Effect of Slag Basicity on Dephosphorization at Lower Basicity and Lower Temperature Based on Industrial Experiments and Ion-Molecular Coexistence Theory

Abstract

In the present work, the effect of dephosphorization slag basicity on the dephosphorization of hot metal has been studied in the lower temperature range of 1370 °C to 1420 °C and the lower basicity of 1.26 to 2.20 with new double slag converter steelmaking process (NDSP). Based on the ion-molecule coexistence theory (IMCT), the thermodynamic model IMCT-N_i of dephosphorization slag is established. With increasing basicity from 1.26 to 2.20, the phosphorus distribution ratio L_P between hot metal and slag increases. The dephosphorization ratio and the decarbonization ratio both increase, while the demanganization ratio decreases. The morphologies of P-rich phase change from long strip shape (B = 1.26-1.37) to dendritic shape (B = 1.50) and to massive shape (B = 1.71-2.20). The area of P-rich phase increases from about 4 μm² to about 8000 μm². The content of P₂O₅ in the P-rich phase increases and the value of the coefficient n in nC₂S-C₃P of the P-rich phase decreases from 6-20 to 1-2. The phosphorus-enrichment contribution ratio of calcium silicate is in the order of $R_{{{\text{C2S}}}}$>$R_{{{\text{CS}}}}$>$R_{{{\text{C3S}}}}$>$R_{{{\text{C3S2}}}}$. The phosphorus-enrichment degree in dephosphorization slag is enhanced mainly by C₂S-C₃P. With increasing basicity, the calculated results of IMCT-(pct C₂S-C_jP) and $R_{{{\text{C2S}}}}$ are well consistent with the measurement results of A^{P-rich phase} and (pct P₂O₅)^{P-rich phase} of industrial experiment, indicating that the IMCT calculated results can correctly express the phosphorus-enrichment degree of dephosphorization slag.

Introduction

The multi-refining converter (MURC)[1,2,3] developed by Nippon Steel in 2001 is a representative new double slag converter steelmaking process(NDSP). Firstly, desiliconization and dephosphorization are carried out at lower basicity and lower temperature in the converter. After intermediate deslagging of dephosphorization slag, the decarburization are conducted in the same converter, with the decarburization slag left in the furnace for dephosphorization in the next heat,[1,2,3,4,5] so that the lime consumption and slag emission amount can be greatly reduced.

Some scholars have studied the effect of dephosphorization slag basicity on hot metal dephosphorization in NDSP. Fang et al.[6] optimized the process parameters of the dephosphorization stage in NDSP. When the dephosphorization endpoint temperature is 1328 °C, the dephosphorization slag basicity is 1.5, T.Fe content is 12 to 16 pct, and the oxygen supply intensity is 2.0 to 2.7 m³/(t min), the dephosphorization ratio reaches 67.3 pct and the phosphorus content reaches 0.011 pct at the endpoint of dephosphorization. Liu et al.[7] carried out the industrial experiments on NDSP by 80 t converter. With the slag basicity of 1.2 to 2.0 at the dephosphorization stage, the dephosphorization ratio of hot metal is higher, and the optimal deslagging temperature range is 1327 °C to 1427 °C. Using the hot metal with a high phosphorus content in NDSP, Wang et al.[8] showed that with increasing dephosphorization slag basicity from 1.75 to 2.22, the phosphorus content of hot metal decreases linearly at the endpoint of dephosphorization. Based on the 180 ton industrial experiments on NDSP, our previous work[9] studied the behavior of phosphorus enrichment in dephosphorization slag. With increasing basicity, the morphologies of different phases in the dephosphorization slag change greatly, and the area fractions and P₂O₅ content of the P-rich phase also increase.

In the process of dephosphorization in NDSP, the slag is in the coexistence state of solid phase and liquid phase. Many research results[4,5,6,7,8,9,10,11,12,13,14,15,16,17] showed that the phosphorus oxide combines with calcium silicate in slag to form a solid solution, 2CaO·SiO₂-3CaO·P₂O₅(C₂S-C₃P), which makes phosphorus exist in slag stably. Xie et al.[10] studied the crystallization kinetics of C₂S-C₃P solid solution in multiphase slag. The content of C₂S-C₃P solid solution in multiphase slag increases with increasing P₂O₅ content and decreasing holding temperature, and decreases with increasing FeO_t content. They further studied the mass transfer behavior of phosphorus in multiphase dephosphorization slag at 1350 °C by adding P₂O₅ powder into CaO-FeO_t-SiO₂ slag saturated with 2CaO·SiO₂(C₂S).[11] The added P₂O₅ powders can form C₂S-C₃P solid solution rapidly with C₂S in the slag, and the rate control step of the process is the mass transfer of phosphorus from C₂S-C₃P solid solution layer to internal C₂S crystal. Kakimoto et al.[12] studied the dissolution behavior of lime in CaO-SiO₂-FeO and CaO-SiO₂-FeO-5.2 pct P₂O₅ slag. Adding P₂O₅ to the slag can promote the dissolution of lime into the slag. The main reason is that part of CaO exists in the slag in the form of C₂S and C₃P in the form of solid solution. Du et al.[13] obtained that the distribution ratio of P₂O₅ in solid solution and liquid phase increases with increasing T.Fe content, and has nothing to do with P₂O₅ content and valence of Fe in CaO-SiO₂-FeO-P₂O₅-Na₂O slag.

On the other hand, the ion-molecule coexistence theory (IMCT) is a slag structure theory based on the possible compounds of simple ions, simple molecules and complex molecules in the phase diagram as the structural units, and the mass action law is used to quantitatively calculate the reaction ability of structure units or ion couples in the studied slag.[18,19,20,21,22,23,24,25,26,27,28,29] The coexistence theory model was first proposed by Chuiko[24] and then was further developed by Zhang.[25]

In recent years, some scholars[22,23,25,26] studied the dephosphorization process of steelmaking slag based on IMCT. Yang et al.[22] established the phosphorus distribution ratio prediction model IMCT-logL_P of CaO-FeO-Fe₂O₃-SiO₂-MgO-MnO-Al₂O₃-P₂O₅, and compared the calculation results with the empirical formula values and the measured values. The IMCT-logL_P model can accurately predict the phosphorus distribution ratio of the slag, and the corresponding phosphorus distribution ratio of each component with dephosphorization ability in slag, indicating that C₃P is the main contribution component of L_P, and its contribution ratio is 96.01 pct. They further established the phosphorus capacity prediction model ${\text{IMCT}} - \log C_{{{\text{PO}}_{4}^{{3 - }} }}$ and the phosphorus capacity index prediction model ${\text{IMCT}} - {\text{log}}C_{{{\text{PO}}_{4}^{{3 - }} \;{\text{index}}}}$ under the same slag condition based on IMCT.[23] The results show that the dephosphorization reaction is controlled by the basic compositions of converter slag and iron oxide. CaO + Fe_tO is the main contribution component for phosphorus capacity or phosphorus capacity index of slag, and its contribution ratio reaches 99.996 pct. Li et al.[26] established the phosphorus distribution ratio model of IMCT-logL_P which can accurately predict the phosphorus distribution ratio of CaO-FeO-Fe₂O₃-SiO₂-MgO steelmaking slag. With increasing CaO and Fe_tO content and decreasing MgO and SiO₂ content, the predicted values of L_{P, cal} is increased which is consistent with the measured values.

Based on IMCT, some scholars studied the phosphorus-enrichment capacity of calcium silicate in slag. Xie et al.[27] discussed the phosphorus-enrichment capacity of calcium silicate in multiphase slag through the phosphorus-enrichment contribution ratio of calcium silicate $R_{{Ci}}$ (refer to Eq. [16]) defined by IMCT. In CaO-FeO-Fe₂O₃-SiO₂-MgO-MnO-Al₂O₃-P₂O₅ slag with the temperature of 1350 °C and the basicity of 0.5 to 4, the phosphorus-enrichment contribution ratio of dicalcium silicate $R_{{{\text{C2S}}}}$ will be significantly increased by increasing the basicity of slag, and the value of $R_{{{\text{C2S}}}}$ reaches the maximum value when FeO content is 25 pct. In addition, with increasing m(FeO)/m(Fe₂O₃) ratio, the value of $R_{{{\text{C2S}}}}$ increases, while with increasing P₂O₅ content in slag, the value of $R_{{{\text{C2S}}}}$ decreases slightly. Li et al.[28] studied the phosphorus-enrichment behavior in CaO-FeO-Fe₂O₃-SiO₂-MgO steelmaking slag at 1450 °C to 1600 °C based on IMCT. C₃P formed in slag can combine with C₂S easily to form C₂S-C₃P solid solution at 1500 °C. Under the fixed cooling condition with basicity of 2.5 and the value of (pct Fe_tO)/(pct CaO) of 0.955, the phosphorus-enrichment degree in C₂S-C₃P solid solution $R_{{{\text{C2S - C3P}}}}$ (refer to Eq. [15]) defined by IMCT is 0.844. They further studied the phosphorus-enrichment behavior in CaO-FeO-Fe₂O₃-SiO₂-MgO slag at 1500 °C and basicity in the range of 1.0 to 2.0.[29] There is an asymmetric inverted V-shape relationship between the enrichment degree of phosphorus in slag and the binary basicity. When the basicity is 1.3, the maximum content of P₂O₅ in C₂S-C₃P solid solution is about 30.0 pct.

From our previous work,[5,9,30,31] the lower temperature range of 1370 °C to 1420 °C and the lower basicity range of 1.26 to 2.20 are the optimal dephosphorization ranges for the NDSP. According to the above literatures, it can be seen that in these temperature and basicity ranges, the researches on the dephosphorization of hot metal and the phosphorus-enrichment capacity of calcium silicate in the dephosphorization slag are quite limited using NDSP.

In the present work, the industrial experiments were carried out by 180 ton top-bottom combined blowing converter for NDSP. When the dephosphorization slag basicity is 1.26 to 2.20 and the dephosphorization endpoint temperature is 1370 °C to 1420 °C, the effect of dephosphorization slag basicity on dephosphorization of hot metal was studied. The effect of dephosphorization slag basicity on the mass action concentration, N_i, of CaO, SiO₂, calcium silicate and phosphate in the dephosphorization slag were analyzed by IMCT-N_i thermodynamic model for CaO-FeO-SiO₂-MgO-MnO-Al₂O₃-P₂O₅ slag. The effect of dephosphorization slag basicity on the enrichment degree $R_{{Ci-Pj}}$ of P₂O₅ containing solid solution and the phosphorus-enrichment contribution ratio of calcium silicate $R_{{Ci}}$ were studied. In addition, X-ray diffraction (XRD) was used to detect the phase compositions of dephosphorization slag under different basicities. The morphological evolution of P-rich phase in dephosphorization slag was observed and analyzed by SEM, and the P-rich phase compositions were determined by SEM-EDS under different basicities. Combined with the IMCT thermodynamic calculation results and dephosphorization reaction of molten slag, the effect of dephosphorization slag basicity on phosphorus-enrichment behavior was clarified, which was verified by the experimental analysis results.

Industrial Experiments

New Double Slag Converter Steelmaking Process

The industrial experiments were carried out with 180 ton top-bottom combined blowing converter in a steelmaking plant of China. Figure 1 shows the NDSP flow chart. The NDSP is mainly divided into eight steps: slag splashing protection → slag solidification confirmation → adding lime and scrap → pouring hot metal → dephosphorization stage → deslagging → decarburization stage → tapping and retaining decarburization slag. According to the silicon content of the hot metal, the quantitatively calculated amounts of auxiliary materials are added in the dephosphorization and decarbonization stages, respectively. Light burned dolomite is used as slag adjusting agent in slag splashing protection.

Fig. 1

New double slag converter steelmaking process flow chart

Industrial Experiment Parameters and Auxiliary Materials

Table I shows the consumptions of auxiliary materials for 180 ton top-bottom combined blowing converter. Lime is put into the bottom of furnace for preheating before dephosphorization stage, so as to improve the utilization rate of lime. The OG(Oxygen converter Gas recovery) slag pellets contain T.Fe of 55 pct, CaO of 12.4 pct and SiO₂ of 3.8 pct, mainly including the mud produced by oxygen converter gas recovery.

Table I Consumptions of Auxiliary Materials of 180 Ton Top-Bottom Combined Blowing Converter

The experimental converter capacity is 180 ton, the actual amount of hot metal added is 186 to 196 t, and the amount of scrap added is 29 to 33 t. Table II shows oxygen flow rates, blowing times, oxygen consumptions in dephosphorization stage and decarburization stage of 180 ton top-bottom combined blowing converter for the heat numbers of S1 to S6. Low-high-low lance position is used for dephosphorization stage blowing. The initial low lance position (1.7 to 1.8 m) promotes oxygen lance ignition, the subsequent high lance position (1.9 to 2.0 m) promotes rapid slagging in the early stage of dephosphorization, and the low lance position (1.65 to 1.75 m) in the later stage of dephosphorization promotes the agitation in dephosphorization. After the dephosphorization stage, the slag is poured out, and then lime, dolomite and other auxiliary materials are added for decarburization blowing. After decarburization, steel is tapped and decarburization slag is left for the dephosphorization of the next heat.

Table II Oxygen Flow Rates, Blowing Times, Oxygen Consumptions in Dephosphorization Stage and Decarburization Stage

Compositions of the Initial Hot Metal, the Hot Metal at the Endpoint of Dephosphorization and Dephosphorization Slag

In the smelting process of steel grade Q235B, the hot metal after desulfurization pretreatment is used for dephosphorization. The initial compositions and temperatures of hot metal in 180 ton top-bottom combined blowing converter are shown in Table III.

Table III Initial Compositions and Temperatures of Hot Metal in 180 Ton Top-Bottom Combined Blowing Converter

After the dephosphorization stage, the slag samples were taken from inclined converter by sticking onto a long inserted iron bars, cooling in air and being collected at room temperature. The whole process is very short with about 1 to 2 minutes, so the cooling rate is above 700 °C/ min, especially at the high temperature range. Part of the slag samples were crushed by crusher and passed through a 200-mesh sieve to remove the residual iron particles. The compositions of slag samples were analyzed by M4 TORNADO fluorescence spectrometer of Bruker company in Germany. The temperatures were measured and the hot metal was sampled with a sub-gun. Then, the hot metal samples were analyzed by SPECTROMAXx direct reading spectrometer of German SPECTRO company. The basicities and chemical compositions of dephosphorization slag, chemical compositions and temperatures of hot metal at the endpoint of dephosphorization are shown in Table IV. The dephosphorization slag basicity, B, is calculated by binary basicity, which is expressed as Eq. [1]:

$$ B = \frac{{({\text{pct}} {\text{CaO}})}}{{({\text{pct}} {\text{SiO}}_{{\text{2}}} )}} $$

(1)

Table IV Basicities and Chemical Compositions of Dephosphorization Slags, Chemical Compositions and Temperatures of Hot Metal at the Endpoint of Dephosphorization

Figure 2 shows the dephosphorization slag compositions with different basicities in CaO-SiO₂-FeO-8 pct MgO-8 pct MnO-4 pct P₂O₅ pseudo ternary phase diagram. The industrial experiments were carried out at the temperature between 1370 °C and 1420 °C. The liquidus projection sections of dephosphorization slag at 1370 °C and 1420 °C were drawn with FactSage8.0 using the database of phase diagram. The compositions of dephosphorization slags selected in the present work are marked in Figure 2. The compositions of six groups of dephosphorization slag all locate outside the liquidus projection area, which indicates that the dephosphorization slags should be in the multiphase state of solid-liquid coexistence.

Fig. 2

Dephosphorization slag compositions with different basicities in CaO-SiO₂-FeO-8 pct MgO-8 pct MnO-4 pct P₂O₅ pseudo ternary phase diagram

The phase analysis of dephosphorization slags were carried out by D8 Advance X-ray powder diffractometer (XRD) of Bruker company in Germany. In the range of 2θ = 10 to 90 deg and step size of 0.04°s⁻¹, XRD data were collected by Cu-Kα radiation. A small amount of massive dephosphorization slag was embedded in epoxy resin. Then it was ground and polished by automatic grinding and polishing machine of PRESI company in France. The surface was carbonized by magnetron sputtering MC1000 of HITACHI company in Japan. The morphology of P-rich phase of dephosphorization slags were observed by Zeiss EVO 18 electronic scanning microscope of Zeiss company of Germany, and the chemical compositions of P-rich phase in dephosphorization slags were analyzed by X-Max^N large area energy dispersive spectrometer (SEM-EDS) of Oxford Instruments Company in UK.

Thermodynamic Model IMCT-N _i for Calculating Mass Action Concentrations of Structural Units Or Ion Couples In Cao-Sio₂-Feo-Mgo-Mno-P₂o₅-Al₂o₃ Slags

Hypotheses

According to the classical hypothesis of IMCT summarized by Zhang et al.[25] and Yang et al.,[22] in the thermodynamic model IMCT-N_i for calculating the mass action concentration of structural unit or ion couple in the dephosphorization slag of CaO-SiO₂-FeO-MgO-MnO-P₂O₅-Al₂O₃ which reacts with hot metal, the main assumptions can be summarized as follows:

• In the dephosphorization slag in the NDSP, the structural units Ca^{2 +}, Mg^{2 +}, Fe^{2 +}, Mn^{2 +} and O²⁻ exist as simple ions, SiO₂, P₂O₅ and Al₂O₃ exist as simple molecules; silicate and phosphate are complex molecules. Each structural unit has its own position in the dephosphorization slag.

• Each kind of cation and anion generated by the same component will participate in the chemical reaction of forming complex molecules in the form of (Me^{2 +} + O²⁻) ion couple. The chemical reaction of forming complex molecule obeys the mass action law.

• The structural units in dephosphorization slag which reacts with hot metal have continuity in the studied concentration range.

• The reaction between simple ions and simple molecules to form complex molecules by bonding ion couples is in chemical dynamic equilibrium.

Selection of Structural Units in CaO-SiO₂-FeO-MgO-MnO-P₂O₅-Al₂ O ₃ Dephosphorization Slag

At the endpoint of the dephosphorization stage in the NDSP, the dephosphorization slag containing phosphorus reacted with hot metal is chosen as CaO-FeO-SiO₂-MgO-MnO-Al₂O₃-P₂O₅. According to the binary and ternary phase diagrams[25] of CaO-SiO₂, MgO-SiO₂, FeO-SiO₂, MnO-SiO₂, MgO-P₂O₅, CaO-P₂O₅, FeO-P₂O₅, MnO-P₂O₅, CaO-Al₂O₃, CaO-MgO-SiO₂, CaO-Al₂O₃-MgO, etc., and other binary and ternary phase diagrams related to dephosphorization slag, it is found that there are 32 complex molecules in dephosphorization slag, such as CaO·SiO₂, 3CaO·P₂O₅, 2FeO·SiO₂. In Table V, all simple ions, simple molecules and complex molecules in CaO-FeO-SiO₂-MgO-MnO-Al₂O₃-P₂O₅ dephosphorization slag at 1370 °C to 1420 °C are summarized and assigned specific numbers.

Table V Expression of Structural Units as Ion Couples, Simple or Complex Molecules, Their Numbers, Mole Numbers and Mass Action Concentration of N_i in 100 g Dephosphorization Slag of CaO-FeO-SiO₂-MgO-MnO-Al₂O₃-P₂O₅ Based on the IMCT

In 100 g dephosphorization slag of CaO-FeO-SiO₂-MgO-MnO-Al₂O₃-P₂O₅ , the initial mole numbers of seven components are expressed as $a_{{\text{1}}} = n_{{{\text{CaO}}}}^{{\text{0}}}$, $a_{{\text{2}}} = n_{{{\text{MnO}}}}^{{\text{0}}}$, $a_{{\text{3}}} = n_{{{\text{MgO}}}}^{{\text{0}}}$, $a_{{\text{4}}} = n_{{{\text{FeO}}}}^{{\text{0}}}$, $b_{1} = n_{{{\text{SiO}}_{2} }}^{0}$, $b_{2} = n_{{{\text{P}}_{2} {\text{O}}_{5} }}^{0}$, $b_{3} = n_{{{\text{Al}}_{2} {\text{O}}_{3} }}^{0}$, respectively. The total equilibrium mole number ∑n_i of all structural units can be expressed as Eq. [2].

$$ \sum n_{i} = 2n{\text{1}} + 2n2 + 2n3 + 2n4 + n5 + n6 + n7 + n{\text{c1}} + n{\text{c}}2 + \cdot \cdot \cdot + n{\text{c}}32 $$

(2)

According to the definition of mass action concentration N_i[18,19,20,21,22,23,24,25,26,27,28,29] of structural unit or ion couples in slag, N_i is the ratio of equilibrium mole number of structural unit i to the total equilibrium mole numbers ∑N_i of all structural units in slag with a fixed amount. The calculation formula of mass action concentration of structural unit i and ion couples (Me^{2 +} + O^{2 -}) in slag is expressed as Eqs. [3] and [4].[22,23,25]

$$ N_{i} = \frac{{n_{i} }}{{\sum n_{i} }} $$

(3)

$$ N_{{{\text{MeO}}}} = N_{{{\text{Me}}^{{{\text{2}} + }} {\text{, MeO}}}} + N_{{{\text{O}}^{{2 - }} {\text{, MeO}}}} = \frac{{n_{{{\text{Me}}^{{{\text{2}} + }} {\text{, MeO}}}} + n_{{{\text{O}}^{{2 - }} {\text{, MeO}}}} }}{{\sum n_{i} }} = \frac{{2n_{{{\text{MeO}}}} }}{{\sum n_{i} }} $$

(4)

Table V also lists the ion couples formed by simple ions in the dephosphorization slag of CaO-FeO-SiO₂-MgO-MnO-Al₂O₃-P₂O₅, as well as the equilibrium mole number n_i of simple ions, simple and complex molecules and the corresponding mass action concentration N_i.

The chemical reaction for the formation of 32 complex molecules ci in the dephosphorization slag of CaO-FeO-SiO₂-MgO-MnO-Al₂O₃-P₂O₅ are listed in Table VI, and the relationship between the variation of standard molar Gibbs free energy $\Delta _{{\text{r}}} G_{{{\text{m,c}}i}}^{\Theta }$ and temperature T are also given. The expressions of the corresponding standard reaction equilibrium constants $K_{{{\text{c}}i}}^{\Theta }$ are also listed in Table VI. In addition, the mass action concentrations N_ci for all complex molecules expressed using N₁ ($N_{{{\text{CaO}}}}$), N₂ ($N_ {\text{MnO}}$), N₃ ($N_ {\text{MgO}}$), N₄ ($N_{{\text{FeO}}}$), N₅ ($N_{{{\text{SiO}}_{{\text{2}}} }}$), N₆ ($N_{{{\text{P}}_{2} {\text{O}}_{5} }}$), N₇ ($N_{{\text{Al}}2{\text{O}}3}$) and $K_{{{\text{c}}i}}^{\Theta }$ are summarized in Table VI.

Table VI Chemical Reaction of Formed Complex Molecules in the Dephosphorization Slag of CaO-FeO-SiO₂-MgO-MnO-Al₂O₃-P₂O₅, Their Standerd Molar Gibbs Free Energy $\Delta _{{\text{r}}} G_{{{\text{m,c}}i}}^{\Theta }$ Changed With T, Standard Equilibrium Constant $K_{{{\text{c}}i}}^{\Theta }$ and Complex Molecular Mass Action Concentration N_ci Expressed by N₁-N₇ and Equilibrium Constant $K_{{{\text{c}}i}}^{\Theta }$

Establishment of IMCT-N_i Thermodynamic Model for Calculating Mass Action Concentrations of Structural Units or Ion Couples in CaO-FeO-SiO₂-MgO-MnO-Al₂O₃-P₂ O ₅ Dephosphorization Slag

With the dephosphorization reaction going on, the phosphorus in hot metal gradually enters the dephosphorization slag and partially removed at the end of dephosphorization stage. Combined with IMCT, N_i and $\sum n_{i}$ in Tables V and VI, the mass conservation equations of seven components in 100 g dephosphorization slag of CaO-FeO-SiO₂-MgO-MnO-Al₂O₃-P₂O₅ are established, which are expressed as Eqs. [5] through [11], respectively.

$$ \begin{gathered} a_{1} = (0.5N_{{\text{1}}} + N_{{{\text{c}}1}} + 2N_{{{\text{c}}2}} + 3N_{{{\text{c}}3}} + 3N_{{{\text{c}}4}} + 3N_{{{\text{c}}5}} + N_{{{\text{c}}6}} + N_{{{\text{c}}7}} + N_{{{\text{c}}8}} \hfill \\ + 12N_{{{\text{c}}9}} + 2N_{{{\text{c}}19}} + N_{{{\text{c}}20}} + N_{{{\text{c}}21}} + N_{{{\text{c}}22}} + 2N_{{{\text{c}}23}} + 3N_{{{\text{c}}24}} + 2N_{{{\text{c}}26}} + 3N_{{{\text{c}}27}} \hfill \\ + 4N_{{{\text{c}}28}} )\sum n_{i} = (0.5N_{{\text{1}}} + K_{{c{\text{1}}}}^{\Theta } N_{{\text{1}}} N_{{\text{5}}} + 2K_{{c{\text{2}}}}^{\Theta } N_{{\text{1}}}^{{\text{2}}} N_{{\text{5}}} + 3K_{{c{\text{3}}}}^{\Theta } N_{{\text{1}}}^{{\text{3}}} N_{{\text{5}}} + 3K_{{c{\text{4}}}}^{\Theta } N_{{\text{1}}}^{{\text{3}}} N_{{\text{5}}}^{{\text{2}}} \hfill \\ + 3K_{{c{\text{5}}}}^{\Theta } N_{{\text{1}}}^{{\text{3}}} N_{{\text{7}}}^{{}} + K_{{c{\text{6}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{7}}}^{{}} + K_{{c{\text{7}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{7}}}^{{\text{2}}} + K_{{c{\text{8}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{7}}}^{{\text{6}}} + 12K_{{c{\text{9}}}}^{\Theta } N_{{\text{1}}}^{{{\text{12}}}} N_{{\text{7}}}^{{\text{7}}} + 2K_{{c{\text{19}}}}^{\Theta } N_{{\text{1}}}^{{\text{2}}} N_{{\text{5}}}^{{}} N_{{\text{7}}}^{{}} \hfill \\ + K_{{c{\text{20}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{5}}}^{{\text{2}}} N_{{\text{7}}}^{{}} + K_{{c{\text{21}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{3}}}^{{}} N_{{\text{5}}}^{{}} + K_{{c{\text{22}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{3}}}^{{}} N_{{\text{5}}}^{2} + 2K_{{c{\text{23}}}}^{\Theta } N_{{\text{1}}}^{{\text{2}}} N_{{\text{3}}}^{{}} N_{{\text{5}}}^{2} + 3K_{{c{\text{24}}}}^{\Theta } N_{{\text{1}}}^{{\text{3}}} N_{{\text{3}}}^{{}} N_{{\text{5}}}^{2} \hfill \\ + 2K_{{c{\text{26}}}}^{\Theta } N_{{\text{1}}}^{{\text{2}}} N_{{\text{6}}}^{{}} + 3K_{{c{\text{27}}}}^{\Theta } N_{{\text{1}}}^{{\text{3}}} N_{{\text{6}}}^{{}} + 4K_{{c{\text{28}}}}^{\Theta } N_{{\text{1}}}^{{\text{4}}} N_{{\text{6}}}^{{}} )\sum n_{i} = n_{{{\text{CaO}}}}^{{\text{0}}} {\text{(mol)}} \hfill \\ \end{gathered} $$

(5)

$$ \begin{gathered} a_{2} = (0.5N_{{\text{2}}} + 2N_{{{\text{c}}15}} + N_{{{\text{c}}16}} + N_{{{\text{c}}17}} )\sum n_{i} \hfill \\ = (0.5N_{{\text{2}}} + 2K_{{c{\text{15}}}}^{\Theta } N_{{\text{2}}}^{{\text{2}}} N_{{\text{5}}}^{{}} + K_{{c{\text{16}}}}^{\Theta } N_{{\text{2}}}^{{}} N_{{\text{5}}}^{{}} + K_{{c{\text{17}}}}^{\Theta } N_{{\text{2}}}^{{}} N_{{\text{7}}}^{{}} )\sum n_{i} = n_{{{\text{MnO}}}}^{{\text{0}}} {\text{(mol)}} \hfill \\ \end{gathered} $$

(6)

$$ \begin{gathered} a_{3} = (0.5N_{{\text{3}}} + N_{{{\text{c}}10}} + 2N_{{{\text{c}}11}} + N_{{{\text{c}}12}} + N_{{{\text{c}}21}} + N_{{{\text{c}}22}} + N_{{{\text{c}}23}} + N_{{{\text{c}}24}} \hfill \\ + 2N_{{{\text{c}}25}} + 2N_{{{\text{c}}31}} + 3N_{{{\text{c}}32}} )\sum n_{i} = (0.5N_{{\text{3}}} + K_{{c{\text{10}}}}^{\Theta } N_{{\text{3}}}^{{}} N_{{\text{5}}}^{{}} + 2K_{{c{\text{11}}}}^{\Theta } N_{{\text{3}}}^{{\text{2}}} N_{{\text{5}}}^{{}} \hfill \\ + K_{{c{\text{12}}}}^{\Theta } N_{{\text{3}}}^{{}} N_{{\text{7}}}^{{}} + K_{{c{\text{21}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{3}}}^{{}} N_{{\text{5}}}^{{}} + K_{{c{\text{22}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{3}}}^{{}} N_{{\text{5}}}^{2} + K_{{c{\text{23}}}}^{\Theta } N_{{\text{1}}}^{{\text{2}}} N_{{\text{3}}}^{{}} N_{{\text{5}}}^{2} + K_{{c{\text{24}}}}^{\Theta } N_{{\text{1}}}^{{\text{3}}} N_{{\text{3}}}^{{}} N_{{\text{5}}}^{2} \hfill \\ + 2K_{{c{\text{25}}}}^{\Theta } N_{{\text{3}}}^{{\text{2}}} N_{{\text{5}}}^{{\text{5}}} N_{{\text{7}}}^{2} + 2K_{{c{\text{31}}}}^{\Theta } N_{{\text{3}}}^{{\text{2}}} N_{{\text{6}}}^{{}} + 3K_{{c{\text{32}}}}^{\Theta } N_{{\text{3}}}^{{\text{3}}} N_{{\text{6}}}^{{}} )\sum n_{i} = n_{{{\text{MgO}}}}^{{\text{0}}} ({\text{mol}}) \hfill \\ \end{gathered} $$

(7)

$$ \begin{gathered} a_{4} = (0.5N_{{\text{4}}} + 2N_{{{\text{c}}13}} + N_{{{\text{c}}14}} + 3N_{{{\text{c}}29}} + 4N_{{{\text{c}}30}} )\sum n_{i} \hfill \\ = (0.5N_{{\text{4}}} + 2K_{{c{\text{13}}}}^{\Theta } N_{{\text{4}}}^{{\text{2}}} N_{{\text{5}}}^{{}} + K_{{c{\text{14}}}}^{\Theta } N_{{\text{4}}}^{{}} N_{{\text{7}}}^{{}} + 3K_{{c{\text{29}}}}^{\Theta } N_{{\text{4}}}^{{\text{3}}} N_{{\text{6}}}^{{}} + 4K_{{c{\text{30}}}}^{\Theta } N_{{\text{4}}}^{{\text{4}}} N_{{\text{6}}}^{{}} )\sum n_{i} = n_{{{\text{FeO}}}}^{{\text{0}}} {\text{(mol)}} \hfill \\ \end{gathered} $$

(8)

$$ \begin{gathered} b_{1} = (N_{{\text{5}}} + N_{{{\text{c}}1}} + N_{{{\text{c}}2}} + N_{{{\text{c}}3}} + 2N_{{{\text{c}}4}} + N_{{{\text{c}}10}} + N_{{{\text{c}}11}} + N_{{{\text{c}}13}} + N_{{{\text{c}}15}} \hfill \\ + N_{{{\text{c}}16}} + 2N_{{{\text{c}}18}} + N_{{{\text{c}}19}} + 2N_{{{\text{c}}20}} + N_{{{\text{c}}21}} + 2N_{{{\text{c}}22}} + 2N_{{{\text{c}}23}} + 2N_{{{\text{c}}24}} + 5N_{{{\text{c}}25}} )\sum n_{i} \hfill \\ = (N_{{\text{5}}} + K_{{c{\text{1}}}}^{\Theta } N_{{\text{1}}} N_{{\text{5}}} + K_{{c{\text{2}}}}^{\Theta } N_{{\text{1}}}^{{\text{2}}} N_{{\text{5}}} + K_{{c{\text{3}}}}^{\Theta } N_{{\text{1}}}^{{\text{3}}} N_{{\text{5}}} + 2K_{{c{\text{4}}}}^{\Theta } N_{{\text{1}}}^{{\text{3}}} N_{{\text{5}}}^{{\text{2}}} + K_{{c{\text{10}}}}^{\Theta } N_{{\text{3}}}^{{}} N_{{\text{5}}}^{{}} \hfill \\ + K_{{c{\text{11}}}}^{\Theta } N_{{\text{3}}}^{{\text{2}}} N_{{\text{5}}}^{{}} + K_{{c{\text{13}}}}^{\Theta } N_{{\text{4}}}^{{\text{2}}} N_{{\text{5}}}^{{}} + K_{{c{\text{15}}}}^{\Theta } N_{{\text{2}}}^{{\text{2}}} N_{{\text{5}}}^{{}} + K_{{c{\text{16}}}}^{\Theta } N_{{\text{2}}}^{{}} N_{{\text{5}}}^{{}} + 2K_{{c{\text{18}}}}^{\Theta } N_{{\text{5}}}^{{\text{2}}} N_{{\text{7}}}^{{\text{3}}} \hfill \\ + K_{{c{\text{19}}}}^{\Theta } N_{{\text{1}}}^{{\text{2}}} N_{{\text{5}}}^{{}} N_{{\text{7}}}^{{}} + 2K_{{c{\text{20}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{5}}}^{{\text{2}}} N_{{\text{7}}}^{{}} + K_{{c{\text{21}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{3}}}^{{}} N_{{\text{5}}}^{{}} + {\text{2}}K_{{c{\text{22}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{3}}}^{{}} N_{{\text{5}}}^{2} \hfill \\ + 2K_{{c{\text{23}}}}^{\Theta } N_{{\text{1}}}^{{\text{2}}} N_{{\text{3}}}^{{}} N_{{\text{5}}}^{2} + 2K_{{c{\text{24}}}}^{\Theta } N_{{\text{1}}}^{{\text{3}}} N_{{\text{3}}}^{{}} N_{{\text{5}}}^{2} + 5K_{{c{\text{25}}}}^{\Theta } N_{{\text{3}}}^{{\text{2}}} N_{{\text{5}}}^{{\text{5}}} N_{{\text{7}}}^{2} )\sum n_{i} = n_{{{\text{SiO}}_{2}}}^{{\text{0}}} {\text{(mol)}} \hfill \\ \end{gathered} $$

(9)

$$ \begin{gathered} b_{2} = (N_{{\text{6}}} + N_{{{\text{c}}26}} + N_{{{\text{c}}27}} + N_{{{\text{c}}28}} + N_{{{\text{c}}29}} + N_{{{\text{c}}30}} + N_{{{\text{c}}31}} + N_{{{\text{c}}32}} )\sum n_{i} \hfill \\ = (N_{{\text{6}}} + K_{{c{\text{26}}}}^{\Theta } N_{{\text{1}}}^{{\text{2}}} N_{{\text{6}}}^{{}} + K_{{c{\text{27}}}}^{\Theta } N_{{\text{1}}}^{{\text{3}}} N_{{\text{6}}}^{{}} + K_{{c{\text{28}}}}^{\Theta } N_{{\text{1}}}^{{\text{4}}} N_{{\text{6}}}^{{}} + K_{{c{\text{29}}}}^{\Theta } N_{{\text{4}}}^{{\text{3}}} N_{{\text{6}}}^{{}} \hfill \\ + K_{{c{\text{30}}}}^{\Theta } N_{{\text{4}}}^{{\text{4}}} N_{{\text{6}}}^{{}} + K_{{c{\text{31}}}}^{\Theta } N_{{\text{3}}}^{{\text{2}}} N_{{\text{6}}}^{{}} + K_{{c{\text{32}}}}^{\Theta } N_{{\text{3}}}^{{\text{3}}} N_{{\text{6}}}^{{}} )\sum n_{i} = n_{{{ {\text{P}}_{2} {\text{O}}_{5} }}}^{{\text{0}}} {\text{(mol)}} \hfill \\ \end{gathered} $$

(10)

$$ \begin{gathered} b_{3} = (N_{{\text{7}}} + N_{{{\text{c}}5}} + N_{{{\text{c}}6}} + 2N_{{{\text{c}}7}} + 6N_{{{\text{c}}8}} + 7N_{{{\text{c}}9}} + N_{{{\text{c}}12}} + N_{{{\text{c}}14}} + N_{{{\text{c}}17}} \hfill \\ + 3N_{{{\text{c}}18}} + N_{{{\text{c}}19}} + 2N_{{{\text{c}}20}} + 2N_{{{\text{c}}25}} )\sum n_{i} \hfill \\ = (N_{{\text{7}}} + K_{{c{\text{5}}}}^{\Theta } N_{{\text{1}}}^{{\text{3}}} N_{{\text{7}}}^{{}} + K_{{c{\text{6}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{7}}}^{{}} + 2K_{{c{\text{7}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{7}}}^{{\text{2}}} + 6K_{{c{\text{8}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{7}}}^{{\text{6}}} \hfill \\ + 7K_{{c{\text{9}}}}^{\Theta } N_{{\text{1}}}^{{{\text{12}}}} N_{{\text{7}}}^{{\text{7}}} + K_{{c{\text{12}}}}^{\Theta } N_{{\text{3}}}^{{}} N_{{\text{7}}}^{{}} + K_{{c{\text{14}}}}^{\Theta } N_{{\text{4}}}^{{}} N_{{\text{7}}}^{{}} + K_{{c{\text{17}}}}^{\Theta } N_{{\text{2}}}^{{}} N_{{\text{7}}}^{{}} + 3K_{{c{\text{18}}}}^{\Theta } N_{{\text{5}}}^{{\text{2}}} N_{{\text{7}}}^{{\text{3}}} \hfill \\ + K_{{c{\text{19}}}}^{\Theta } N_{{\text{1}}}^{{\text{2}}} N_{{\text{5}}}^{{}} N_{{\text{7}}}^{{}} + K_{{c{\text{20}}}}^{\Theta } N_{{\text{1}}}^{{}} N_{{\text{5}}}^{{\text{2}}} N_{{\text{7}}}^{{}} + 2K_{{c{\text{25}}}}^{\Theta } N_{{\text{3}}}^{{\text{2}}} N_{{\text{5}}}^{{\text{5}}} N_{{\text{7}}}^{2} )\sum n_{i} = n_{{{ {\text{Al}}_{2} {\text{O}}_{3} }}}^{{\text{0}}} {\text{(mol)}} \hfill \\ \end{gathered} $$

(11)

According to the mass conservation law, the sum of mole fractions of all structural units in the dephosphorization slag of CaO-FeO-SiO₂-MgO-MnO-Al₂O₃-P₂O₅ with fixed total mass under equilibrium condition is equal to 1.0, and Eq. [12] can be obtained.

$$ \begin{gathered} N_{{\text{1}}} + N_{{\text{2}}} + N_{{\text{3}}} + N_{{\text{4}}} + N_{{\text{5}}} + N_{{\text{6}}} + N_{{\text{7}}} + N_{{{\text{c}}1}} + N_{{{\text{c}}2}} + N_{{{\text{c}}3}} + N_{{{\text{c}}4}} + \cdot \cdot \cdot + N_{{{\text{c}}30}} \hfill \\ + N_{{{\text{c}}31}} + N_{{{\text{c}}32}} = (N_{{\text{1}}} + N_{{\text{2}}} + N_{{\text{3}}} + N_{{\text{4}}} + N_{{\text{5}}} + N_{{\text{6}}} + N_{{\text{7}}} + K_{{c{\text{1}}}}^{\Theta } N_{{\text{1}}} N_{{\text{5}}} + K_{{c{\text{2}}}}^{\Theta } N_{{\text{1}}}^{{\text{2}}} N_{{\text{5}}} \hfill \\ + K_{{c{\text{3}}}}^{\Theta } N_{{\text{1}}}^{{\text{3}}} N_{{\text{5}}} + K_{{c{\text{4}}}}^{\Theta } N_{{\text{1}}}^{{\text{3}}} N_{{\text{5}}}^{{\text{2}}} + \cdot \cdot \cdot + K_{{c{\text{30}}}}^{\Theta } N_{{\text{4}}}^{{\text{4}}} N_{{\text{6}}}^{{}} + K_{{c{\text{31}}}}^{\Theta } N_{{\text{3}}}^{{\text{2}}} N_{{\text{6}}}^{{}} + K_{{c{\text{32}}}}^{\Theta } N_{{\text{3}}}^{{\text{3}}} N_{{\text{6}}}^{{}} ) = \sum N_{i} = 1.0 \hfill \\ \end{gathered} $$

(12)

Eqs. Eqs. [5] through [12] are the governing equations for calculating the mass action concentration N_i of structural units or ion couples in the dephosphorization slag of CaO-FeO-SiO₂-MgO-MnO-Al₂O₃-P₂O₅. According to Eqs. [5] through [12], there are eight unknown parameters of N₁, N₂, N₃, N₄, N₅, N₆, N₇ and ∑n_i, combined with the eight independent governing equations built by IMCT. The mass action concentration N_i of simple components and the total equilibrium mole number ∑n_i can be obtained, thus the mass action concentration N_ci of complex components can be calculated, and the reaction ability of complex components can be further studied. The solution of the Eqs. (5-12) can be obtained by Jupyter Notebook in Anaconda, and the accuracy of the solution of nonlinear equations by calling Fsolve Function can reach to be smaller than 10⁻²⁵. Therefore, it can be considered that the obtained N_i is very accurate.

Definition of Enrichment Possibility $N_{{Ci-Pj}}$, Enrichment Degree $R_{{Ci - Pj}}$ of Solid Solution Containing P₂O₅ and Phosphorus-Enrichment Contribution Ratio of Calcium Silicate $R_{{Ci}}$

Senlin Xie et al.[27] and Jingyan Li et al.[28,29] both studied the enrichment behavior of phosphorus in calcium silicate based on IMCT. P₂O₅ is mainly concentrated in calcium silicate complex molecules, so the solid phase rich in P₂O₅ can be regarded as the reaction product of calcium silicate and phosphate, independent of other structural units.[27] There are four kinds of calcium silicate molecules and seven kinds of phosphate in the dephosphorization slag in the present work. Therefore, the product of mass action concentration $N_{{Ci}}$ of calcium silicate and $N_{{Pj}}$ of containing P₂O₅ component can be used to describe the enrichment possibility $N_{{Ci-Pj}}$ of solid solution containing P₂O₅ in dephosphorization slag,[27,28,29] as shown in Eq. [13]:

$$ N_{{Ci-Pj}} {\text{ = }}N_{{Ci}} \times N_{{Pj}} \;{\text{with}}\;i = {\text{1,2,3,4,}}\;j = {\text{1,2,3,4,5,6,7}} $$

(13)

Ci includes CS, C₂S, C₃S, 3CaO·2SiO₂(C₃S₂).

Pj includes 2CaO·P₂O₅(C₂P), 3CaO·P₂O₅(C₃P), 4CaO·P₂O₅(C₄P), 3FeO·P₂O₅(F₃P), 4FeO·P₂O₅(F₄P), 2MgO·P₂O₅(M₂P), 3MgO·P₂O₅(M₃P).

The sum of the enrichment possibility $N_{{Ci - Pj}}$ of the above-mentioned twenty-eight components containing P₂O₅ components is expressed by Eq. [14]:

$$ \sum\limits_{\begin{subarray}{l} i = 1,2,3,4 \\ j = 1,2,3,4,5,6,7 \end{subarray} } {\left( {N_{{{\text{C}}i{\text{ - P}}j}} \frac{{M_{{ {\text{P}}_{2} {\text{O}}_{5} }} }}{{M_{{Ci - Pj}} }}} \right)} = N_{{{\text{C1 - P1}}}} \frac{{M_{{{ {\text{P}}_{2} {\text{O}}_{5} }}} }}{{M_{{{\text{C1 - P1}}}} }} + N_{{{\text{C1 - P2}}}} \frac{{M_{{ {\text{P}}_{2} {\text{O}}_{5} }} }}{{M_{{{\text{C1 - P2}}}} }} + \ldots + N_{{{\text{C4 - P7}}}} \frac{{M_{{ {\text{P}}_{2} {\text{O}}_{5} }} }}{{M_{{{\text{C4 - P7}}}} }} $$

(14)

M_i is the relative atomic or molecular mass of i. The ratio of $N_{{Ci - Pj}} \frac{{M_{{{\text{P}}_{2} {\text{O}}_{5} }} }}{{M_{{Ci - Pj}} }}$ of a certain components to the sum of the enrichment possibility for all the components containing P₂O₅, $\sum\limits_{\begin{subarray}{l} i = 1,2,3,4 \\ j = 1,2,3,4,5,6,7 \end{subarray} } {\left( {N_{{Ci - Pj}} \frac{{M_{{{\text{P}}_{{\text{2}}} {\text{O}}_{{\text{5}}} }} }}{{M_{{Ci - Pj}} }}} \right)}$, can be defined as the enrichment degree $R_{{Ci - Pj}}$ of solid solution containing P₂O₅.[27,28,29] Taking C₂S-C₃P as an example, the enrichment degree $R_{{{\text{C2S - C3P}}}}$ is expressed as Eq. [15]:

$$ R_{{{\text{C2S - C3P}}}} = \frac{{\left( {N_{{{\text{C2S - C3P}}}} \frac{{M_{{{\text{P2O5}}}} }}{{M_{{{\text{C2S - C3P}}}} }}} \right)}}{{\sum\limits_{\begin{subarray}{l} i = 1,2,3,4 \\ j = 1,2,3,4,5,6,7 \end{subarray} } {\left( {N_{{Ci - Pj}} \frac{{M_{{{\text{P2O5}}}} }}{{M_{{Ci - Pj}} }}} \right)} }} $$

(15)

In order to describe the phosphorus-enrichment capacity of a certain calcium silicate in the dephosphorization slag, the sum of the enrichment degree $R_{{Ci - Pj}}$ of all components containing P₂O₅ in a certain calcium silicate is defined as the phosphorus-enrichment contribution ratio $R_{{Ci}}$ of calcium silicate.[27] Taking C₂S as an example, the phosphorus-enrichment contribution ratio $R_{{{\text{C2S}}}}$ can be expressed as Eq. [16]:

$$ R_{{{\text{C2S}}}} = R_{{{\text{C2S}} - {\text{C2P}}}} + R_{{{\text{C2S}} - {\text{C3P}}}} + \ldots + R_{{{\text{C2S}} - {\text{M3P}}}} = \frac{{\sum\limits_{\begin{subarray}{l} i = 2 \\ j = 1,2,3,4,5,6,7 \end{subarray} } {\left( {N_{{{\text{C2S - }}Pj}} \frac{{M_{{{\text{P2O5}}}} }}{{M_{{{\text{C2S - }}Pj}} }}} \right)} }}{{\sum\limits_{\begin{subarray}{l} i = 1,2,3,4 \\ j = 1,2,3,4,5,6,7 \end{subarray} } {\left( {N_{{Ci - Pj}} \frac{{M_{{{\text{P2O5}}}} }}{{M_{{Ci - Pj}} }}} \right)} }} $$

(16)

Analysis and Discussion of Hot Metal Samples and Dephosphorization Slag Samples from Industrial Experiments

Effect of Dephosphorization Slag Basicity on Element Removal Ratio in Hot Metal, Phosphorus Distribution Ratio Between Slag and Hot Metal

In industrial experiment, it is difficult to control all the other parameters to be constants for investigating the effect of dephosphorization slag basicity on hot metal dephosphorization. In the heats of industrial experiments selected in the present work, the dephosphorization endpoint temperatures were 1370 °C to 1420 °C. From the previous industrial experiment results,[5,9,30,31] the slagging effect of dephosphorization slag was favorable in this temperature range, and the thermodynamic conditions were conducive to dephosphorization. The FeO contents changed in a narrow range of 17.04 to 20.48 pct, which ensured a relatively close oxidation capacity. The contents of MgO, MnO and Al₂O₃ changed little, and these changes did not have a great impact on the dephosphorization results. The changes in the removal ratios of phosphorus, silicon, carbon and manganese in hot metal, phosphorus distribution ratio between dephosphorization slag and hot metal at the different dephosphorization slag basicities from 1.26 to 2.20 were studied.

Figure 3 shows the effect of dephosphorization slag basicity on removal ratios of elements in hot metal. $\eta _{i}$ is the removal ratio of element i in hot metal, which is calculated by Eq. [17]. [pct i]₀ represents the mass fraction of i in the hot metal at the initial point of dephosphorization and [pct i]_e represents that at the endpoint of dephosphorization. The chemical reactions of dephosphorization, desilication, demanganization and decarbonization in hot metal are expressed as Eqs. [18] through [21].[32,33,34,35,36]

$$ \eta _{i} = \frac{{[{\text{pct}}\;i]_{0} - [{\text{pct}}\;i]_{e} }}{{[{\text{pct}}\;i]_{0} }} \times 100\;{\mkern 1mu} {\text{pct}} $$

(17)

$$ 2[{\text{P}}] + 5({\text{FeO}}) + 3{\text{CaO}} = (3{\text{CaO}} \cdot {\text{P}}_{2} {\text{O}}_{5} ) + 5[{\text{Fe}}] $$

(18)

$$ [{\text{Si}}] + 2({\text{FeO}}) = ({\text{SiO}}_{2} ) + 2[{\text{Fe}}] $$

(19)

$$ [{\text{Mn}}] + ({\text{FeO}}) = ({\text{MnO}}) + [{\text{Fe}}] $$

(20)

$$ [{\text{C}}] + [{\text{O}}] = {\text{CO}} $$

(21)

Fig. 3

Effect of dephosphorization slag basicity on removal ratios of elements in hot metal

It can be seen from Figure 3 that with increasing dephosphorization slag basicity, the dephosphorization ratio and the decarbonization ratio both increases, and the demanganization ratio gradually decreases, while the desiliconization ratio does not change significantly and remains at a relatively high level. With increasing dephosphorization slag basicity, the activity of CaO in slag increases, and the calcium silicate is easier to form in the slag, which is conducive to the formation of C₂S-C₃P solid solution. According to the chemical reaction of Eq. [18], increasing the dephosphorization slag basicity is beneficial to reduce the activity of P₂O₅ in the slag, so as to improve the phosphorus distribution ratio between slag and hot metal, and further improve the dephosphorization ratio.

With increasing dephosphorization slag basicity, the oxygen potential at the interface between slag and hot metal is increased, and the decarburization reaction is also promoted. However, the decarburization reaction is weak in the dephosphorization stage, and the decarburization ratio is from 28.46 to 33.95 pct. In the dephosphorization stage, the combination ability of silicon and manganese with oxygen is stronger than that of phosphorus, so that silicon and manganese will be oxidized prior to phosphorus. With increasing dephosphorization slag basicity, the activity of SiO₂ in the slag decreases, which is conducive to the desilication reaction. The desilication ratio at the end of dephosphorization is always above 94 pct, so that silicon in hot metal is removed to trace at the end of dephosphorization stage. The increase of basicity leads to the existence of a large amount of free CaO in the dephosphorization slag. CaO will replace the MnO in 2MnO·SiO₂ to generate the stabler C₂S,[36] thus increasing the activity of MnO. This will lead to the occurrence of remanganization reaction, reducing the demanganization ratio. When the dephosphorization slag basicity is 2.20, the dephosphorization ratio can reach 66.20 pct. The desilication ratio, demanganization ratio and the decarburization ratio are 94.22, 35.65 and 33.95 pct, respectively.

Figure 4 shows the effect of dephosphorization slag basicity on P₂O₅ content in dephosphorization slag, phosphorus content in hot metal and phosphorus distribution ratio L_P. Phosphorus distribution ratio L_P is calculated by Eq. [22].

$$ {L_{\text{P}}} = \frac{{({\text{pct}}\;{\text{P}}_{2} {\text{O}}_{5} )}}{{[{\text{pct}}\;{\text{P]}}}} $$

(22)

Fig. 4

Effect of dephosphorization slag basicity on P₂O₅ content in dephosphorization slag, phosphorus content in hot metal and phosphorus distribution ratio L_P

With increasing the dephosphorization slag basicity, the phosphorus distribution ratio L_P increases, the content of P₂O₅ in dephosphorization slag increases as a whole and the phosphorus content in hot metal decreases. When the dephosphorization slag basicity is 1.90, the P₂O₅ content in the slag can reach 5.10 pct. When the dephosphorization slag basicity is further increased to 2.20, the phosphorus distribution ratio increases to 81.3 and the phosphorus content in hot metal decreases to 0.048 pct. The increase of dephosphorization slag basicity improves the apparent diffusion coefficient of phosphorus in solid solution,[37] which makes the phosphorus in hot metal more easily fixed in C₂S-C₃P solid solution. This increases the content of P₂O₅ in slag and reduces the phosphorus content in hot metal.

XRD Analysis of Dephosphorization Slag Under Different Basicities

Figure 5 shows the XRD analysis results of dephosphorization slag with basicities of 1.26 to 2.20. At the endpoint of the dephosphorization stage in the NDSP, the dephosphorization slag mainly contains dicalcium silicate Ca₂SiO₄(C₂S), silicate phase Ca₃Mg(SiO₄)₂, calcium ferrite phase Ca₂Fe₂O₅, the Ca(Fe_xMg_y)(SiO₄)(x+y=1) mixture of Ca₃Mg(SiO₄)₂ and Ca₂Fe₂O₅, metal oxide phase RO and the solid solution of (Ca₂(SiO₄))6(Ca₃(PO₄)₂)(C₂S-6C₃P) and Ca₁₅(PO₄)₂(SiO₄)₆(6C₂S-C₃P) containing phosphorus.

Fig. 5

XRD analysis results of dephosphorization slag with basicities of 1.26 to 2.20

By comparing the XRD results of dephosphorization slags with different basicites, it is found that the mixed phase of Ca(Fe_xMg_y)(SiO₄)(x + y = 1) is widely existed in dephosphorization slag when basicity is 1.26 to 1.37, and there is no oxide phase and the solid solution phase containing phosphorus. Combined with the dephosphorization results in Figure 3 and our previous mineralogical analysis[9] of the dephosphorization slag under low basicity, a reasonable explanation can be obtained. Because there is a large amount of liquid slag matrix phase in the slag at lower basicity, phosphorus in hot metal is difficult to be effectively fixed in dephosphorization slag. Large-area P-rich phase in the dephosphorization slag is hard to form, which leads to the low dephosphorization ratio at lower basicity.

When the basicity range of dephosphorization slag is 1.37 to 1.71, C₂S, Ca₃Mg(SiO₄)₂, Ca₂Fe₂O₅ and RO are mainly detected in the dephosphorization slag, which indicates that the dephosphorization slag changes from liquid slag matrix phase to silicate and calcium ferrite. However, the solid solution containing phosphorus has not been detected by XRD in this range. When the basicity range of dephosphorization slag is further increased to 1.90 to 2.20, the diffraction peaks of C₂S-6C₃P and 6C₂S-C₃P phases appear, which is consistent with the higher dephosphorization ratio as shown in Figure 3.

Analysis of P-Rich Phase Morphologies and Areas in Dephosphorization Slag at Different Basicities by SEM-EDS

The typical morphologies, areas and map scanning results of P-rich phase in dephosphorization slag at different basicities are shown in Figure 6. When the dephosphorization slag basicity is in the range of 1.26 to 1.37, the P-rich phases are in long strip shape, and their area is between 4 and 36 μm². The content of P₂O₅ in the P-rich phase is less than 10 pct and it contains high contents of Ca and Si. The map scanning result is not obvious for the identification of phosphorus element in each phase. Therefore, it is inferred that the solid solution containing phosphorus is not formed in the basicity range of 1.26 to 1.37.

Fig. 6

Typical morphologies, areas and map scanning results of P-rich phase in dephosphorization slag at different basicities

When the dephosphorization slag basicity is 1.50, the P-rich phases are dispersed into several small block P-rich phases, which are mainly distributed in dendrite shape, and their areas are mainly concentrated in 8 to 25 μm². When the dephosphorization slag basicity is further increased to the range of 1.71 to 2.20, the dispersed small block P-rich phase grows rapidly, irregular blocks gradually grow into the blocks with smooth edge, and the area of P-rich phase grows from 142 μm² at basicity of 1.71 to 8000 μm² at the basicity of 2.20. It can be seen from Figure 6 that the Ca, Si and P are mainly concentrated in the P-rich phase. Therefore, according to the results of Figures 5 and 6, the solid solution containing phosphorus is formed in the basicity range of 1.90 to 2.20.

Analysis of P-Rich Phase at Different Basicities

In order to determine the existing form of phosphorus containing solid solution (C_iS-C_jP) in P-rich phase of dephosphorization slag, five groups of P-rich phase composition data were obtained by SEM-EDS analysis under each basicity, and the results were averaged to reduce the element content differences caused by different points in the P-rich phase. Because phosphorus mainly exists in the form of C₃P in the solid solution,[16,17] and the sum of the masses of CaO, SiO₂ and P₂O₅ in the P-rich phase is equal to the sum of C_iS and C₃P, the average mass fraction of C_iS and C₃P can be calculated. According to the mass fraction ratio of CaO and SiO₂ in the P-rich phase, it can be seen that the calcium silicate existing in the P-rich phase is mainly the mixture of CS and C₂S. Table VII shows the average mass fractions of different compositions in P-rich phase of dephosphorization slag and the average mass fractions of C₃P and C_iS at the different basicities.

Table VII Average Mass Fractions of Different Compositions in P-Rich Phase of Dephosphorization Slag and the Average Mass Fractions of C_iS and C₃P at Different Basicities/(Pct)

Figure 7(a) shows the Gibbs free energy changes of C_iS(i=1, 2) and C_jP(j=1,2,3) under different basicities of dephosphorization slag, Figure 7(b) shows the effect of dephosphorization slag basicity on C₃P content, basicity, C_iS content in P-rich phase of dephosphorization slag and Figure 7(c) shows the determination of coefficient n in nC₂S-C₃P of the P-rich phase at different basicities. The Gibbs free energy of each substance in Figure 7(a) is calculated according to Table VI. With increasing dephosphorization slag basicity, the content of C₃P and basicity of P-rich phase increase, the content of C_iS decreases as a whole. The basicity in P-rich phase increases from 1.21 to 1.97, which corresponds to the actual basicity change of dephosphorization slag. It also shows that calcium silicate in P-rich phase is a mixture of CS and C₂S. By comparing the free energy of formation of C_iS(i = 1, 2) and C_jP(j = 1,2,3) at different basicities, C_iS is stabler than C_jP at 1370 °C to 1420 °C, and the combination ability of CaO with P₂O₅ is stronger than that with SiO₂.[38,39,40] With the increase of P₂O₅ content in the P-rich phase, CaO will first combine with P₂O₅ to form C₃P. Therefore, with increasing dephosphorization slag basicity, the content of C₃P increases and the content of C_iS decreases in P-rich phase.

Fig. 7

(a) Gibbs free energy changes of C_iS (i=1,2) and C_jP (j=1,2,3) under different basicities of dephosphorization slag; (b) Effect of dephosphorization slag basicity on C₃P content, basicity, C_iS content in P-rich phase of dephosphorization slag; (c) Determination of coefficient n in nC₂S-C₃P of the P-rich phase at different basicities

The phosphorus containing solid solution in dephosphorization slag may exist in the form of C₂S-C₃P, 2C₂S-C₃P, 4.8C₂S-C₃P, 6C₂S-C₃P and 20C₂S-C₃P.[30] Therefore, taking nC₂S-C₃P (n = 1, 2, 4.8, 6, 20) as the judgment standard, the coefficient n in nC₂S-C₃P of P-rich phase under different basicities is roughly determined, as shown in Figure 7(c). When the dephosphorization slag basicity is 1.26 to 1.37, the values of n are 6 to 20. When the basicity is 1.50 to 1.90, the values of n are 2 to 4.8. When the basicity further increases to 2.20, the values of n are 1 to 2. The results show that with increasing the basicity, the coefficient n of nC₂S-C₃P presents a decreasing trend, which indicates that the phosphorus content in nC₂S-C₃P increases gradually with increasing basicity, and the phosphorus-enrichment ability of the dephosphorization slag increases.

Analysis and Discussion of IMCT Thermodynamic Calcuation Results

Effect of Dephosphorization Slag Basicity on Mass Action Concentration N_i of Components in Dephosphorization Slag

According to the IMCT-N_i thermodynamic calculation model, the mass action concentration N_i of each component in Table VI was calculated. The mass action concentration N_i in IMCT can be used to characterize the reaction capacity of the composition like the activity a_i in molecular theory.[18,19,20,21,25] In order to study the relationship between mass action concentration N_i and the basicity of dephosphorization slag, the best fitting method was selected according to the data changing rule, and the goodness of fit was expressed by the fitting coefficient r².

In order to analyze the phosphorus-enrichment capacity of calcium silicate in dephosphorization slag, the effect of dephosphorization slag basicity on mass action concentration of CaO , SiO₂ and the their ratio are analyzed. Figure 8 shows the effect of dephosphorization slag basicity on $N_{\text{CaO}}$, $N_{{{\text{SiO}}_{2} }}$ and $N_{{{\text{CaO}}}} /N_{{{\text{SiO}}_{2} }}$. With increasing dephosphorization slag basicity, $N_{{{\text{CaO}}}}$ increases exponentially and $N_{{{\text{SiO}}_{2} }}$ decreases exponentially. The fitting coefficient r² of both is greater than 0.97, which indicates that there is a good mathematical relationship between the dephosphorization slag basicity and $N_{{{\text{CaO}}}}$ and $N_{{{\text{SiO}}_{2} }}$.

Fig. 8

Effect of dephosphorization slag basicity on $N_{\text{CaO}}$, $N_{{{\text{SiO}}_{2} }}$ and $N_{{{\text{CaO}}}} /N_{{{\text{SiO}}_{2} }}$

With increasing dephosphorization slag basicity, $N_{{{\text{CaO}}}} /N_{{{\text{SiO}}_{2} }}$ increases exponentially, and its fitting coefficient is greater than 0.999, reaching the fitting convergence. The results show that both basicities of B and $N_{{{\text{CaO}}}} /N_{{{\text{SiO}}_{2} }}$ have the similar effect in dephosphorization slag at temperature of 1370 °C to 1420 °C and basicity of 1.26 to 2.20. The relationship between B and $N_{{{\text{CaO}}}} /N_{{{\text{SiO}}_{2} }}$ is Eq. [23]. It should be noted that the range of $N_{{{\text{CaO}}}} /N_{{{\text{SiO}}_{2} }}$ has large values of 4 to 1202, so that Eq. [23] can only reflect the their change trends.

$$ N_{{{\text{CaO}}}} /N_{{{\text{SiO}}_{2} }} = 6.774 \times 10^{{ - 5}} \times \exp \left( {\frac{B}{{0.1403}}} \right) + 5.674 $$

(23)

Four kinds of calcium silicate complex molecules CS, C₂S, C₃S, C₃S₂ formed by CaO and SiO₂ are further considered. The effect of dephosphorization slag basicity on the mass action concentration of calcium silicates were analyzed under the conditions of lower temperature range of 1370 °C to 1420 °C and lower basicity range of 1.26 to 2.20.

Figure 9 shows the effect of dephosphorization slag basicity on the mass action concentration of calcium silicates. With increasing dephosphorization slag basicity, $N_{{{\text{CS}}}}$ decreases exponentially, $N_{{{\text{C2S}}}}$ increases first and then decreases, $N_{{{\text{C3S}}}}$ increases exponentially and $N_{{{\text{C3S2}}}}$ shows a decreasing trend as a whole. The variation trend of $N_{{{\text{CS}}}}$, $N_{{{\text{C2S}}}}$ and $N_{{{\text{C3S}}}}$ is consistent with the results obtained by Jingyan Li et al.[28] At the conditions of CaO-15 pct SiO₂-FeO-Fe₂O₃-5 pct P₂O₅ slag, 1450 °C to 1600 °C, basicity of 1.8 to 3.7. The increase of dephosphorization slag basicity can reduce $N_{{{\text{C3S2}}}}$, and there is no obvious mathematical relationship between them.

Fig. 9

Effect of dephosphorization slag basicity on the mass action concentration of calcium silicate of $N_{{{\text{CS}}}}$, $N_{{{\text{C2S}}}}$, $N_{{{\text{C3S}}}}$ and $N_{{{\text{C3S2}}}}$

Figure 9 shows that $N_{{{\text{CS}}}}$ and $N_{{{\text{C2S}}}}$ are one order of magnitude higher than $N_{{{\text{C3S}}}}$ and $N_{{{\text{C3S2}}}}$, indicating that the former two have strong reaction ability in the dephosphorization slag, being the main components in the dephosphorization slag. Between $N_{{{\text{CS}}}}$ and $N_{{{\text{C2S}}}}$, the value of $N_{{{\text{C2S}}}}$ is always higher than that of $N_{{{\text{CS}}}}$, which indicates that C₂S has the strongest reaction ability in the dephosphorization slag, and the phosphorus in hot metal is easier to combine with C₂S to form phosphorus containing solid solution.

With increasing dephosphorization slag basicity from 1.26 to 2.20, it is calculated that $N_{{{\text{C2P}}}}$ varies from 7.52 × 10⁻⁷ to 2.88×10⁻⁶, $N_{{{\text{C3P}}}}$ varies from 0.012 to 0.026, and $N_{{{\text{C4P}}}}$ varies from 2.14 × 10⁻⁵ to 2.20×10⁻⁴. In addition, the variation range of $N_{{{\text{F3P}}}}$ is 2.57 × 10⁻¹⁴ to 3.29 × 10⁻¹², the variation range of $N_{{{\text{F4P}}}}$ is 4.32 × 10⁻¹⁴ to 6.90 × 10⁻¹², the variation range of $N_{{{\text{M2P}}}}$ ranging from 3.13 × 10⁻¹⁰ to 8.43 × 10⁻⁹ and that of $N_{{{\text{M3P}}}}$ from 3.58 × 10⁻⁹ to 5.82 × 10⁻⁸. Considering the above range value, the variation range of $N_{{{\text{C2P}}}}$, $N_{{{\text{C4P}}}}$, $N_{{{\text{F3P}}}}$, $N_{{{\text{F4P}}}}$, $N_{{{\text{M2P}}}}$ and $N_{{{\text{M3P}}}}$ is less than 10⁻⁴ in the dephosphorization slag with the basicity from 1.26 to 2.20, so it is reasonable to ignore the effect of the above components on the phosphorus-enrichment effect. According to the above description, in the low temperature range of 1370 °C to 1420 °C and the low basicity range of 1.26 to 2.20, the P₂O₅ containing components in the dephosphorization slag mainly combined with calcium silicate are C₃P.

Effect of Dephosphorization Slag Basicity on Phosphorus-Enrichment Contribution Ratio $R_{{Ci}}$ of Calcium Silicate

The phosphorus-enrichment contribution ratio $R_{{Ci}}$ can well indicate the enrichment degree of P₂O₅ containing solid solution by different calcium silicate in slag.[27] According to Eq. [16], the phosphorus-enrichment contribution ratios of four kinds of calcium silicate of $R_{{{\text{CS}}}}$, $R_{{{\text{C2S}}}}$, $R_{{{\text{C3S}}}}$ and $R_{{{\text{C3S2}}}}$ are calculated. The effect of dephosphorization slag basicity on phosphorus-enrichment capacity of different calcium silicate in dephosphorization slag is further studied under the conditions of low temperature range of 1370 to 1420 °C and low basicity range of 1.26 to 2.20.

Figure 10 shows the changes in the phosphorus-enrichment contribution ratio $R_{{Ci}}$ under different basicities of dephosphorization slags. From the proportion of different strip areas in Figure 10(a), it can be seen that the phosphorus-enrichment contribution ratio of $R_{{{\text{C2S}}}}$ is the largest. With increasing dephosphorization slag basicity from 1.26 to 2.20, the $R_{{{\text{C2S}}}}$ increases from 0.56 to 0.84, the $R_{{{\text{CS}}}}$ significantly reduces, and the value of $R_{{{\text{CS}}}}$ decreases from 0.41 to 0.11, while the proportions of $R_{{{\text{C3S}}}}$ and $R_{{{\text{C3S2}}}}$ have very small values. This indicates that with increasing dephosphorization slag basicity, phosphorus tends to combine with C₂S to be enriched. It can be seen from Figure 10(b) and (c) that the change trend of $R_{{{\text{C2S}}}}$ is the same as dephosphorization ratio, but the change trend of $R_{{{\text{CS}}}}$ is opposite to dephosphorization ratio. Therefore, the increase of dephosphorization slag basicity mainly will increase the phosphorus-enrichment capacity of C₂S and decrease the phosphorus-enrichment capacity of CS.

Fig. 10

Changes in the phosphorus-enrichment contribution ratio $R_{{Ci}}$ under different basicities of dephosphorization slags. (a) Effect of dephosphorization slag basicity to the phosphorus-enrichment contribution ratio $R_{{Ci}}$; Effect of dephosphorization slag basicity on (b) $R_{{{\text{CS}}}}$, (c) $R_{{{\text{C2S}}}}$, (d) $R_{{{\text{C3S}}}}$, (e) $R_{{{\text{C3S2}}}}$

The mathematical relationship between dephosphorization slag basicity and phosphorus-enrichment contribution ratio of calcium silicate are further studied. Figure 10(b-e) shows that with increasing dephosphorization slag basicity, $R_{{{\text{CS}}}}$ and $R_{{{\text{C3S2}}}}$ decrease exponentially, $R_{{{\text{C2S}}}}$ and $R_{{{\text{C3S}}}}$ increase exponentially. The regression coefficients, r², of $R_{{{\text{CS}}}}$, $R_{{{\text{C2S}}}}$ and $R_{{{\text{C3S}}}}$ against dephosphorization slag basicity are greater than 0.99. There is an obvious exponential relationship between dephosphorization slag basicity and $R_{{{\text{CS}}}}$, $R_{{{\text{C2S}}}}$ and $R_{{{\text{C3S}}}}$, which can be expressed by Eqs. [24] through [26]:

$$ R_{{{\text{CS}}}} = {\text{1}}{\text{.598}} \times {\text{exp}}(\frac{{{\text{ - B}}}}{{{\text{1}}{\text{.121}}}}){\text{ - 0}}{\text{.11}} $$

(24)

$$ R_{{{\text{C2S}}}} = -1{\text{.835}} \times {\text{exp}}(\frac{{{\text{ - B}}}}{{{\text{0}}{\text{.854}}}}) + {\text{0}}{\text{.982}} $$

(25)

$$ R_{{{\text{C3S}}}} = {\text{1}}{\text{.123}} \times {\text{10}}^{{{\text{ - 4}}}} \times {\text{exp}}(\frac{{\text{B}}}{{{\text{0}}{\text{.381}}}}) + {\text{0}}{\text{.0018}} $$

(26)

Effect of Dephosphorization Slag Basicity on Phosphorus-Enrichment Behavior

It has been shown that C₂S is the main phosphorus-enrichment component in the dephosphorization slag. Therefore, the phosphorus-enrichment behavior of C₂S in the dephosphorization slag can represent the phosphorus-enrichment behavior in the dephosphorization slag. Based on the enrichment degree $R_{{Ci - Pj}}$ of P₂O₅ containing solid solution, the effect of the dephosphorization slag basicity on the phosphorus-enrichment behavior of C₂S in dephosphorization slag was analyzed under the conditions of low temperature range of 1370 °C to 1420 °C and low basicity range of 1.26 to 2.20.

In the dephosphorization reaction of slag, CaO reacts with SiO₂ to generate C₂S. FeO and CaO react with P₂O₅ to form F₃P and C₃P, respectively, which initially fixes phosphorus in dephosphorization slag.[41] Further, P₂O₅ in F₃P is easy to react with CaO to form more stable C₃P,[27] the chemical reaction is expressed as Eq. [27]. According to the standard Gibbs free energy of the above reactions summarized in Table VI, the actual Gibbs free energy of F₃P reacting with CaO to produce C₃P is derived, which is expressed as Eq. [28]. The substituted FeO diffuses into CaO solid through the reaction interface and forms CaO-FeO layer.

$$ 3({\text{CaO}}) + (3{\text{FeO}} \cdot {\text{P}}_{2} {\text{O}}_{5} ) = 3({\text{FeO}}) + (3{\text{CaO}} \cdot {\text{P}}_{2} {\text{O}}_{5} ) $$

(27)

$$ \Delta {\text{G}}_{{{\text{F}}3{\text{P}} - {\text{C}}3{\text{P}}}} = - 279486 - 86.558T + RT\ln \left( {\frac{{(N{\text{FeO}})^{3} \times (N_{{3{\text{CaO}} \cdot {\text{P}}_{2} {\text{O}}_{5} }} )}}{{(N{\text{CaO}})^{3} \times (N_{{3{\text{FeO}} \cdot {\text{P}}_{2} {\text{O}}_{5} }} )}}} \right) $$

(28)

Under the conditions of lower temperature and lower basicity in the dephosphorization stage of the NDSP, the existence state of C₂S is α’_H-C₂S state,[42] and α’_H-C₂S mainly exists in the form of 2Ca²⁺ and [SiO₄]^4-. C₃P mainly exists in the form of 3Ca²⁺ and 2[PO₄]^3-. The radii of [SiO₄]^4- and [PO₄]^3- are 2.79 Å and 2.76 Å, respectively, and their crystal structures are tetrahedral.[43] This shows that the structure and size of [SiO₄]^4- and [PO₄]^3- are very similar and can replace each. In the range of 1370 °C to 1420 °C, the Gibbs free energy of the reaction of CaO with P₂O₅ to produce C₃P is much smaller than that of the reaction of CaO with SiO₂ to produce C₂S. The affinity of CaO with P₂O₅ is much stronger than that with SiO₂. P can replace part of Si in the tetrahedral structure, resulting in the change of its coordination structure, which shows that [PO₄]^3- replaces [SiO₄]^4- in the solvent C₂S lattice.

Furthermore, $\Delta {\text{G}}_{{{\text{F3P}} - {\text{C3P}}}}$ is always less than 0 in the NDSP. C₂S-F₃P can not exist stably, and F₃P will spontaneously transform into C₃P. Therefore, it can be considered that the formation of C₂S-C₃P solid solution is through the replacement of [SiO₄]^4- in C₂S phase by [PO₄]^3- in slag, or transformation of the unstable C₂S-F₃P phase into the stable C₂S-C₃P.

Figure 11 shows the effect of dephosphorization slag basicity on $R_{{{\text{C2S - C3P}}}}$, $R_{{{\text{C2S - C4P}}}}$ and $R_{{{\text{C2S - F3P}}}}$. With increasing dephosphorization slag basicity, $R_{{{\text{C2S - C3P}}}}$, $R_{{{\text{C2S - C4P}}}}$ both increase exponentially, while $R_{{{\text{C2S - F3P}}}}$ decreases exponentially. This is because the increase of basicity will promote the formation of C₂S-C₃P solid solution in slag, and the coefficient n of nC₂S-C₃P solid solution will decrease with increasing basicity, thus improving the enrichment degree of phosphorus in C₂S-C₃P solid solution in dephosphorization slag. In addition, under the conditions of lower temperature and lower basicity in the dephosphorization stage of the NDSP, F₃P spontaneously transforms to C₃P, and with increasing dephosphorization slag basicity, this change trend will become more obvious. Therefore, it can be concluded that increasing dephosphorization slag basicity is beneficial to the enhancement of phosphorus-enrichment degree in dephosphorization slag, and the phosphorus-enrichment ability of C₂S-C₃P and C₂S-C₄P will be significantly improved.

Fig. 11

Effect of dephosphorization slag basicity on $R_{{{\text{C2S - C3P}}}}$, $R_{{{\text{C2S - C4P}}}}$ and $R_{{{\text{C2S - F3P}}}}$

Comparison Between the Measurement Results of Industrial Experiment and the Calculated Results of IMCT

In Section IV–C, the mass fraction of CaO, SiO₂ and P₂O₅ in the P-rich phase is analyzed by SEM-EDS. The sum of the mass fraction of CaO, SiO₂ and P₂O₅ represents the mass fraction of phosphorus containing solid solution in the P-rich phase, expressed as (pct C_iS-C_jP). According to the conclusion in Section V–C, C₂S is the main component of phosphorus enrichment in the dephosphorization slag. Therefore, the product of the mass fraction of phosphorus containing solid solutions (pct C_iS-C_jP) and the phosphorus-enrichment contribution ratio $R_{{{\text{C2S}}}}$ of C₂S is regarded as the mass fraction of C₂S-C_jP solid solution in P-rich phase(IMCT-(pct C₂S-C_jP)), which is calculated by Eq. [29]. The areas of P-rich phase in dephosphorization slag with different basicities can be calculated using Image Pro Plus software under three viewing fields of SEM at the magnification of 1500 times, and Eq. [30] is used to calculate the average area fraction of P-rich phase(A^{P-rich phase}). The calculated results of IMCT-(pct C₂S-C_jP) and $R_{{{\text{C2S}}}}$ can illustrate the phosphorus-enrichment degree. Both the calculation results are compared with the measurement results of A^{P-rich phase}, and (pct P₂O₅)^{P-rich phase} to verify the rationality of the IMCT calculation results.

$$\text{IMCT}-(\%{\text{C}_{2}}{\text{S}}-{\text{C}_{j}}{\text{P}})=(\%{\text{C}_{i}}{\text{S}}-{\text{C}_{j}}{\text{P}})^{\text{P-rich \ phase}} \,\times\, R_{{{\text{C}_{2}}{\text{S}}}}$$

(29)

$$ {\text{A}}_{{}}^{{{\text{P - rich \ phase}}}} = \frac{{{\text{Area}}^{{{\text{P - rich\ phase}}}} }}{{{\text{Area}}^{{{\text{Total\ field\ of\ view}}}} }} $$

(30)

Figure 12 shows the comparison between the calculated results of IMCT-(pct C₂S-C_jP) and $R_{{{\text{C}_{2}{\text{S}}}}}$, and the measurement results of A^{P-rich phase}, and (pct P₂O₅)^{P-rich phase} of industrial experiment. With increasing dephosphorization slag basicity, IMCT calculated results and experimental results are all increased. The trends of the enrichment degree of phosphorus in dephosphorization slag are well consistent among the results characterized by different ways. Therefore, the IMCT calculated results can correctly express the phosphorus-enrichment degree of dephosphorization slag, and further reveal the phosphorus-enrichment degree of the different calcium silicates in dephosphorization slag.

Fig. 12

Comparison between the calculated results of IMCT-(pct C₂S-C_jP) and $R_{{{\text{C2S}}}}$, and the measurement results of A^{P-rich phase}, and (pct P₂O₅)^{P-rich phase} of industrial experiment

Conclusions

In the percent work, the dephosphorization experiments using new double slag converter steelmaking process(NDSP) has been carried out in a 180 ton top-bottom combined blowing converter under the low temperature range of 1370 °C to 1420 °C and low basicity of 1.26 to 2.20. Based on the ion-molecule coexistence theory (IMCT) and phase analysis of dephosphorization slag, the effect of dephosphorization slag basicity on the hot metal dephosphorization and the phosphorus-enrichment behavior in slag is studied, and the following conclusions are obtained:

• 1. With increasing basicity, the phosphorus distribution ratio L_P between hot metal and slag increases. The dephosphorization ratio and the decarbonization ratio both increase, while the demanganization ratio decreases. The desiliconization ratio has no obvious change and remains at a high level. When the basicity is 2.20, the phosphorus content in hot metal decreases from 0.142 to 0.048 pct, the dephosphorization ratio increases to 66.2 pct and the phosphorus distribution ratio increases to 81.33.

• 2. With increasing basicity from 1.26 to 2.20, the morphologies of P-rich phase change from long strip shape (B = 1.26 to 1.37) to dendritic shape (B = 1.50) and to massive shape(B = 1.71 to 2.20). The area of P-rich phase increases from about 4 μm² to about 8000 μm². The content of P₂O₅ in the P-rich phase increases and the value of the coefficient n in nC₂S-C₃P of P-rich phase decreases from 6-20 to 1-2.

• 3. With increasing basicity, $N_{\text{CaO}}$ and $N_{{{\text{SiO}}_{2} }}$ increases and decreases exponentially, respectively, and $N_{{{\text{CaO}}}} /N_{{{\text{SiO}}_{2} }}$ also increases exponentially. The phosphorus-enrichment contribution ratio of calcium silicate is in the order of $R_{{{\text{C2S}}}}$>$R_{{{\text{CS}}}}$>$R_{{{\text{C3S}}}}$>$R_{{{\text{C3S2}}}}$. C₂S is the main phosphorus-enrichment calcium silicate in dephosphorization slag, and $R_{{{\text{C2S}}}}$ has the value of 0.56 to 0.84. The phosphorus-enrichment degree in dephosphorization slag is enhanced mainly by C₂S-C₃P.

• 4. In the dephosphorization stage of the NDSP, C₂S is in the existence state of α’H-C₂S state. The formation of C₂S-C₃P solid solution is through the replacement of [SiO₄]^4- in C₂S phase by [PO₄]^3- in slag, or transformation of the unstable C₂S-F₃P phase into the stable C₂S-C₃P.

• 5. With increasing basicity, the calculated results of IMCT-(pct C₂S-C_jP) and $R_{{{\text{C2S}}}}$ are well consistent with the measurement results of A^{P-rich phase} and (pct P₂O₅)^{P-rich phase} of industrial experiment, indicating that the IMCT calculated results can correctly express the phosphorus-enrichment degree of dephosphorization slag. It is possible to use the enrichment contribution ratio $R_{{{\text{C}}i}}$ to qualitatively predict the phosphorus-enrichment degree of calcium silicate in dephosphorization slag.

• 6. From the present results, it is reasonable to deduce that the method combining laboratory phase analysis and IMCT thermodynamic calculation can facilitate optimizing the dephosphorization process parameters of NDSP under low temperature and low basicity, which has a guiding significance for industrial production.