Activity of P₂O₅ in Solid Solution between Di-calcium Silicate and Tri-calcium Phosphate at 1823 and 1873 K

Abstract

By applying the chemical equilibrium method, the equilibrium between liquid iron and 2CaO∙SiO₂-3CaO∙P₂O₅ solid solution has been measured with oxygen partial pressure of 5.22×10⁻¹² atm at 1823 K and 1.41×10⁻¹¹ atm or 4.25×10⁻¹⁰ atm at 1873 K. The phosphorus partition ratio between 2CaO∙SiO₂-3CaO∙P₂O₅ solid solution and liquid iron was observed. The activity of P₂O₅ relative to hypothetical pure liquid P₂O₅ was determined from the phosphorus content in liquid iron and the reported thermodynamic data. The activity of P₂O₅ in 2CaO∙SiO₂-3CaO∙P₂O₅ solid solution increased with the increase of 3CaO∙P₂O₅ content in solid solution. The activity coefficient of P₂O₅ in 2CaO∙SiO₂-3CaO∙P₂O₅ solid solution also increased with the increase of 3CaO∙P₂O₅ content in solid solution.

1. Introduction

Generally speaking phosphorus is a harmful element for steel. It could cause embrittlement.^1,2,3) In order to meet the requirement of high quality steel, phosphorus should be removed as much as possible. The CaO–SiO₂–FeO_x slag system is commonly used for BOF process, and usually extra CaO is added to remove phosphorus from molten hot metal and steel. Due to the unreacted CaO, the BOF slag is difficult to be reused meanwhile the amount of slag increases. Although fluorite could enhance CaO dissolution into slag, use of fluorite is restricted due to its toxicity for human and environment.

Recently, multi-phase fluxes are adopted in the hot metal dephosphorization process, in which di-calcium silicate and tri-calcium phosphate could form a solid solution over a wide composition range at the steelmaking temperature range as reported by Fix et al.⁴⁾ Suito and Inoue⁵⁾ confirmed the existence of 2CaO·SiO₂-3CaO·P₂O₅ solid solution during the reaction between solid CaO and CaO–Fe_tO–P₂O₅(–SiO₂) slag. The 2CaO·SiO₂-3CaO·P₂O₅ solid solution was found between the solid CaO and CaO–Fe_tO–P₂O₅(–SiO₂) slag. They also studied the phosphorous transfer behavior from CaO–Fe_tO–P₂O₅(–SiO₂) slag to 2CaO·SiO₂ particles⁶⁾ and the phosphorous partition between 2CaO·SiO₂ particles and CaO–SiO₂–Fe_tO slag with the similar experimental method.⁷⁾ Kitamura et al.⁸⁾ studied the mass transfer of P₂O₅ between CaO–SiO₂–FeO–P₂O₅ slag and 2CaO·SiO₂-3CaO·P₂O₅ solid solution by immersing 2CaO·SiO₂ or 3CaO·P₂O₅ rod into CaO–SiO₂–FeO–P₂O₅ slag for various reaction duration. Pahlevani et al.⁹⁾ estimated the activity coefficient of P₂O₅ in 2CaO·SiO₂-3CaO·P₂O₅ solid solution by applying the regular solution model and chemical equilibrium method. For the reaction mechanisms between solid CaO or 2CaO·SiO₂ and CaO–SiO₂–FeO_x–P₂O₅ slag, Fukagai et al.¹⁰⁾ and Hamano et al.¹¹⁾ studied the reaction mechanisms between solid CaO and CaO–SiO₂–FeO_x–P₂O₅ slag, and Yang et al.^12,13,14,15) studied the reaction mechanisms between 2CaO·SiO₂ and molten CaO–SiO₂–FeO_x–P₂O₅ slag with the similar experimental method like Suito and Inoue’s experiments. Gao et al.^16,17,18) studied the phase relationship of the CaO-SiO₂-FeO-5 mass% P₂O₅ system by applying the chemical equilibrium method similar to the study reported by Pahlevani et al. Takeshita et al.¹⁹⁾ measured the free energies of the formation of 2CaO·SiO₂-3CaO·P₂O₅ solid solution by applying the gas equilibrium technique. Hasegawa et al.²⁰⁾ estimated the thermodynamic properties of 2CaO·SiO₂-3CaO·P₂O₅ solid solution by applying chemical equilibrium method and phase relationship.

For estimating the activity of P₂O₅ in 2CaO·SiO₂-3CaO·P₂O₅ solid solution by Pahlevani et al.,⁹⁾ the regular solution model was adopted. However, other components such as FeO, MgO, Al₂O₃ etc. were contained in the 2CaO·SiO₂-3CaO·P₂O₅ solid solution. In the study by Hasegawa et al.,²⁰⁾ the metal phase was Cu base rather than Fe base and the activities of P₂O₅ in some compositions were deduced by the measured activities of P₂O₅ of other compositions by applying the phase relationship and the appropriate simplification for calculation. In order to eliminate the deviation caused by applying the regular solution model and the appropriate simplification for calculating the activity of P₂O₅, in current research by conducting the equilibration between molten iron and 2CaO·SiO₂-3CaO·P₂O₅ solid solution at 1823 and 1873 K, the activity of P₂O₅ was measured directly.

2. Experimental

A chemical equilibrium method was adopted in the present study, in which 2CaO·SiO₂-3CaO·P₂O₅ solid solution was equilibrated with molten iron and the activity of P₂O₅ relative to hypothetical liquid P₂O₅ was observed. Reaction (1) was used to obtain the activity of P₂O₅.   

$${\mathrm{P}}_2{\mathrm{O}}_5\left(\mathrm{l}\right)=2\underset{\_}{\mathrm{P}}\left(\text{mass\%}\right)+5\underset{\_}{\mathrm{O}}\left(\text{mass\%}\right)$$(1)

  

$$\mathrm{\Delta }{G}_1°=832\hspace{0.17em}384-632.65T\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\text{J}/\text{mol}$$(2) ²¹⁾

  

$$K_1=\frac{f_{\text{P}}^2{\left[\text{mass\%P}\right]}^2{f}_{\text{O}}^5{\left[\text{mass\%O}\right]}^5}{a_{{\text{P}}_2{\text{O}}_5}}$$(3)

f_P and f_O are the activity coefficients of phosphorus and oxygen in liquid iron relative to 1 mass%, respectively, and $a_{{\text{P}}_2{\text{O}}_5}$ is the activity of P₂O₅ relative to hypothetical pure liquid P₂O₅. T is absolute temperature. The values of f_P and f_O could be estimated by using the interaction parameters in liquid iron, respectively. In the present experiment, liquid Fe–P–C alloy was equilibrated with 2CaO·SiO₂-3CaO·P₂O₅ solid solution pellet in an MgO crucible, and the oxygen partial pressure was controlled by CO–CO₂ gas atmosphere according to reaction (4).   

$$\text{CO}\left(\text{g}\right)+\frac{1}{2}{\text{O}}_2\left(\text{g}\right)={\text{CO}}_2\left(\text{g}\right)$$(4)

  

$$\mathrm{\Delta }{G}_4°=-281\mathrm{\hspace{0.17em} }000+85.23T\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\text{J}/\text{mol}$$(5) ²²⁾

The 2CaO·SiO₂-3CaO·P₂O₅ solid solution pellet was prepared by sintering the mixture of the reagent grade SiO₂, CaHPO₄·2H₂O and CaO obtained by the calcination of reagent grade CaCO₃ with various ratios. Firstly the mixture of raw materials was charged into a Pt crucible and put in a resistance furnace for 24 hours at 1873 K in air. The sample quenched with Ar gas flow was ground into fine powder. The powder was charged into a Pt crucible and put in a resistance furnace for 24 hours at 1873 K again. The ground sample was obtained. About 1.5 g of fine powder was charged into an alloy steel mold and pressed into a pellet shape at 50 MPa. For some samples the pellets were heated for another 24 hours at 1873 K. The formation of each solid solution was confirmed by XRD and after sintering for 24 hours for twice at 1873 K the 2CaO·SiO₂-3CaO·P₂O₅ solid solution was detected and the CaO, SiO₂ and P₂O₅ was not detected as shown in Fig. 1.

Fig. 1.

The XRD data of 80mass%2CaO·SiO₂-20mass%3CaO·P₂O₅ solid solution.

A vertical resistance furnace with an Al₂O₃ tube (outer diameter: 60 mm, inner diameter: 50 mm, length: 1000 mm) was used. Temperature was controlled at 1823 K ± 1 K or 1873 K ± 1 K by a thermocouple placed at the bottom of the MgO crucible. The partial pressure of oxygen was controlled by CO–CO₂ gas according to reaction (4). The CO/CO₂ ratio was 110/1 (P_O2=5.22×10⁻¹² atm at 1823 K or 1.41×10⁻¹¹ atm at 1873 K) with the total flow rate of 366 mL/min or 20/1 (P_O2=4.25×10⁻¹⁰ atm at 1873 K) with the total flow rate of 347 mL/min. The CO/CO₂ ratio was 20/1 in order to obtain a suitable content of P after reaction for the experiments with the large 3CaO·P₂O₅ content tablet at 1873 K and the CO/CO₂ ratio was 110/1 for the other experiments. About 10 g electrolytic iron was equilibrated with about 1.5 g synthesized pellet in an MgO crucible at 1823 or 1873 K. As explained in section 3, the equilibrium duration of 24 hours was adopted to ensure equilibrium for various compositions of solid solution. After the equilibrium was established, the crucible was taken out from the furnace and quenched in Ar flow. Phosphorus content in iron was analyzed by the molybdenum-blue spectrophotometric solvent extraction method or the phosphomolybdate blue spectrophotometric method depending on the content of P in iron. Phosphorus content in solid solution was analyzed by the phosphomolybdate blue spectrophotometric method. ICP-OES was adopted for the analysis of Ca, Mg and Fe. Gravimetry was used for SiO₂ in solid solution. Table 1 shows the initial composition of solid solution, temperature, the ratio between CO and CO₂ gases and the initial content of phosphorus in iron. Figure 2 shows the projection of the initial compositions of solid solution on the CaO–SiO₂–P₂O₅ ternary phase diagram near the CaO corner.

Table 1. Experimental conditions and initial compositions of solid solutions.

No.	T/K	CO/CO2	P in iron/ mass%	Solid solution
				CaO/ mass%	SiO2/ mass%	P2O5/ mass%	3CaO·P2O5/ mass%
1	1823	110/1	0.0003	64.7	33.5	1.8	4.0
2	1823	110/1	0.0003	64.2	32.1	3.7	8.0
3	1823	110/1	0.0003	63.8	30.7	5.5	12.0
4	1823	110/1	0.0003	62.9	27.9	9.2	20.0
5	1823	110/1	0.0003	61.9	24.4	13.7	30.0
6	1823	110/1	0.0003	60.8	20.9	18.3	40.0
7	1823	110/1	0.0003	60.0	18.6	21.4	46.7
8	1823	110/1	0.0003	59.0	15.2	25.8	56.5
9	1823	110/1	0.0003	57.9	11.9	30.2	66.0
10	1823	110/1	0.0003	57.0	8.7	34.3	75.0
11	1823	110/1	0.0003	55.9	5.2	38.9	85.0
12	1823	110/1	0.0003	54.8	1.7	43.5	95.0
13	1823	110/1	0.0003	54.2	0.0	45.8	100.0
14	1873	110/1	0.0077	64.2	32.1	3.7	8.0
15	1873	110/1	0.0268	62.9	27.9	9.2	20.0
16	1873	110/1	0.0393	61.9	24.4	13.7	30.0
17	1873	110/1	0.0551	60.8	20.9	18.3	40.0
18	1873	110/1	0.5304	59.7	17.4	22.9	50.0
19	1873	110/1	1.0736	58.6	13.9	27.5	60.0
20	1873	100/5	0.1785	57.5	10.5	32.0	70.0
21	1873	100/5	0.6773	56.4	7.0	36.6	80.0
22	1873	100/5	1.6298	55.3	3.5	41.2	90.0
23	1873	100/5	3.7796	54.2	0.0	45.8	100.0

Fig. 2.

The phase diagram of the CaO–SiO₂–P₂O₅ system near the CaO corner and the projections of initial experimental compositions of 2CaO·SiO₂-3CaO·P₂O₅ solid solution. The boundary lines and tie lines in the phase diagram of the CaO–SiO₂–P₂O₅ system were tested at 1773 K by Gutt.²³⁾

3. Results and Discussion

According to Fig. 3, for the 60mass%2CaO·SiO₂-40mass%3CaO·P₂O₅ solid solution at 1823 K and the 92mass%2CaO·SiO₂-8mass%3CaO·P₂O₅ solid solution at 1873 K, the equilibrium was attained within 12 hours. For the 3CaO·P₂O₅ at 1873 K, the equilibrium was attained within 24 hours. Finally 24 hours was adopted for the subsequent experiments in order to ensure equilibrium for various compositions of solid solution.

Fig. 3.

Time for attainment of equilibrium.

The results of the chemical analysis of the solid solution and the content of P in iron were presented in Table 2. The content of iron oxide was calculated as FeO. Due to the inevitable analytical error, the total mass percent of solid solution was not 100% but near to 100%. Powder of 2CaO·SiO₂-3CaO·P₂O₅ solid solution was contaminated with more or less MgO and metallic Fe particles, which would be the reason of larger MgO and FeO contents in some solid solutions. After normalizing the contents of CaO, SiO₂ and P₂O₅, the normalized compositions were projected on the CaO–SiO₂–P₂O₅ phase diagram near to CaO corner which were shown in Fig. 4. In Fig. 4(A), the compositions after reaction diverged from the initial compositions more or less, and some compositions moved to the CaO corner or away from CaO corner. The materials after reaction were tested by XRD as shown in Fig. 5, and the CaO, SiO₂, P₂O₅ or other phases were not detected, which means the 2CaO·SiO₂-3CaO·P₂O₅ solid solution has certain solubility for the other component in the composition range of current research. In Fig. 4(B), although the compositions after reaction diverged from the initial compositions as shown in Fig. 4(A), the compositions were still solid phase after reaction and no liquid phase was observed for all the samples.

Table 2. The composition of solid solution and the content of P in metal phase after experiments.

No.	Solid solution/mass%						P in iron/ mass%
	P2O5	SiO2	CaO	MgO	FeO	Total
1	1.83	32.8	67.1	0.566	0.216	102.5	0.00276
2	3.59	31.3	60.6	0.589	0.354	96.4	0.00282
3	5.44	29.6	64.5	0.721	0.351	100.6	0.00501
4	9.18	27.3	60.7	0.502	0.299	98.0	0.0081
5	13.6	23.9	59.8	0.383	0.489	98.2	0.0059
6	18.2	19.7	63.1	0.397	0.268	101.7	0.0124
7	21.8	18.9	60.8	0.476	0.231	102.2	0.0175
8	25.5	14.8	56.7	0.398	0.328	97.7	0.0238
9	30.2	11.5	59.2	0.273	0.286	101.5	0.0178
10	31.9	8.82	57.1	0.811	0.697	99.3	0.111
11	37.2	5.16	57.3	0.353	2.32	102.3	0.128
12	43.4	1.72	57.2	0.294	0.436	103.1	0.150
13	45.8	0.00	56.4	0.266	0.467	102.9	0.221
14	3.47	29.5	61.1	4.28	0.174	98.5	0.0201
15	8.60	25.1	58.0	4.19	0.331	96.2	0.0498
16	12.1	22.0	56.9	5.66	0.575	97.2	0.109
17	16.8	19.7	57.9	3.67	0.317	98.4	0.261
18	21.6	16.7	57.4	2.72	0.261	98.7	0.661
19	25.3	12.5	56.6	2.86	0.319	97.6	1.26
20	31.8	10.8	55.3	0.510	0.209	98.6	0.127
21	36.3	7.18	53.6	0.626	0.276	98.0	0.557
22	41.9	3.49	52.7	0.850	0.704	99.6	1.49
23	46.5	0.00	51.5	1.10	0.319	99.4	3.52

Fig. 4.

A: The projections of compositions after reaction on the phase diagram of CaO–SiO₂–P₂O₅. B: The projections of compositions after reaction on the liquidus surface in the CaO rich region of the CaO–SiO₂–P₂O₅ system.²⁴⁾

Fig. 5.

The XRD data of 80mass%2CaO·SiO₂-20mass%3CaO·P₂O₅ solid solution after reaction.

In the present study, the partial pressure of oxygen was controlled by the ratio of CO and CO₂. Because of the segregation of C and O in a solidified iron sample resulting in the possible formation of CO gas bubbles and the inevitable analytical error, the analyzed concentrations of C and O were not stable. Therefore, the concentrations of C and O in iron after reaction were calculated according to reactions (6) and (8) and the reported interaction coefficients shown in Table 3. The segregation of P does not influence the analyzed concentration of P in iron from the current analytical method.   

$$\underset{\_}{\mathrm{O}}\left(\text{mass\%}\right)+\text{CO}\left(\text{g}\right)={\text{CO}}_2\left(\text{g}\right)$$(6)

  

$$\mathrm{\Delta }{G}_6°=-166\mathrm{\hspace{0.17em} }900+91.16T\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\text{J}/\text{mol}$$(7) ²⁵⁾

  

$$\underset{\_}{\mathrm{C}}\left(\text{mass\%}\right)+{\text{CO}}_2\left(\text{g}\right)=2\text{CO}\left(\text{g}\right)$$(8)

  

$$\mathrm{\Delta }{G}_8°=144\mathrm{\hspace{0.17em} }700-129.5T\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }\text{J}/\text{mol}$$(9) ²⁵⁾

Table 3. The reference data about interaction coefficient.

$e_i^j$		j
		P	C	O
i	P	0.05426)	0.12627)	0.1328)
	C	0.05127)	0.24325)	−0.3225)
	O	0.0728)	−0.42125)	−0.1729)

3.1. The Equilibrium Content of P with 2CaO·SiO₂-3CaO·P₂O₅ Solid Solution at 1823 and 1873 K with CO/CO₂=110 or 20

Figure 6 shows the relationship between the equilibrium content of P in iron and the 3CaO·P₂O₅ content in solid solution. The contents of 3CaO·P₂O₅ in solid solution were calculated from the analyzed content P₂O₅ and the normalized compositions were shown in Table 4. The content of P in iron increased with the increase of the 3CaO·P₂O₅ content in solid solution. And for a constant composition of solid solution, equilibrium content of P in iron increased with the increase of temperature from 1823 K to 1873 K. At 1873 K, when the ratio between CO/CO₂ changed from 110/1 to 20/1, the equilibrium content of P in iron decreased.

Fig. 6.

The content of P in iron equilibrated with the 2CaO·SiO₂-3CaO·P₂O₅ solid solution at 1823 and 1873 K with different partial pressure of oxygen.

Table 4. The normalized compositions of solid solution calculated from P₂O₅ and SiO₂ content by assuming 2CaO·SiO₂-3CaO·P₂O₅, phosphorus partition ratios between 2CaO·SiO₂-3CaO·P₂O₅ solid solution and liquid iron, and the activity and the activity coefficient of P₂O₅ in 2CaO·SiO₂-3CaO·P₂O₅ solid solution.

No.	3CaO·P2O5/mol%	$\frac{\left(\text{mass\%P}\right)}{\left[\text{mass\%P}\right]}$	$a_{{\text{P}}_2{\text{O}}_5}$	${\gamma }_{{\text{P}}_2{\text{O}}_5}$
1	2.3	2.84×102	2.74×10−25	3.73×10−23
2	4.6	5.82×102	2.86×10−25	1.84×10−23
3	7.2	4.76×102	9.06×10−25	3.97×10−23
4	12.5	5.1×102	2.4×10−24	5.9×10−23
5	19.4	1.0×103	1.3×10−24	2.0×10−23
6	28.1	6.35×102	5.59×10−24	6.90×10−23
7	32.8	5.36×102	1.12×10−23	1.13×10−22
8	42.2	4.82×102	2.09×10−23	1.67×10−22
9	52.6	7.34×102	1.16×10−23	7.95×10−23
10	60.5	1.28×102	4.97×10−22	3.07×10−21
11	75.3	1.27×102	6.73×10−22	3.52×10−21
12	91.4	1.23×102	9.46×10−22	4.19×10−21
13	100.0	8.85×101	2.21×10−21	9.11×10−21
14	4.7	8.01×101	1.45×10−23	9.55×10−22
15	12.7	8.22×101	9.21×10−23	2.30×10−21
16	18.9	5.33×101	4.70×10−22	8.08×10−21
17	26.5	2.99×101	3.16×10−21	3.95×10−20
18	35.4	1.49×101	3.09×10−20	2.95×10−19
19	46.1	9.29	2.11×10−19	1.65×10−18
20	55.5	1.12×102	3.10×10−18	1.92×10−17
21	68.2	2.93×101	9.38×10−17	4.88×10−16
22	83.6	1.25×101	1.79×10−15	7.87×10−15
23	100.0	5.89	8.53×10−14	3.24×10−13

3.2. The Activity of P₂O₅ in 2CaO·SiO₂-3CaO·P₂O₅ Solid Solution at 1823 and 1873 K

The activity of P₂O₅ calculated by reaction (1) and interaction coefficients shown in Table 3 were shown in Table 4. Figure 7 shows the relationship between the activity of P₂O₅ relative to hypothetical pure liquid P₂O₅ in solid solution and the 3CaO·P₂O₅ content in solid solution. The activity of P₂O₅ increased with the increase of the 3CaO·P₂O₅ content in solid solution at both 1823 and 1873 K. The activity of P₂O₅ at 1873 K is larger than that at 1823 K.

Fig. 7.

The change in the activity of P₂O₅ relative to hypothetical pure liquid P₂O₅ in 2CaO·SiO₂-3CaO·P₂O₅ solid solution with mol% of the 3CaO·P₂O₅ in solid solution.

3.3. The Activity Coefficient of P₂O₅ in 2CaO·SiO₂-3CaO·P₂O₅ Solid Solution

Pahlevani et al.⁹⁾ studied the activity coefficient of P₂O₅ in 2CaO·SiO₂-3CaO·P₂O₅ solid solution by conducting the slag and solid solution equilibrium and applying the regular solution model. Figure 8 shows the activity coefficient of P₂O₅ in solid solution measured in the present study compared with those reported by Pahlevani et al. and Hasegawa et al. In Fig. 8, the dashed line means the pure 3CaO·P₂O₅ whose mole percent of P₂O₅ is 25%. Due to the analytical error, P₂O₅ contents for some samples were beyond 25 mol%. The activity coefficient of P₂O₅ in large 3CaO·P₂O₅ content region increased from about 10⁻²⁰ to 10⁻¹² when the temperature increased from 1823 K to 1873 K. At both temperatures, the activity coefficient of P₂O₅ increased with the increase of P₂O₅ content in solid solution. On the contrary, Pahlevani et al. reported that the activity coefficient of P₂O₅ measured at 1673 and 1573 K showed no obvious difference. The activity coefficient of P₂O₅ in solid solution was in the range between 10⁻¹⁷ and 10⁻¹³. There was no clear relationship between the activity coefficient of P₂O₅ and the content of P₂O₅ in solid solution. Comparing with the values reported by Pahlevani et al., the current values of the activity coefficient of P₂O₅ were smaller. Besides, the activity coefficient of P₂O₅ measured at 1573 K by Hasegawa et al. increased with the increase of P₂O₅ content in solid solution and the current values were larger than those because of the higher temperature.

Fig. 8.

The activity coefficient of P₂O₅ in 2CaO·SiO₂-3CaO·P₂O₅ solid solution.

4. Conclusions

By applying chemical equilibrium method, the equilibrium between liquid iron and 2CaO·SiO₂-3CaO·P₂O₅ solid solution pellet has been measured at 1823 and 1873 K with the oxygen partial pressure of 5.22×10⁻¹², 1.41×10⁻¹¹ or 4.25×10⁻¹⁰ atm. The equilibrium P content in iron increased with the increase of the 3CaO·P₂O₅ content in solid solution. The phosphorus partition ratios between 2CaO·SiO₂-3CaO·P₂O₅ solid solution and liquid iron decreased with the increase of the 3CaO·P₂O₅ content in solid solution. The activity of P₂O₅ relative to hypothetical pure liquid in 2CaO·SiO₂-3CaO·P₂O₅ solid solution changed from 2.74×10⁻²⁵ to 2.21×10⁻²¹ at 1823 K and from 1.45×10⁻²³ to 8.53×10⁻¹⁴ at 1873 K with the increase of the 3CaO·P₂O₅ content in solid solution. The activity coefficient of P₂O₅ in 2CaO·SiO₂-3CaO·P₂O₅ solid solution was also calculated.

Acknowledgment

This research was partially supported by Steel Foundation for Environmental Protection Technology. Authors greatly appreciate the financial support.

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