**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:


Table 10. The *GT* of forming ternary compounds ( *G A BT <sup>T</sup>* , J/mol)

Thermodynamics of Reactions Among


Fig. 12. Relationships between

can react with wustite (FeO) to form FeO·Al2O3.



2CaO + Al

2CaO+SiO2=2CaO·SiO2**(**γ**)**

2CaO+SiO2=2CaO·SiO2**(**

CaO + 1/3Al

CaO+SiO2

CaO+SiO2

CaO + Al

1/2CaO + 1/2Al2O3 +

2CaO+Fe2O3=2CaO·Fe2O3

3CaO+Al

2CaO + Al

12/7CaO+Al

3/2Al2O3+ SiO2= (1/2)3Al2O3·2SiO**<sup>2</sup>**

2O3=3CaO·Al

> 2O3 +

2O3 + SiO2=

=CaO·SiO2

=CaO·SiO2

2O3 +

**(**

2O3 +

> (wollastonite)

CaO·SiO2+ CaO·Al

2O3

Al2O3+ SiO2= Al2O3·SiO2**(**andalusite)

Al2O3+ SiO2= Al2O3·SiO2**(**kyanite)

=(1/7)12CaO

2O3

> SiO2=2CaO·Al

(

ß

**)**

SiO2=CaO·Al

1/3

pseud-wollastonite

)

SiO2=2CaO·Al

2·7Al

Al

2O3+FeO=FeO·Al

Al2O3+ SiO2= Al2O3·SiO2**(**fibrolite)

3CaO·Al

(3/2)CaO+SiO

2O3·SiO2

SiO2=(1/2)CaO·Al2O3·2SiO2

2O3

> 2O3·3SiO2**(**Hessonite

**)**

2O3·SiO2

2O3=2CaO·Al

> 2O3=CaO2·Al

CaO+Al

2CaO·Fe2O3+Fe2O3=CaO·Fe2O3

> **(**Anorthite**)**

2O3·2SiO2

2O3=(1/2)CaO2·2Al

2O3 2O3

1/2CaO+Al

2O3

CaO+Fe2O3=CaO·Fe2O3




△G/(KJ·Mol-1

/(KJ·Mol-1)

*T G* 

)




0

Al2O3, CaO, SiO2 and Fe2O3 During Roasting Processes 837

200 400 600 800 1000 1200 1400 1600 1800

T/K

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

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

2O3·SiO2**(**Gehlenite

4CaO+Al

3CaO+SiO2=3CaO·SiO2

2=(1/2)3CaO·2SiO2

> 2O3+Fe2O3

*GT* and temperature in Al2O3-CaO-SiO2-Fe2O3 system

**)**

=4CaO·Al

**)**

2O3·Fe2O3

The relationships between *GT* and temperature (T) are shown in figure 11. Figure 11 shows that, except for C3AS3(Hessonite), all the *GT* 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 *GT* 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.

Fig. 11. Relationships between *GT* 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-toaluminum ratio calcium aluminates. Fe2O3 reacts with CaO easily to form2CaO·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.

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.

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,

**Al**

**2O3**

**Al**

**Al**

·

**Al**

**2O3**

**2O3**

·

·

**SiO2**

**SiO2**

**2SiO2(**Anorthite**)**

·

**2O3**

**2SiO2**

·

**200 400 600 800 1000 1200 1400 1600 1800**

**T/K**

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

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-toaluminum ratio calcium aluminates. Fe2O3 reacts with CaO easily to form2CaO·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

**2O3+Fe2O3=4CaO**

*GT* of ternary compounds and temperature

**3SiO2(**Hessonite**)**

·

**Al**

**2O3**

·

**Fe2O3**

**4CaO+Al**

**2O3**

·

**SiO2(**Gehlenite**)**

**Al**

*GT* and temperature (T) are shown in figure 11. Figure 11

*GT* of reaction (Al2O3+CaO+SiO2) is lower than that of reaction

*GT* of the reactions get more negative with

**CaO** ·

**1/2CaO + 1/2Al**

**2CaO + Al**

**2O3 + SiO2=2CaO** ·

can react with calcium ferrites to form CaO·Al2O3 or CaO·2Al2O3.

**SiO2+ CaO** ·

**2CaO + Al**

> **CaO + Al**

**CaO + 1/3Al2O3 + SiO2=**

**Al**

**2O3 + SiO2=2CaO** ·

**2O3 + SiO2=CaO**

> ( **1/3** ) **3CaO** · **Al2O3** ·

**2O3 + SiO2=(1/2**)**CaO** ·

**2O3=2CaO** ·

shows that, except for C3AS3(Hessonite), all the

**-200**

**-150**

**-100**

△G/(KJ·Mol-1

*T G* 

/(KJ·Mol-1)

Fig. 11. Relationships between

ferrites are generated.

**4. Summary** 

)

**-50**

**0**

The relationships between

Figure 11 shows that, the

as shown in figure 12.

Fig. 12. Relationships between *GT* 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

**0**

**31**

*France*

**of Simple Liquids**

Jean-Louis Bretonnet

**Thermodynamic Perturbation Theory**

*Laboratoire de Physique des Milieux Denses, Université Paul Verlaine de Metz*

This chapter is an introduction to the thermodynamics of systems, based on the correlation function formalism, which has been established to determine the thermodynamic properties of simple liquids. The article begins with a preamble describing few general aspects of the liquid state, among others the connection between the phase diagram and the pair potential *u*(*r*), on one hand, and between the structure and the pair correlation function *g*(*r*), on the other hand. The pair correlation function is of major importance in the theory of liquids at equilibrium, because it is required for performing the calculation of the thermodynamic properties of systems modeled by a given pair potential. Then, the article is devoted to the expressions useful for calculating the thermodynamic properties of liquids, in relation with the most relevant features of the potential, and provides a presentation of the perturbation theory developed in the four last decades. The thermodynamic perturbation theory is founded on a judicious separation of the pair potential into two parts. Specifically, one of the greatest successes of the microscopic theory has been the recognition of the quite distinct roles played by the repulsive and attractive parts of the pair potential in predicting many properties of liquids. Much attention has been paid to the hard-sphere potential, which has proved very efficient as natural reference system because it describes fairly well the local order

in liquids. As an example, the Yukawa attractive potential is also mentioned.

The ability of the liquids to form a free surface differs from that of the gases, which occupy the entire volume available and have diffusion coefficients (<sup>∼</sup> 0, 5 cm2s−1) of several orders of magnitude higher than those of liquids (<sup>∼</sup> <sup>10</sup>−<sup>5</sup> cm2s−1) or solids (<sup>∼</sup> <sup>10</sup>−<sup>9</sup> cm2s−1). Moreover, if the dynamic viscosity of liquids (between 10−<sup>5</sup> Pa.s and 1 Pa.s) is so lower compared to that of solids, it is explained in terms of competition between *configurational* and *kinetic* processes. Indeed, in a solid, the displacements of atoms occur only after the breaking of the bonds that keep them in a stable configuration. At the opposite, in a gas, molecular transport is a purely kinetic process perfectly described in terms of exchanges of energy and momentum. In a liquid, the continuous rearrangement of particles and the molecular transport combine together in appropriate proportion, meaning that the liquid is an intermediate state between

**1. Introduction**

**2. An elementary survey**

the gaseous and solid states.

**2.1 The liquid state**

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: *GT* ,J

### **6. References**

