2 = X2/ | X2 = N2 | |
5 | (Ca2+ + O2−) + SiO2 = CaSiO3 | −92,500 − 2.5 T | N5 = K1N1N3 | X5 = N5 |
6 | 2(Ca2+ + O2−) + SiO2 = Ca2SiO4 | −118,800 − 11.3 T | N6 = K2N3 | X6 = N6 |
7 | 3(Ca2+ + O2−) + SiO2 = Ca3SiO5 | −118,800 − 6.7 T | N7 = K3N3 | X7 = N7 |
8 | (Mg2+ + O2) + SiO2 = MgSiO3 | −41,100 + 6.1 T | N8 = K4N3N4 | X8 = N8 |
9 | 2(Mg2+ + O2) + SiO2 = Mg2SiO4 | −67,200 + 4.31 T | N9 = K5N3 | X9 = N9 |
10 | (Ca2+ + O2−) + Al2O3 = CaO·Al2O3 | −18,000 − 18.83 T | N10 = K6N1N2 | X10 = N10 |
11 | 12(Ca2+ + O2−) + 7Al2O3 = 12CaO·7Al2O3 | −86,100 − 205.1 T | N11 = K7 | X11 = N11 |
12 | 3(Ca2+ + O2−) + Al2O3 = 3CaO·Al2O3 | −12,600 − 24.69 T | N12 = K8N2 | X12 = N12 |
13 | (Ca2+ + O2−) + 2Al2O3 = CaO·2Al2O3 | −16,700 − 25.52 T | N13 = K9N1 | X13 = N13 |
14 | 3(Ca2+ + O2−) + 6Al2O3 = 3CaO·6Al2O3 | −16,380 − 37.58 T | N14 = K10 | X14 = N14 |
15 | 2(Ca2++ O2−) + Al2O3 + SiO2 = 2CaO·Al2O3·SiO2 | −61,964.64 − 60.29 T | N15 = K11N2N3 | X15 = N15 |
16 | (Ca2++ O2−) + Al2O3 + 2SiO2 = CaO·Al2O3·2SiO2 | −13,816.44 − 55.266 T | N16 = K12N1N2 | X16 = N16 |
17 | 3Al2O3 + 2SiO2 = 3Al2O3·2SiO2 | −8600 − 17.41 T | N17 = K13 | X17 = N17 |
18 | (Ca2+ + O2−) + (Mg2+ + O2) + SiO2 = CaO·MgO·SiO2 | −124,766.6 + 3.768 T | N18 = K14N1N3N4 | X18 = N18 |
19 | 3(Ca2+ + O2−) + (Mg2+ + O2) + 2SiO2 = 3CaO·MgO·2SiO2 | −315,469 + 24.786 T | N19 = K15N4 | X19 = N19 |
20 | (Ca2+ + O2−) + (Mg2+ + O2) + 2SiO2 = CaO·MgO·2SiO2 | −80,387 − 51.916 T | N20 = K16N1N4 | X20 = N20 |
21 | 2(Ca2+ + O2−) + (Mg2+ + O2) + 2SiO2 = 2CaO·MgO·2SiO2 | −73,688 − 63.639 T | N21 = K17N4 | X21 = N21 |
22 | (Mg2+ + O2) + Al2O3 = MgO·Al2O3 | −35,600 − 2.09 T | N22 = K18N2N4 | X22 = N22 |
Slag Composition | Activity | |||||||
---|---|---|---|---|---|---|---|---|
Sample No. | ||||||||
1 | 0.660 | 0.103 | 0.092 | 0.145 | 0.0936 | 0.1199 | 0.0432 | 0.0029 |
2 | 0.648 | 0.126 | 0.083 | 0.143 | 0.1005 | 0.1256 | 0.0348 | 0.0028 |
3 | 0.652 | 0.152 | 0.076 | 0.120 | 0.0950 | 0.1334 | 0.0210 | 0.0034 |
4 | 0.648 | 0.177 | 0.068 | 0.107 | 0.0999 | 0.1359 | 0.0203 | 0.0032 |
5 | 0.646 | 0.199 | 0.060 | 0.095 | 0.1405 | 0.1218 | 0.0161 | 0.0019 |
6 | 0.641 | 0.225 | 0.052 | 0.082 | 0.1090 | 0.1074 | 0.0150 | 0.0031 |
7 | 0.636 | 0.248 | 0.044 | 0.070 | 0.0968 | 0.1254 | 0.0143 | 0.0036 |
8 | 0.537 | 0.158 | 0.119 | 0.186 | 0.0603 | 0.1051 | 0.0811 | 0.0044 |
9 | 0.560 | 0.157 | 0.110 | 0.173 | 0.0669 | 0.1250 | 0.0524 | 0.0046 |
10 | 0.584 | 0.156 | 0.101 | 0.159 | 0.0807 | 0.1221 | 0.0509 | 0.0034 |
11 | 0.607 | 0.155 | 0.093 | 0.145 | 0.0840 | 0.1268 | 0.0390 | 0.0036 |
12 | 0.630 | 0.153 | 0.084 | 0.133 | 0.1013 | 0.1261 | 0.0339 | 0.0027 |
13 | 0.652 | 0.152 | 0.076 | 0.120 | 0.0906 | 0.1242 | 0.0227 | 0.0038 |
14 | 0.675 | 0.151 | 0.068 | 0.106 | 0.1348 | 0.1191 | 0.0260 | 0.0018 |
15 | 0.633 | 0.160 | 0.032 | 0.174 | 0.2006 | 0.1163 | 0.0168 | 0.000867 |
16 | 0.666 | 0.157 | 0.031 | 0.146 | 0.1980 | 0.1169 | 0.0117 | 0.000942 |
17 | 0.689 | 0.155 | 0.031 | 0.125 | 0.1221 | 0.1248 | 0.0175 | 0.0023 |
18 | 0.706 | 0.153 | 0.031 | 0.110 | 0.1116 | 0.1244 | 0.0159 | 0.0028 |
19 | 0.719 | 0.152 | 0.030 | 0.099 | 0.1698 | 0.1120 | 0.0081 | 0.0014 |
20 | 0.730 | 0.151 | 0.030 | 0.089 | 0.1127 | 0.1012 | 0.0120 | 0.0030 |
21 | 0.740 | 0.149 | 0.030 | 0.081 | 0.1053 | 0.1084 | 0.0130 | 0.0033 |
Sample No. | R (Alkalinity) | Slag Composition | Activity | ||||||
---|---|---|---|---|---|---|---|---|---|
1 | 1.0 | 0.478 | 0.446 | 0.030 | 0.046 | 0.0118 | 0.0037 | 0.0100 | 0.1159 |
2 | 1.1 | 0.499 | 0.424 | 0.050 | 0.045 | 0.0171 | 0.0049 | 0.0124 | 0.0720 |
3 | 1.25 | 0.529 | 0.395 | 0.030 | 0.046 | 0.0309 | 0.0090 | 0.0213 | 0.0327 |
4 | 1.5 | 0.570 | 0.355 | 0.030 | 0.045 | 0.0768 | 0.0229 | 0.0167 | 0.0080 |
5 | 2 | 0.630 | 0.295 | 0.029 | 0.046 | 0.2840 | 0.0974 | 0.0054 | 0.0005372 |
6 | 2.5 | 0.674 | 0.251 | 0.029 | 0.046 | 0.1203 | 0.0892 | 0.0100 | 0.0026 |
7 | 3 | 0.706 | 0.220 | 0.029 | 0.045 | 0.1179 | 0.1326 | 0.0105 | 0.0026 |
8 | 3.5 | 0.731 | 0.195 | 0.029 | 0.045 | 0.1603 | 0.1029 | 0.0069 | 0.0016 |
9 | 4 | 0.750 | 0.175 | 0.029 | 0.046 | 0.1437 | 0.1063 | 0.0057 | 0.0020 |
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Lin, Y.; Yi, Y.; Fang, M.; Ma, W.; Liu, W. Prediction Model for SiO2 Activity in the CaO-Al2O3-SiO2-MgO Quaternary Slag System. Minerals 2023, 13, 509. https://doi.org/10.3390/min13040509
Lin Y, Yi Y, Fang M, Ma W, Liu W. Prediction Model for SiO2 Activity in the CaO-Al2O3-SiO2-MgO Quaternary Slag System. Minerals. 2023; 13(4):509. https://doi.org/10.3390/min13040509
Chicago/Turabian StyleLin, Yue, Yuanrong Yi, Minghang Fang, Wenqing Ma, and Wei Liu. 2023. "Prediction Model for SiO2 Activity in the CaO-Al2O3-SiO2-MgO Quaternary Slag System" Minerals 13, no. 4: 509. https://doi.org/10.3390/min13040509