Neodymium Distribution between Cu-rich and Fe-rich Phases in Two Immiscible Liquids in Fe–Cu–C System

Abstract

Recovery of Nd from used products is a crucial problem to be solved for a stable supply of Nd resource. In the present work, the use of two immiscible liquids, i.e. a Cu-rich phase and an Fe-rich phase, in an Fe–Cu–C system was regarded as one of the solutions for this purpose and the distributions of Nd between two immiscible liquids in an Fe–Cu–C system were measured. We found Nd is distributed in the Cu-rich phase more than in the Fe-rich phase in an Fe–Cu–C system and Nd is more concentrated at low temperatures than at high temperatures. In addition, the thermodynamic parameters for Nd were obtained based on the experimental results.

1. Introduction

In the past two decades, the use of two immiscible liquids in Fe–Cu–C systems in several kinds of metal recycling has been investigated. It is known that a uniform liquid in an Fe–Cu system separates into two immiscible phases, i.e., a Cu-rich phase and an Fe-rich phase, when C is added to the system.^1,2,3,4,5) Based on this phenomenon, the recovery of Cu and Fe from Fe–Cu mixed scraps such as motor cores and polychlorinated biphenyl transformers has been investigated by Marukawa and Tanaka et al.^6,7) It has also been reported that the minor metals contained in an Fe–Cu–C system are distributed between the Cu-rich and Fe-rich phases.^{8,9,10,11,12,13)} This behavior can be used to recover the minor metals from the phase in which they are concentrated, and to remove impurities from phases in which impurities are concentrated. From this viewpoint, Yamaguchi et al.⁸⁾ have conducted the fundamental experiments on the copper enrichment of low grade copper scraps such as ashes of shredder dust and trash, and the recovery of precious metals, i.e. Au, Ag, Pd, Pt and Rh. The recovery of valuable metals from speiss generated in the smelting process of metals based on this phenomenon has been investigated by Voisin et al.^9,10) Gonzalez et al.¹¹⁾ made an suggestion that molybdenum is concentrated in the Fe-rich phase by applying the two immiscible liquids to the Cu slag. Recently, Lu et al.¹²⁾ have focused on municipal solid wastes as the target material which the two immiscible liquids are applied to. The removal of Ni from low-grade Cu scraps has been studied by Sano et al.¹³⁾ with respect to impurity removal.

The recovery of valuable metals from used products is important for stable supplies of metal resources. In this study, we focus on the use of two immiscible liquids in an Fe–Cu–C system as the seed technology for the treatment of used products because the motors in automobiles, electric appliances and so on consist of Fe, Cu, and various valuable metals. Nd is a particularly significant metal since Nd-based magnets are used in many electronic devices and Nd supplies are unstable. In this study, the temperature dependence of the distribution of Nd between the two immiscible liquids in an Fe–Cu–C system was investigated. In addition, the interaction parameters for Nd were evaluated based on experimental data on the distribution of Nd in the two immiscible liquids in an Fe–Ag–C system, as well as that in an Fe–Cu–C system.

2. Experimental

2.1. Distribution of Nd between Cu-rich and Fe-rich Phases in Fe–Cu–C System

An Fe–C_sat alloy, Cu–Nd alloy, and Cu were used in the experiments. The Fe–C_sat alloy was prepared by melting 100 g of electrolytic Fe (Toho Zinc Co., Ltd.: C 36 ppm, P <10 ppm, 12 ppm, Si <5 ppm, Mn 1 ppm, Cu 1 ppm, N 10 ppm, O 200 ppm) and 4 g of C powder (Sigma-Aldrich Co. LLC) in a carbon-crucible at 1573 K under Ar gas for 3 h. The Cu–Nd alloy was prepared by melting 27 g of Cu (Nilaco Corp.: > 99.99%) and 3 g of Nd (Mitsuwa Chemicals Co., Ltd: > 99.9%) in a carbon-crucible at 1523 K under Ar gas for 3 h. The weight of Fe–C_sat alloy in the sample was 10 g and the total weight of Cu–Nd alloy and Cu in the sample was 10 g; the proportion of Nd in the Cu–Nd was varied by varying the amount of Nd. The sample was melted in a carbon- crucible at a target temperature under an Ar gas flow 50 ml/min (s.t.p.) for more than 10 h. The target temperatures were 1523, 1623, and 1723 K. After the holding time, the sample was quenched with water, and the compositions of the Cu-rich and Fe-rich phases were analyzed using inductively- coupled plasma atomic emission spectrometry (ICPAES) and infrared absorptiometry.

2.2. Distribution of Nd between Ag-rich and Fe-rich Phases in Fe–Ag–C System

The Fe–C_sat alloy, Ag (Nilaco Corp.: > 99.99%), and Nd were used in the experiments. The Fe–C_sat alloy (6 g), Ag (6 g), and different amounts of Nd were melted in a carboncrucible at 1623 K under an Ar gas flow 50 ml/min (s.t.p.) for more than 10 h. After the holding time, the sample was quenched with water, and the compositions of the Ag-rich and Fe-rich phases were analyzed using ICP-AES and infrared absorptiometry.

3. Results

3.1. Distribution of Nd between Cu-rich and Fe-rich Phases in Fe–Cu–C System

The compositions of the Cu-rich and Fe-rich phases as mass percentages and mole fractions are shown in Table 1. The Nd content in the Cu-rich phase is higher than that in the Fe-rich phase, regardless of the temperature and the amount of Nd. We found that Nd is distributed in the Curich phase more than in the Fe-rich phase. Figure 1 shows the relationship between the mass percentage of Nd in the Cu-rich phase and that of Nd in the Fe-rich phase. The plots for different amounts of Nd at 1523 K and at 1623 K give straight lines. This means that the distribution ratio of Nd between the Cu-rich and Fe-rich phases does not change in the Nd concentration range used in the present experiments. The distribution ratio of Nd, defined as [mass%Nd]_{in Cu-rich}/ [mass%Nd]_{in Fe-rich}, is determined by the slope of the fitted line through the origin for the plots. The distribution ratios are 18.8 at 1523 K, 10.4 at 1623 K, and 6.2 at 1723 K. The distribution ratio of Nd between the Cu-rich and Fe-rich phases increases with decreasing temperature; i.e., Nd is more concentrated at low temperatures than at high temperatures. Sano et al.¹²⁾ reported that the distribution of Ni between the two immiscible liquids in an Fe–Cu–C system has the similar tendency as that of Nd in the present work. They found that Ni is more concentrated in the Fe-rich phase at low temperatures than at high temperatures.

Fig. 1.

Relationships between mass percentages of Nd in Cu-rich and Fe-rich phases in two immiscible liquids in Fe–Cu–C system.

Table 1. Compositions of Fe-rich and Cu-rich phases as (a) mass percentages and (b) mole fractions.

3.2. Distribution of Nd between Ag-rich and Fe-rich Phases in Fe–Ag–C System

The compositions of the Ag-rich and Fe-rich phases as mass percentages and mole fractions are shown in Table 2. The content of Nd in the Ag-rich phase is higher than that in the Fe-rich phase, regardless of the amount of Nd, which means that Nd is distributed in the Ag-rich phase more than in the Fe-rich phase. The mass percentage of Nd in the Agrich phase is plotted against the mass percentage of Nd in the Fe-rich phase in Fig. 2. The plot shows a linear relationship. This suggests that the distribution ratio of Nd between the Ag-rich and Cu-rich phases is constant under our experimental conditions. The distribution ratio of Nd, defined as [mass%Nd]_{in Ag-rich}/[mass%Nd]_{in Fe-rich}, is 6.3 at 1623 K, so Nd is concentrated in the Ag-rich phase in the two immiscible liquids in the Fe–Ag–C system.

Fig. 2.

Relationship between mass percentages of Nd in Ag-rich and Fe-rich phases in two immiscible liquids in Fe–Cu–C system at 1623 K.

Table 2. Compositions of Fe-rich and Ag-rich phases as (a) mass percentages and (b) mole fractions at 1623 K.

3.3. Thermodynamic Evaluation of Distribution of Nd between Cu-rich and Fe-rich Phases in Two Immiscible Liquids in Fe–Cu–C System

The reaction between Nd in the Cu-rich phase and Nd in the Fe-rich phase is expressed by Eq. (1).

  

$${\text{Nd}}_{\left(\text{Cu}\right)}={\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}$$(1)

The Cu-rich and Fe-rich phases are denoted by the subscripts (Cu) and (Fe–C), respectively. Both phases have the same Nd chemical potentials at equilibrium. The activity of Nd in the Cu-rich phase, a_Nd(Cu), is equal to the that in the Fe-rich phase, a_Nd(Fe–C), when the standard chemical potential of Nd is the same in both phases:

  

$$a_{{\text{Nd}}_{\left(\text{Cu}\right)}}=a_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}$$(2)

Using the relationship a_i = γ_iX_i, where a_i is the activity of i, γ_i is the activity coefficient of i and X_i is mole fraction of i, Eq. (2) is rewritten as Eq. (3).

  

$${\gamma }_{{\text{Nd}}_{\left(\text{Cu}\right)}}{X}_{{\text{Nd}}_{\left(\text{Cu}\right)}}={\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}{X}_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}$$(3)

γ_Nd(Cu) is the activity coefficient of Nd in the Cu-rich phase, based on Raoult's law, X_Nd(Cu) is the mole fraction of Nd in the Cu-rich phase, γ_Nd(Fe–C) is the activity coefficient of Nd in the Fe-rich phase, based on Raoult's law, and X_Nd(Fe–C) is the mole fraction of Nd in the Fe-rich phase. γ_Nd(Fe–C) and γ_Nd(Cu) are given as Eqs. (4) and (5), based on Taylor expansions.¹⁴⁾   

$$\text{ln}{\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}=\text{ln}{\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}+{\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Nd}}{X}_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}+{\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}{X}_{{\text{Cu}}_{\left(\text{Fe}-\text{C}\right)}}$$(4)

  

$$\text{ln}{\gamma }_{{\text{Nd}}_{\left(\text{Cu}\right)}}=\text{ln}{\gamma }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{o}}+{\epsilon }_{\text{Nd}}^{\text{Nd}}{X}_{{\text{Nd}}_{\left(\text{Cu}\right)}}+{\epsilon }_{\text{Nd}}^{\text{Fe}}{X}_{{\text{Fe}}_{\left(\text{Cu}\right)}}$$(5)

where ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ is the activity coefficient of Nd in an infinitely dilute solution of the Fe-rich phase, based on Raoult's law, ${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Nd}}$ is the interaction coefficient of Nd with Nd itself in the Fe-rich phase, X_Nd(Fe–C) is the mole fraction of Nd in the Fe-rich phase, ${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}$ is the interaction coefficient of Cu with Nd in the Fe-rich phase, X_Cu(Fe–C) is the mole fraction of Cu in the Fe-rich phase. ${\gamma }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{o}}$ is the activity coefficient of Nd in an infinitely dilute solution of Cu, based on Raoult's law, ${\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Nd}}$ is the interaction coefficient of Nd with Nd itself in Cu, and X_Nd(Cu) is the mole fraction of Nd in the Cu-rich phase, ${\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Fe}}$ is the interaction coefficient of Fe with Nd in Cu, and X_Fe(Cu) is the mole fraction of Fe in the Cu-rich phase. In this thermodynamic assessment, the Fe-rich phase is treated as a C-saturated Fe alloy; in other words, γ_Nd(Fe–C) is the activity coefficient of Nd in C-saturated Fe, ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ is the activity coefficient of Nd in an infinitely dilute solution (X_Nd(Fe–C) → 0) of C-saturated Fe, and ${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}$ is the interaction coefficient of Cu with Nd in C-saturated Fe. In this treatment, the interaction of C with Nd in the Fe-rich phase is taken into account in the first term of the right-hand side of Eq. (4), i.e., ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ . In addition, it is defined that ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ is not dependent on the content of C of the alloy in the vicinity of the carbon content of C-saturated Fe binary alloy although the existences of Cu^15,16) and Nd¹⁷⁾ can change the C content in C-saturated Fe alloy to some extent. The content of C in the Cu-rich phase was not analyzed in this work and the interaction of C on the activity coefficient of Nd in the Cu-rich phase was ignored because the content of C in the Cu-rich phase was considered to be negligibly small as described below. Nishi¹⁸⁾ and Horiguchi et al.¹⁹⁾ reported that the C solubilities in Cu–C system and Cu– Nd–C system, where C and NdC2 are equilibrated, are expressed as log (C/mass ppm) = 4.97 − 7.04×10³/T and log (C/mass ppm) = 7.86 − 9.73×10³/T, respectively. From these relations, the C solubility in the Cu-rich phase is estimated to be small like around 0.001 mass% although the effect of Fe on the C content in the Cu-rich phase is not taken into consideration.

By combining Eqs. (3), (4), and (5) and using a relation $L_{\text{Nd}}=X_{{\text{Nd}}_{\left(\text{Cu}\right)}}/X_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}$ = const., the natural logarithm of the distribution ratio in mole fraction, ln $X_{{\text{Nd}}_{\left(\text{Cu}\right)}}/X_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}$ , is expressed as a next equation:

  

$$\begin{array}{l}\text{ln}\left(X_{{\text{Nd}}_{\left(\text{Cu}\right)}}/X_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}\right)= \text{ln}\left({\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}/{\gamma }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{o}}\right)\\ +\left({\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Nd}}/L_{\text{Nd}}-{\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Nd}}\right)X_{{\text{Nd}}_{\left(\text{Cu}\right)}}\\ +{\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}{X}_{{\text{Cu}}_{\left(\text{Fe}-\text{C}\right)}}-{\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Fe}}{X}_{{\text{Fe}}_{\left(\text{Cu}\right)}}\end{array}$$(6)

Here, we considered that the influence of $\left({\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Nd}}/L_{\text{Nd}}-{\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Nd}}\right)X_{{\text{Nd}}_{\left(\text{Cu}\right)}}$ on Eq. (6) can be neglected because the influence of Nd on its distribution is negligibly small, at least under the conditions of the present experiments, as the distribution ratio of Nd shows a constant in spite of considerably larger change in X_Nd(Cu) than those in X_Cu(Fe–C) and X_Fe(Cu). The distribution ratio of Nd should increase or decrease monotonously if the influence of $\left({\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Nd}}/L_{\text{Nd}}-{\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Nd}}\right)X_{{\text{Nd}}_{\left(\text{Cu}\right)}}$ is large. Remove of $\left({\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Nd}}/L_{\text{Nd}}-{\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Nd}}\right)X_{{\text{Nd}}_{\left(\text{Cu}\right)}}$ in Eq. (6) and deformation of Eq. (6) give

  

$$\begin{array}{l}\text{ln}\left({\gamma }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{o}}{X}_{{\text{Nd}}_{\left(\text{Cu}\right)}}/{\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}{X}_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}\right)/X_{{\text{Fe}}_{\left(\text{Cu}\right)}}\\ ={\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}{X}_{{\text{Cu}}_{\left(\text{Fe}-\text{C}\right)}}/X_{{\text{Fe}}_{\left(\text{Cu}\right)}}-{\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Fe}}\end{array}$$(7)

Equation (7) shows that ${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}$ and ${\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Fe}}$ can be calculated from the relationship between the left-hand side in Eq. (7) and $X_{{\text{Cu}}_{\left(\text{Fe}-\text{C}\right)}}/X_{{\text{Fe}}_{\left(\text{Cu}\right)}}$ when ${\gamma }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{o}}$ and ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ are known. That is to say, ${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}$ and ${\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Fe}}$ correspond to the slope and the negative value of the intercept in the linear relationship between the left-hand side and $X_{{\text{Cu}}_{\left(\text{Fe}-\text{C}\right)}}/X_{{\text{Fe}}_{\left(\text{Cu}\right)}}$ , respectively.   

$$\begin{array}{c}\text{log}\left({\gamma }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{o}}\right)=0.638-3.15\times {10}^{-4}T-4.98\times {10}^3/T\\ (1523-1775\hspace{0.17em}\text{K})\end{array}$$(8)

was derived by Horiguchi et al.¹⁹⁾ However, ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ has not yet been derived. In this study, therefore, ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ was obtained based on data on the distribution of Nd in the two immiscible liquids in an Fe–Ag–C system. By analogy with Eq. (6), in an Fe–Cu–C system, the natural logarithm of the ratio of the mole fraction of Nd in the Ag-rich phase, X_Nd(Ag), to the mole fraction of Nd in the Fe-rich phase, X_Nd(Fe–C), is expressed by Eq. (9).   

$$\begin{array}{l}\text{ln}\left(X_{{\text{Nd}}_{\left(\text{Ag}\right)}}/X_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}\right)= \text{ln}\left({\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}/{\gamma }_{{\text{Nd}}_{\left(\text{Ag}\right)}}^{\text{o}}\right)\\ +{\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Ag}}{X}_{{\text{Ag}}_{\left(\text{Fe}-\text{C}\right)}}-{\epsilon }_{{\text{Nd}}_{\left(\text{Ag}\right)}}^{\text{Fe}}{X}_{{\text{Fe}}_{\left(\text{Ag}\right)}}\end{array}$$(9)

where ${\gamma }_{{\text{Nd}}_{\left(\text{Ag}\right)}}^{\text{o}}$ is the activity coefficient of Nd in an infinitely dilute solution of Ag, based on Raoult's law, ${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Ag}}$ is the interaction coefficient of Ag with Nd in C-saturated Fe, X_Ag(Fe–C) is the mole fraction of Ag in the Fe-rich phase, ${\epsilon }_{{\text{Nd}}_{\left(\text{Ag}\right)}}^{\text{Fe}}$ is the interaction coefficient of Fe with Nd in Ag, X_Fe(Ag) and is the mole fraction of Fe in the Ag-rich phase. Here, the Ferich phase is treated as a C-saturated Fe alloy, as in the Fe– Cu–C system. In Eq. (9), the terms of interactions between Nd elements were neglected because Nd does not affect the distribution of Nd in the Fe–Ag–C system, as mentioned above. In addition, the interaction of C on the activity coefficient of Nd in the Ag-rich phase was ignored because the content of C in the Ag-rich phase was considered to be negligibly small as well as in the Cu-rich phase in Fe–Cu–C system. Although there are no investigations on the solubility of C in Ag–Nd–C system, it is estimated that the content of C in the Ag-rich phase is quite small since the C solubility in Ag–C system, which is expected to be around 0.0001 masss% from Ag–C phase diagram,²⁰⁾ is smaller than that in Cu–C system. Moreover, the terms ${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Ag}}$ · X_Ag(Fe–C) and ${\epsilon }_{{\text{Nd}}_{\left(\text{Ag}\right)}}^{\text{Fe}}$ · X_Fe(Ag) were not taken into account in the calculation because the values of X_Ag(Fe–C) and X_Fe(Ag) are very low, as shown in Table 2. Thus, ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ is calculated from ${\gamma }_{{\text{Nd}}_{\left(\text{Ag}\right)}}^{\text{o}}$ , X_Nd(Ag), and X_Nd(Fe–C). Ivanov and Lukashenko²¹⁾ has reported that ${\gamma }_{{\text{Nd}}_{\left(\text{Ag}\right)}}^{\text{o}}$ = 0.00265 at 1363 K. Using the relationship lnγ^o·T = const.,²²⁾ ${\gamma }_{{\text{Nd}}_{\left(\text{Ag}\right)}}^{\text{o}}$ at 1623 K is 0.00687. ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ = 0.104 at 1623 K is calculated from ${\gamma }_{{\text{Nd}}_{\left(\text{Ag}\right)}}^{\text{o}}$ , and X_Nd(Ag) and X_Nd(Fe–C) in Table 2. With the values of ${\gamma }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{o}}$ , which is 0.00114 at 1623 K from Eq. (8), and ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ , and the compositional data for the Cu-rich and Fe-rich phases listed in Table 1, the relationship in Eq. (7); i.e., the relationship between the left-hand side and $X_{{\text{Cu}}_{\left(\text{Fe}-\text{C}\right)}}/X_{{\text{Fe}}_{\left(\text{Cu}\right)}}$ in Eq. (7) is plotted in Fig. 3. Figure 3 shows a reasonable linear relationship between the left-hand side and $X_{{\text{Cu}}_{\left(\text{Fe}-\text{C}\right)}}/X_{{\text{Fe}}_{\left(\text{Cu}\right)}}$ . From the slope and intercept of the linear equation, ${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}$ = −57.6 and ${\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Fe}}$ = −11.8, respectively, are obtained. There is no data for ${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}$ and ${\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Fe}}$ to our knowledge. The large negative value of ${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}$ like minus several dozen means that the elements Nd and Cu have a stronger affinity for each other than for Fe–C. This can be qualitatively inferred from the following equation with the properties of the binary limiting system in the regular solution model:¹⁴⁾

Fig. 3.

Relationship between left-hand side and X_Cu(Fe–C)/X_Fe(Cu) in Eq. (7) at 1623 K.

  

${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}=\text{ln}{\gamma }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{o}}-\text{ln}{\gamma }_{{\text{Cu}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}-\text{ln}{\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$(10)

where ${\gamma }_{{\text{Cu}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ is the activity coefficient of Cu in an infinitely dilute solution of C-saturated Fe. The values of ${\gamma }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{o}}$ , ${\gamma }_{{\text{Cu}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ and ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ at 1623 K are 0.00114, 39.6 which is estimated by ${\gamma }_{{\text{Cu}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ = 35.5 at 1673 K²³⁾ and lnγ^o·T = const. and 0.104, respectively. The smaller ${\gamma }_{i_{\left(j\right)}}^{\text{o}}$ in case of ${\gamma }_{i_{\left(j\right)}}^{\text{o}}$ < 1 represents a stronger affinity of interaction between i and j, the larger ${\gamma }_{i_{\left(j\right)}}^{\text{o}}$ in case of ${\gamma }_{i_{\left(j\right)}}^{\text{o}}$ > 1 represents a stronger repulsive force between i and j, and ${\gamma }_{i_{\left(j\right)}}^{\text{o}}$ = 1 represents no interaction between i and j. The order of ${\gamma }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{o}}$ < ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ < ${\gamma }_{{\text{Cu}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ corresponds to the negative value of ${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}$ although its absolute value cannot be evaluated.

The dependence of distribution of Nd between Cu-rich and Fe-rich phases in Fe–Cu–C system on temperature was evaluated by using the thermodynamic parameters obtained in the present work. Here, we assumed that the temperature dependence of ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ is calculated by lnγ^o·T = const., and those of ${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}$ and ${\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Fe}}$ are by ε·T = const. ${\gamma }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{o}}$ is a function of temperature as shown in Eq. (8). The calculated $\left(X_{{\text{Nd}}_{\left(\text{Cu}\right)}}/X_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}\right)$ are plotted with an inverse of temperature in Fig. 4. The experimental values are also shown in the figure. As well as the calculated results at 1623 K, where the thermodynamic parameters were determined, those at 1523 K are in relatively-good agreement with the experimental results. On the other hand, the calculated value at 1723 K is much lower than the experimental one. This difference is considered to be attributable to the temperature dependence of thermodynamic parameters and the lack of higher order interaction parameters. In this work, we conducted the calculation under assumption of lnγ^o·T = const. and ε·T = const. However, the real temperature dependence of thermodynamic parameters can be different from this assumption. In addition, X_Cu(Fe–C) and X_Fe(Cu) at 1723 K are as high as 0.08 in comparisons with those at 1623 and 1523 K. In such cases, the activity coefficient cannot be expressed by the interaction parameter of first order and the term on the interaction parameter for higher order should be included in the expression for activity coefficient.

Fig. 4.

Relationship between ln(X_Nd(Cu)/X_Nd(Fe–C)) and 1/T.

3.4. Formation of Nd Carbide

In our experiment, several % of Nd is contained in the Cu-rich phase in Fe–Cu–C system and in the Ag-rich phase in Fe–Ag–C system. The maximum Nd contents in the Curich phase and the Ag-rich phase were as high as 5.89 and 2.93 mass%. This magnitude of Nd content reminds us of the possibility of NdC₂ formation. Therefore, we discussed the formation of NdC₂ under our experimental conditions. Here, the binary M–Nd alloy (M=Cu or Ag) is treated for simplicity. The reaction of Nd in M–Nd alloy (M=Cu or Ag) and C to form NdC₂ is expressed as below:

  

$${\text{Nd}}_{(\text{M})}+2\text{C}={\text{NdC}}_2$$(11)

  

$$\mathrm{\Delta }{G}_{{\text{NdC}}_2}^{\text{O}}=-95\mathrm{\hspace{0.17em} }240-23.57T (\text{J}/\text{mol})$$ ^19,24) (12)

Equation (12) is changed into Eq. (13).

  

$$\mathrm{\Delta }{G}_{{\text{NdC}}_2}^{\text{O}}=-\text{R}T\text{ln}\left\{a_{{\text{NdC}}_2}/\left(a_{{\text{Nd}}_{(\text{M})}}\cdot a_{\text{C}}^2\right)\right\}$$(13)

Here, both a_C and a_NdC2 are defined as 1. By using a_Nd(M) = γ_Nd(M) · X_Nd(M), Eq. (14) was obtained.

  

$$\mathrm{\Delta }{G}_{{\text{NdC}}_2}^{\text{O}}=\text{R}T\text{ln}\left({\gamma }_{{\text{Nd}}_{(\text{M})}}\cdot X_{{\text{Nd}}_{(\text{M})}}\right)$$(14)

This equation means the solubility of Nd in M–Nd alloy (M=Cu or Ag) is calculated when the activity coefficient of Nd in M–Nd alloy (M=Cu or Ag) is known. When Eq. (8) is used as the activity coefficient of Nd in Cu–Nd system, the Nd solubility in Cu–Nd system in the presence of C and NdC₂ at 1523, 1623 and 1723 K are estimated to be 8.9, 9.5 and 10.2 mass% from Eqs.11, 13 and 14, respectively. It is expected that NdC₂ does not appear in the Cu-rich phase in Fe–Cu–C system in our experiment even if the effect of Fe on the solubility of Nd is considered. This is because γ_Nd(Cu) decreases with the content of Fe in Cu–Nd system due to the negative value of ${\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Fe}}$ .

On the other hand, there is no data on the activity coefficient of Nd in Ag–Nd–C system with the presence of C and NdC₂. Thus, the formation of NdC₂ in the Ag-rich phase in Fe–Ag–C system was discussed based on the activity coefficient of Nd in Ag–Nd system. The activity coefficient of Nd in an infinitely dilute solution of Ag, ${\gamma }_{{\text{Nd}}_{\left(\text{Ag}\right)}}^{\text{o}}$ , is 0.00687 at 1623 K as described above. This value leads to 0.98 mass% of Nd solubility in the presence of C and NdC₂ in Ag–Nd system. The contents of Nd in the Ag-rich phase in the present work are higher than 0.98 mass%, which suggests the possibility of the formation of NdC₂. However, it is considered that the formation of NdC₂ does not occur in the experiment by the following reason. If NdC₂ is formed, the content of Nd in “Ag-rich phase” should show a constant value, i.e. solubility of Nd in the presence of C and NdC₂. Here, “Ag-rich phase” means a liquid part, which does not contain any NdC₂, in the Ag-rich phase. In addition, the content of Nd in the Fe-rich phase also shows a constant value determined by the distribution ratio of Nd between “Ag-rich phase” and Fe-rich phase in case of the existence of NdC₂. From this viewpoint, the increase of Nd content in the Ferich phase in the present work is not in accordance with the phenomenon predicted by the existence of NdC₂. Further work like the investigation on the solubility of Nd in Ag– Nd system with the presence of C and NdC₂ needs to be conducted in order to elucidate this point.

4. Conclusions

In this study, the distribution of Nd between the two immiscible liquids in an Fe–Cu–C system was investigated at 1523, 1623, and 1723 K. In addition, the distribution behavior of Nd between the two immiscible liquids in an Fe–Ag–C system was investigated at 1623 K. The activity coefficient of Nd in an infinitely dilute solution of C-saturated Fe, the interaction parameter of Fe with Nd in Cu, and the interaction parameter of Cu with Nd in C-saturated Fe were determined from the experimental results. We found the following. Nd is concentrated in the Cu-rich phase in the two immiscible liquids in an Fe–Cu–C system and the tendency of Nd to concentrate in the Cu-rich phase becomes strong at low temperatures. In the two immiscible liquids in an Fe– Ag–C system, Nd is distributed in the Ag-rich phase more than in the Fe-rich phase. The thermodynamic parameters obtained in the present work are ${\gamma }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{o}}$ = 0.104, ${\epsilon }_{{\text{Nd}}_{\left(\text{Fe}-\text{C}\right)}}^{\text{Cu}}$ = −57.6, and ${\epsilon }_{{\text{Nd}}_{\left(\text{Cu}\right)}}^{\text{Fe}}$ = −11.8 at 1623 K.

Acknowledgments

This work was supported by the New Energy and Industrial Technology Development Organization (NEDO). We wish to thank them for financial assistance. The authors also are grateful to Dr. Hideki Ono (Associate Professor, Graduate School of Engineering, Osaka University), and Dr. Katsuhiro Yamaguchi (formerly with the Graduate School of Engineering, Osaka University is now with Kobe Steel, Ltd.) for their valuable discussions on thermodynamic assessment.

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