ISIJ International
Online ISSN : 1347-5460
Print ISSN : 0915-1559
ISSN-L : 0915-1559
Regular Article
Retraction: Representation of Dephosphorization Ability for CaO–Containing Slags Based on the Ion and Molecule Coexistence Theory
Peng-cheng LiJian-liang Zhang
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2014 Volume 54 Issue 3 Pages 567-577

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Abstract

A thermodynamic model for calculating phosphorous distribution between several slag systems and hot metal has been developed by coupling with a developed thermodynamic model for calculating mass action concentrations of iron oxides based on the ion and molecule coexistence theory (IMCT). The calculated mass action concentrations of iron oxides in the several CaO–containing slags can be applied to represent reaction ability of iron oxides, like classic concept of activity. The developed thermodynamic model for calculating phosphorus distribution can quantitatively calculate the respective contribution of free components, and the sum of the respective contribution of free components. The comparison of the calculated total phosphorous distribution with all available measured phosphorous distribution reported in literatures shows that the agreement between the calculated total phosphorous distribution and measured phosphorous distribution is good. This reliable agreement indicates that the IMCT–LP model can be successfully applied to predict the phosphorous distribution for CaO–FeO–Fe2O3–P2O5 slags, CaO–SiO2–FeO–Fe2O3–P2O5 slags, CaO–SiO2–FeO–Fe2O3–Al2O3–P2O5 slags, CaO–SiO2–FeO–MgO–P2O5 slags, CaO–SiO2–FeO–Fe2O3–MgO–P2O5 slags and CaO–SiO2–MgO–FeO–Fe2O3–MnO–P2O5 slags in a temperature range from 1823 K to 1973 K.

1. Introduction

Dephosphorization is one of the most important reaction in the steelmaking process, assessing the distribution of phosphorous ratio between metallurgical slag and hot metal always attract many researchers’ attention.1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19) Many studies have been carried out to measure phosphorous distribution between various slags and hot metal since the 1940 s.1,2,9) However, the measurement of phosphorous distribution between molten slag and hot metal is costly and difficult11,12) in the operation. It is therefore very necessary to develop a reliable model for predicting phosphorous distribution between molten slag and hot metal. Several attempts9,10,11,12,13,14,15,16) have been made to treat slag–metal phosphorus equilibrium empirically and theoretically based on the concept of ionic or molecular constituents in the slags. However, these attempts are generally associated with artificial parameters, and most of the regressed parameters are valid only within certain limits of concentration.20)

The ion and molecule coexistence theory (IMCT) has been successfully applied to predict sulphur distribution ratio between CaO–SiO2–MgO–Al2O3 BF slags and hot metal,21) and sulphide capacity of CaO–SiO2–MgO–Al2O3 BF slags.22) In addition, Zhang23,24,25,26,27,28,29,30) et al. and other researchers28) have proved that the calculated mass action concentrations of structural units by the IMCT model in various slags have a good agreement with the measured activities of the corresponding components in MnO–SiO2 slags,23,24) FeO–Fe2O3–SiO2 slags,23,25) Na2O–SiO2 slags,23,26) CaO–MgO slags, NiO–MgO slags,23,27) and CaO–MgO–SiO2–Al2O3–Cr2O3 slags.28) To expand the application fields of IMCT, in the present study, a thermodynamic model was developed for calculating phosphorous distribution between several slags and hot metal, i.e., CaO–FeO–Fe2O3–P2O5 slags,29) CaO–SiO2–FeO–Fe2O3–P2O5 slags,20) CaO–FeO–Fe2O3–Al2O3–P2O5 slags,20) CaO–SiO2–FeO–MgO–P2O5 slags,7) CaO–SiO2–FeO–Fe2O3–MgO–P2O5 slags,30) and CaO–SiO2–MgO–FeO–Fe2O3–MnO–P2O5 slags.31) All available experimental data of measured phosphorous distribution reported in literatures were used to examine the reliability of the developed IMCT–LP model in predicting the phosphorous distribution.

2. Model for Calculating Mass Action Concentrations of Structural Units in CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 Slags

2.1. Hypotheses

According to classical hypotheses of IMCT described in detail elsewhere,21,22) the six slag systems equilibrated with hot metal, i.e., CaO–FeO–Fe2O3–P2O5 slags,29) CaO–SiO2–FeO–Fe2O3–P2O5 slags,20) CaO–FeO–Fe2O3–Al2O3–P2O5 slags,20) CaO–SiO2–FeO–MgO–P2O5 slags,7) CaO–SiO2–FeO–Fe2O3–MgO–P2O5 slags,30) and CaO–SiO2–MgO–FeO–Fe2O3–MnO–P2O5 slags,31) can be classified as a virtual CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slag system. To improve the readability, the developed IMCT–LP model for CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slag system was briefly described in the following text.

The main assumptions in the developed thermodynamic model for calculating mass action concentrations of structural units in CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags equilibrated with hot metal can be simply summarized as follows: 1) Structural units in the studied slags equilibrated with hot metal are composed of Ca2+, Mg2+, Fe2+, Mn2+ and O2− as simple ions, SiO2, Fe2O3, Al2O3 and P2O5 as simple molecules, silicates, aluminates and so on as complex molecules. Each structural unit has its independent position in the slags. Every cation and anion generated from the same component will take part in reactions of forming complex molecules in the form of ion couple as (Me2++O2−). 2) Reactions of forming complex molecules are under chemically dynamic equilibrium between bonded ion couples from simple ions and simple molecules. 3) Structural units in the selected slags equilibrated with molten steel bear continuity in the range of investigated concentration range. 4) Chemical reactions of forming complex molecules obey the mass action law.

2.2. Model for Calculating Mass Action Concentrations of Structural Units in the Six Selected CaO–Containing Slags

2.2.1. Structural Units in CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 Slags

Generally speaking from the view point of traditional metallurgical physicochemistry, there are eight components as CaO, SiO2, MgO, FeO, Fe2O3, MnO, Al2O3 and P2O5 in CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags, while the extracted phosphorus from molten steel gradually enter into the slags with the proceeding of dephosphorization reactions until dephosphorization reactions reach equilibrium. However, the IMCT21,22) suggests that the extracted phosphorus from hot metal into the slags exists as P2O5 can be bonded with ion couples (Fe2++O2−), (Ca2++O2−), (Mg2++O2−) and (Mn2++O2−) to form molecules as P2O5, 3FeO·P2O5, 4FeO·P2O5, 2CaO·P2O5, 3CaO·P2O5, 4CaO·P2O5, 2MgO·P2O5, 3MgO·P2O5 and 3MnO·P2O5 in oxidizing slags containing iron oxides FetO, respectively.

From above mentioned discussion, it can be obviously deduced that there are 5 simple ions as Ca2+, Mg2+, Fe2+, Mn2+ and O2−, 4 simple molecules as SiO2, Fe2O3, Al2O3 and P2O5 in the slags under dephosphorization equilibrium at metallurgical temperatures based on IMCT.21,22,23,24,25,26,27,28) According to the reported binary and ternary phase diagrams69,70) of CaO–SiO2 slags, CaO–Al2O3 slags, CaO–Al2O3–SiO2 slags, CaO–Al2O3–MgO slags, CaO–MgO–SiO2 slags, MgO–Al2O3–SiO2 slags, CaO–FeO–SiO2 slags, Al2O3–SiO2–MnO slags and Al2O3–SiO2–FeO slags and so on in a temperature range from 1673 K to 1986 K, about 36 kinds of complex molecules, such as 3CaO·SiO2, 2CaO·SiO2, CaO·SiO2 and so on can be formed in the slags as listed in Table 1.

Table 1. Chemical reaction formulas of possibly formed complex molecules, their standard molar Gibbs free energy changes, mole numbers, mass action concentrations and equilibrium constants in virtual CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags.

2.2.2. Model for Calculating Mass Action Concentrations of Structural Units in CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 Slags

The mole number of above–mentioned eight components, such as CaO, SiO2, MgO, FeO, Fe2O3, MnO, Al2O3, P2O5 in 100 g of CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags is assigned as b 1 = n CaO 0 , b 2 = n SiO 2 0 , b 3 = n MgO 0 , b 4 = n FeO 0 , b 5 = n Fe 2 O 3 0 , b 6 = n MnO 0 , b 7 = n Al 2 O 3 0 and b 8 = n P 2 O 5 0 to present chemical composition of the slags. The defined21,22) equilibrium mole numbers ni of all above-mentioned structural units in 100 g slags equilibrated with hot metal at metallurgical temperatures have been also given out in Table 1. According to the ion and molecule coexistence theory,21,22) each ion couple is electroneutral and can be electrolyzed into cation and anion based on electrovalence balance principle. Hence, the equilibrium mole number of each ion couple is defined as the sum of equilibrium mole number of the separated cation and anion. Choosing ion couple (Ca2++O2–) as an example, (Ca2++O2–) can be separated into Ca2+ and O2–, the equilibrium mole number of Ca2+ and O2– can be expressed as n 1 = n Ca 2+ ,CaO = n O 2- ,CaO = n CaO . Therefore, ion couple (Ca2++O2–) with a fixed amount under equilibrium condition can produce two times amount of structural units, i.e., n Ca 2+ ,CaO + n O 2- ,CaO =2 n CaO =2 n 1 . The total equilibrium mole number Σni of all structural units in 100 g slags equilibrated with molten steel can be expressed as follows   

n i =2 n CaO + n SiO 2 +2 n MgO +2 n FeO + n Fe 2 O 3 +2 n MnO + n Al 2 O 3 + n P 2 O 5 + n c1 + n c2 ++ n c36 (mol) (1)

With respect to the definition of mass action concentrations21,22) Ni for structural units, which is a ratio of equilibrium mole number of structural units i to the total equilibrium mole numbers of all structural units in a close system with a fixed amount, Ni of structural units i and ion couples (Me2++O2−) in molten slags can be calculated by   

N i = n i n i   (–) (2a)
  
N MeO = N Me 2+ ,MeO + N O 2- ,MeO = n Me 2+ ,MeO + n O 2- ,MeO n i = 2 n MeO n i   (–) (2b)

All definitions of Ni for formed ion couples from simple ions, simple and complex molecules in CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags were listed in Table 1.

The chemical reaction formulas of 36 kinds of possibly formed complex molecules, their standard molar Gibbs free energy Δ r G m,ci Θ of formation reactions as a function of absolute temperature T, reaction equilibrium constant K ci Θ and presentation of mass action concentration of all complex molecules Nci expressed by using K ci Θ , N1 (NCaO), N2 (NSiO2), N3 (NMgO), N4 (NFeO), N5 (NFe2O3) N6 (NMnO), N7 (NAl2O3), and N8 (NP2O5) based on the mass action law were summarized in Table 1.

The mass conservation equations of eight components in 100 g of CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags equilibrated with liquid iron can be established according to the definitions21,22) of ni and mass action concentrations Ni of all structural units listed in Table 1 as follows   

b 1 =( 1 2 N 1 +3 N c1 +2 N c2 + N c3 +3 N c4 +12 N c5 + N c6 + N c7 + N c8 +2 N c18 + N c19 + N c20 + N c21 +2 N c22 +3 N c23 +2 N c25 +2 N c29 +3 N c30 +4 N c31 ) n i =( 1 2 N 1 +3 K c1 Θ N 1 3 N 2 +2 K c2 Θ N 1 2 N 2 + K c3 Θ N 1 N 2 +3 K c4 Θ N 1 3 N 7 +12 K c5 Θ N 1 12 N 7 7 + K c6 Θ N 1 N 7 + K c7 Θ N 1 N 7 2 + K c8 Θ N 1 N 7 6 +2 K c18 Θ N 1 2 N 2 N 7 + K c19 Θ N 1 N 7 N 2 2 + K c20 Θ N 1 N 2 N 3 + K c21 Θ N 1 N 3 N 2 2 +2 K c22 Θ N 1 2 N 3 N 2 2 +3 K c23 Θ N 1 3 N 2 2 N 3 +2 K c25 Θ N 1 2 N 5 +2 K c29 Θ N 1 2 N 8 +3 K c30 Θ N 1 3 N 8 +4 K c31 Θ N 1 4 N 8 ) n i = n CaO 0 (mol) (3a)
  
b 2 =( N 2 + N c1 + N c2 + N c3 + N c9 + N c10 + N c12 + N c14 + N c15 +2 N c17 + N c18 +2 N c19 + N c20 +2 N c21 +2 N c22 +2 N c23 +5 N c24 ) n i =( N 2 + K c1 Θ N 1 3 N 2 + K c2 Θ N 1 2 N 2 + K c3 Θ N 1 N 2 + K c9 Θ N 2 N 3 2 + K c10 Θ N 2 N 3 + K c12 Θ N 2 N 4 2 + K c14 Θ N 2 N 6 + K c15 Θ N 2 N 6 2 +2 K c17 Θ N 2 2 N 7 3 + K c18 Θ N 1 2 N 2 N 7 +2 K c19 Θ N 1 N 2 2 N 7 + K c20 Θ N 1 N 2 N 3 +2 K c21 Θ N 1 N 3 N 2 2 +2 K c22 Θ N 1 2 N 2 2 N 3 +2 K c23 Θ N 1 3 N 2 2 N 3 +5 K c24 Θ N 3 2 N 7 2 N 2 5 ) n i = n SiO 2 0 (mol) (3b)
  
b 3 =( 1 2 N 3 +2 N c9 + N c10 + N c11 + N c20 + N c21 + N c22 + N c23 +2 N c24 + N c27 +2 N c35 +3 N c36 ) n i =( 1 2 N 3 +2 K c9 Θ N 2 N 3 2 + K c10 Θ N 2 N 3 + K c11 Θ N 3 N 7 + K c20 Θ N 1 N 2 N 3 + K c21 Θ N 1 N 3 N 2 2 + K c22 Θ N 1 2 N 2 2 N 3 + K c23 Θ N 1 3 N 2 2 N 3 +2 K c24 Θ N 3 2 N 7 2 N 2 5 + K c27 Θ N 3 N 5 +2 K c35 Θ N 3 2 N 8 +3 K c36 Θ N 3 3 N 8 ) n i = n MgO 0 (mol) (3c)
  
b 4 =( 1 2 N 4 +2 N c12 + N c13 + N c26 +3 N c32 +4 N c33 ) n i =( 1 2 N 4 +2 K c12 Θ N 2 N 4 2 + K c13 Θ N 4 N 7 + K c26 Θ N 4 N 5 +3 K c32 Θ N 4 3 N 8 +4 K c33 Θ N 4 4 N 8 ) n i = n FeO 0 (mol) (3d)
  
b 5 =( N 5 + N c25 + N c26 + N c27 + N c28 ) n i =( N 5 + K c25 Θ N 1 N 5 + K c26 Θ N 4 N 5 + K c27 Θ N 3 N 5 + K c28 Θ N 6 N 5 ) n i = n Fe 2 O 3 0 (mol) (3e)
  
b 6 =( 1 2 N 6 + N c14 +2 N c15 + N c16 + N c28 +3 N c34 ) n i =( 1 2 N 6 + K c14 Θ N 2 N 6 +2 K c15 Θ N 2 N 6 2 + K c16 Θ N 6 N 7 + K c28 Θ N 6 N 5 +3 K c34 Θ N 6 3 N 8 ) n i = n MnO 0 (mol) (3f)
  
b 7 =( N 7 + N c4 +7 N c5 + N c6 +2 N c7 +6 N c8 + N c11 + N c13 + N c16 +3 N c17 + N c18 + N c19 +2 N c24 ) n i =( N 7 + K c4 Θ N 1 3 N 7 +7 K c5 Θ N 1 12 N 7 7 + K c6 Θ N 1 N 7 +2 K c7 Θ N 1 N 7 2 +6 K c8 Θ N 1 N 7 6 + K c11 Θ N 3 N 7 + K c13 Θ N 4 N 7 + K c16 Θ N 6 N 7 +3 K c17 Θ N 2 2 N 7 3 + K c18 Θ N 1 2 N 2 N 7 + K c19 Θ N 1 N 2 2 N 7 +2 K c24 Θ N 3 2 N 7 2 N 2 5 ) n i = n Al 2 O 3 0 (mol) (3g)
  
b 8 =( N 8 + N c29 + N c30 + N c31 + N c32 + N c33 + N c34 + N c35 + N c36 ) n i =( N 8 + K c29 Θ N 1 2 N 8 + K c30 Θ N 1 3 N 8 + K c31 Θ N 1 4 N 8 + K c32 Θ N 4 3 N 8 + K c33 Θ N 4 4 N 8 + K c34 Θ N 6 3 N 8 + K c35 Θ N 3 2 N 8 + K c36 Θ N 3 3 N 8 ) n i = n P 2 O 5 0 (mol) (3h)

According to the principle that the sum of mole fraction for all structural units in a fixed amount of CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags under equilibrium condition is equal to 1.0, the following equation can be obtained   

N 1 + N 2 + N 3 + N 4 + N 5 + N 6 + N 7 + N 8 + N c1 + N c2 ++ N c36 = N 1 + N 2 ++ N 8 + K c1 Θ N 1 3 N 2 + K c2 Θ N 1 2 N 2 ++ K c36 Θ N 3 3 N 8 = N i =1.0 (–) (4)

The equation group of Eqs. (3) and (4) is the governing equations of the developed thermodynamic model for calculating mass action concentrations Ni of structural units in CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags equilibrated or reacted with liquid iron. Obviously, there are nine unknown parameters as N1, N2, N3, N4, N5, N6, N7, N8 and Σni with 9 independent equations in the developed equation group of Eqs. (3) and (4). The unique solution of Ni, Σni and ni can be calculated by solving these algebraic equation group of Eqs. (3) and (4) by combining with definition of Ni in Eq. (2).

3. Definition of Mass Action Concentration for Iron Oxides FetO in the CaO–Containing Slag Systems

It’s well-known that high oxygen potential and basicity oxides of the slags are needed to remove phosphorus from steel melts below the up-to-date limits. In this study, the mass action concentration of iron oxides FetO, i.e., NFetO, is recommended to present slag oxidization ability. The IMCT21,22,23,24,25,26,27,28) proposed that all iron oxides in metallurgical slags are composed of ion couple (Fe2++O2−), simple molecule Fe2O3 and complex molecule FeO·Fe2O3, therefore, the related structural units of iron oxides can dynamically equilibrate among those structural units as follows   

( F e 2 O 3 ) +[ Fe ]=3(F e 2+ + O 2- ) (5a)
  
(FeO·F e 2 O 3 )+[ Fe ]=4(F e 2+ + O 2- ) (5b)

Obviously, the contribution of simple molecule Fe2O3 to oxygen potential of slags or slag oxidization ability is equivalent to 3 times as that of ion couple (Fe2++O2–) from Eq. 5(a), in other words, 1 mole of molecule Fe2O3 is equivalent to 3 mole of ion couple (Fe2++O2–), meanwhile, 3 mole of FeO can produce 6 mole of ion. Similarly, the contribution of 1 mole of complex molecule FeO·Fe2O3 to slags oxidization ability is 4 times as that of ion couple (Fe2++O2–) from Eq. 5(b), and 4 mole of FeO can produce 8 mole of ion. Therefore, the slags oxidization ability of NFetO can be defined as   

N Fe t O = N FeO + 3( n Fe 2+  ,Fe 2 O 3 FeO + n O 2-  ,Fe 2 O 3 FeO ) n i + 4( n Fe 2+  ,Fe 3 O 4 FeO + n O 2-  ,Fe 3 O 4 FeO ) n i = N FeO + 6 n Fe 2 O 3 n i + 8 n  Fe 3 O 4 n i = N FeO +6 N Fe 2 O 3 +8 N Fe 3 O 4 (–) (6)

In order to examine the reliability of the IMCT–Ni model developed in the present study based on the ion and molecule coexistence theory, the calculated mass action concentrations of iron oxides NFetO in CaO–FeO–Fe2O3 slags,32,59,60) CaO–SiO2–FeO–Fe2O3 slags,33,38,61,62,63,64,65,66) CaO–SiO2–FeO–Fe2O3–Al2O3 slags,34) CaO–SiO2–FeO–Fe2O3–MgO slags,35,67) CaO–SiO2–MgO–FeO–Fe2O3–MnO slags,36) CaO–SiO2–MgO–FeO–P2O5 slags,37) MgO–FeO–Fe2O3–P2O5 slags,38) CaO–FeO–Fe2O3–P2O5 slags39) and CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags40) were compared with all available measured FetO activities aFetO, measured at different temperatures reported in various literatures by different investigators, respectively. The experimental techniques employed by these investigators for FetO activity measurements in different slags were summarized in Table 2.

Table 2. Summary of previous investigations on FetO activity measurements.
SlagsResearcher(s)Experimental TechniqueRef.
CaO–FeO–Fe2O3Iwase et al.EMF electrochemical measurements of the solid-oxide electrolyte galvanic cell at 1673 K32)
Ban-ya et al.Equilibrated the slags in iron crucible with H2/H2O mixture at 1673 K58)
Taylor and
Chipman
Equilibrated liquid iron in a rotating induction furnace with the slags at 1873 K; measuring the equilibrium oxygen content of the metal phase59)
Fujita et al.Determining the oxygen distribution between the slags and liquid iron at 1833 K60)
CaO–FeO–Fe2O3–P2O5Ban-ya et al.Slag–gas (H2/H2O mixture) equilibrium at 1673 K39)
MgO–FeO–Fe2O3– P2O5Ban-ya et al.Slag–gas (H2/H2O mixture) equilibrium at 1673 K39)
CaO–SiO2–FeO–Fe2O3Ogura et al.Electrochemical measurements using ZrO2 as electrolyte and Mo+MoO2 as reference electrode at 1673 K33)
Bodsworth et al.Equilibrated H2/H2O mixture with the molten slags in iron crucible in the temperature range of 1538–1638 K61)
Fredriksson et al.Gas equilibration method involving equilibration between the partial pressure of oxygen defined by CO–CO–Ar gas mixtures and molten slags in a Pt crucible at 1823, 1873 and 1923 K62)
Bygdén et al.Employing ZrO2–CaO solid-electrolyte galvanic cell method in the temperature range of 1473, 1523, 1573 and 1623 K63)
Wanibe et al.Electrochemical determination by measuring oxygen activity in silver in equilibrium with the slags by a ZrO2(CaO) solid electrolyte in the temperature range of 1573–1673 K64)
CaO–SiO2–FeO–Fe2O3–Al2O3Taniguchi et al.Equilibrated the slags with copper-iron alloys in a controlled oxygen partial pressure at 1673 K; determining activity coefficients of FeO34)
CaO–SiO2–MgO–FeO–Fe2O3Lv et al.Electrochemical measurements of the solid electrolyte cell for oxygen potential determination at 1673 K35)
Liu et al.Measurement of the oxygen potential of liquid iron equilibrated with molten slags using EMF technique at 1823 K67)
CaO–SiO2–MgO–FeO–Fe2O3–P2O5Basu et al.Slag–metal equilibrium in the temperature range of 1873–1923 K37)
CaO–SiO2–MgO–FeO–Fe2O3–MnOFredriksson et al.Equilibrated the slags in iron crucible with H2/H2O mixtures at 1723 K36)
CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5Young et al.Slag–metal equilibrium in the temperature range of 1858–1975 K40)

The comparison between the calculated NFetO from the developed IMCT–Ni model and reported aFetO in the five FeO–containing slags systems was illustrated in Fig. 1, respectively. It can be obviously observed from Figs. 1(a) to 1(b) that the calculated NFetO has a reliable 1:1 corresponding relationship with the reported aFetO in eight CaO–containing slag systems without P2O5 components. Basically speaking, the calculated NFetO from the developed IMCT–Ni model can replace the reported aFetO in the above–mentioned five FeO–containing slag systems without P2O5 components.

Fig. 1.

Comparison between measured activity of iron oxides aFetO from various literatures and calculated mass action concentration of ion oxides NFetO based on IMCT at different temperatures.

Principally speaking, the developed thermodynamic IMCT–Ni model for calculating mass action concentrations Ni of structural units in CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3 slags cannot be reasonably applied to CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags. Two methods were used in this study to verify the adaptability of the developed thermodynamic IMCT–Ni model in CaO–SiO2–MgO–FeO–P2O5 slags,37) MgO–FeO–Fe2O3–P2O5 slags,38) CaO–FeO–Fe2O3–P2O5 slags39) and CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O540) slags: one method is directly using the normalized mass percentages of components in CaO–SiO2–MgO–FeO–P2O5 slags,37) MgO–FeO–Fe2O3–P2O5 slags,38) CaO–FeO–Fe2O3–P2O5 slags39) and CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags40) including P2O5 as the initial conditions, the calculated mass action concentrations Ni is assigned as N i including P 2 O 5 ; while, the other method is using the normalized mass percentages of components in CaO–SiO2–MgO–FeO–P2O5 slags,37) MgO–FeO–Fe2O3–P2O5 slags,38) CaO–FeO–Fe2O3–P2O5 slags39) and CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags40) ignoring P2O5 as the initial conditions, the calculated mass action concentrations Ni is labeled as N i ignoring P 2 O 5 . Theoretically speaking, the inevitable error between the calculated N Fe t O including P 2 O 5 using the first method and the calculated N Fe t O ignoring P 2 O 5 using the second method will be generated for CaO–SiO2–MgO–FeO–P2O5 slags,37) MgO–FeO–Fe2O3–P2O5 slags,38) CaO–FeO–Fe2O3–P2O5 slags39) and CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags.40) However, the magnitude of the generated error between the calculated N Fe t O including P 2 O 5 and N Fe t O ignoring P 2 O 5 is the key factor for a conclusion whether the developed thermodynamic IMCT–Ni model of the P2O5 free CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3 slags can be reliably applied to substitute CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags, such as to CaO–SiO2–MgO–FeO–P2O5 slags,37) MgO–FeO–Fe2O3–P2O5 slags,38) CaO–FeO–Fe2O3–P2O5 slags39) and CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags.40)

As shown in Fig. 2, a good agreement was observed between the calculated mass action concentrations N Fe t O ignoring P 2 O 5 and the calculated mass action concentrations N Fe t O including P 2 O 5 , i.e., the calculated N Fe t O ignoring P 2 O 5 based on thermodynamic IMCT–Ni model of the P2O5 free CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3 slags can be reliably applied to substitute the calculated N Fe t O including P 2 O 5 from thermodynamic IMCT–Ni model of the CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags. This phenomenon can be explained as that the physicochemical meaning of mass action concentration NP2O5 is almost consistent with the traditionally applied activity aP2O5 of component P2O5 in slags relative to liquid matter as standard state, i.e., N P 2 O 5 = n P 2 O 5 n i a P 2 O 5 = x P 2 O 5 γ P 2 O 5 , meanwhile, many researchers68,71,72,73,74,75) have reported that the value of activity coefficient γP2O5 of P2O5 in metallurgical slags is less than 10−17. Therefore, the value of NP2O5 is very small, i.e., the equilibrium mole number nP2O5 of P2O5 is also very low and have little effect on other calculated Ni value.

Fig. 2.

Comparison of measured activity of iron oxides aFetO from various literatures with calculated mass action concentration of ion oxides N Fe t O including P 2 O 5 based on IMCT in four slag systems with P2O5 content at different temperatures, and the comparison of calculated mass action concentration of iron oxides N Fe t O including P 2 O 5 with calculated mass action concentration of iron oxides N Fe t O including P 2 O 5 in above mentioned P2O5 containing slags.

Therefore it can be easily concluded that the defined NFetO from IMCT21,22,23,24,25,26,27,28) has the similar meaning with aFetO from viewpoint of traditionally metallurgical physicochemistry, which can be calculated according to (FetO–O) equilibrium as   

T[ Fe ]+[ O ]=( F e t O ) Δ r G m, Fe t O Θ =116100+48.79 T   (j/mol) (7a) 41)
  
K Fe t O Θ = a Fe t O a Fe t a O       a Fe t O = K Fe t O Θ a O = K Fe t O Θ [%O] f O (7b)
where fO is oxygen activity coefficient (–), and can be determined by   
lg f O = e O O [%O]+ e O C [%C]+ e O S [%S] (8)

The related values of interaction coefficients are chosen as e O O =−0.2, e O C =−0.45, e O S =−0.133.42)

4. Model for Calculating Phosphorus Distribution Ratio between CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 Slags and Hot Metal

4.1. Establishment of LP Prediction Model Based on Slag Oxidizing Ability

According to the ion and molecule coexistence theory that only free ion couples (Ca2++O2−), (Mg2++O2−) and (Mn2++O2−), which can be combined with iron oxides FetO in CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags, can take roles in dephosphorization reactions in terms of forming 9 dephosphorization products or molecules as P2O5, 3FeO·P2O5, 4FeO·P2O5, 2CaO·P2O5, 3CaO·P2O5, 4CaO·P2O5, 2MgO·P2O5, 3MgO·P2O5 and 3MnO·P2O5 according to IMCT21,22,23,24,25,26,27,28) as follows   

2[ P ]+5( F e t O ) =( P 2 O 5 ) +5t[ Fe ] Δ r G m, P 2 O 5 Θ =-122412+312.522T   (J/mol) (9a)
  
2[ P ]+5( F e t O ) +3( Fe 2+ + O 2- )=( 3FeO· P 2 O 5 ) +5t[ Fe ] Δ r G m, 3FeO P 2 O 5 Θ =-552816+405.23T   (J/mol) (9b)
  
2[ P ]+5( F e t O ) +4(F e 2+ + O 2- )=( 4FeO· P 2 O 5 ) +5t[ Fe ] Δ r G m, 4FeO P 2 O 5 Θ =-504243+359.889T   (J/mol) (9c)
  
2[ P ]+5( F e t O ) +2(C a 2+ + O 2- )=( 2CaO· P 2 O 5 ) +5t[ Fe ] Δ r G m, 2CaO P 2 O 5 Θ =-484372-26.569T  (J/mol) (9d)
  
2[ P ]+5( F e t O ) +3(C a 2+ + O 2- )=( 3CaO· P 2 O 5 ) +5t[ Fe ] Δ r G m, 3CaO P 2 O 5 Θ =-832302+318.672T  (J/mol) (9e)
  
2[ P ]+5( F e t O ) +4(C a 2+ + O 2- )=( 4CaO· P 2 O 5 ) +5t[ Fe ] Δ r G m, 4CaO P 2 O 5 Θ =-783768+309.049T  (J/mol) (9f)
  
2[ P ]+5( F e t O ) +2(M g 2+ + O 2- )=( 2MgO· P 2 O 5 ) +5t[ Fe ] Δ r G m, 2MgO P 2 O 5 Θ =45957-26.835T  (J/mol) (9g)
  
2[ P ]+5( F e t O ) +3(M g 2+ + O 2- )=( 3MgO· P 2 O 5 ) +5t[ Fe ] Δ r G m, 3MgO P 2 O 5 Θ =-390053+197.336T  (J/mol) (9h)
  
2[ P ]+5( F e t O ) +3(M n 2+ + O 2- )=( 3MnO· P 2 O 5 ) +5t[ Fe ] Δ r G m, 3MnO P 2 O 5 Θ =-665671+354.344T  (J/mol) (9i)

According to IMCT,21,22,23,24,25,26,27,28) the mass action concentration Ni of component i in slags is used to represent its reaction ability, and the corresponding equilibrium constants of Eq. (9) can be expressed as   

K P 2 O 5 Θ = a P 2 O 5 a Fe 5t a Fe t O 5 a P 2 = N P 2 O 5 ×1 N Fe t O 5 [%P] 2 f P 2 = ( (% P 2 O 5 ) P 2 O 5 / M P 2 O 5 / n i ) N Fe t O 5 [%P] 2 f P 2   (–) (10a)
  
K 3FeO P 2 O 5 Θ = a 3FeO P 2 O 5 a Fe 5t a Fe t O 5 a FeO 3 a P 2 = N 3FeO P 2 O 5 ×1 N Fe t O 5 N FeO 3 [%P] 2 f P 2 = ( (% P 2 O 5 ) 3FeO P 2 O 5 / M P 2 O 5 / n i ) N Fe t O 5 N FeO 3 [%P] 2 f P 2   (–) (10b)
  
K 4FeO P 2 O 5 Θ = a 4FeO P 2 O 5 a Fe 5t a Fe t O 5 a FeO 4 a P 2 = N 4FeO P 2 O 5 ×1 N Fe t O 5 N FeO 4 [%P] 2 f P 2 = ( (% P 2 O 5 ) 4FeO P 2 O 5 / M P 2 O 5 / n i ) N Fe t O 5 N FeO 4 [%P] 2 f P 2   (–) (10c)
  
K 2CaO P 2 O 5 Θ = a 2CaO P 2 O 5 a Fe 5t a Fe t O 5 a CaO 2 a P 2 = N 2CaO P 2 O 5 ×1 N Fe t O 5 N CaO 2 [%P] 2 f P 2 = ( (% P 2 O 5 ) 2CaO P 2 O 5 / M P 2 O 5 / n i ) N Fe t O 5 N CaO 2 [%P] 2 f P 2   (–) (10d)
  
K 3CaO P 2 O 5 Θ = a 3CaO P 2 O 5 a Fe 5t a Fe t O 5 a CaO 3 a P 2 = N 3CaO P 2 O 5 ×1 N Fe t O 5 N CaO 3 [%P] 2 f P 2 = ( (% P 2 O 5 ) 3CaO P 2 O 5 / M P 2 O 5 / n i ) N Fe t O 5 N CaO 3 [%P] 2 f P 2   (–) (10e)
  
K 4CaO P 2 O 5 Θ = a 4CaO P 2 O 5 a Fe 5t a Fe t O 5 a CaO 4 a P 2 = N 4CaO P 2 O 5 ×1 N Fe t O 5 N CaO 4 [%P] 2 f P 2 = ( (% P 2 O 5 ) 4CaO P 2 O 5 / M P 2 O 5 / n i ) N Fe t O 5 N CaO 4 [%P] 2 f P 2   (–) (10f)
  
K 2MgO P 2 O 5 Θ = a 2MgO P 2 O 5 a Fe 5t a Fe t O 5 a MgO 2 a P 2 = N 2MgO P 2 O 5 ×1 N Fe t O 5 N MgO 2 [%P] 2 f P 2 = ( (% P 2 O 5 ) 2MgO P 2 O 5 / M P 2 O 5 / n i ) N Fe t O 5 N MgO 2 [%P] 2 f P 2   (–) (10g)
  
K 3MgO P 2 O 5 Θ = a 3MgO P 2 O 5 a Fe 5t a Fe t O 5 a MgO 3 a P 2 = N 3MgO P 2 O 5 ×1 N Fe t O 5 N MgO 3 [%P] 2 f P 2 = ( (% P 2 O 5 ) 3MgO P 2 O 5 / M P 2 O 5 / n i ) N Fe t O 5 N MgO 3 [%P] 2 f P 2   (–) (10h)
  
K 3MnO P 2 O 5 Θ = a 3MnO P 2 O 5 a Fe 5t a Fe t O 5 a MnO 3 a P 2 = N 3MnO P 2 O 5 ×1 N Fe t O 5 N MnO 3 [%P] 2 f P 2 = ( (% P 2 O 5 ) 3MnO P 2 O 5 / M P 2 O 5 / n i ) N Fe t O 5 N MnO 3 [%P] 2 f P 2   (–) (10i)
where MP2O5 is molecular mass of P2O5 as 141.94 (–). According to Eq. (10), the respective phosphorus distribution ratio of structural units as basic components in the slags LP,i can be expressed by   
L P, P 2 O 5 = (% P 2 O 5 ) P 2 O 5 [%P] 2 = M P 2 O 5 K P 2 O 5 Θ N Fe t O 5 f P 2 n i   (–) (11a)
  
L P, 3FeO P 2 O 5 = (% P 2 O 5 ) 3FeO P 2 O 5 [%P] 2 = M P 2 O 5 K 3FeO P 2 O 5 Θ N Fe t O 5 N FeO 3 f P 2 n i   (–) (11b)
  
L P, 4FeO P 2 O 5 = (% P 2 O 5 ) 4FeO P 2 O 5 [%P] 2 = M P 2 O 5 K 4FeO P 2 O 5 Θ N Fe t O 5 N FeO 4 f P 2 n i   (–) (11c)
  
L P, 2CaO P 2 O 5 = (% P 2 O 5 ) 2CaO P 2 O 5 [%P] 2 = M P 2 O 5 K 2CaO P 2 O 5 Θ N Fe t O 5 N CaO 2 f P 2 n i   (–) (11d)
  
L P, 3CaO P 2 O 5 = (% P 2 O 5 ) 3CaO P 2 O 5 [%P] 2 = M P 2 O 5 K 3CaO P 2 O 5 Θ N Fe t O 5 N CaO 3 f P 2 n i   (–) (11e)
  
L P, 4CaO P 2 O 5 = (% P 2 O 5 ) 4CaO P 2 O 5 [%P] 2 = M P 2 O 5 K 4CaO P 2 O 5 Θ N Fe t O 5 N CaO 4 f P 2 n i   (–) (11f)
  
L P, 2MgO P 2 O 5 = (% P 2 O 5 ) 2MgO P 2 O 5 [%P] 2 = M P 2 O 5 K 2MgO P 2 O 5 Θ N Fe t O 5 N MgO 2 f P 2 n i   (–) (11g)
  
L P, 3MgO P 2 O 5 = (% P 2 O 5 ) 3MgO P 2 O 5 [%P] 2 = M P 2 O 5 K 3MgO P 2 O 5 Θ N Fe t O 5 N MgO 3 f P 2 n i   (–) (11h)
  
L P, 3MnO P 2 O 5 = (% P 2 O 5 ) 3MnO P 2 O 5 [%P] 2 = M P 2 O 5 K 3MnO P 2 O 5 Θ N Fe t O 5 N MnO 3 f P 2 n i   (–) (11i)
where fP is activity coefficient of the dissolved phosphorus in liquid iron (–), and can be calculated by considering chemical composition of hot metal and temperature as   
lg f P = e P j [%j]   (–) (12a)
  
e P j = A T +B   (–) (12b)
where A and B are two parameters related to temperature, (–). Therefore, the total phosphorus distribution ratio between CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags and hot metal can be obtained from Eq. (11) as follows   
L P = L P, P 2 O 5 + L P, 3FeO P 2 O 5 + L P, 4FeO P 2 O 5 + L P, 2CaO P 2 O 5 + L P, 3CaO P 2 O 5 + L P, 4CaO P 2 O 5 + L P, 2MgO P 2 O 5 + L P, 3MgO P 2 O 5 + L P, 3MnO P 2 O 5 = (% P 2 O 5 ) P 2 O 5 [%P] 2 + (% P 2 O 5 ) 3FeO P 2 O 5 [%P] 2 + (% P 2 O 5 ) 4FeO P 2 O 5 [%P] 2 + (% P 2 O 5 ) 2CaO P 2 O 5 [%P] 2 + (% P 2 O 5 ) 3CaO P 2 O 5 [%P] 2 + (% P 2 O 5 ) 4CaO P 2 O 5 [%P] 2 + (% P 2 O 5 ) 2MgO P 2 O 5 [%P] 2 + (% P 2 O 5 ) 3MgO P 2 O 5 [%P] 2 + (% P 2 O 5 ) 3MnO P 2 O 5 [%P] 2 = M P 2 O 5 N Fe t O 5 f P 2 ( K P 2 O 5 Θ + K 3FeO P 2 O 5 Θ N FeO 3 + K 4FeO P 2 O 5 Θ N FeO 4 + K 2CaO P 2 O 5 Θ N CaO 2 + K 3CaO P 2 O 5 Θ N CaO 3 + K 4CaO P 2 O 5 Θ N CaO 4 + K 2MgO P 2 O 5 Θ N MgO 2 + K 3MgO P 2 O 5 Θ N MgO 3 + K 3MnO P 2 O 5 Θ N MnO 3 ) n i (–) (13)

Therefore, the developed LP prediction model by NFetO to present slag oxidizing ability is composed of Eqs. (11) and (13) based on IMCT.21,22,23,24,25,26,27,28) According to the calculated Ni and Σni in Section 3, K i Θ by Eq. (10) and fP by Eq. (12), the total phosphorus distribution ratio LP of the slags which equals to the sum of respective phosphorus distribution ratio LP,i of basic ion couples in the slags can be calculated. The standard molar Gibbs free energy Δ r G m, i Θ of dephosphorization reactions in Eq. (9) for forming dephosphorization products i is determined from the reported data and summarized in Table 3.

Table 3. Calculation of standard molar Gibbs free energy for 9 dephosphorization reactions from the reported data of standard molar Gibbs free energy.
Dephosphorization reactionsResource reactions Δ r G m, i Θ (J/mol)
2[P]+5(FetO)=(P2O5)+5t[Fe]
Δ r G m, i Θ =−122412+312.522T
1 / 2 P2=[P]−157700+5.4T52)
1 / 2 O2=[O]−117110−3.39T52)
2[P]+5[O]=(P2O5)(l)−702912+556.472T53)
P2+ 5 / 2 O2=(P2O5)(l)−1603862+550.322T52,53)
t[Fe]+[O]=(FetO)−116100+48.79T54)
2[P]+5(FetO)+3(Fe2++O2−)=(3FeO·P2O5)+5t[Fe]
Δ r G m, i Θ =−552816+405.23T
3(FeO)+(P2O5)=(3FeO·P2O5)−430404+92.708T14)
2[P]+5(FetO)=(P2O5)+5t[Fe]−122412+312.522T
2[P]+5(FetO)+4(Fe2++O2−)=(4FeO·P2O5)+5t[Fe]
Δ r G m, i Θ =−504243+359.889T
4(Fe2++O2−)+(P2O5)=(4FeO·P2O5)−381831+47.367T14)
2[P]+5(FetO)=(P2O5)+5t[Fe]−122412+312.522T
2[P]+5(FetO)+2(Ca2++O2−)=(2CaO·P2O5)+5t[Fe]
Δ r G m, i Θ =−606784+285.953T
2(CaO)+P2+ 5 / 2 O2=(2CaO·P2O5)(s)−2189069+585.76T55)
(2CaO·P2O5)(s)=(2CaO·P2O5)(l)100834.4−62.0069T23)
P2+ 5 / 2 O2=(P2O5)(l)−1603862+550.322T52,53)
2[P]+5(FetO)=(P2O5)+5t[Fe]−122412+312.522T
2[P]+5(FetO)+3(Ca2++O2−)=(3CaO·P2O5)+5t[Fe]
−832302+318.672T
3(CaO)+P2+ 5 / 2 O2=(3CaO·P2O5)(s)−2313752+556.472T55)
P2+ 5 / 2 O2=(P2O5)(l)−1603862+550.322T52,53)
2[P]+5(FetO)=(P2O5)+5t[Fe]−122412+312.522T
2[P]+5(FetO)+4(Ca2++O2−)=(4CaO·P2O5)+5t[Fe]
−783768+309.049T
4(CaO)+(P2O5)(l)=(4CaO·P2O5)(l)−661356−3.473T56)
2[P]+5(FetO)=(P2O5)+5t[Fe]−122412+312.522T
2[P]+5(FetO)+2(Mg2++O2−)=(2MgO·P2O5)+5t[Fe]
45957−26.835T
2(Mg2++O2–)+(P2O5)=(2MgO·P2O5)168369−339.357T14)
2[P]+5(FetO)=(P2O5)+5t[Fe]−122412+312.522T
2[P]+5(FetO)+3(Mg2++O2−)=(3MgO·P2O5)+5t[Fe]
−390053+197.336T
3(MgO)+P2+ 5 / 2 O2=(3MgO·P2O5)(s)−1992839+510.0296T55)
(3MgO·P2O5)(s)=(3MgO·P2O5)(l)121336−74.8936T55)
P2+ 5 / 2 O2=(P2O5)(l)−1603862+550.322T52,53)
2[P]+5(FetO)=(P2O5)+5t[Fe]−122412+312.522T
2[P]+5(FetO)+3(Mn2++O2−)=(3MnO·P2O5)+5t[Fe]
−665671+354.344T
2[P]+5[O]+3(MnO)=(3MnO·P2O5)−1248715+598.312T57)
2[P]+5[O]=(P2O5)(l)−702912+556.472T53)
2[P]+5(FetO)=(P2O5)+5t[Fe]−122412+312.522T

4.2. Comparison of Measured LP, measured and Calculated L P, calculated IMCT

In order to examine the applicability of the IMCT–LP model developed in the present study based on the ion and molecule coexistence theory, the calculated phosphorous distribution L P, calculated IMCT between several slag systems and hot metal, i.e., CaO–FeO–Fe2O3–P2O5 slags,29) CaO–SiO2–FeO–Fe2O3–P2O5 slags,20) CaO–FeO–Fe2O3–Al2O3–P2O5 slags,20) CaO–SiO2–FeO–MgO–P2O5 slags,7) CaO–SiO2–FeO–Fe2O3–MgO–P2O5 slags,30) and CaO–SiO2–MgO–FeO–Fe2O3–MnO–P2O5 slags31) were compared with all available measured phosphorous distribution LP, measured at different temperatures reported in various literatures by different investigators, respectively. The experimental techniques employed by these investigators for phosphorous distribution measurements were summarized in Table 4.

Table 4. Summary of previous investigations on phosphorus distribution measurements.
SlagsResearcher(s)Experimental TechniqueRef.
CaO–FeO–Fe2O3–P2O5Nagabayashi et al.Equilibrated the slags in CaO crucible with liquid iron has been studied at a temperature range from 1573 to 1953 K29)
CaO–SiO2–FeO–Fe2O3–P2O5Wrampelmeyer et al.Around 50 g of metal and 12 g of slag were held in pure CaO crucibles for 30 to 100 min in most cases20)
CaO–Al2O3–FeO–Fe2O3–P2O5Wrampelmeyer et al.Around 50 g of metal and 12 g of slag were held in pure CaO crucibles for 30 to 100 min in most cases20)
CaO–SiO2–MgO–FeO–Fe2O3–P2O5Basu et al.Ten grams each of electrolytic iron and synthetic slag premix, of specified chemical composition, were put in the magnesia crucible. The crucible was then placed in a high-temperature furnace and heated to the desired temperature7)
CaO–SiO2–MgO–FeO–Fe2O3–P2O5Ting et al.Equilibrated the slags in MgO crucible with liquid iron has been studied at a temperature range from 1823 to 1873 K30)
CaO–SiO2–MgO–FeO–Fe2O3–MnO–P2O5Suito et al.Equilibrated the slags in iron crucible with liquid iron under the condition of high purity argon gas31)

The logarithm of the calculated L P, calculated IMCT by IMCT–LP model for the six CaO–containing slag systems has been compared with the measured phosphorous distribution LP, measured in logarithm form, which is equal to (%P2O5)/[%P]2, as shown in Fig. 3, a relative agreement between phosphorous distribution log L P, calculated N FetO , IMCT and log LP, measured in logarithm form can be obtained for the six CaO–containing slag systems, respectively.

Fig. 3.

Comparison between measured phosphorus distribution log LP, measured from various literatures and calculated phosphorus distribution log L P, calculated N FetO , IMCT based on IMCT–LP model, respectively.

The chosen values of log LP, measured between CaO–FeO–Fe2O3–P2O5 slags and liquid iron are reported data from Nagabayashi29) et al. in a temperature range from 1823 K to 1973 K, respectively. As shown in Fig. 4(a) that a relative agreement between phosphorous distribution log L P, calculated N FetO , IMCT and log LP, measured can be obtained for CaO–FeO–Fe2O3–P2O5 slags.29) However, the disagreement between the phosphorous distribution log L P, calculated N FetO , IMCT and log LP, measured in a narrow range of the measured LP, measured at about 5.1 for some experimental points can be obviously found in Fig. 4(a). It should be pointed out that Nagabayashi68) had confirmed his regular solution model68) was satisfied for all experimental results except for composition extreamly rich in iron oxide, meanwhile, the disagreement between the log LP, calculated by Nagabayashi’s regular solution model68) and log LP, measured in a narrow range of the measured log LP, measured at about 5.1 can also be found in his latter publication.68) Therefore, it can be deduced that the experimental error is the main reason for the disagreements.

Fig. 4.

Comparison between measured phosphorus distribution log LP, measured from various literatures and calculated phosphorus distribution log L P, calculated N FetO , IMCT based on IMCT–LP model at different temperatures, respectively.

The value of measured phosphorous distribution between CaO–SiO2–FeO–Fe2O3–P2O5 slags20) and molten steel or the value of measured phosphorous distribution between CaO–FeO–Fe2O3–Al2O3–P2O5 slags20) and molten steel at 1823 K, 1873 K and 1973 K were reported by Wrampelmeyer20) et al. The comparison between phosphorous distribution log L P, calculated N FetO , IMCT and log LP, measured in CaO–SiO2–FeO–Fe2O3–P2O5 slags20) and CaO–FeO–Fe2O3–Al2O3–P2O5 slags20) at 1823 K, 1873 K and 1973 K were shown in Figs. 4(b) and 4(c), Both good 1:1 corresponding relationship between phosphorous distribution log L P, calculated N FetO , IMCT and log LP, measured can be found for most experimental data, respectively.

The selected values of phosphorous distribution log LP, measured between CaO–SiO2–FeO–MgO–P2O5 slags and liquid iron at 1873 K and 1923 K were reported by Basu7) et al. An excellent linear relationship between the phosphorous distribution log L P, calculated N FetO , IMCT and log LP, measured for all experimental data can be obviously obtained in Fig. 4(d).

The comparison between measured phosphorous distribution log LP, measured for CaO–SiO2–FeO–Fe2O3–MgO–P2O5 slags at 1823 K and 1873 K by Ting30) et al. and log L P, calculated N FetO , IMCT was illustrated in Fig. 4(e). A reasonable agreement was observed, but the calculated value of log L P, calculated N FetO , IMCT are slightly higher than the measured value of log LP, measured in a narrow range of the measured log LP, measured at about 4.

The comparison between measured phosphorous distribution log LP, measured for CaO–SiO2–MgO–FeO–Fe2O3–MnO–P2O5 slags31) at 1823 K, 1873 K and 1923 K by Ting30) et al. and log L P, calculated N FetO , IMCT was illustrated in Fig. 4(f). A scattered linear agreement can be observed, but some calculated value of log L P, calculated N FetO , IMCT are slightly higher than the measured value of log LP, measured in a narrow range from 4 to 5.

Therefore, the developed IMCT–LP prediction model can be basically applied to predict phosphorous distribution LP for the above-mentioned six CaO–containing slag systems. However, it should be pointed out that the mass action concentration of iron oxides FetO, i.e., NFetO, is applied to present slag oxidization ability in IMCT–LP prediction model. Considering the large different contribution of ion couple (Fe2++O2–) and simple molecule Fe2O3 to the mass action concentration of iron oxides NFetO, i.e., the contribution of simple molecule Fe2O3 to NFetO is equivalent to 3 times that of ion couple (Fe2++O2–). Hence, the chemical analysis error of mass content of Fe2O3 can result in relatively large calculation error of phosphorous distribution.

5. Conclusions

A thermodynamic model for calculating mass action concentration for several CaO–containing slags within CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 slags was developed based on the ion and molecule coexistence theory. The defined comprehensive mass action concentration of iron oxides NFetO as NFetO+6NFe2O3+8NFeO·Fe2O3 according to the IMCT has a reliable 1:1 corresponding relationship with the measured activity of iron oxides aFetO in the FetO–containing slag systems. Therefore, the defined comprehensive mass action concentration of iron oxides NFetO can be applied to represent the oxidation ability of the FetO–containing slag systems, like the measured activity of iron oxides aFetO. Using the calculated mass action concentration of iron oxides as a presentation of slag oxidization ability, a thermodynamic model for calculating phosphorous distribution between several slag systems and hot metal has been developed. The comparison of the calculated total phosphorous distribution with all available measured phosphorous distribution reported in literatures shows that the agreement between the calculated total phosphorous distribution and measured phosphorous distribution is good, this results indicate that the developed IMCT–LP model can be applied reliably to calculate the phosphorus distribution ratio between CaO–FeO–Fe2O3–P2O5 slags, CaO–SiO2–FeO–Fe2O3–P2O5 slags, CaO–FeO–Fe2O3–Al2O3–P2O5 slags, CaO–SiO2–FeO– MgO–P2O5 slags, CaO–SiO2–FeO–Fe2O3–MgO–P2O5 slags, CaO–SiO2–MgO–FeO–Fe2O3–MnO–P2O5 slags and hot metal, respectively.

References
 
© 2014 by The Iron and Steel Institute of Japan
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