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Page 14 of 25 Park et al. J Mater Inf 2023;3:5 https://dx.doi.org/10.20517/jmi.2022.37

where τ = T/T and T is the critical temperature (Néel or Curie) and β is the average magnetic moment
Cr
Cr
0
per atom.
The intermetallic phases - FeSn, FeSn , Fe Sn and Fe Sn - were treated as stoichiometric compounds.
3
5
2
3
3
RESULTS OF THERMODYNAMIC OPTIMIZATION
Table 3 shows the assessed parameters in the present study. Data for pure elements were taken from the
work of Dinsdale . The calculated results are critically compared with the selected Fe-Sn assessments of
[65]
Kumar et al. and Miettinen , which have been widely accepted until recently.
[19]
[20]
Thermodynamic properties of the liquid phase
The enthalpy of mixing in the liquid phase (∆h) was measured using calorimetry. Batalin et al.
[67]
determined the ∆h in the whole composition at 1,600 °C. Also, a full range of compositions of ∆h was
investigated by Petrushevskiy et al. at 1,677 °C. Lück and Predel measured ∆h at 1,547 °C in a limited
[68]
[69]
composition range (X < 0.229). They mentioned that it was difficult to obtain the data because of the high
Sn
evaporation rate of Sn in the liquid alloy.
Figure 9A shows the calculated partial enthalpy of mixing (∆h ∆h ) and Figure 9B the integral enthalpy of
Sn
Fe,
mixing (∆h) of the liquid alloy along with experimental data and calculated results. Petrushevskiy et al.
[68]
measured slightly negative values for the ∆h on the Fe side. The data show inconsistencies with the values
Fe
obtained by Batalin et al. . The data of Batalin et al. were considered more reliable. As also for ∆h, a
[67]
[67]
reasonable agreement can be identified with the measurements of Lück and Predel . The large positive
[69]
enthalpy of mixing indicates the stability of the miscibility gap. In the present study, both data sets by
[69]
Batalin et al. and Lück and Predel were considered to model the liquid phase at X < 0.25, representing
[67]
Sn
[20]
[19]
the main difference from the previous work of Kumar et al. and Miettinen .
Activities of Fe and Sn in liquid alloys were investigated with Electromotive Force (EMF) measurement,
vapor pressure measurement, mass spectrometric method, and transportation method. Kozuka et al.
[32]
conducted the EMF measurement with Fe, FeO, and ZrO -CaO solid electrolytes and used Sn-Fe alloys to
2
measure the activities of Fe and Sn at 1,100 °C and 1,200 °C, respectively. Wagner and St. Pierre
[70]
conducted the mass spectrometric method to measure the ionic intensities of the Fe and Sn and obtained
the activities of Fe and Sn at 1,287 °C and 1,537 °C. Also, Nunoue and Kato and Yamamoto et al. used a
[42]
[44]
mass spectrometric method to determine the activity at 1,550 °C and 1,600 °C. By vapor-liquid equilibrium,
[71]
Maruyama and Ban-ya conducted a transportation method, which was used to measure the concentration
ratios of the Fe and Sn in the vapor and metal phases to obtain the activity. Eremenko et al. measured the
[72]
[74]
[73]
vapor pressure with the effusion technique and Federenko and Brovkin and Shiraishi and Bell
measured with the transportation method at 1,100-1,300 °C. Yazawa and Koike determined the activity of
[75]
Sn by distribution of Sn between Fe and Pb alloys at 1,350 to 1,500 °C.
The activities of each component in the liquid alloys at 1,100-1,600 °C are represented as ∆μ = RT ln a in
M
M
Figure 10. As shown in Figure 10A, the present calculation and previous studies [19,20] show good accordance
[70]
[32]
with data from Kozuka et al. at 1,200 °C. Data from Wagner and St. Pierre seem to differ up to
X = 0.15 due to the fcc phase appearance. Data from Shiraishi and Bell show a slight deviation up to X
[74]
Sn
Sn
= 0.3, and this might have been attributed to the condensation of SnO during the experiment, as mentioned