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

In the past, researchers assessed the Fe-Sn system [18-22] using the Bragg-Williams (BW) model for the liquid
phase. The Gibbs energies of the solid solutions were formulated by the Compound Energy Formalism
[23]
(CEF) , and intermetallic phases were considered as stoichiometric compounds. Particularly for the
miscibility gap in the liquid phase, information reported in the Fe-Sn system shows inconsistencies between
the calculated results and the experimental data. Also, experimental results are scattered, most likely due to
the experimental difficulty such as fast crystallization during the quenching of liquid alloys. Further, Kang
and Pelton demonstrated that the BW model is often inadequate for elucidating the miscibility gap as the
[24]
calculated phase boundaries show higher and rounded shapes. The present study used three different
experimental techniques to determine the binodal of the miscibility gap. Also, the Fe-Sn binary system was
re-optimized using the Modified Quasichemical Model (MQM) in the pair approximation [25,26] for the liquid
phase. The MQM was chosen due to its better performance in optimizing systems showing positive
deviations from ideal mixing and forming a miscibility gap with fewer parameters . The CEF was
[24]
[23]
employed to describe the fcc and bcc solid solution phases . Polynomial functions were used for the
temperature dependence of the Gibbs energies of the stoichiometric compounds, FeSn, FeSn , Fe Sn , and
2
3
2
Fe Sn .
3
5
The crystallographic data of all stable phases in the binary Fe-Sn system are listed in Table 1 . The phase
[27]
diagram consists of the liquid solution, the face-centered cubic (fcc) and body-centered cubic (bcc) Fe solid
solutions, pure Sn, as well as four intermetallic compounds (FeSn, FeSn , Fe Sn , and Fe Sn ).
2
5
3
3
2
The binary Fe-Sn system optimized in the present study is shown in Figure 1, along with the literature
data [28-46] . An essential feature of the phase diagram is a stable miscibility gap (Liquid + Liquid ). During
2
1
cooling in the composition range of mole fraction Sn (X ) between 0.31 and 0.80, the homogeneous melt
Sn
separates into a Fe-rich melt (Liquid ) and an Sn-rich melt (Liquid ). The assessed consolute temperature is
2
1
1,365 °C at X = 0.542; the monotectic temperature is 1,140 °C . In the Fe-rich part, bcc and fcc form a
Sn
[47]
closed fcc single-phase region, also known as “γ-loop” . The fcc phase shows a maximum solubility of
X = 0.0079 at T = 1,167 °C. The solid/liquid equilibria on the Fe side are characterized by a bcc/liquid two-
Sn
phase region between X = 0.099-0.313 above the monotectic temperature. Below this temperature, the bcc
Sn
+ liquid phase region exists over a wide composition range. Complex phase equilibria can be identified
between the intermetallic compounds FeSn, FeSn , Fe Sn and Fe Sn and liquid Sn or the Sn-rich melt,
3
2,
5
2
3,
respectively. Several transitions of the stoichiometric compounds are observed, discussed in detail in the
Section “RESULTS OF THERMODYNAMIC OPTIMIZATION”.
MATERIALS AND METHODS
In the present study, the liquid phase miscibility gap was measured to provide key data for the modeling of
the liquid phase. The sample preparation and methods were carefully selected. The present authors
conducted well-established Differential Scanning Calorimetry (DSC) [48,49] in combination with the less
common electromagnetic levitation technique and contact angle measurement . This section
[51]
[50]
summarizes the sample preparation and experimental approaches used to evaluate the miscibility gap.
Sample preparation
Master alloys were prepared using an electromagnetic levitation furnace, as shown in Figure 2. Thanks to
the small chamber size of a fused silica tube (outer diameter 17.5 mm × inner diameter 16.9 mm × height
300 mm), it was easier to control the inner atmosphere against oxidation of the alloy. Conventional
induction or resistance furnaces were rejected to prepare the master alloys because of the considerable
chamber volume to maintain the reducing atmosphere since oxygen can prohibit the accurate
determination of the phase equilibria. The miscibility gap reported in the previous studies [18-22] exists in
XSn = 0.31-0.81. Detailed information on sample composition is listed in Table 2.