RETRACTION - JST

2663 © 2014 ISIJ

RETRACTION

The following three articles were withdrawn upon request of their authors on October 3, 2014, becausethey were submitted without the consent of all the authors.

Retraction: Representation of Dephosphorization Ability for CaO–Containing Slags Based on the Ion and Molecule Coexistence Theory

Peng-cheng LI1,2) and Jian-liang ZHANG1)

1) State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing, 100083 P. R. China.2) State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences,Beijing, 100190 P. R. China.

This article was published in ISIJ Int., 54 (2014), No. 3, 567–577.

Retraction: A Prediction Model of Phosphorus Distribution between CaO–SiO2–MgO–FeO–Fe2O3–P2O5 Slags and Liquid Iron

Peng-cheng LI1,2,3) and Jian-liang ZHANG1,2)

1) State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing, 100083 P. R. China.2) School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing, 100083 P. R.China.3) State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences,Beijing, 100190 P. R. China.


Retraction: Representation of Reaction Ability for Structural Units in Fe–Al Binary Melts

Peng-cheng LI1,2,3) and Jian-liang ZHANG1,2)

1) State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing, 100083 P. R. China.2) School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing, 100083 P. R.China.3) State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences,Beijing, 100190 P. R. China.


© 2014 ISIJ 756

ISIJ International, Vol. 54 (2014), No. 4, pp. 756–765

A Prediction Model of Phosphorus Distribution between CaO–SiO2–MgO–FeO–Fe2O3–P2O5 Slags and Liquid Iron

Peng-cheng LI1,2,3)* and Jian-liang ZHANG1,2)

1) State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing, 100083 P. R. China.2) School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing, 100083 P. R.China. 3) State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy ofSciences, Beijing, 100190 P. R. China.

(Received on September 8, 2013; accepted on December 1, 2013)

CaO−SiO2−MgO−FeO−Fe2O3−P2O5 slags is typical in the basic oxygen steelmaking(BOS) process. Phos-phate distribution between slags and liquid iron is an index of the phosphorus holding capacity of theslag, which determines the phosphorus content achievable in the finished steel. In this study, a thermo-dynamic model for calculating phosphorus distribution between CaO−SiO2−MgO−FeO−Fe2O3−P2O5 slagsand liquid iron, i.e., IMCT−Lp model, has been developed coupled with a developed thermodynamic modelfor calculating mass action concentrations of structural units, i.e., IMCT−Ni model, based on ion and mol-ecule coexistence theory. Simple binary basicity R have a large effect on equilibrium mole number Σni ofstructural units in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags, the formula of equilibrium mole number Σni

against the simple binary basicity R of slags can be regressed as Σni = 2.604 – 3.029*exp(–R/2.339), andthe fitting degree is 0.995. The comparison of the calculated phosphorous distribution by IMCT−Lp modelwith the measured phosphorous distribution reported from different literatures shows that the agreementbetween the calculated phosphorous distribution and measured phosphorous distribution is good. Mean-while, some other Lp prediction models have also been taken into consideration for calculating phosphatedistribution between CaO−SiO2−MgO−FeO−Fe2O3−P2O5 slags and liquid iron, and the results shows thatIMCT−Lp model have more accuracy compared with other Lp prediction models. The developed IMCT−Lp

model can quantitatively calculate the respective contribution of FetO, CaO+FetO and MgO+FetO in theslags. A significant difference of dephosphorziation abilities among FetO, CaO+FetO and MgO+FetO canbe found as approximately 0.00%, 99.98%, 0.01%. Meanwhile, the phosphorus in liquid iron can be effec-tively extracted by CaO+FetO in slags to form complex molecules 3CaO·P2O5 which made the main con-tribution to dephosphorizaiton in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags.

KEY WORDS: phosphorous distribution; mass action concentration; structural units; ion and molecule coex-istence theory.

1. Introduction

Phosphorus can make the steel prone to embrittlementduring heat treatment and cause degradation of electricalproperties. It’s therefore useful to study suitable metal-slagreactions with the objective to remove phosphorus fromsteel melts below up-to-date limits. Many studies werecarried out to measure phosphorous distribution betweenvarious slags and liquid iron.1–6) Colclough1,2) have madeexperiments involving the dephosphorization from the liq-uid iron in a basic open-hearth furnace, and he proposed thatthe phosphorus in liquid iron was mainly extracted in theform of tetra-calcium phosphate (4CaO·P2O5). Herty3) car-ried out a series of experiments using an experimental fur-nace as well as 200 T basic open-hearth furnace and cameto the conclusion that P2O5 formed tri-calcium phosphate(3CaO·P2O5), but not tetra-calcium phosphate (4CaO·P2O5).Considering the fact that the measurement of phosphorousdistribution between molten slag and liquid iron was costlyand difficult in the operation, several attempts4–8) were madeto describe and predict phosphorus partition ratios as a func-tion of slag composition. Healy4) conducted a series ofexperiments involving the measurement of phosphorusdistribution between slags and liquid iron, and publishedthe famous correlation for equilibrium phosphorus partition

in a wide range of slag compositions and temperatures as

. Sim-

ilarly, many phosphorous distribution prediction models havebeen developed based on some empirical regressions of themeasured data, such as Suito’s models,6,7) Sommerville’smodel8) and Balajiva’s model.9) All the above-mentionedphosphorous distribution prediction models4,6–9) have beenevaluated in the following sections.

Many researchers5,6,12,35–40) have worked towards estimationof in metallurgical slags with different chemical compo-sitions. Turkdogan and Pearson5) proposed an expression ofactivity coefficient of P2O5 as a function of slag compositionsi.e., lgγ P2O5 = –1.12(22XCaO + 15XMgO + 13XMnO + 12XFeO –

2XSiO2) – + 23.58. In 1981, on the basis of the mea-

sured phosphorus distribution between MgO–saturatedCaO–MgO–FeO–SiO2 slags, containing 30–40% CaO, inthe temperature range from 1 823 K to 1 923 K, Suito et al.6)

modified Turkdogan’s correlation5) as that lgγ P2O5 = –1.01

(23XCaO + 17XMgO + 8XFeO) – + 1.12. The correlation

proposed by Suito et al.6) indicates significantly lower tem-perature dependence of γ P2O5, compared with Turkdogan’sexpression.5) Basu et al.10) observed that the relationshipbetween the measured γ P2O5 and the calculated γ P2O5 byTurkdogan’s γ P2O5 prediction model5) or Suito’s γ P2O5 predic-

* Corresponding author: E-mail: [email protected]: http://dx.doi.org/10.2355/isijinternational.54.756

lg(% )[% ]

. (% ) . lg(% )PP

CaO T Fe= + + ⋅ −22 350

0 08 2 5 16T

γ P O2 5

42000

T

26 000

T

ISIJ International, Vol. 54 (2014), No. 4

757 © 2014 ISIJ

tion model6) was not good, and developed two γ P2O5

prediction models as lgγ P2O5 = –6.775NCaO – 4.995NFeO +

2.816NMgO – 1.377NSiO2 + and lgγ P2O5 =

– 8.172XCa2+ – 7.169XFe2+ + 1.323XMg2+ –

11.66 (r2 =0.86). Both of Basu’s models12) were satisfac-torily applicable to the data of other previous workers.5,6)

Suito et al.11) and Kobayashi et al.12) made extensive workon the dephosphorizaion ability of steelmaking slags con-taining MnO, and they observed that the addition of MnOhad a negative effect on dephosphorization. In 2007, Basuet al.10) conducted experiments to establish for equilibriumphosphorus partition between CaO–SiO2–MgO–FeO–P2O5slags and molten Fe which is free from Al2O3 or MnO, andproposed the correlation for equilibrium phosphorus parti-tion in terms of ionic.

From the above discussion, it can be obviously observedthat much of the previous work was carried out using arti-ficial parameters, and most of the regressed parameters werevalid only within certain limits of concentration. The presentstudy developed a fresh model without artificial regressedparameters to establish phosphorus partition between CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags and liquid iron based onthe ion and molecule coexistence theory. The measured dataof phosphorus distribution of CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags equilibrated with liquid iron in a temper-ature range from 1 823 K to 1 923 K reported byNagabayashi et al.13) and the measured data of phosphorusdistribution of CaO–SiO2–MgO–FeO–P2O5 slags equilibrat-ed with liquid iron in a temperature range from 1 873 K to1 923 K by Basu et al.10) were both selected to verify theaccuracy of the developed IMCT–Lp prediction model. Itshould be pointed out that CaO–SiO2–MgO–FeO–P2O5slags was a special CaO–SiO2–MgO–FeO–Fe2O3–P2O5slags with the assumption that the content of Fe2O3 equal tozero. However, the major aim of this study is to represent aninvestigation of true characteristics of dephosphorization inCaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags. Hence, only thereported data of CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slagsby Nagabayashi et al.13) was taken into consideration forrepresentation of reaction abilities of structure units in thefollowing sections.

2. Model for Calculating Mass Action Concentrationsof Structural Units in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 Slags

2.1. HypothesesIn view of the fact that there are ions and molecules in

molten metallurgical slags simultaneously,13–19,22) the mainviewpoints of the ion and molecule coexistence theory ofslag structures in the developed thermodynamic model canbe simply summarized as follows: 1) Molten slags of CaO–SiO2–MgO–FeO–Fe2O3–P2O5 are composed of Ca2+, Mg2+,Fe2+, and O2− as simple ions, SiO2 and P2O5 as simple mol-ecules, silicates, aluminates as complex molecules. Eachstructural unit has its independent position in the slags.Every cation and anion generated from the same componentwill take part in reactions of forming complex molecules inthe form of ion couple as (Me2++O2−). 2) Reactions of form-ing complex molecules are under chemically dynamic equi-librium between bonded ion couples from simple ions andsimple molecules. 3) Structural units in the selected slagsequilibrated with liquid iron bear continuity in the range of

investigated concentration range. 4) Chemical reactions offorming complex molecules obey the mass action law.

2.2. Model for Calculating Mass Action Concentrationsof Structural Units in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 Slags

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

According to traditional metallurgical physicochemistry,CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags is composed ofCaO, SiO2, MgO, FeO, Fe2O3 and P2O5, while the extractedphosphorus gradually enter into the slags with the proceed-ing of dephosphorization reactions until dephosphorizationreactions reach equilibrium. However, the IMCT14–20,23) sug-gests that the extracted phosphorus from liquid iron into theslags exists as P2O5 can be bonded with ion couples(Fe2++O2−), (Ca2++O2−) and (Mg2++O2−) to form moleculesas P2O5, 3FeO·P2O5, 4FeO·P2O5, 2CaO·P2O5, 3CaO·P2O5,4CaO·P2O5, 2MgO·P2O5, and 3MgO·P2O5 in oxidizing slagscontaining iron oxides FetO, respectively.

In view of the reported binary and ternary phasediagrams20,21) of CaO–SiO2 slags, CaO–P2O5 slags, FeO–P2O5 slags, MgO–P2O5 slags, CaO–MgO slags, CaO–MgO–SiO2 slags, MgO–SiO2 slags, and CaO–FeO–SiO2 slags in atemperature range from 1 673 K to 1 986 K, about 20 kindsof complex molecules can be formed in the slags as listedin Table 1.

2.2.2. Model for Calculating Mass Action Concentrationsof Structural Units in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 Slags

The mole number of above–mentioned six components,such as CaO, SiO2, MgO, FeO, Fe2O3 and P2O5 in 100 g ofCaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags is assigned as b1 =

, , , , and to b6 =

present chemical composition of the slags. Thedefined14–20,23) equilibrium mole numbers ni of all above-mentioned structural units in 100 g slags equilibrated withliquid iron at metallurgical temperatures have been also giv-en out in Table 1. According to the ion and molecule coex-istence theory,14–20,23) each ion couple is electroneutral andcan be electrolyzed into cation and anion based on electrov-alence balance principle. Hence, ion couple (Me2++O2–)with a fixed amount under equilibrium condition canproduce two times amount of structural units, i.e.,

. The total equilibrium molenumber Σni of all structural units in 100 g slags equilibratedwith liquid iron can be expressed as follows

...... (1)

With respect to the definition of mass actionconcentrations14–20,23) Ni for structural units, which is a ratioof equilibrium mole number of structural units i to the totalequilibrium mole numbers of all structural units in a closesystem with a fixed amount, Ni of structural units i and ioncouples (Me2++O2−) in molten slags can be calculated by

.........................(2a)

........ (2b)

100713 992 0 772

Tr− =. ( . )

− +−1.377SiO4

4XT

340

nCaO0

b n2 = SiO0

2b n3 = MgO

0b n4 = FeO

0 b n5 = Fe O0

2 3

nP O0

2 5

n n nMe ,MeO O ,MeO MeO2+ 2-+ = 2

n n n n n n

n n n n

i∑ = + + + +

+ + + + +

2 2 2CaO SiO MgO FeO Fe O

P O c1 c2 c20

2 2 3

2 5mo( ll)

Nn

nii

i

= −∑

( )

N N N

n n

n

n

ni i

MeO Me ,MeO O ,MeO

Me ,MeO O ,MeO MeO

2+ 2-

2+ 2-

= +

=+

= −∑ ∑

2( )

© 2014 ISIJ 758


All definitions of Ni for formed ion couples from simpleions, simple and complex molecules in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags were listed in Table 1. Meanwhile,it should be pointed out that the physicochemistry meaningof Ni is almost consistent with the traditionally appliedactivity ai of component i in slags, in which pure matter ischosen as standard state and mole fraction is selected asconcentration unit.14–20,23)

The chemical reaction formulas of 20 kinds of possiblyformed complex molecules, their standard molar Gibbs freeenergy of formation reactions as a function of abso-lute temperature T, reaction equilibrium constant andpresentation of mass action concentration of all complexmolecules Nci expressed by using , N1 (NCaO), N2 ( ),N3 (NMgO), N4 (NFeO), N5 ( ) and N6 ( ) based on themass action law were summarized in Table 1.

The mass conservation equations of six components in100 g of CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags equili-

brated with liquid iron can be established according to thedefinition14–20,23) of ni and mass action concentrations Ni ofall structural units listed in Table 1 as follows

...(3a)

..... (3b)

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 CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags.

Reactions (J/mol) Mole numbers ofstructural units (mol)

Mass action concentrationsof structural units (–)

3(Ca2++O2−)+(SiO2)=(3CaO·SiO2) −118 826−6.694T 24)

2(Ca2++O2−)+(SiO2)=(2CaO·SiO2) −102 090−24.267T 25)

(Ca2++O2−)+(SiO2)=(CaO·SiO2) −21 757−36.819T 25)

2(Mg2++O2−)+(SiO2)=(2MgO·SiO2) −56 902−3.347T 25)

(Mg2++O2−)+(SiO2)=(MgO·SiO2) 23 849−29.706T 25)

2(Fe2++O2−)+(SiO2)=(2FeO·SiO2) −9 395−0.227T 24,27,28)

(Ca2++O2−)+(Mg2++O2−)+(SiO2)=(CaO·MgO·SiO2) −124 683+3.766T 24)

(Ca2++O2−)+(Mg2++O2−)+2(SiO2)=(CaO·MgO·2SiO2) −80 333−51.882T 25)

2(Ca2++O2−)+(Mg2++O2−)+2(SiO2)=(2CaO·MgO·2SiO2) −73 638−63.597T 25)

3(Ca2++O2−)+(Mg2++O2−)+2(SiO2)=(3CaO·MgO·2SiO2) −205 016−31.798T 25)

2(Ca2++O2−)+(Fe2O3)=(2CaO·Fe2O3) −53 137−2.510T 24)

(Fe2++O2−)+(Fe2O3)=(FeO·Fe2O3) −78 451+30.813T 26,27)

(Mg2++O2−)+(Fe2O3)=(MgO·Fe2O3) −19 246−2.092T24)

2(Ca2++O2−)+(P2O5)=(2CaO·P2O5) −484 372−26.569T 24)

3(Ca2++O2−)+(P2O5)=(3CaO·P2O5) −709 890+6.150T 24)

4(Ca2++O2−)+(P2O5)=(4CaO·P2O5) −661 356−3.473T29)

3(Fe2++O2−)+(P2O5)=(3FeO·P2O5) −587 683−71.706T 27,28)

4(Fe2++O2−)+(P2O5)=(4FeO·P2O5) −512 251+128.083T 27,28)

2(Mg2++O2−)+(P2O5)=(2MgO·P2O5) 168 369−339.357T 24)

3(Mg2++O2−)+(P2O5)=(3MgO·P2O5) −267 641−115.186T 24)

Δ Θr m, cG i K ic

Θ

n nc1 3CaO SiO2= ⋅ N

n

nN

ic1

c13CaO SiO2

= =∑ ⋅ K

N

N Nc1

c1Θ =13

2

n nc2 2CaO SiO2= ⋅ N

n

nN

ic2

c22CaO SiO2

= =∑ ⋅ K

N

N Nc2

c2Θ =12

2

n nc3 CaO SiO2= ⋅ N

n

nN

ic3

c3CaO SiO2

= =∑ ⋅ K

N

N Nc3

c3Θ =1 2

n nc4 2MgO SiO2= ⋅ N

n

nN

ic4

c42MgO SiO2

= =∑ ⋅ K

N

N Nc4

c4Θ =2 3

2

n nc5 MgO SiO2= ⋅

Nn

nN

ic5

c5MgO SiO2

= =∑ ⋅ K

N

N Nc5c5Θ =

2 3

n nc6 2FeO SiO2= ⋅

Nn

nN

ic6

c62FeO SiO2

= =∑ ⋅ K

N

N Nc6

c6Θ =2 4

2

n nc7 CaO MgO SiO2= ⋅ ⋅ N

n

nN

ic7

c7CaO MgO SiO2

= =∑ ⋅ ⋅ K

N

N N Nc7

c7Θ =1 2 3

n nc8 CaO MgO SiO2= ⋅ ⋅2 N

n

nN

ic8

c8CaO MgO SiO2

= =∑ ⋅ ⋅2 K

N

N N Nc8

c8Θ =1 3 2

2

n nc9 2CaO MgO SiO2= ⋅ ⋅2

Nn

nN

ic9

c92CaO MgO SiO2

= =∑ ⋅ ⋅2 K

N

N N Nc9

c9Θ =12

22

3

n nc10 3CaO MgO SiO2= ⋅ ⋅2 N

n

nN

ic10

c103CaO MgO SiO2

= =∑ ⋅ ⋅2 K

N

N N Nc10

c103

Θ =1 2

23

n nc11 2CaO Fe O2 3= ⋅ N

n

nN

ic11

c112CaO Fe O2 3

= =∑ ⋅

KN

N Nc11

c112

Θ =1 5

n nc12 FeO Fe O2 3= ⋅ N

n

nN

ic12

c12FeO Fe O2 3

= =∑ ⋅ K

N

N Nc12

c12Θ =4 5

n nc13 MgO Fe O2 3= ⋅ N

n

nN

ic13

c13MgO Fe O2 3

= =∑ ⋅ K

N

N Nc13

c13Θ =3 5

n nc14 2CaO P O2 5= ⋅ N

n

nN

ic14

c142CaO P O2 5

= =∑ ⋅ K

N

N Nc14

c14Θ =12

6

n nc15 3CaO P O2 5= ⋅

Nn

nN

ic15

c153CaO P O2 5

= =∑ ⋅ K

N

N Nc15

c15Θ =13

6

n nc16 4CaO P O2 5= ⋅ N

n

nN

ic16

c164CaO P O2 5

= =∑ ⋅ K

N

N Nc16

c16Θ =14

6

n nc17 3FeO P O2 5= ⋅ N

n

nN

ic17

c173FeO P O2 5

= =∑ ⋅ K

N

N Nc17

c17Θ =43

6

n nc18 4FeO P O2 5= ⋅ N

n

nN

ic18

c184FeO P O2 5

= =∑ ⋅ K

N

N Nc18

c18Θ =44

6

n nc19 2MgO P O2 5= ⋅ N

n

nN

ic19

c192MgO P O2 5

= =∑ ⋅ K

N

N Nc19

c19Θ =32

6

n nc20 3MgO P O2 5= ⋅ N

n

nN

ic20

c203MgO P O2 5

= =∑ ⋅ K

N

N Nc20

c20Θ =33

6

Δ Θr m,cG i

K icΘ

K icΘ NSiO2

NFe O2 3NP O2 5

b N N N N N N N N

N N N

1 1

1

23 2 2 3

2 3 4

= + + + + + + +

+ + +

( c1 c2 c3 c7 c8 c9 c10

c14 c15 c166 c1

c2 c3 c7 3 2 c8

) (n N K N N

K N N K N N K N N N K

i∑ = +

+ + + +

1

23

2

1 13

2

12

2 1 2 1

Θ

Θ Θ Θ ΘΘ

Θ Θ Θ

Θ

N N N

K N N N K N N N K N N

K N

1

1 6

13

2 3

3

3 22

c9 12

3 2 c10 13

3 22

c142

c15

+ + ++ NN K N N n ni6 1

46

04+ =∑c16 CaO molΘ ) ( )

b N N N N N N N N N

N N n Ni

2 2

2

2

2 2

= + + + + + + + ++ + =∑(

) (c1 c2 c3 c4 c5 c6 c7 c8

c9 c10 ++ ++ + + +

K N N K N N

K N N K N N K N N K N Nc1 c2

c3 c4 c5 c6

Θ Θ

Θ Θ Θ Θ13

2 12

2

1 2 2 32

2 3 2 422

1 3 1 3 22

12

3 22

13

3 22

2 2

2

+ + ++K N N N K N N N K N N N

K N N N ni

c7 2 c8 c9

c10

Θ Θ Θ

Θ )∑∑ = nSiO0

2mol( )


759 © 2014 ISIJ

......(3c)

...... (3d)

.......(3e)

... (3f)

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

.... (4)

The equation group of Eqs. (3) and (4) is the governingequations of the developed thermodynamic model for calcu-lating mass action concentrations Ni of structural units inCaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags equilibrated withliquid iron. Obviously, there are seven unknown parametersas N1, N2, N3, N4, N5, N6 and Σni with 7 independent equa-tions in the developed equation group of Eqs. (3) and (4).The unique solution of Ni, Σni and ni can be calculated bysolving these algebraic equation group of Eqs. (3) and (4)by combining with the definition of Ni in Eq. (2).

2.3. Definition of Mass Action Concentration for IronOxides FetO in the CaO–SiO2–MgO–FeO–Fe2O3–P2O5 Slags

It’s well-known that high oxygen potential and basicity ofthe slags are needed to remove phosphorus from steel melts.In this study, the mass action concentration of iron oxidesFetO, i.e., , is recommended to present slag oxidizationability. Meanwhile, it should be pointed out that the definedcomprehensive mass action concentration of ironoxides in slags can be applied to accurately replace activityof relative pure liquid matter as standard state in pre-vious publication.23)

The IMCT14–20,23) proposed that all iron oxides in metal-lurgical slags are composed of ion couple (Fe2++O2−), sim-ple molecule Fe2O3 and complex molecule FeO·Fe2O3,therefore, the related structural units of iron oxides candynamically equilibrate among those structural units as fol-lows

...................(5a).............. (5b)

Obviously, when the reactions of Eqs. (5a) and (5b) reachequilibrium, increase of single molcule of Fe2O3 will lead tothe changing of balance with increase of one third ion cou-

ple since the equilibirum constant is kept constant. There-fore, the mass action concentration of free ion couple(Fe2++O2−) can directly represent present slag oxidizationability. Meanwhile, it should be pointed out that the symbolof is applied in this study to keep consistent with tra-ditional symbol of iron oxides “FetO” in the related refer-ence. Therefore, the slags oxidization ability or can bedefined as

................... (6)According to IMCT, the defined from IMCT23) has

the similar meaning with from viewpoint of tradition-ally metallurgical physicochemistry, which can be calculat-ed according to (FetO–O) equilibrium as

.............(7a)

.............. (7b)

where fO is oxygen activity coefficient (–), and can be deter-mined by

....................... (8)The related values of interaction coefficients are chosen as

=–0.2, =–0.07.

3. Results of Mass Action Concentrations for StructuralUnits in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 Slags

3.1. Relation between Mass Percent of Six Componentsand Mass Action Concentrations of Related StructuralUnits in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 Slags

The relationship between mass percentage of CaO, SiO2,MgO, FeO, Fe2O3 and P2O5 as components and the calcu-lated mass action concentrations Ni of structural units, i.e.,(Ca2++O2−), SiO2, (Mg2++O2−), (Fe2++O2−), Fe2O3 and P2O5,in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags in a tempera-ture range from 1 823 K to 1 923 K was shown in Fig. 1,respectively. The good scatter linear relationship can beobserved for (Ca2++O2−), SiO2, (Mg2++O2−), (Fe2++O2−) andFe2O3 as components in Figs. 1(a), 1(b), 1(c), 1(d) and 1(e).The scatter corresponding relationship can be found forP2O5 in Fig. 1(f). The good scatter linear relationship for(Ca2++O2−), SiO2, (Mg2++O2−), (Fe2++O2−) and Fe2O3 can beexplained as follows 1) some basic oxides such as(Ca2++O2−) and (Mg2++O2−) can react with SiO2 to formcomplex molecules 3CaO·SiO2, 2CaO·SiO2, CaO·SiO2,2MgO·SiO2, MgO·SiO2, CaO·MgO·2SiO2, 2CaO·MgO·2SiO2and 3CaO·MgO·2SiO2 as shown in Table 1; 2) (Fe2++O2−)and Fe2O3 can also be consumed as iron oxides in the pro-cess of dephosphorization.

3.2. Relation between Mass Percent of Six Componentsand Equilibrium Mole Numbers of Related StructuralUnits in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 Slags

The relationship between mass percentage of CaO, SiO2,MgO, FeO, Fe2O3 and P2O5 as components and the calcu-lated equilibrium mole numbers ni of structural units, i.e.,(Ca2++O2−), SiO2, (Mg2++O2−), (Fe2++O2−), Fe2O3 and P2O5,in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags in a tempera-ture range from 1 823 K to 1 923 K was illustrated in Fig.2, respectively. Obviously, the calculated equilibrium molenumbers ni of all 6 structural units have some relation withmass percentage of the corresponding components. Thegood linear relationship can be found for SiO2 and FeO in

b N N N N N N N n

N K N N K

i3 3

3 2 32

1

22

1

22

= + + + + + +

= + +

∑( )

(

c4 c5 c7 c8 c9 c10

c4 cΘ

55 c7

c8 c9

c10

Θ Θ

Θ Θ

Θ

N N K N N N

K N N N K N N N

K N N N

2 3 1 3 2

1 3 22

12

3 22

13

32

22

+

+ ++ )) ( )n ni∑ = MgO

0 mol

b N N N N n

N K N N K N N

i4 4

4 2 42

43

6

1

22 3 4

1

22 3

= + + +

= + +

∑( )

(

c6 c17 c18

c6 c17Θ Θ

++ =∑4 44

6K N N n nic18 FeO0 molΘ ) ( )

b N N N N n

N K N N K N N

K N

i5 5

5 12

5 4 5

3

= + + += + ++

∑( )

(c11 c12 c13

c11 c12

c13

Θ Θ

Θ NN n ni5 ) ( )∑ = Fe O0

2 3mol

b N N N N N N N N n

N K N

i6 6

6 12

= + + + + + + +

= +

∑( )

(

c14 c15 c16 c17 c18 c19 c20

c14Θ NN K N N K N N

K N N K N N K N N

6 13

6 14

6

43

6 44

6 32

6

+ +

+ + +c15 c16

c17 c18 c19

Θ Θ

Θ Θ Θ

++ =∑K N N n nic20 P O0

2 5molΘ

33

6 ) ( )

N N N N N N N N N

N N N K N N K

1 2 3 4 5 6

1 2 5 13

2

+ + + + + + + + +

= + + + + +c1 c2 c20

c1 c2Θ ΘNN N

K N N Ni

12

2

33

6 1 0+ + = = −∑c20Θ . ( )

NtFe O

NtFe O

atFe O

( ) [ ] ( )Fe O Fe Fe +O2 3 + = + −3 2 2

( ) [ ] ( )FeO Fe O Fe Fe +O2 3⋅ + = + −4 2 2

NtFe O

NtFe O

N N at tFe O FeO Fe O= ≈ −( )

NtFe O

atFe O

t

G Tt

[ ] [ ] Fe O

. ()

Fe O

J/mol)r m, Fe O

+ =

= − +t

Δ Θ 116 100 48 79 22

Ka

a aa K a K f

t

t

t t ttFe OFe O

Fe OFe O Fe O O Fe O OOΘ Θ Θ= = = [% ]

lg [% ] [% ]f e eO OO

OPO P= +

eOO eO

P

© 2014 ISIJ 760


Figs. 2(b) and 2(d), this phenomenon can be explained asthat not so many molecules of SiO2 or FeO can be boundedto form complex molecules. The scatter relationship can beobserved for (Ca2++O2−), (Mg2++O2−), Fe2O3 and P2O5 ascomponents in Figs. 2(a), 2(c), 2(e) and 2(f). However, a lin-ear relationship can be correlated for (Ca2++O2−), (Mg2++O2−),Fe2O3 and P2O5 in Figs. 2(a), 2(c), 2(e) and 2(f) althoughsome mass of above mentioned components can be found asvarious complex molecules. Therefore, the calculated equi-librium mole number ni of structural units in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags can be applied to representchemical composition of the slags.14–20,23)

3.3. Relation between Equilibrium Mole Numbers andBasicity in CaO–SiO2–MgO–FeO–Fe2O3–P2O5Slags

The relationship between the calculated equilibrium molenumbers ni and simple binary basicity R of slags, i.e.,((%CaO)/(%SiO2)) was illustrated in Fig. 3. Total equilibri-um mole number Σni has a very good linear relationshipwith simple binary basicity R of slags, i.e., ((%CaO)/(%SiO2)). The formula of equilibrium mole number Σniagainst the simple binary basicity R of slags can beregressed as Σni = 2.604–3.029*exp(–R/2.339), and the fit-ting degree is 0.995. This reliable fitting degree results sug-gest that changing the simple binary basicity R of slags havea large effect on Σni.

4. Model for Calculating Phosphorus Distributionbetween CaO–SiO2–MgO–FeO–Fe2O3–P2O5 Slagsand Liquid Iron

According to the ion and molecule coexistence theorythat only free ion couples (Ca2++O2−), and (Mg2++O2−),which can be combined with iron oxides FetO in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags, can take roles indephosphorization reactions in terms of forming 8 dephos-phorization molecules as P2O5, 3FeO·P2O5, 4FeO·P2O5,2CaO·P2O5, 3CaO·P2O5, 4CaO·P2O5, 2MgO·P2O5 and3MgO·P2O5 according to IMCT14–20,23) as follows

.........(9a)

.......... (9b)

..........(9c)

Fig. 1. Relationship between mass percent of CaO, SiO2, MgO,FeO, Fe2O3 and P2O5 as components and calculated massaction concentrations of (Ca2++O2−), SiO2, (Mg2++O2−),(Fe2++O2−), Fe2O3 and P2O5 as structural units in 100 gCaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags equilibrated withliquid iron at elevated temperatures, respectively.

Fig. 2. Relationship between mass percent of CaO, SiO2, MgO,FeO, Fe2O3 and P2O5 as components and calculated equilib-rium mole numbers of (Ca2++O2−), SiO2, (Mg2++O2−),(Fe2++O2−), Fe2O3 and P2O5 as structural units in 100 gCaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags equilibrated withliquid iron at elevated temperatures, respectively.

Fig. 3. Relationship between binary basicity R and calculated totalequilibrium mole number of structural units Σni in 100 gCaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags equilibrated withliquid iron at elevated temperatures.

2 5 5

122 412 312 522

2 5P Fe O P O Fe

J/mor m, P O2 5

[ ]+ ( ) = ( ) + [ ]= − +t t

TGΔ Θ . ll( )

2 5 3 3 52 22 5P Fe O Fe O FeO P O Fe

r m, 3FeO P O2 5

[ ] ( ) ( ) + [ ]+ + + =+ −

⋅

t t

G

( ) ·

Δ ΘΘ = +− ( )552 816 405 23. T J/mol

2 5 4 4 52 22 5P Fe O Fe O FeO P O Fe

r m, 4FeO P O2 5

[ ] ( ) ( ) + [ ]+ + + =+ −

⋅

t t

G

( ) ·

Δ ΘΘ = +− ( )504 243 359 889. T J/mol

Total


761 © 2014 ISIJ

.......... (9d)

..........(9e)

.......... (9f)

........... (9g)

........... (9h)

The corresponding equilibrium constants of Eq. (9) canbe expressed according to IMCT14–20,23) as

......(10a)

............ (10b)

............(10c)

........... (10d)

............(10e)

............ (10f)

.......... (10g)

.......... (10h)

where is molecular mass of P2O5 as 141.94 (–).According to Eq. (10), the respective phosphorus distribu-tion of structural units as basic components in the slags LP, ican be expressed by

..........(11a)

............(11b)

............(11c)

...........(11d)

............(11e)

........... (11f)

............(11g)

............(11h)

where fP is activity coefficient of the dissolved phosphorusin liquid iron (–), and can be calculated as follows

...................(12a)..................... (12b)

The related values of interaction coefficients of [P][22] arechosen as =0.062, =0.13 at 1 873 K. Therefore, the totalphosphorus distribution between CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags and liquid iron can be obtained from Eq.(11) as follows

.. (13)

2 5 2 2 52 22 5P Fe O Ca O CaO P O Fe

r m, 2CaO P O2 5

[ ] ( ) ( ) + [ ]+ + + =+ −

⋅

t t

G

( ) ·

Δ ΘΘ = − − ( )484 372 26 569. T J/mol

2 5 3 3 52 22 5P Fe O Ca O CaO P O Fe

r m, 3CaO P O2 5

[ ] ( ) ( ) + [ ]+ + + =+ −

⋅

t t

G

( ) ·

Δ ΘΘ = +− ( )832 302 318 672. T J/mol

2 5 4 4 52 22 5P Fe O Ca O CaO P O Fe

r m, 4CaO P O2 5

[ ] ( ) ( ) + [ ]+ + + =+ −

⋅

t t

G

( ) ·

Δ ΘΘ = +− ( )783 768 309 049. T J/mol

2 5 2 2 52 22 5P Fe O Mg O MgO P O Fe

r m, 2MgO P O2 5

[ ] ( ) ( )+ [ ]+ + + =+ −

⋅

t t

G

( ) ·

Δ ΘΘ = − ( )45957 26 835. T J/mol

2 5 3 3 52 2P Fe O Mg O MgO P O Fe2 5

r m, 3MgO P O2 5

[ ] ( ) ( )+ [ ]+ + =+ −

⋅

t t

G

+ ( ) ·

Δ ΘΘ = +− ( )390053 197 318. T J/mol

Ka a

a a

N

N f

t

t t

P OP O Fe

Fe O P

P O

Fe O P

2 5 P

2 5

2 5 2 5

2

P

P O

Θ = =×

=

5

5 2 5 2 2

1

[% ]

(% ) OO P O

Fe O P

5 2 5

P

/

[% ]( )

Mn

N f

i

t

∑⎛

⎝⎜

⎞

⎠⎟

−5 2 2

Ka a

a a a

N

N

t

t t

3FeO P O3FeO P O Fe

Fe O FeO P

3FeO P O

Fe2 5

2 5 2 5

⋅⋅ ⋅= =

×Θ

5

5 3 2

1

OO FeO P

2 5 3FeO P O P O

Fe O FeO

P

P O2 5 2 5

5 3 2 2

5

N f

Mn

N N

i

t

[% ]

(% ) /

=

⎛

⎝⎜

⎞

⎠⎟

⋅

∑33 2 2[% ]

( )P Pf

−

Ka a

a a a

N

N

t

t t

4FeO P O4FeO P O Fe

Fe O FeO P

4FeO P O

Fe2 5

2 5 2 5

⋅⋅ ⋅= =

×Θ

5

5 4 2

1

OO FeO P

2 5 4FeO P O P O

Fe O FeO

P

P O2 5 2 5

5 4 2 2

5

N f

Mn

N N

i

t

[% ]

(% ) /

=

⎛

⎝⎜

⎞

⎠⎟

⋅

∑44 2 2[% ]

( )P Pf

−

Ka a

a a a

N

N

t

t t

2CaO P O2CaO P O Fe

Fe O CaO P

2CaO P O

Fe2 5

2 5 2 5

⋅⋅ ⋅= =

×Θ

5

5 2 2

1

OO CaO P

2 5 2CaO P O P O

Fe O CaO

P

P O2 5 2 5

5 2 2 2

5

N f

Mn

N N

i

t

[% ]

(% ) /

=

⎛

⎝⎜

⎞

⎠⎟

⋅

∑22 2 2[% ]

( )P Pf

−

Ka a

a a a

N

N

t

t t

3CaO P O3CaO P O Fe

Fe O CaO P

3CaO P O

Fe2 5

2 5 2 5

⋅⋅ ⋅= =

×Θ

5

5 3 2

1

OO CaO P

2 5 3CaO P O P O

Fe O CaO

P

P O2 5 2 5

5 3 2 2

5

N f

Mn

N N

i

t

[% ]

(% ) /

=

⎛

⎝⎜

⎞

⎠⎟

⋅

∑33 2 2[% ]

( )P Pf

−

Ka a

a a a

N

N

t

t t

4CaO P O4CaO P O Fe

Fe O CaO P

4CaO P O

Fe2 5

2 5 2 5

⋅⋅ ⋅= =

×Θ

5

5 4 2

1

OO CaO P

2 5 4CaO P O P O

Fe O CaO

P

P O2 5 2 5

5 4 2 2

5

N f

Mn

N N

i

t

[% ]

(% ) /

=

⎛

⎝⎜

⎞

⎠⎟

⋅

∑44 2 2[% ]

( )P Pf

−

Ka a

a a a

N

N

t

t t

2MgO P O2MgO P O Fe

Fe O MgO P

2MgO P O

Fe2 5

2 5 2 5

⋅⋅ ⋅= =

×Θ

5

5 2 2

1

OO MgO P

2 5 2MgO P O P O

Fe O MgO

P

P O2 5 2 5

5 2 2 2

5

N f

Mn

N N

i

t

[% ]

(% ) /

=

⎛

⎝⎜

⎞

⎠⎟

⋅

∑22 2 2[% ]

( )P Pf

−

Ka a

a a a

N

N

t

t t

3MgO P O3MgO P O Fe

Fe O MgO P

3MgO P O

Fe2 5

2 5 2 5

⋅⋅ ⋅= =

×Θ

5

5 3 2

1

OO MgO P

2 5 3MgO P O P O

Fe O MgO

P

P O2 5 2 5

5 3 2 2

5

N f

Mn

N N

i

t

[% ]

(% ) /

=

⎛

⎝⎜

⎞

⎠⎟

⋅

∑33 2 2[% ]

( )P Pf

−

MP O2 5

L M K N f nt iP, P O

2 5 P OP O P O Fe O P2 5

2 5

2 5 2 5

P O

P= = −∑

(% )

[% ]( )

25 2Θ

L

M K Nt

P, 3FeO P O2 5 3FeO P O

P O 3FeO P O Fe O

2 5

2 5

2 5 2 5

P O

P⋅

⋅

⋅

=

=

(% )

[% ]2

5Θ NN f niFeO P3 2∑ −( )

L

M K Nt

P, 4FeO P O2 5 4FeO P O

P O 4FeO P O Fe O

2 5

2 5

2 5 2 5

P O

P⋅

⋅

⋅

=

=

(% )

[% ]2

5Θ NN f niFeO P4 2∑ −( )

L

M K Nt

P, 2CaO P O2 5 2CaO P O

P O 2CaO P O Fe O

2 5

2 5

2 5 2 5

P O

P⋅

⋅

⋅

=

=

(% )

[% ]2

5Θ NN f niCaO P2 2∑ −( )

L

M K Nt


P O 3CaO P O Fe O

2 5

2 5

2 5 2 5

P O

P⋅

⋅

⋅

=

=

(% )

[% ]2


L

M K Nt


P O 4CaO P O Fe O

2 5

2 5

2 5 2 5

P O

P⋅

⋅

⋅

=

=

(% )

[% ]2


L

M K Nt

P, 2MgO P O2 5 2MgO P O

P O 2MgO P O Fe O

2 5

2 5

2 5 2 5

P O

P⋅

⋅

⋅

=

=

(% )

[% ]2

5Θ NN f niMgO P2 2∑ −( )

L

M K Nt

P, 3MgO P O2 5 3MgO P O

P O 3MgO P O Fe O

2 5

2 5

2 5 2 5

P O

P⋅

⋅

⋅

=

=

(% )

[% ]2

5Θ NN f niMgO P3 2∑ −( )

lg [% ] ( )f e jPj= −∑ P

e TjP const= −( )

ePP eP

O

L L L L L

LP P, P O P, 3FeO P O P, 4FeO P O P, 2CaO P O

P,

2 5 2 5 2 5 2 5= + + ++

⋅ ⋅ ⋅

33CaO P O P, 4CaO P O P, 2MgO P O P, 3MgO P O

2

2 5 2 5 2 5 2 5

P O⋅ ⋅ ⋅ ⋅+ + +

=

L L L

(% 55 P O 2 5 3FeO P O 2 5 4FeO P O2 5 2 5 2 5

P

P O

P

P O

P

)

[% ]

(% )

[% ]

(% )

[% ](

2 2 2+ + +⋅ ⋅

%% )

[% ]

(% )

[% ]

(% )P O

P

P O

P

P O2 5 2CaO P O 2 5 3CaO P O 2 5 4CaO P2 5 2 5 2⋅ ⋅ ⋅+ +2 2

OO

2 5 2MgO P O 2 5 3MgO P O

P O

5

2 5 2 5

2 5

PP O

P

P O

P

[% ](% )

[% ]

(% )

[% ]

2

2 2

+

+

=

⋅ ⋅

M NN f K K N K N

KtFe O P P O 3FeO P O FeO 4FeO P O FeO

2CaO

2 5 2 5 2 5

5 2 3 4( Θ Θ Θ+ + +⋅ ⋅

⋅PP O CaO 3CaO P O CaO 4CaO P O CaO

2MgO P O

2 5 2 5 2 5

2 5

Θ Θ Θ

Θ

N K N K N

K N

2 3 4+ + +⋅ ⋅

⋅ MMgO 3MgO P O MgO2 5

2 3+ −⋅ ∑K N niΘ ) ( )

© 2014 ISIJ 762


Therefore, the developed LP prediction model by topresent slag oxidizing ability is composed of Eqs. (11) and(13). According to the calculated Ni and Σni in Section 3,

by Eq. (10) and fP by Eq. (12), the total phosphorus dis-tribution LP of the slags which equals to the sum of respec-tive phosphorus distribution LP, i of basic ion couples in theslags can be calculated. The standard molar Gibbs free ener-gy of dephosphorization reactions in Eq. (9) forforming dephosphorization products i is determined fromthe reported data and summarized in Table 2.

5. Results and Discussion

5.1. Comparison of Measured Phosphorous Distribu-tion LP, measured and Calculated Phosphorous Distri-bution LP, calculated

In order to examine the applicability of the IMCT−LPmodel developed in the present study based on the ion andmolecule coexistence theory, both methods have beenadopted to evaluate the accuracy of the calculated .One is directly comparing the measured LP, measured from pre-vious references10,13) and the calculated based onthe ion and molecule coexistence theory; the other is com-paring the IMCT−LP model with some other reported phos-phorous distribution prediction models,4,6–9) such as Healy’smodel,4) Suito’s models,6,7) Sommerville’s model,8) andBalajiva’s model.9)

The comparisons between the measured phosphorous dis-tribution LP, measured for CaO–SiO2–MgO–FeO–P2O5 slagsequilibrated with liquid iron at 1 873 K and 1 923 K reportedby Basu et al.10) or the measured phosphorous distributionLP, measured for the CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slagsat 1 823 K, 1 873 K and 1 923 K reported by Nagabayashiet al.13) and the calculated phosphorous distribution

based on ion and molecule coexistence theory

was illustrated in Fig. 4, respectively.As shown in Fig. 4, an excellent 1:1 agreement between

phosphorous distribution lg LP, measured reported by Basu etal.10) and based on the ion and molecule coex-istence theory can be obtained, meanwhile, a good 1:1 linearrelationship between phosphorous distribution lg LP, measuredreported by Nagabayashi et al.13) and based onthe ion and molecule coexistence theory can also be found.It should be pointed out CaO–SiO2–MgO–FeO–P2O5 slagswas treated as a special CaO–SiO2–MgO–FeO–Fe2O3–P2O5slags in this paper with the assumption that the content ofFe2O3 equal to zero. This result indicates that the developedIMCT–LP prediction model can be applied to reliably pre-dict the phosphorous distribution LP of CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags equilibrated with liquid iron.

5.2. Comparison of Calculated Phosphorous Distribu-tion by Different Models

The comparisons between the measured LP, measured and

Table 2. Calculation of standard molar Gibbs free energy for 8 dephosphorization reactions from the reported data of stan-dard molar Gibbs free energy.

Dephosphorization reactions Resource reactions (J/mol)

2[P]+5(FetO)=(P2O5)+5t[Fe]

=–122 412+312.522T

P2=[P] –157 700+5.4T 30)

O2=[O] –117 110–3.39T 30)

2[P]+5[O]=(P2O5)(l) –702 912+556.472T 31)

P2+ O2=(P2O5)(l) –1 603 862+550.322T 30,31)

t[Fe]+[O]=(FetO) –116 100+48.79T 32)

2[P]+5(FetO)+3(Fe2++O2−)=(3FeO·P2O5)+5t[Fe]

=–552 816+405.23T

3(FeO)+(P2O5)=(3FeO·P2O5) –430 404+92.708T 9)

2[P]+5(FetO)=(P2O5)+5t[Fe] –122 412+312.522T

2[P]+5(FetO)+4(Fe2++O2−)=(4FeO·P2O5)+5t[Fe]

=–504 243+359.889T

4(Fe2++O2−)+(P2O5)=(4FeO·P2O5) –381 831+47.367T 9)

2[P]+5(FetO)=(P2O5)+5t[Fe] –122 412+312.522T

2[P]+5(FetO)+2(Ca2++O2−)=(2CaO·P2O5)+5t[Fe]

=–606 784+285.953T

2(CaO)+P2+ O2=(2CaO·P2O5)(s) –2 189 069+585.76T 33)

(2CaO·P2O5)(s)= (2CaO·P2O5)(l) 100 834.4–62.0069T 16)

P2+ O2=(P2O5)(l) –1 603 862+550.322T 30,31)

2[P]+5(FetO)=(P2O5)+5t[Fe] –122 412+312.522T


=–832 302+318.672T

3(CaO)+P2+ O2=(3CaO·P2O5)(s) –2 313 752+556.472T 33)

P2+ O2=(P2O5)(l) –1 603 862+550.322T 30,31)

2[P]+5(FetO)=(P2O5)+5t[Fe] –122 412+312.522T


=–783 768+309.049T

4(CaO)+(P2O5)(l)=(4CaO·P2O5)(l) –661 356–3.473T 34)

2[P]+5(FetO)=(P2O5)+5t[Fe] –122 412+312.522T

2[P]+5(FetO)+2(Mg2++O2−)=(2MgO·P2O5)+5t[Fe]

=45 957–26.835T

2(Mg2++O2-)+(P2O5)=(2MgO·P2O5) 168 369–339.357T 9)

2[P]+5(FetO)=(P2O5)+5t[Fe] –122 412+312.522T

2[P]+5(FetO)+3(Mg2++O2−)=(3MgO·P2O5)+5t[Fe]

=–390 053+197.336T

3(MgO)+P2+ O2=(3MgO·P2O5)(s) –1 992 839+510.0296T 33)

(3MgO·P2O5)(s)= (3MgO·P2O5)(l) 121 336–74.8936T 32)

P2+ O2=(P2O5)(l) –1 603 862+550.322T 30,31)

2[P]+5(FetO)=(P2O5)+5t[Fe] –122 412+312.522T

Δ Θr m, G i

Δ Θr m, G i

12

12

52

Δ Θr m, G i

Δ Θr m, G i

Δ Θr m, G i

52

52

Δ Θr m, G i

52

52

Δ Θr m, G i

Δ Θr m, G i

Δ Θr m, G i

52

52

NtFe O

KiΘ

Δ Θr m, G i

LP, calculatedIMCT

LP, calculatedIMCT

LP, calculatedIMCT

Fig. 4. Comparison between calculated and measured phosphorusdistribution of CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slagsequilibrated with liquid iron in a temperature range from1 823 K to 1 923 K.10,13)

lgLP, calculatedIMCT


LiP, calculated


763 © 2014 ISIJ

calculated in logarithmic form by various modelslisted in Table 3 were shown in Fig. 5. Obviously, allprediction models have good agreement with the measuredLP, measured for CaO–SiO2–MgO–FeO–P2O5 slags at 1 873 Kand 1 923 K reported by Ban–ya et al.10) except Suito’s No.2 LP model.5,6) However, only by IMCT–LPmodel have 1:1 reliable linear relationship with the mea-sured LP, measured for CaO–SiO2–MgO–FeO–Fe2O3–P2O5slags at 1 823 K, 1 873 K and 1 923 K reported byNagabayashi et al.,13) compared with other prediction mod-els such as by Healy’s LP model,4) by Suito’s No. 1 LP model,6,7) by Suito’s No. 2LP model,6,7) by Sommerville’s LP model8) and

by Balajiva’s LP model.9)

It should be specially emphasized that the calculated by various models listed in Table 3 has been

transferred into (%P2O5)/[%P]2, rather than the definedphosphorus distribution as (%P)/[%P] in Healy’s model,4) or(%P2O5)/[%P]2(%FetO)5 in Suito’s No. 1 and No. 2 mod-els,6,7) or (%P2O5)/[%P] in Sommerville’s model8) as listedin Table 3.

5.3. Relation between Mass Action Concentrations ofComponents and lg LP, measured or

The influence of the calculated mass action concentra-tions of components upon lg LP, measured or for theCaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags equilibrated withliquid iron at 1 823 K, 1 873 K and 1 923 K was shown inFig. 6, respectively. It was seen in Figs. 6(a) and 6(c) thatincreasing NCaO and NMgO can lead to an increase of phos-phorus distribution lg LP, measured or ; improving

will result in decreasing of phosphorus distributionlg LP, measured or from Fig. 6(b). Meanwhile,clearly corresponding relationship between lg LP, measured or

and NFeO or can be observed from Figs.6(d) and 6(e). This phenomenon can be explained as thatdephosphorization process is controlled by the comprehen-sive effect of basic oxides and iron oxides. Therefore, undercircumstance of adequate basicity oxides, increasing ironoxides can effectively increase dephosphorization ability ofslags. However, increasing iron oxides without enoughbasicity oxides can only lead to a slightly increasing ofphosphorus distribution.

There are some extreme proofs to support this results asfollows: 1) A slags with high iron oxides but very low CaO,which is applied in desiliconization pretreatment of liquidiron, can only extract silicon but not phosphorus; 2) A slagswith high CaO but very low FetO, which is applied at reduc-

Table 3. Formulas of phosphorus distribution prediction models reported in related literatures.

LP model Slags Formulas of LP models

Healy’smodel4) CaO–SiO2–MgO–FetO–MnO–Al2O3 slags

Suito’s No.1model6,7) CaO–SiO2–MgO–FetO–P2O5 slags

Suito’s No.2model6,7) CaO–SiO2–MgO–FetO–P2O5 slags

Sommerville’smodel8) CaO–SiO2–MgO–FeO–MnO –P2O5 slags

Balajiva’smodel9) CaO–SiO2–MgO–FetO–MnO–P2O5 slags

lg(% )

[% ]. (% ) . lg(% )

P

PCaO T Fe= + + ⋅ −

22 3500 08 2 5 16

T

lg(% )

[% ] (% ). [(% ) . (% ) . (% )

P O

P Fe OCaO MgO P O2 5

2 52 50 145 0 3 0 5 0

t

= + − + .. %(

.

6

22 81020 506

MnO)]

+ −T

lg(% )

[% ] (% ). lg[(% ) . (% ) . (% )

P O

P Fe OCaO MgO Fe O2 5

2 57 87 0 3 0 05

tt= + − −− +

+ −

0 5 0 6

22 24027 124

. (% ) . %(

.

P O MnO)]2 5

T

lg(% )

[% ]. lg(% )

[ (% ) . (% )P O

PFeO

CaO MgO2 5 = + ++ +11 000

2 5162 127 5 28

T

.. (% )]

. . lg(% ) .

5

0 0006287 04 10 402

MnO

SiO2

T

− −

lg(% )

[% ]lg( ) . [(% ) . (% ) . (%

P O

P%Fe O CaO MgO P O2 5

2 525 0 145 0 3 0 5= + + −t ))

. (% )] .

+

+ −0 622 810

20 506MnOT

LiP, calculated


lgLP, calculatedHealy

lgLP, calculatedSuito's No.1

lgLP, calculatedSuito's No.2

lgLP, calculated

Sommerville

lgLP, calculatedBalajiva

LiP, calculated

lg LP, calculatedIMCT



NSiO2


lgLP, calculatedIMCT NFe O2 3

Fig. 5. Comparison between the measured phosphorus distributionlg LP, measured by previous literatures10,13) and the calculatedphosphorus distribution by various phosphorusdistribution prediction models4,6–9) of CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags equilibrated with liquid iron at ele-vated temperatures.

lgLiP, calculated

© 2014 ISIJ 764


tion period during electric arc furnace steelmaking process,can only extract sulfur but not phosphorus. Therefore, thecomprehensive effect of basic components, especially CaOand FetO, can make the main controlling contribution todephosphorization in the slags.

5.4. Relationship between Slag Basicity and lg LP, measuredor

No Al2O3 exists in the selected slags, the commonlyapplied complex basicity ((%CaO)+1.4(%MgO)/(%SiO2)+(%P2O5)+/(%Al2O3))22) can be simplified as ((%CaO)+1.4(%MgO)/(%SiO2)+(%P2O5)). The relationship betweenlg LP, measured or and binary basicity ((%CaO)/(%SiO2)) or complex basicity ((%CaO)+1.4(%MgO)/(%SiO2)+(%P2O5)) were illustrated in Figs. 7(a) and 7(b). Itcan be observed from Fig. 7(a) that increasing binary basic-ity from 1.25 to 2.7 can effectively improve lg LP, measured or

, further increasing binary basicity from 2.7 to

9 cannot bring an obvious increasing tendency oflg LP, measured or due to saturation with solidphase; as shown in Fig. 7(b), increasing complex basicityfrom 1.5 to 2.5 can lead to an obvious increasing tendencyof LP, further increasing complex basicity from 2.5 to 3.5have little influence on lg LP, measured or owing tosaturation with solid phase;.

5.5. Contribution of Basic Oxides to Dephosphoriza-tion Ability of CaO–SiO2–MgO–FeO–Fe2O3–P2O5Slags

According to IMCT,14–20,23) the structural unit P2O5 is gen-erated from FetO in the slags or [O] in liquid iron, mean-while, three components as CaO, MgO, and FeO in the slagscan react with P2O5 to generate 3FeO·P2O5, 4FeO·P2O5,2CaO·P2O5, 3CaO·P2O5, 4CaO·P2O5, 2MgO·P2O5, and3MgO·P2O5 as complex molecules. As shown in Eq. (11),the respective phosphorus distribution LP, i of above-men-tioned eight molecules can be calculated from the developedIMCT−LP model.

The relationship between the calculated respective phos-phorus distribution of 8 structural units con-taining phosphorus and the measured of theslags was illustrated in Fig. 8(a), respectively. Obviously,the contribution of P2O5, 3FeO·P2O5, 4FeO·P2O5, 2MgO·P2O5,and 3MgO·P2O5 to the total dephosphorization ability isvery small, therefore, the contribution of above mentionedcomplex molecules can be ignored compared with the con-tribution of 3CaO·P2O5 as 97.88%, 4CaO·P2O5 as 2.10%and 2CaO·P2O5 as 0.0013%.

Since 3CaO·P2O5 made the main contribution to dephos-phorizaiton in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags,and the 1:1 corresponding relationship between and can be found in Fig. 8(b), meanwhile, the

formula of against was regressed

as = 0.00697 + 0.99577 . Hence, itcan be concluded that P2O5 formed tri-calcium phosphate(3CaO·P2O5), but not tetra-calcium phosphate, (4CaO·P2O5)in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags.

6. Conclusions

A thermodynamic model for calculating phosphate distri-bution between CaO−SiO2−MgO−FeO−Fe2O3−P2O5 slagsand liquid iron, i.e., IMCT−LP model, has been developedcoupled with a developed thermodynamic model for calcu-lating mass action concentrations of structural units, i.e.,IMCT−Ni model, based on ion and molecule coexistencetheory. The main information can be summarized as follows:

Fig. 6. Effect of calculated mass action concentrations of ion cou-ples or simple molecules of (Ca2++O2−), SiO2, (Mg2++O2−),(Fe2++O2−), and Fe2O3 on lg LP, measured and atelevated temperatures.

Fig. 7. Effects of binary basicity (%CaO)/(%SiO2) (a) and com-plex basicity ((%CaO)+1.4(%MgO)/(%SiO2)+(%P2O5)) (b)on lg LP, measured and at elevated temperatures.



lg LP, calculatedIMCT



Fig. 8. Contribution of 8 structural units containing P2O5 in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags to the total dephospho-rization ability (a), and the relationship between

and at elevated temperatures (b).lgLP, calculatedIMCT

lgLP, CaO P OIMCT

2 53 ⋅



lgL iP, , calculatedIMCT



lgLP, 3CaO P OIMCT

2 5⋅

lgLP, calculatedIMCT lgLP, 3CaO P O

IMCT

2 5⋅

lgLP, calculatedIMCT lgLP, 3CaO P O

IMCT

2 5⋅


765 © 2014 ISIJ

(1) The calculated results from IMCT−Ni model showsthat the calculated mass action concentrations of structuralunits, rather than mass percentage of components, are rec-ommended to represent reaction ability of components inCaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags. Simple binarybasicity R of slags have a large effect on total equilibriummole number Σni of structural units in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags, the formula of total equilibriummole number Σni against the simple binary basicity R ofslags can be regressed as Σni = 2.604–3.029*exp(–R/2.339),and the fitting degree is 0.995.

(2) The developed IMCT–LP prediction model can beapplied to reliably predict the phosphorous distribution LP ofCaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags equilibrated withliquid iron. Meanwhile, some other phosphorous distributionprediction models have also been taken into consideration forcalculating phosphate distribution between CaO–SiO2−MgO−FeO−Fe2O3−P2O5 slags and liquid iron, and the resultsshows that IMCT−LP model have more accuracy comparedwith other phosphorous distribution prediction models.

(3) The developed IMCT−LP model can quantitativelycalculate the respective contribution of FetO, CaO+FetO andMgO+FetO in the slags. A significant difference of dephos-phorziation abilities among FetO, CaO+FetO and MgO+FetOcan be found as approximately 0.00%, 99.98%, 0.01%.Meanwhile, the phosphorus in liquid iron can be effectivelyextracted by CaO+FetO in slags to form complex molecules3CaO·P2O5 which made the main contribution to dephos-phorizaiton in CaO–SiO2–MgO–FeO–Fe2O3–P2O5 slags.

NomenclatureA: Constant, (–);

ai : Activity of components i in liquid iron or inslags, (–);

B: Constant, (–);bi: Mole number of component i in 100 g slags, (mol);

: Interaction coefficient of component j on compo-nent i in liquid iron, (–);

fi : Activity coefficient of component i in liquid iron,(–);

: Standard molar Gibbs free energy of formingcomplex molecule i in slags, (J/mol);

(%i): Mass percentage of component i in the slags,(mass%);

[%i]: Mass percentage of component i in liquid iron,(mass%);

: Equilibrium constant of chemical reaction forforming component i or structural unit i, (–);

LP: Phosphorus distribution between slags and liquidiron, (–);

LP, i: Calculated respective phosphorus distribution ofgenerated structural unit i containing P2O5 inslags based on slag oxidization ability by IMCTmodel, (–);: Calculated total phosphorus distribution

between slags and liquid iron based on slagoxidization ability by IMCT model, (–);

LP, measured: Measured phosphorus distribution, (–);: Calculated respective phosphorus distribution

between generated structural unit i containingP2O5 in slags and liquid iron based on slag oxi-dization ability by IMCT model from calculat-ed data, (–);

: Calculated phosphorus distribution between

slags and liquid iron by model i, (–);Me: Metal, (–);

MeO: Oxide component in slags, (–);Mi: Molecular mass of element i or component i, (g/

mol);: Mole number of component i in 100 g slags, (mol);

ni: Equilibrium mole number of structural unit i in100 g slags, (mol);

Ni: Mass action concentrations of structural unit i inthe slags, (–);

Σni: Total equilibrium mole number of all structuralunits in 100 g slags, (mol);

R: simple binary basicity, (–);R: Gas constant, (8.314 J/(mol⋅K));T: Absolute temperature, (K);

Subscriptsci: Complex molecule i, (–);

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eij

Δ Θr m, G i

KiΘ

LP, calculatedIMCT

L iP, , calculatedIMCT

LiP, calculated

ni0

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