Investigating the Phase Diagram of SiO₂–CaO–CrO_x System to Evaluate Distribution of Platinum between Slag and Molten Copper

Abstract

In the hydrometallurgical process used for recycling platinum group metals (PGMs), a residue containing mainly Cr₂O₃ and a small amount of PGMs is generated. In the present work, a pyrometallurgical process was applied in which PGMs from the residue generated in the hydrometallurgical process are concentrated in a molten copper phase as a collector-metal, and Cr₂O₃ is separated into a slag phase with SiO₂ and CaO as a flux. To reduce the loss of PGMs to the slag, it is necessary to have a homogenous liquid and a lower dissolution of PGMs into the slag. Therefore, the phase diagram of the SiO₂–CaO–CrO_x system was investigated at 1773 and 1873 K in an oxygen partial pressure $p_{\text{O}_{2}} = 10^{ - 10}$ to obtain knowledge of the homogeneous melts. Based on the determined phase diagram, the distribution ratios of Pt as representative PGMs between the liquid SiO₂–CaO–Al₂O₃–CrO_x or the liquid SiO₂–CaO–CrO_x slag and molten copper were measured at 1773 K in $p_{\text{O}_{2}} = 10^{ - 10}$. The experimental results showed that CrO_x solubility in the slag increased with decreasing slag basicity, B defined as B = (mass%CaO)/(mass%SiO₂). Furthermore, the results showed that the distribution of Pt in the slag increased with increasing CrO_x concentration in the slag.

Fig. 8 Iso-activity coefficient curves of PtO(s) in the SiO₂–CaO–CrO_x system (1773 K, $p_{\text{O}_{2}} = 10^{ - 10}$).

1. Introduction

The demand for platinum group metals (PGMs) has been increasing owing to the growth in the manufacturing of industrial products that require them, such as catalysts.¹⁾ Natural resources of PGMs are concentrated in South Africa and Russia, which account for more than 75% of PGMs production from their ores.²⁾ Therefore, recycling PGMs is essential for ensuring a stable supply of resources. In the hydrometallurgical process used for recycling, a residue containing Cr₂O₃ and PGMs is generated. In the present study, an additional pyrometallurgical process was employed to selectively recover PGMs from the residue, in which PGMs are concentrated in the metal phase with Cu as the collector-metal, while Cr₂O₃ separates into the slag phase.

In general, Cr₂O₃ has a high melting point and low solubility in a slag. The presence of a solid phase in the slag during melting increases the viscosity of the slag, inhibiting the separation of slag and metal, and causing the loss of valuable metals to the slag. Even when a homogeneous slag is formed and there is no physical suspension of the metallic phase, a part of the valuable metals is oxidized and chemically dissolved in the slag. Therefore, it is important to investigate the operating conditions of the pyrometallurgical process for Cr₂O removal with minimal loss of PGMs to the slag. In the present work, because of the low cost of the fluxes, the SiO₂–CaO–CrO_x slag system was used for the experimental study. A homogenous melt of SiO₂–CaO–CrO_x system was prepared, and the phase diagram of the SiO₂–CaO–CrO_x system was studied to examine the distribution ratio of Pt as representative PGMs between the liquid SiO₂–CaO–Al₂O₃–CrO_x or the SiO₂–CaO–CrO_x slag and molten copper. Based on the thermodynamic data, the $p_{\text{O}_{2}} = 10^{ - 10}$ was chosen as an experimental condition, which oxidizes Cr but hardly oxidizes PGMs, where $p_{\text{O}_{2}}$ is a dimensionless number obtained by dividing the oxygen partial pressure by the standard atmosphere (1.01325 × 10⁵ Pa).

Many studies have been conducted on chromium oxides in slags because of their relevance to the steel industry. It is known that the oxidation states of Cr in its oxides in slag are mainly divalent and trivalent, and the proportion of divalent Cr oxide increases under low basicity and low oxygen partial pressures. For example, the following studies are available:^3–5) Degterov et al. reported the phase diagram for the CaO–CrO_x, the Al₂O₃–CrO_x, and the SiO₂–CaO–CrO_x systems, and Arnout et al. reported a phase diagram for the CaO–SiO₂–MgO–Al₂O₃–CrO_x system.^6–9) Pretorius et al. reported a phase diagram for the CaO–SiO₂–CrO_x system at 1773 K in varying oxygen partial pressures.¹⁰⁾ In the present study, phase diagram for the SiO₂–CaO–CrO_x system at 1773 K and 1873 K were studied in $p_{\text{O}_{2}} = 10^{ - 10}$ and compared with the phase diagrams from the previous studies.

The dissolution of PGMs in slags have been investigated in a few studies. Nakamura et al. reported on the relationship between slag basicity and the solubility of Pt in slag.^11,12) Wiraseranee et al. and Morita et al. investigated the solubility of PGMs in slag in air.^13–16) Baba et al., Avarmaa et al., and Klemettinen et al. reported the solubility of precious metals in the FeO–SiO₂ slag system, which is mainly used in smelting of non-ferrous metals.^17–20) Borisov et al. and Nisijima et al. reported the solubility of precious metals in the Al₂O₃–CaO–SiO₂ slag system.^21,22) However, to the best of our knowledge, there have been no reports on the solubility of PGMs in slag systems containing CrO_x. In the present study, the distribution behavior of Pt between the slag phase and metal phase was investigated in a slag system containing CrO_x. Crucibles made of Al₂O₃ or SiO₂ were used for preparing the slag, and the SiO₂–CaO–Al₂O₃–CrO_x or the SiO₂–CaO–CrO_x slag systems was allowed to equilibrate with Pt-containing Cu alloy at 1773 and 1873 K in $p_{\text{O}_{2}} = 10^{ - 10}$. Slag systems with varying compositions were prepared and analyzed in a similar manner.

2. Experimental Procedure

2.1 Phase diagram of SiO₂–CaO–CrO_x system

Approximately 0.5 g of SiO₂ (>99.5 mass% purity), CaO calcined from CaCO₃ (>99.5 mass% purity), Cr₂O₃ (>99.9 mass% purity), Cr (>98 mass% purity), and Pt (no purity statement available) powders of special reagent grade were mixed according to the target composition and placed in a Pt crucible (>99.9 mass% purity) with an inner diameter of 7 mm and height of 25 mm. Metallic Cr and Pt powders were added to facilitate the measurement of the concentration of Pt–Cr alloy after attaining equilibrium. The sample was then inserted into an alumina reaction tube, held at 1773 K (±3 K) or 1873 K (±3 K) in a furnace, heated using SiC heating elements. A preliminary experiment was conducted to determine the time required to achieve equilibrium, in which the samples were allowed to reach equilibrium for two time periods: 24 h and 60 h. On comparing the results, it was found that 24 h is sufficient to attain equilibrium. The oxygen partial pressure of $p_{\text{O}_{2}} = 10^{ - 10}$ was controlled with CO and CO₂ mixture gases at a combined flow rate of 150 mL/min for 24 h. After quenching with water, a microstructural analysis was first performed by embedding the samples in an ethyl acetate resin, polishing, and coating with carbon, then by determination of the equilibrium compositions for each phase by scanning electron microscopy coupled with energy-dispersive X-ray spectra analyzer (SEM-EDX; JEOL, JSM-6510A). The SEM-EDX was set at an accelerating voltage of 15 kV, and the characteristic X-rays obtained were corrected by taking into account the following three effects: (1) atomic number effect, (2) absorption effect, and (3) fluorescence excitation effect (ZAF method). To ensure statistical reliability, at least five points were measured for each phase using SEM-EDX. Additionally, the equilibrium phases were identified by X-ray diffraction (XRD; RIGAKU, SmartLab) with Cu Kα radiation.

2.2 Distribution ratio of Pt between liquid SiO₂–CaO–Al₂O₃–CrO_x or liquid SiO₂–CaO–CrO_x slag phase and Cu–Pt molten alloy

Two types of crucibles made of SiO₂ (no purity statement) and Al₂O₃ (>99.6 mass% purity) were used for this measurement. 0.2 g of Pt (>99.95 mass% purity) and 1.8 g of Cu (>99.5 mass% purity) wires were put into the SiO₂ or Al₂O₃ crucible, Additionally, 8 g of a mixture of SiO₂ (>99.5 mass% purity), CaO calcined from CaCO₃ (>99.9 mass% purity), and Cr₂O₃ (>99.9 mass% purity) was added to the crucible to cover the Pt and Cu metals. Case of the Al₂O₃ crucible, excess Al₂O₃ powder (>99 mass% purity) was added to the crucible for the purpose of preventing melting of the crucible. The sample was then inserted into a reaction tube, held at 1773 K (±3 K) in a furnace, and heated using SiC heating elements. Oxygen partial pressure was controlled to $p_{\text{O}_{2}} = 10^{ - 10}$ with 150 mL/min of CO and CO₂ mixture gases for 20 h. After attaining equilibrium, the sample was quenched with water.

In this study, basicity of a slag is defined by eq. (1) as follows:   

\begin{equation} B = \frac{(\text{mass%CaO})}{(\text{mass%SiO$_{2}$})} \end{equation} (1)

The SiO₂ crucible was dissolved in the slag. Therefore, the compositions were fixed to the liquidus of SiO₂(s) saturation. As shown in the SiO₂–CaO–Cr₂O₃ system phase diagram to be described later, the slag basicity of SiO₂ saturation is fixed at about 0.5 regardless of the Cr₂O₃ concentration in the slag. Al₂O₃ derived from the Al₂O₃ crucible was also dissolved in the slag. The initial composition of the slag was chosen to be within the homogeneous liquid range based on the SiO₂–CaO–Cr₂O₃ phase diagram determined in this experiment.

Subsequently, the slag and alloy phases in the crucible were carefully separated. Two types of dissolution methods with the alkali fusion method using Li₂B₄O₇ and the aqua-regia were employed to achieve total dissolution of the sample for complete and accurate characterization by instrumental methods. The Si, Ca, Cr, and Al in the slag were dissolved by the alkali fusion method using Li₂B₄O₇ as a flux. The Cu and Pt in the slag, which have low concentrations and cannot be analyzed by alkali fusion, were dissolved in aqua regia. The Cu, Pt, and Cr in the metal phase were also dissolved in aqua regia. The Pt concentration in the slag sample was quantified by inductively coupled plasma mass spectrometry (ICP-MS; Agilent Technologies, 7700x). To correct for any interferences, In¹¹⁵ was used as an internal standard for ICP-MS. The Cu, Si, Ca, Cr, and Al concentrations in the slag sample and Cu, Pt, and Cr concentrations in the alloy phase were quantified by inductively coupled plasma optical emission spectrometry (ICP-OES; Agilent Technologies, 5100). Pt¹⁹⁵ was monitored by ICP-MS as the mass of Pt. Additionally, wavelengths of Si (252.851 nm), Ca (422.637 nm), Cr (267.716 nm), Al (308.215 nm), Cu (267.395 nm), and Pt (214.424 nm) were used for concentration determination by ICP-OES.

3. Results and Discussion

3.1 Phase diagram of SiO₂–CaO–CrO_x system

The phase diagram of the SiO₂–CaO–CrO_x system was determined at 1773 and 1873 K in $p_{\text{O}_{2}} = 10^{ - 10}$. Table 1 shows the initial compositions, composition of the equilibrium oxide phases, and standard deviations for different samples of SiO₂–CaO–CrO_x system. Table 2 shows the equilibrium alloy phase compositions and standard deviations for each sample. The backscattered electron images obtained by SEM-EDX, and the diffraction patterns obtained by XRD are shown in Figs. 1–3. Figure 1(a) shows the backscattered electron image of a sample in which the liquid phase and SiO₂ solid phase are in equilibrium, and Fig. 1(b) shows the XRD pattern for this sample. Figures 2 and 3 represent analogous results for equilibrium conditions involving (liquid + Cr₂O₃(s) + Pt–Cr(s)) and (liquid + SiO₂(s) + Cr₂O₃(s) + Pt–Cr(s)), respectively. Similarly, the equilibrium phase and composition of each phase of all samples were determined by SEM-EDX and XRD.

Table 1 Experimentally determined equilibrium oxide phase compositions of the SiO₂–CaO–CrO_x system.

Table 2 Experimentally determined equilibrium alloy phase composition.

Fig. 1

Equilibrium with the liquid phase and SiO₂(s); (a) backscattered electron image, and (b) diffraction pattern.

Fig. 2

Equilibrium with the liquid phase and Cr₂O₃(s); (a) backscattered electron image, and (b) diffraction pattern.

Fig. 3

Equilibrium with the liquid phase, SiO₂(s), and Cr₂O₃(s); (a) backscattered electron image, and (b) diffraction pattern.

According to the Gibbs phase rule, the number of degree of freedom is given by eq. (2) as follows:   

\begin{equation} f = c - p + 2 \end{equation} (2)

where f is the number of degree of freedom, c is the number of components, and p is the number of phases. In this study, c = 5 because there are five components of Si, Ca, Cr, Pt, and O in the system. Therefore, there were seven maximum possible degrees of freedom. When the sample contained two solid oxide phases different from the liquid phase, in addition to the gas phase and the single phase of solid solution in the Pt–Cr alloy, p = 5, and hence f = 2. When the partial pressure of oxygen in the gas phase and at a temperature of 1773 or 1873 K are specified, f = 0, and hence the composition of the liquid phase is fixed. When the sample contained one solid oxide phase different from the liquid phase, f = 1, and hence, the composition of the liquid phase changes, which is represented as the liquidus line in the phase diagram.

In the present study, the oxidation state of Cr in the liquid slag phase was not determined because the samples obtained were heterogeneous of liquid and solid phases. According to the previous studies conducted under similar experimental conditions, the Cr³⁺/Cr²⁺ ratio increases with increasing slag basicity and increasing $p_{\text{O}_{2}}$.^3–5) When Cr₂O₃(s) and the liquid phase are in equilibrium, the oxidation states of Cr differ, and both divalent and trivalent states of Cr are present in the slag. For this reason, all Cr in the solid and liquid phase were assumed to be in trivalent oxidation state in this study. The phase diagram of SiO₂–CaO–CrO_x system at 1773 and 1873 K in $p_{\text{O}_{2}} = 10^{ - 10}$ is shown in Fig. 4. Figure 4(a) represents the phase diagram at 1773 K, and Fig. 4(b) represents the phase diagram at 1873 K. The plot of the SiO₂–CaO line was obtained from the literature.²³⁾ The phase diagram in Fig. 4(a) agrees well with the phase diagram at 1773 K in $p_{\text{O}_{2}} = 10^{ - 9.56}$ reported by Pretorius et al.¹⁰⁾ Figure 4 shows that the solubility of Cr is greater in slag with lower basicity. A maximum of 12 mass% and 29 mass% of Cr₂O₃ dissolves in the slag at 1773 and 1873 K, respectively. The results suggest that low basicity compositions are suitable for removing Cr from the slag.

Fig. 4

Phase diagram of the SiO₂–CaO–CrO_x system $p_{\text{O}_{2}} = 10^{ - 10}$; (a) 1773 K, and (b) 1873 K.

3.2 Distribution ratio of Pt between liquid SiO₂–CaO–Al₂O₃–CrO_x or liquid SiO₂–CaO–CrO_x slag phase and Cu–Pt molten alloy

Table 3 shows the results of the chemical analysis of the slag phase and the Cu–Pt alloy phase. As discussed in the previous section, the oxidation state of Cr in the slag phase was assumed to be trivalent.

Table 3 Compositions of the slag phase and the Cu–Pt alloy phase.

3.2.1 Solubility of Al₂O₃ in the SiO₂–CaO–Cr₂O₃ slag

Solubility of Al₂O₃ in SiO₂–CaO–Cr₂O₃ slag as a function of basicity, B is shown in Fig. 5. The solubility of Al₂O₃ in SiO₂–CaO–Cr₂O₃ slag was 20.0–32.1 mass%. The solubility of Al₂O₃ increased with increasing basicity, B. This trend is consistent with the fact that the liquid phase line of Al₂O₃ saturation in SiO₂–CaO–Al₂O₃ slag approaches high Al₂O₃ concentration with increasing basicity (0.52 ≤ B ≤ 1).²⁴⁾

Fig. 5

Solubility of Al₂O₃ in the SiO₂–CaO–CrO_x system (1773 K, $p_{\text{O}_{2}} = 10^{ - 10}$).

3.2.2 Distribution ratios of Cu, Pt, and Cr between liquid SiO₂–CaO–Al₂O₃–CrO_x or liquid SiO₂–CaO–CrO_x slag phase and Cu–Pt molten alloy

In the present study, the distribution ratios of Cu, Pt, and Cr between the slag phase and liquid copper were defined by eq. (3) as follows:   

\begin{equation} L_{\text{X}} = \frac{(\text{mass%X})}{[\text{mass%X}]} \end{equation} (3)

where, X = Cu, Pt, or Cr. ( ) and [ ] represent values for slag and alloy phases in this study. Figure 6 shows the relationship between the distribution ratio of each element and the concentration of Cr₂O₃ in the slag. Figure 7 shows the relationship between the distribution ratio of each element and the basicity of the slag under Al₂O₃ saturation. The distribution ratio of Pt between the SiO₂–CaO–Al₂O₃–CrO_x or SiO₂–CaO–CrO_x slag and liquid copper was 6.5 × 10⁻⁷ to 1.6 × 10⁻⁵, value of Cu was 1.3 × 10⁻³ to 3.9 × 10⁻³, and distribution of Cr was 10 to 69. The results show that Pt was concentrated in the Cu–Pt alloy phase, and Cr was removed in the slag phase. Figure 6 shows that the distribution ratio of Pt between the SiO₂–CaO–Al₂O₃–CrO_x or SiO₂–CaO–CrO_x slag and liquid copper tends to increase with increasing CrO_x concentration in the slag. However, Fig. 7 shows that the distribution ratio of Pt between the SiO₂–CaO–Al₂O₃–CrO_x slag and liquid copper was constant regardless of the basicity of the slag.

Fig. 6

Relationship between the distribution ratio of each element and the concentration of Cr₂O₃ in the slag (1773 K, $p_{\text{O}_{2}} = 10^{ - 10}$).

Fig. 7

Relationship between the distribution ratio of each element and the basicity of the slag under Al₂O₃ saturation (1773 K, $p_{\text{O}_{2}} = 10^{ - 10}$).

3.2.3 Activity coefficient of Pt between SiO₂–CaO–Al₂O₃–CrO_x or SiO₂–CaO–CrO_x slag

Platinum is thought to exist as metallic platinum, platinum cations, or platinate ions in slag. The equilibrium conditions for slag phase and alloy phase in which platinum exists in different oxidation states are in eqs. (4)–(6). The solubility of metallic platinum is independent of the oxygen partial pressure, whereas that of platinum cations and platinate ions is dependent on the oxygen partial pressure.^11,25)   

\begin{equation} [\text{Pt}] = (\text{Pt}) \end{equation} (4)

  

\begin{equation} [\text{Pt}] + \text{$m$O$_{2}$ (g)} + \text{$n$(O$^{2-}$)} = (\text{PtO}_{(2m + n)}^{2n-}) \end{equation} (5)

  

\begin{equation} [\text{Pt}] + \text{$m$O$_{2}$ (g)} = (\text{Pt$^{4m+}$}) + \text{2$m$(O$^{2-}$)} \end{equation} (6)

In this study, both platinum cations and platinate ions were considered oxides without distinction, and the solubility of metallic platinum was assumed to be sufficiently small and negligible compared to that of oxides. The activity coefficient of PtO in each slag composition was calculated by assuming that the oxidation state of platinum is PtO, using eq. (7) for the oxidation reaction of platinum reported in the thermodynamic database HSC.²⁶⁾   

\begin{equation} \text{Pt (s)} + \frac{1}{2}\text{O$_{2}$ (g)} = \text{PtO (s)}:\Delta G_{1773\,\text{K}}^{\circ} = \text{65631 (J)} \end{equation} (7)

where $\Delta G^{\circ}_{1773\,\text{K}}$ is the standard Gibbs free energy change for the reaction at 1773 K. The equilibrium constant K for the reaction is calculated from activity a and oxygen partial pressure $p_{\text{O}_{2}}$, using eq. (8) as follows:   

\begin{equation} K = \frac{a_{\text{PtO}}}{a_{\text{Pt}} \cdot p_{\text{O${_{2}}$}}^{\frac{1}{2}}} \end{equation} (8)

Because there is no thermodynamic data on the dissolution of PtO(s) into PtO(l), the activity coefficient of PtO solid standard was calculated. The activity coefficient, (γ_PtO) is calculated from eq. (9) as follows:   

\begin{equation} (\gamma_{\text{PtO}}) = \frac{[\gamma_{\text{Pt}}] \cdot p_{\text{O${_{2}}$}}^{\frac{1}{2}} \cdot (n_{\text{T}}) \cdot K}{[n_{\text{T}}] \cdot L_{\text{Pt}}} \end{equation} (9)

where [γ_Pt] and (γ_PtO) are the activity coefficients of Pt in the alloy and PtO(s) in the slag, respectively, and [n_T] and (n_T) are the total molarities per 100 g in the alloy phase and slag phase, respectively.

The concentration of Cr in alloy phase is less compared to that of Cu and Pt. The interaction of Cr with Cu and Pt is negligible; therefore, the alloy can be considered as the Cu–Pt binary alloy. The activity coefficient of Pt in the alloy phase at 1773 K was calculated from the results of the quantitative analysis of each element in the Cu–Pt alloy using SGnobl of the FactSage database.²⁷⁾ Table 4 shows the Gibbs free energy change, $\Delta G^{\circ}_{1773\,\text{K}}$²⁶⁾ of PtO used in the calculation of the equilibrium constant, K. According to eq. (7), Pt is present in the solid state, but the Cu–10 mass%Pt binary alloy is liquid at 1773 K.²⁸⁾ Therefore, the change in the state of Pt is considered, and the $\Delta G^{\circ}_{1773\,\text{K}}$ for melting reaction of Pt(s) = Pt(l) is shown in Table 4. The values of [n_T], (n_T), L_Pt [γ_Pt], and (γ_PtO) are listed in Table 5. Figure 8 shows the iso-activity coefficient curves of PtO(s) obtained using the thermodynamic data. The curves were drawn on the phase diagram projected onto the SiO₂–CaO–CrO_x system, excluding Al₂O₃. The activity coefficient of PtO(s) tends to increase as the concentration of Cr₂O₃ in the slag decreases. The activity coefficient of PtO(s) was almost constant regardless of the basicity of the slag. When the slag composition had a low Cr₂O₃ concentration and low basicity (high basicity causes CaSiO₃ to precipitate out), the activity coefficient of PtO(s) increased, indicating that the loss of Pt to slag can be minimized. The change in the concentration of Cr₂O₃ in the slag had a greater effect on the change in the activity coefficient of PtO(s) than the change in the basicity of the slag. Therefore, a high Cr₂O₃ concentration in the slag allows a large amount of Cr₂O₃ to be processed but increases the Pt loss to the slag.

Table 4 Standard free energy change of formation.

Table 5 Activity Coefficients of Pt in SiO₂–CaO–Al₂O₃–CrO_x or SiO₂–CaO–CrO_x system.

Fig. 8

Iso-activity coefficient curves of PtO(s) in the SiO₂–CaO–CrO_x system (1773 K, $p_{\text{O}_{2}} = 10^{ - 10}$).

4. Conclusion

The phase diagram of the SiO₂–CaO–CrO_x system was determined in the experimental study. The solubility of Cr₂O₃ was higher in the slag with low basicity. A maximum of 12.42 mass% and 28.96 mass% of Cr₂O₃ was dissolved in the slag at 1773 and 1873 K in $p_{\text{O}_{2}} = 10^{ - 10}$, respectively. Furthermore, the distribution of Pt between the liquid SiO₂–CaO–Al₂O₃–CrO_x or liquid SiO₂–CaO–CrO_x slag systems and molten copper was investigated. Pt and Cr were concentrated in the alloy and the slag phases, respectively. The solubility of Pt in the slag increased with increasing Cr₂O₃ concentration. In the case of a constant Cr₂O₃ concentration in the slag, the solubility of Pt was approximately constant and independent of basicity.

Acknowledgments

The authors would like to thank Tanaka Kikinzoku Kogyo K.K. for their helpful suggestions and discussions, Kagami Memorial Research Institute for Materials Science and Technology of Waseda University for the use of XRD, Environmental Safety Center of Waseda University for the use of ICP-OES and ICP-MS, and Editage (www.editage.com) for language support during the preparation of this paper.

REFERENCES

• 1)   D.  Xun,  H.  Hao,  X.  Sun,  Z.  Liu and  F.  Zhao: J. Clean. Prod. 266 (2020) 121942. doi:10.1016/j.jclepro.2020.121942
• 2)  A. Cowley: PGM Market Report February 2021, (Johnson Matthey Plc., 2021). https://platinum.matthey.com/market-research (accessed 2022–04–08).
• 3)   E.B.  Pretorius,  R.  Snellgrove and  A.  Muan: J. Am. Ceram. Soc. 75 (1992) 1378–1381. doi:10.1111/j.1151-2916.1992.tb04197.x
• 4)   Y.  Xiao,  L.  Holappa and  M.A.  Reuter: Metall. Mater. Trans. B 33 (2002) 595–603. doi:10.1007/s11663-002-0039-9
• 5)   K.  Morita,  K.  Tsukiashi,  M.  Kimura and  N.  Sano: Steel Res. Int. 76 (2005) 279–283. doi:10.1002/srin.200506009
• 6)   S.  Degterov and  A.D.  Pelton: J. Phase Equilib. 17 (1996) 476–487. doi:10.1007/BF02665994
• 7)   S.  Degterov and  A.D.  Pelton: Metall. Mater. Trans. B 28 (1997) 235–242. doi:10.1007/s11663-997-0089-0
• 8)   S.  Arnout,  D.  Durinck,  M.  Guo,  B.  Blanpain and  P.  Wollants: J. Am. Ceram. Soc. 91 (2008) 1237–1243. doi:10.1111/j.1551-2916.2007.02249.x
• 9)   S.  Arnout,  M.  Guo,  I.  Jung,  B.  Blanpain and  P.  Wollants: J. Am. Ceram. Soc. 92 (2009) 1831–1839. doi:10.1111/j.1551-2916.2009.03115.x
• 10)   E.B.  Pretorius and  A.  Muan: J. Am. Ceram. Soc. 75 (1992) 1364–1377. doi:10.1111/j.1151-2916.1992.tb04196.x
• 11)   S.  Nakamura and  N.  Sano: Metall. Mater. Trans. B 28 (1997) 103–108. doi:10.1007/s11663-997-0132-1
• 12)   S.  Nakamura,  K.  Iwasawa,  K.  Morita and  N.  Sano: Metall. Mater. Trans. B 29 (1998) 411–414. doi:10.1007/s11663-998-0118-7
• 13)   C.  Wiraseranee,  T.H.  Okabe and  K.  Motira: Metall. Mater. Trans. B 44 (2013) 584–592. doi:10.1007/s11663-013-9816-x
• 14)   C.  Wiraseranee,  T.  Yoshikawa,  T.H.  Okabe and  K.  Motira: J. Min. Metall. Sect. B-Metall. 49 (2013) 131–138. doi:10.2298/JMMB121221018W
• 15)   C.  Wiraseranee,  T.  Yoshikawa,  T.H.  Okabe and  K.  Motira: Mater. Trans. 55 (2014) 1083–1090. doi:10.2320/matertrans.M2014042
• 16)   K.  Morita,  C.  Wiraseranee,  H.  Shuto,  S.  Nakamura,  K.  Iwasawa,  T.H.  Okabe and  N.  Sano: Miner. Process. Extr. Metall. 123 (2014) 29–34. doi:10.1179/0371955313Z.00000000070
• 17)   K.  Baba and  K.  Yamaguchi: J. MMIJ 129 (2013) 208–212. doi:10.2473/journalofmmij.129.208
• 18)   K.  Avarmaa,  H.  Johto and  P.  Taskinen: Metall. Mater. Trans. B 47 (2016) 244–255. doi:10.1007/s11663-015-0498-4
• 19)   K.  Avarmaa,  L.  Klemettinen,  H.  O’Brien and  P.  Taskinen: Miner. Eng. 133 (2019) 95–102. doi:10.1016/j.mineng.2019.01.006
• 20)   L.  Klemettinen,  K.  Avarmaa,  H.  O’Brien,  A.  Jokilaakso and  P.  Taskinen: JOM 72 (2020) 2770–2777. doi:10.1007/s11837-019-03960-4
• 21)   A.  Borisov and  L.  Danyushevsky: Eur. J. Mineral. 23 (2011) 355–367. doi:10.1127/0935-1221/2011/0023-2107
• 22)   W.  Nishijima and  K.  Yamaguchi: J. Japan Inst. Met. Mater. 78 (2014) 267–273. doi:10.2320/jinstmet.JA201404
• 23)   J.R.  Taylor and  A.T.  Dinsdale: Calphad 14 (1990) 71–88. doi:10.1016/0364-5916(90)90041-W
• 24)   G.  Eriksson and  A.D.  Pelton: Metall. Mater. Trans. B 24 (1993) 807–816. doi:10.1007/BF02663141
• 25)  S. Nakamura: Doctoral thesis, The University of Tokyo, (1997).
• 26)  A. Roine (Ed.): HSC Chemistry 6.1 Software, (Outokumpu, Finland).
• 27)   C.W.  Bale et al.: Calphad 54 (2016) 35–53. doi:10.1016/j.calphad.2016.05.002
• 28)  H. Okamoto: Desk Handbook: Phase Diagrams for Binary Alloys, 2nd Edition, (ASM International, Ohio, 2010) p. 318.