Thermodynamics of Reactions Among Al2O3, CaO, SiO2 and Fe2O3 During Roasting Processes

1. Introduction

The thermodynamic of the chemical reactions among Al₂O₃, CaO, SiO₂ and Fe₂O₃ in the roasting processes was investigated in this chapter. The chemical reactions are classified into SiO₂-Al₂O₃ system, Fe₂O₃-Al₂O₃ system, SiO₂-Fe₂O₃ system, CaO-Al₂O₃ system, SiO₂-CaO system, SiO₂-calcium aluminates system, CaO-Fe₂O₃ system, Al₂O₃-calcium ferrites system and Al₂O₃-CaO-SiO₂-Fe₂O₃ system. When the roasting temperature is over 1100K, 3Al₂O₃ 2SiO₂ is preferentially formed in SiO₂-Al₂O₃ system; FeO Al₂O₃ can be formed in Fe₂O₃-Al₂O₃ system; ferric oxide and SiO₂ could not generate iron silicate; 12CaO 7Al₂O₃ is preferentially formed in CaO-Al₂O₃ system when one mole Al₂O₃ reacts with CaO; 2CaO SiO₂ is preferentially formed in SiO₂-CaO system; except for CaO 2Al₂O₃ and CaO Al₂O₃, the other calcium aluminates can transform into calcium silicate by reacting with SiO₂ in SiO₂-calcium aluminates system; 2CaO Fe₂O₃ is preferentially formed in CaO-Fe₂O₃ system; alumina is unable to form 3CaO Al₂O₃ with calcium ferrites(2CaO Fe₂O₃ and CaO Fe₂O₃), but able to form 12CaO 7Al₂O₃ with 2CaO Fe₂O₃; when CaO, Fe₂O₃, Al₂O₃,SiO₂ coexist, they are more likely to form ternary compound 2CaO Al₂O₃ SiO₂ and 4CaO Al₂O₃ Fe₂O₃.

2. Binary compounds

2.1. Fe₂O₃-Al₂O₃-CaCO₃ system

Fe₂O₃ and Al₂O₃ can all react with limestone during roasting to generate corresponding aluminates and ferrites. In Fe₂O₃-Al₂O₃-CaO system, the reaction Fe₂O₃ and Al₂O₃ with CaCO₃ coexist, and the reactions equations are as followed:

Reactions	A, J/mol	B, J/K.mol	Temperature, K
CaCO3+Al2O3=CaO·Al2O3+CO2	161088.3	-244.1	298~1200
CaCO3+Fe2O3=CaO·Fe2O3+CO2	151677.8	-220.9	298~1200

Table 1.

The $$\Delta G_T^{\theta }$$of Fe₂O₃-Al₂O₃-CaCO₃ system（$$\Delta G_T^{\theta }=A+BT$$, J/mol;$$P_{C{O}_2}$$=30Pa, i.e., the partial pressure of CO₂ in the air）

The relationships between Gibbs free energy ($$\Delta G_T^{\theta }$$) and temperature (T) are as shown in figure 1.

Figure 1.

Relationships between$$\Delta G_T^{\theta }$$and temperature in Fe₂O₃-Al₂O₃-CaCO₃ system

Figure 1 shows that, the Gibbs free energy of reactions on Fe₂O₃ and Al₂O₃ with CaCO₃ decreased with the rise of temperature in normal roasting process (due to decomposition of CaCO₃ over 1200K, so the curve has no drawing above 1200K), and the reactions all can automatically react to generate the corresponding calcium aluminate and calcium ferrite. The $$\Delta G_T^{\theta }$$of reaction with Al₂O₃ is more negative than the $$\Delta G_T^{\theta }$$of reaction with Fe₂O₃ at the same temperature. CaCO₃ has actually decomposed at 1473~1673K industrial roasting temperature, therefore, only CaO is taken into account on the following analysis.

2.2. SiO₂-Al₂O₃ system

SiO₂ mainly comes from the ore and coke ash in the roasting process. SiO₂ reacts with Al₂O₃ to form aluminium silicates. The aluminium silicates mainly include Al₂O₃ 2SiO₂(AS₂), Al₂O₃ SiO₂(AS,andalusite), AS(kyanite), AS(fibrolite), 3Al₂O₃ 2SiO₂(A₃S₂). Thermodynamic calculation indicates that, AS₂ can not be formed from the reaction of Al₂O₃ and SiO₂ under the roasting condition. The others equations are shown in table 2.

Reactions	A, J/mol	B, J/K.mol	Temperature, K
Al2O3+SiO2=Al2O3·SiO2（kyanite）	-8469.3	9.0	298~1696
Al2O3+SiO2=Al2O3·SiO2（fibrolite）	-4463.8	-0.9	298~1696
Al2O3+SiO2=Al2O3·SiO2（andalusite）	-6786.1	0.6	298~1696
$$\frac{\text{3}}{\text{2}}{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{SiO}}_{\text{2}}=\text{(}\frac{\text{1}}{\text{2}}{\text{)3Al}}_{\text{2}}{\text{O}}_{\text{3}}\cdot {\text{2SiO}}_{\text{2}}$$	12764.7	-16.7	298~1696

Table 2.

The $$\Delta G_T^{\theta }$$of Al₂O₃-SiO₂ system（$$\Delta G_T^{\theta }=A+BT$$, J/mol）

The relationships of $$\Delta G_T^{\theta }$$and temperature in Al₂O₃-SiO₂ system is shown in figure 2.

Figure 2.

Relationships of$$\Delta G_T^{\theta }$$and temperature in Al₂O₃-SiO₂ system

Figure 2 shows that, the $$\Delta G_T^{\theta }$$of kyanite is greater than zero at 1000~1700K, so the reaction cannot happen; the $$\Delta G_T^{\theta }$$of andalusite and fibrolite alter little with temperature changes; the $$\Delta G_T^{\theta }$$of A₃S₂ decreases with the rise of temperature. The thermodynamic order of forming aluminium silicates is A₃S₂, AS(andalusite), AS(fibrolite) at 1100~1700K.

2.3. Fe₂O₃-Al₂O₃ system

Al₂O₃ does not directly react with Fe₂O₃, but Al₂O₃ may react with wustite (FeO) produced during roasting process to form FeO Al₂O₃. No pure ferrous oxide (FeO) exists in the actual process. The ratio of oxygen atoms to iron atoms is more than one in wustite, which is generally expressed as Fe_xO(x=0.83~0.95), whose crystal structure is absence type crystallology. For convenience, FeO is expressed as wustite in this thesis. Al₂O₃ may react with wustite(FeO) to form FeO Al₂O₃ in the roasting process. The relationship of $$\Delta G_T^{\theta }$$and temperature is shown in figure 2, and the chemical reaction of the equation is as followed:

$${\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+\text{FeO}=\text{FeO}·{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}=-\text{3}0\text{172}.\text{2}+\text{9}.\text{3T},\text{J}.{\text{mol}}^{-\text{1}} \text{843}~\text{165}0\text{K}$$E1

Figure 3.

Relationship of$$\Delta G_T^{\theta }$$and temperature in Fe₂O₃-Al₂O₃ system

Figure 3 shows that, the $$\Delta G_T^{\theta }$$is negative at 843~1650K, reaction can happen and generate FeO Al₂O₃; the $$\Delta G_T^{\theta }$$rises with the temperature, the higher temperature is, the lower thermodynamic reaction trends.

2.4. SiO₂-Fe₂O₃ system

SiO₂ also does not directly react with Fe₂O₃, but Al₂O₃ may react with wustite (FeO) to form FeO SiO₂ (FS) and 2FeO SiO₂(F₂S). The relationships of $$\Delta G_T^{\theta }$$and temperature is shown in figure 4, and the chemical reactions of the equations are shown in table 3.

Reactions	A, J/mol	B, J/K.mol	Temperature, K
FeO+SiO2 =FeO·SiO2	26524.6	18.8	847~1413
2FeO+SiO2 =2FeO·SiO2	-13457.3	30.3	847~1493

Table 3.

The $$\Delta G_T^{\theta }$$of SiO₂- Al₂O₃ system（$$\Delta G_T^{\theta }=A+BT$$, J/mol）

Figure 4 shows that, the $$\Delta G_T^{\theta }$$of SiO₂- Al₂O₃ system are above zero at 847~1500K, so all of the reactions can not happen to form ferrous silicates (FS and F₂S).

Figure 4.

Relationships of$$\Delta G_T^{\theta }$$and temperature in SiO₂-Fe₂O₃ system

2.5. CaO-Al₂O₃ system

Al₂O₃ can react with CaO to form calcium aluminates such as 3CaO Al₂O₃(C₃A), 12CaO 7Al₂O₃(C₁₂A₇), CaO Al₂O₃(CA) and CaO 2Al₂O₃ (CA₂). As regard as the calcium aluminates only C₁₂A₇ can be totally soluble in soda solution, C₃A and CA dissolve with a slow speed, and the other calcium aluminates such as CA₂ are completely insoluble. Equations that Al₂O₃ reacted with CaO to form C₃A, C₁₂A₇, CA and CA₂ are presented in table 4.

Figure 5 shows that, the $$\Delta G_T^{\theta }$$of reactions of Al₂O₃ with CaO decreases with the rise of temperature; all reactions automatically proceed to generate the corresponding calcium aluminates at normal roasting temperature (1473~1673K, same as follows); At the same roasting temperature, the thermodynamic order that one mole Al₂O₃ reacts with CaO to generate calcium aluminates such as C₁₂A₇, C₃A, CA, CA₂.

Reactions	A, J/mol	B, J/K.mol	Temperature, K
3CaO+ Al2O3=3CaO·Al2O3	-9.9	-28.4	298~1808
$$\frac{\text{12}}{\text{7}}{\text{CaO+Al}}_{\text{2}}{\text{O}}_{\text{3}}\text{=(}\frac{\text{1}}{\text{7}}\text{)12CaO}\cdot {\text{7Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	318.3	-44.5	298~1800
CaO+ Al2O3=CaO·Al2O3	-15871.5	-18.1	298~1878
$$\frac{\text{1}}{\text{2}}{\text{CaO+Al}}_{\text{2}}{\text{O}}_{\text{3}}\text{=(}\frac{\text{1}}{\text{2}}\text{)CaO}\cdot {\text{2Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-6667.2	-13.8	298~2023

Table 4.

The $$\Delta G_T^{\theta }$$of Al₂O₃-CaO system（$$\Delta G_T^{\theta }=A+BT$$, J/mol）The relationships between $$\Delta G_T^{\theta }$$and temperature (T) are shown in figure 5.

Figure 5.

Relationships between$$\Delta G_T^{\theta }$$and temperature in Al₂O₃-CaO system

Reactions	A, J/mol	B, J/K.mol	Temperature, K
$$\text{(}\frac{\text{4}}{\text{3}}\text{)3CaO}\cdot {\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}{\text{+Al}}_{\text{2}}{\text{O}}_{\text{3}}\text{=(}\frac{\text{1}}{\text{3}}\text{)12CaO}\cdot {\text{7Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	13939.7	-65.8	298~1800
$$\text{(}\frac{\text{1}}{\text{2}}\text{)3CaO}\cdot {\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}{\text{+Al}}_{\text{2}}{\text{O}}_{\text{3}}\text{=(}\frac{\text{3}}{\text{2}}\text{)CaO}\cdot {\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-18843.8	-13.0	298~1878
$$\text{(}\frac{\text{1}}{\text{5}}\text{)3CaO}\cdot {\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}{\text{+Al}}_{\text{2}}{\text{O}}_{\text{3}}\text{=(}\frac{\text{3}}{\text{5}}\text{)CaO}\cdot {\text{2Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-6011.2	-10.9	298~2023
$$\text{(}\frac{\text{1}}{\text{5}}\text{)12CaO}\cdot {\text{7Al}}_{\text{2}}{\text{O}}_{\text{3}}{\text{+Al}}_{\text{2}}{\text{O}}_{\text{3}}\text{=(}\frac{\text{12}}{\text{5}}\text{)CaO}\cdot {\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-38544.8	18.8	298~1878
$$\text{(}\frac{\text{1}}{\text{17}}\text{)12CaO}\cdot {\text{7Al}}_{\text{2}}{\text{O}}_{\text{3}}{\text{+Al}}_{\text{2}}{\text{O}}_{\text{3}}\text{=(}\frac{\text{12}}{\text{17}}\text{)CaO}\cdot {\text{2Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-9541.1	-1.2	298~2023
CaO•Al2O3+ Al2O3=CaO•2Al2O3	2543.8	-9.5	298~2023

Table 5.

. The $$\Delta G_T^{\theta }$$of Al₂O₃-calcium aluminates system（$$\Delta G_T^{\theta }=A+BT$$, J/mol）

When CaO is insufficient, redundant Al₂O₃ may promote the newly generated high calcium-to-aluminum ratio (CaO to Al₂O₃ mole ratio) calcium aluminates to transform into lower calcium-to-aluminum ratio calcium aluminates. The reactions of the equations are presented in table 5:

The relationships between $$\Delta G_T^{\theta }$$of reactions of Al₂O₃-calcium aluminates system and temperature (T) are shown in figure 6.

Figure 6.

Relationships between$$\Delta G_T^{\theta }$$of reactions Al₂O₃-calcium aluminates system and temperature

Figure 6 shows that, Gibbs free energy of the reaction of Al₂O₃-calcium aluminates system are negative at 400~1700K, and all the reactions automatically proceed to generate the corresponding low calcium-to-aluminum ratio calcium aluminates; Except for the reaction of Al₂O₃-C₁₂A₇, the $$\Delta G_T^{\theta }$$of the rest reactions decreases with the rise of temperature and becomes more negative. Comparing figure 4 with figure 5, it can be found that Al₂O₃ reacts with CaO easily to generate C₁₂A₇.

2.6. SiO₂- CaO system

SiO₂ can react with CaO to form CaO SiO₂ (CS), 3CaO 2SiO₂ (C₃S₂), 2CaO SiO₂ (C₂S) and 3CaO SiO₂(C₃S) in roasting process. The reactions are shown in table 6, and the relationships between △G⁰ of the reactions of SiO₂ with CaO and temperature are shown in figure 7.

Reactions	A, J/mol	B, J/K.mol	Temperature, K
CaO+SiO2 = CaO·SiO2(pseud-wollastonite)	-83453.0	-3.4	298~1817
CaO+SiO2 = CaO·SiO2(wollastonite)	-89822.9	-0.3	298~1817
$$\frac{\text{3}}{\text{2}}{\text{CaO+SiO}}_{\text{2}}\text{=(}\frac{\text{1}}{\text{2}}\text{)3CaO}\cdot {\text{2SiO}}_{\text{2}}$$	-108146.6	-3.1	298~1700
3CaO+SiO2 = 3CaO·SiO2	-111011.9	-11.3	298~1800
2CaO+SiO2 = 2CaO·SiO2(β)	-125875.1	-6.7	298~2403
2CaO+SiO2 = 2CaO·SiO2(γ)	-137890.1	3.7	298~1100

Table 6.

The $$\Delta G_T^{\theta }$$of SiO₂-CaO system($$\Delta G_T^{\theta }=A+BT$$, J/mol)

Figure 7.

Relationships between$$\Delta G_T^{\theta }$$and temperature

Figure7 shows that, SiO₂ reacts with CaO to form γ-C₂S when temperature below 1100K, but β-C₂S comes into being when the temperature above 1100K. At normal roasting temperature, the thermodynamic order of forming calcium silicate is C₂S, C₃S, C₃S₂, CS.

Figure 5 ~ figure 7 show that, CaO reacts with SiO₂ and Al₂O₃ firstly to form C₂S, and then C₁₂A₇. Therefore, it is less likely to form aluminium silicates in roasting process.

2.7. SiO₂- calcium aluminates system

In the CaO-Al₂O₃ system, if there exists some SiO₂, the newly formed calcium aluminates are likely to react with SiO₂ to transform to calcium silicates and Al₂O₃ because SiO₂ is more acidity than that of Al₂O₃. The reaction equations are presented in table 7, the relationships between $$\Delta G_T^{\theta }$$and temperature are shown in figure 8.

Figure 8 shows that, the $$\Delta G_T^{\theta }$$of all the reactions increases with the temperature increases; the reaction (3CA₂+SiO₂=C₃S+6Al₂O₃) can not happen when the roasting temperature is above 900K, i.e., the lowest calcium-to-aluminum ratio calcium aluminates cannot transform to the highest calcium-to-silicon ratio (CaO to SiO₂ molecular ratio) calcium silicate; when the temperature is above 1500K, the $$\Delta G_T^{\theta }$$of reaction(3CA+ SiO₂=C₃S+3Al₂O₃) is also more than zero; but the other calcium aluminates all can react with SiO₂ to generate calcium silicates at 800~1700K. The thermodynamic sequence of calcium aluminates reaction with SiO₂ is firstly C₃A, and then C₁₂A₇, CA, CA₂.

Reactions	A, J/mol	B, J/K.mol	Temperature, K
(3)CaO·2Al2O3 +SiO2=3CaO·SiO2+6Al2O3	-69807.8	70.8	298~1800
(3)CaO·Al2O3 +SiO2=3CaO·SiO2+3Al2O3	-62678.8	42.6	298~1800
$$\text{(}\frac{\text{1}}{\text{4}}\text{)12CaO}\cdot {\text{7Al}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{SiO}}_{\text{2}}=\text{3CaO}\cdot {\text{SiO}}_{\text{2}}+\frac{\text{7}}{4}{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-111820.6	66.7	298~1800
(2)CaO·2Al2O3+SiO2 =2CaO·SiO2+4Al2O3	-98418.8	48.1	298~1710
$$\text{(}\frac{\text{3}}{\text{2}}\text{)CaO}\cdot 2{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{SiO}}_{\text{2}}=(\frac{1}{2})\text{3CaO}\cdot 2{\text{SiO}}_{\text{2}}+3{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-87585.9	38.0	298~1700
CaO·2Al2O3+SiO2= CaO·SiO2+2Al2O3	-76146.6	27.1	298~1817
CaO·Al2O3+SiO2 =CaO·SiO2+Al2O3	-73770.2	17.7	298~1817
$$\text{(}\frac{\text{3}}{\text{2}}\text{)CaO}\cdot {\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{SiO}}_{\text{2}}=(\frac{1}{2})\text{3CaO}\cdot 2{\text{SiO}}_{\text{2}}+\frac{3}{2}{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-84021.4	23.8	298~1700
(2)CaO·Al2O3+SiO2 =2CaO·SiO2+2Al2O3	-93666.1	29.2	298~1710
$$\text{(}\frac{\text{1}}{\text{12}}\text{)12CaO}\cdot 7{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{SiO}}_{\text{2}}=\text{CaO}\cdot {\text{SiO}}_{\text{2}}+\frac{7}{12}{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-90150.8	25.7	298~1800
$$\text{(}\frac{\text{1}}{\text{8}}\text{)12CaO}\cdot 7{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{SiO}}_{\text{2}}=(\frac{1}{2})\text{3CaO}\cdot 2{\text{SiO}}_{\text{2}}+\frac{7}{8}{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-108592.3	35.9	298~1700
$$\text{(}\frac{\text{1}}{\text{6}}\text{)12CaO}\cdot {\text{7Al}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{SiO}}_{\text{2}}=\text{2CaO}\cdot {\text{SiO}}_{\text{2}}+\frac{\text{7}}{6}{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-126427.4	45.3	298~1710
$$\text{(}\frac{\text{1}}{\text{3}}\text{)3CaO}\cdot {\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{SiO}}_{\text{2}}=\text{CaO}\cdot {\text{SiO}}_{\text{2}}+\frac{1}{3}{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-86654.2	9.4	298~1808
3CaO·Al2O3+SiO2= 3CaO·SiO2+Al2O3	-100774.6	16.9	298~1808
$$\text{(}\frac{\text{1}}{\text{2}}\text{)3CaO}\cdot {\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{SiO}}_{\text{2}}=(\frac{1}{2})\text{3CaO}\cdot 2{\text{SiO}}_{\text{2}}+\frac{1}{2}{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-103069.3	11.0	298~1700
$$\text{(}\frac{\text{2}}{\text{3}}\text{)3CaO}\cdot {\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{SiO}}_{\text{2}}=\text{2CaO}\cdot {\text{SiO}}_{\text{2}}+\frac{\text{2}}{3}{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$$	-119063.3	12.1	298~1710

Table 7.

Table 7. The $$\Delta G_T^{\theta }$$of the reactions SiO₂ with calcium aluminates($$\Delta G_T^{\theta }=A+BT$$, J/mol)

Figure 8.

Relationships between$$\Delta G_T^{\theta }$$and temperature in SiO₂-calcium aluminates system

2.8. CaO- Fe₂O₃ system

Fe₂O₃ can react with CaO to form CaO Fe₂O₃(CF) and 2CaO Fe₂O₃(C₂F). When Fe₂O₃ is used up, the newly formed C₂F can react with Fe₂O₃ to form CF. The reaction equations are shown in table 8, and the relationships between △G⁰ and temperature are shown in figure 9.

Figure 9 shows that, Fe₂O₃ reacts with CaO much easily to form C₂F; CF is not from the reaction of C₂F and Fe₂O₃, but from the directly reaction of Fe₂O₃ with CaO. When Fe₂O₃ is excess, C₂F can react with Fe₂O₃ to form CF.

Reactions	A, J/mol	B, J/K.mol	Temperature, K
CaO+Fe2O3=CaO·Fe2O3	-19179.9	-11.1	298~1489
2CaO+Fe2O3=2CaO·Fe2O3	-40866.7	-9.3	298~1723
2CaO·Fe2O3+Fe2O3=(2)CaO·Fe2O3	2340.8	-12.6	298~1489

Table 8.

The $$\Delta G_T^{\theta }$$of Fe₂O₃-CaO system($$\Delta G_T^{\theta }=A+BT$$, J/mol)

Figure 9.

Relationships between$$\Delta G_T^{\theta }$$and temperature in Fe₂O₃-CaO system

2.9. Al₂O₃- calcium ferrites system

Figure 1 shows that, the $$\Delta G_T^{\theta }$$of the reaction of Al₂O₃ with CaCO₃ is more negative than that of Fe ₂O₃ with CaCO₃, therefore, the reaction of Fe₂O₃ with CaCO₃ occurs after the reaction of Al₂O₃ with CaCO₃ under the conditions of excess CaCO₃. The new generated calcium ferrites are likely to transform into calcium aluminates when CaCO₃ is insufficient, the reactions are as followed:

Reactions	A, J/mol	B, J/K.mol	Temperature, K
(3)CaO•Fe2O3+ Al2O3 = 3CaO•Al2O3+3Fe2O3	47922.7	4.5	298~1489
$$(\frac{3}{2})2\text{CaO}\cdot {\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}=\text{3CaO}\cdot {\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+\frac{\text{3}}{2}{\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}$$	49.6	-1.2×10-2	298~1723
$$(\frac{12}{7})\text{CaO}\cdot {\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}=\text{(}\frac{\text{1}}{\text{7}}\text{)12CaO}\cdot 7{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+\frac{\text{12}}{7}{\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}$$	32685.1	-24.5	298~1489
$$(\frac{6}{7})2\text{CaO}\cdot {\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}=\text{(}\frac{\text{1}}{\text{7}}\text{)12CaO}\cdot 7{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+\frac{\text{6}}{7}{\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}$$	34514.4	-35.0	298~1723
CaO•Fe2O3+ Al2O3 =CaO•Al2O3+Fe2O3	3626.6	-7.5	298~1489
$$(\frac{1}{2})\text{CaO}\cdot {\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}=(\frac{1}{2}\text{)CaO}\cdot 2{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+\frac{\text{1}}{2}{\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}$$	3215.1	-8.8	298~1489
$$(\frac{1}{4})2\text{CaO}\cdot {\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}=(\frac{1}{2}\text{)CaO}\cdot 2{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+\frac{\text{1}}{4}{\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}$$	3168.6	-11.0	298~1723
$$(\frac{1}{2})2\text{CaO}\cdot {\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}+{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}=\text{CaO}\cdot {\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+\frac{\text{1}}{2}{\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}$$	4009.5	-12.8	298~1723

Table 9.

The $$\Delta G_T^{\theta }$$of the reaction Al₂O₃ with calcium ferrites($$\Delta G_T^{\theta }=A+BT$$, J/mol)

The relationships between $$\Delta G_T^{\theta }$$and temperature (T) are shown in figure 10. Figure 10 shows that, Al₂O₃ cannot replace the Fe₂O₃ in calcium ferrites to generate C₃A, and also cannot replace the Fe₂O₃ in CaO•Fe₂O₃(CF) to generate C₁₂A₇, but it can replace the Fe₂O₃ in 2CaO•Fe₂O₃(C₂F) to generate C₁₂A₇ when the temperature is above 1000K, the higher temperature is, the more negative Gibbs free energy is; Al₂O₃ can react with CF and C₂F to form CA or CA₂, the higher temperature, more negative$$\Delta G_T^{\theta }$$. Because Fe₂O₃ reacts with CaO more easily to generate C₂F (Fig.9), therefore, C₁₂A₇ is the reaction product at normal roasting temperature(1073~1673K) under the conditions that CaO is sufficent in batching and the ternary compounds are not considered.

Figure 10.

Relationship between$$\Delta G_T^{\theta }$$and temperature in Al₂O₃- calcium ferrites system

3. Ternary compounds in Al₂O₃-CaO-SiO₂-Fe₂O₃ system

The ternary compounds formed by CaO, Al₂O₃ and SiO₂ in roasting process are mainly 2CaO Al₂O₃ SiO₂(C₂AS), CaO Al₂O₃ 2SiO₂(CAS₂), CaO Al₂O₃ SiO₂(CAS) and 3CaO Al₂O₃ 3SiO₂(C₃AS₃). In addition, ternary compound 4CaO Al₂O₃ Fe₂O₃(C₄AF) is formed form CaO, Al₂O₃ and Fe₂O₃. The equations are shown in table 10:

Reactions	A, J/mol	B, J/K.mol	Temperature, K
CaO·SiO2+ CaO·Al2O3=2CaO·Al2O3·SiO2	-30809.41	0.60	298~1600
$$\frac{\text{1}}{\text{2}}{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+\frac{\text{1}}{\text{2}}\text{CaO}+{\text{SiO}}_{\text{2}}=\text{(}\frac{\text{1}}{\text{2}}\text{)CaO}\cdot {\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}\cdot {\text{2SiO}}_{\text{2}}$$	-47997.55	-7.34	298~1826
Al2O3 + 2CaO + SiO2=2CaO·Al2O3·SiO2	-50305.83	-9.33	298~1600
Al2O3 + CaO + SiO2=CaO·Al2O3·SiO2	-72975.54	-9.49	298~1700
$$\frac{\text{1}}{\text{3}}{\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}+\text{CaO}+{\text{SiO}}_{\text{2}}=\text{(}\frac{\text{1}}{\text{3}}\text{)3CaO}\cdot {\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}\cdot {\text{3SiO}}_{\text{2}}$$	-112354.51	20.86	298~1700
4CaO +Al2O3 + Fe2O3=4CaO·Al2O3·Fe2O3	-66826.92	-62.5	298~2000
Al2O3 + 2CaO + SiO2=2CaO·Al2O3·SiO2 (cacoclasite)	-136733.59	-17.59	298~1863

Table 10.

The $$\Delta G_T^{\theta }$$of forming ternary compounds ($$\Delta G_T^{\theta }=A+BT$$, J/mol)

The relationships between $$\Delta G_T^{\theta }$$and temperature (T) are shown in figure 11. Figure 11 shows that, except for C₃AS₃(Hessonite), all the $$\Delta G_T^{\theta }$$of the reactions get more negative with the temperature increasing; the thermodynamic order of generating ternary compounds at sintering temperature of 1473K is: C₂AS(cacoclasite), C₄AF, CAS, C₃AS₃, C₂AS, CAS₂.

C₂AS may also be formed by the reaction of CA and CS, the curve is presented in figure 11. Figure 11 shows that, the $$\Delta G_T^{\theta }$$of reaction (Al₂O₃+CaO+SiO₂) is lower than that of reaction of CA and CS to generate C₂AS. So C₂AS does not form from the binary compounds CA and CS, but from the direct combination among Al₂O₃, CaO, SiO₂. Qiusheng Zhou thinks that, C₄AF is not formed by mutual reaction of calcium ferrites and sodium aluminates, but from the direct reaction of CaO, Al₂O₃ and Fe₂O₃. Thermodynamic analysis of figure 1~figure11 shows that, reactions of Al₂O₃, Fe₂O₃, SiO₂ and CaO are much easier to form C₂AS and C₄AF, as shown in figure 12.

Figure 11.

Relationships between$$\Delta G_T^{\theta }$$of ternary compounds and temperature

Figure 12 shows that, in thermodynamics, C₂AS and C₄AF are firstly formed when Al₂O₃, Fe₂O₃, SiO₂ and CaO coexist, and then calcium silicates, calcium aluminates and calcium ferrites are generated.

4. Summary

1) When Al₂O₃ and Fe₂O₃ simultaneously react with CaO, calcium silicates are firstly formed, and then calcium ferrites. In thermodynamics, when one mole Al₂O₃ reacts with CaO, the sequence of generating calcium aluminates are 12CaO 7Al₂O₃, 3CaO Al₂O₃, CaO Al₂O₃, CaO 2Al₂O₃. When CaO is insufficient, redundant Al₂O₃ may promote the newly generated high calcium-to-aluminum ratio calcium aluminates to transform to lower calcium-to-aluminum ratio calcium aluminates. Fe₂O₃ reacts with CaO easily to form 2CaO Fe₂O₃, and CaO Fe₂O₃ is not from the reaction of 2CaO Fe₂O₃ and Fe₂O₃ but form the directly combination of Fe₂O₃ with CaO. Al₂O₃ cannot replace the Fe₂O₃ in calcium ferrites to generate 3CaO Al₂O₃, and also cannot replace the Fe₂O₃ in CaO•Fe₂O₃ to generate 12CaO 7Al₂O₃, but can replace the Fe₂O₃ in 2CaO•Fe₂O₃ to generate 12CaO 7Al₂O₃ when the temperature is above 1000K; Al₂O₃ can react with calcium ferrites to form CaO Al₂O₃ or CaO 2Al₂O₃.

Figure 12.

Relationships between$$\Delta G_T^{\theta }$$and temperature in Al₂O₃-CaO-SiO₂-Fe₂O₃ system

2) One mole SiO₂ reacts with Al₂O₃ much easily to generate 3Al₂O₃ 2SiO₂, Fe₂O₃ can not react with SiO₂ in the roasting process in the air. Al₂O₃ can not directly react with Fe₂O₃, but can react with wustite (FeO) to form FeO Al₂O₃.

3) In thermodynamics, the sequence of one mole SiO₂ reacts with CaO to form calcium silicates is 2CaO SiO₂, 3CaO SiO₂, 3CaO 2SiO₂ and CaO SiO₂. Calcium aluminates can react with SiO₂ to transform to calcium silicates and Al₂O₃. CaO 2Al₂O₃ can not transform to 3CaO SiO₂ when the roasting temperature is above 900K; when the temperature is above 1500K, 3CaO Al₂O₃ can not transform to 3CaO SiO₂; but the other calcium aluminates all can all react with SiO₂ to generate calcium silicates at 800~1700K.

4) Reactions among Al₂O₃, Fe₂O₃, SiO₂ and CaO easily form 2CaO Al₂O₃ SiO₂ and 4CaO Al₂O₃ Fe₂O₃. 2CaO Al₂O₃ SiO₂ does not form from the reaction of CaO Al₂O₃ and CaO SiO₂, but from the direct reaction among Al₂O₃, CaO, SiO₂. And 4CaO Al₂O₃ Fe₂O₃ is also not formed via mutual reaction of calcium ferrites and sodium aluminates, but from the direct reaction of CaO, Al₂O₃ and Fe₂O₃. In thermodynamics, when Al₂O₃, Fe₂O₃, SiO₂ and CaO coexist, 2CaO Al₂O₃ SiO₂ and 4CaO Al₂O₃ Fe₂O₃ are firstly formed, and then calcium silicates, calcium aluminates and calcium ferrites.

5. Symbols used

Thermodynamic temperature: T, K

Thermal unit: J

Amount of substance: mole

Standard Gibbs free energy:$$\Delta G_T^{\theta }$$,J