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Park et al. J Mater Inf 2023;3:5 https://dx.doi.org/10.20517/jmi.2022.37 Page 15 of 25

-1
-1
-1
Table 3. Model parameters for the Fe-Sn system optimized in the present study (J mol or J mol K )
Phase Model
Liquid MQM (Fe,Sn)
2
Δg 14,434.8 - 2.21752T - 7322X - 4184X - 2928.8(X )
FeSn FeFe SnSn FeFe
bcc (α-Fe, δ-Fe) CEF (Fe,Sn) (Va) 3
1
G Fe:Va GHSERFE
G Sn:Va GBCCSN
L Fe,Sn:Va 23,012 + 8.9956T + 23,012(X -X )
Sn
Fe
β Fe:Va 2.22X Fe [64]
T C(Fe:Va) 1043X Fe [65]
fcc (γ-Fe) CEF (Fe,Sn) (Va) 1
1
G Fe:Va GFCCFE
G Sn:Va GFCCSN
L Fe,Sn:Va 23012 - 1.8828T
[66]
β Fe:Va -2.1X Fe
T C(Fe:Va) -201X Fe [66]
Stoichiometric compounds
-4 -3 2 -5 3
FeSn C (1 K < T < 41 K) = 1.0 × 10 T + 5.1 × 10 T + 3.0 ×10 T
p -1 2 -2 -3 2
C (41 K < T < 135 K) = -12.051834 + 6.36436 × 10 T - 3.101986 × 10 T - 1.92343 × 10 T
p
-1
4 -2
-4 2
C (135 K < T < 250 K) = 25.827026 + 1.57530 × 10 T - 6.659823 × 10 T - 2.55233 × 10 T
p
C (250 K < T <1000 K) = 80-500T -0.5
p
H° 298 = -8600, S° 298 = 79.2675, T = 365 K, = 0.37
Cr
0
-2 4 -2 -5 2
FeSn C (250 K < T < 505.08 K) = 55.4363 + 8.427584 × 10 T + 9.3122 × 10 T - 3.710044 × 10 T
2 p -2 6 -2 -5 2
C (505.08 K < T < 800 K) = 40.032397 + 7.605276 × 10 T + 4.170258 × 10 T - 3.112401 × 10 T +
p
27 -10
2.21526 × 10 T
-3 5 -2 -7 2 27
C (800 K < T < 1811 K) = 80.4167 + 8.79504 × 10 T - 1.54718 × 10 T + 3.53562 × 10 T + 2.21526 × 10
p
-10
T
H° = -14750, S° = 128.5
298 298
-2 -3 2 -4 3
Fe Sn 2 C (1 K < T < 50 K) = 1.96 × 10 T + 6.6 × 10 T + 1.0 × 10 T
p
3
0
3 -2
-3 2
C (50 K < T < 150 K) = -23.162953 + 1.286666 × 10 T - 8.076442 × 10 T - 3.253589 × 10 T
p
-1
5 -2
-4 2
C (150 K < T < 250 K) = 51.084372 + 4.385531 × 10 T - 1.400109 × 10 T - 6.38662 × 10 T
p -1 5 -2 -4 2
C (250 K < T < 400 K) = 61.585963 + 2.462198 × 10 T + 3.24163 × 10 T - 1.55945 × 10 T
p
-1 1
-5 2
5 -2
C (400 K < T < 505.08 K) = 103.4649 + 1.018659 × 10 T - 2.16314 × 10 T - 3.63933 × 10 T - 2.28882
p -5 -0.5 -4 -1
× 10 T + 1.83105 × 10 T
-6 2
6 -2
-5
C (505.08 K < T < 800 K) = 346.009961 - 5.53886 × 10 T - 1.308346 × 10 T - 7.38 × 10 T - 8.954057
p
5 -1
3 -0.5
× 10 T + 1.031169 × 10 T
-2 5 -2 -6 2
C (800 K < T < 1811 K) = 130.4253 + 2.638512 × 10 T - 4.64154 × 10 T + 1.060686 × 10 T + 2.21526 ×
p
27 -10
10 T
H° 298 = -2100, S° 298 = 206
5 -2
-1
-5 2
Fe Sn 3 C (250 K < T < 505.08 K) = 165.4545 + 1.571964 × 10 T - 4.01830 × 10 T - 5.441320 × 10 T
5
p
-1
6 -2
-5 2
C (505.08 K < T < 800 K) = 142.348646 + 1.448618×10 T + 5.713874 × 10 T - 4.544854 × 10 T +
p 27 -10
3.32289 × 10 T
-2 5 -2 -6 2
C (800 K < T < 1811 K) = 202.9251 + 4.39752 × 10 T - 7.73590 × 10 T + 1.76781 × 10 T + 3.32289 ×
p
27 -10
10 T
H° 298 = 30,128.19, S° 298 = 356.0416
bcc: Body-centered cubic; CEF: Compound Energy Formalism; fcc: face-centered cubic; MQM: Modified Quasichemical Model.
in this study. In Figure 10B, the experimental data show inconsistencies with the assessments. In the
experiments of Eremenko et al. , Fe and Sn show similar vapor pressure, and this might cause a deviation
[72]
in the activity data. Yazawa and Koike distributed Sn between Pb-Sn and Fe-Sn alloys, expecting slight
[75]
mutual solubility between the two alloys. However, it is a practical problem during the experiment that Fe
could be entrapped and suspended into the Pb melt. This phenomenon might be the reason that shows the
deviation in the liquid activity since the activities diverged from fundamental activity behavior. In
Figure 10C and D, the data of Nunoue and Kato and Yamamoto et al. at 1,600 °C are in good
[42]
[44]