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Ye et al. J Mater Inf 2023;3:15 https://dx.doi.org/10.20517/jmi.2023.08 Page 11 of 37

Table 5. Thermodynamic parameters in the Fe-Y binary system
Phase Thermodynamic parameters* Reference
Liquid This work

bcc-(Fe/Y) This work
hcp-(Y) This work
fcc-(Fe) [142]

This work
Fe Y This work
17 2

[132]
Fe Y This work
23 6

[132]
Fe Y This work
3

[132]
Fe Y This work
2

[132]
[134]
*The Gibbs energies (J/mol) of Fe and Y with liquid, bcc, fcc, and hcp structures are given by Dinsdale . The unit of temperature (T) is Kelvin
(K).

[96]
Figure 6 compares the presently calculated Fe-Dy binary system with the data and the calculations [104,105] .
The calculated temperatures of the invariant reactions in Fe-Dy binary system were seen in Table 7. The
presently calculated results agree well with the reported results and the calculations [104,105] .
[96]

The presently calculated partial enthalpy of mixing and enthalpy of mixing in liquid Fe-Dy alloys are
consistent with the calculations , as given in Figure 7 and Figure 8, respectively. In Figure 9, the enthalpies
[27]
of formation of the Fe-Dy intermetallic compounds in the present calculation at 298 K agree well with the
calculations [19,27,44,83,104,105,141] and the experimental data [54,102,103] . The enthalpy of formation of Fe Dy is
2
calculated as -12.327 kJ/mol-atom. Additionally, the calculated thermodynamic properties [e.g., heat
capacity, entropy of formation and enthalpy difference compares] of Fe Dy, as shown in Figure 10, are
2
much better accordance with the results and show no artificial break point in the heat capacity curve.
[101]
Fe-Er
Figure 11 displays the presently calculated Fe-Er binary system with the earlier calculations [110-112] and the
experimental results [106-108] . As can be seen, Fe Er , Fe Er , Fe Er, and Fe Er are stable at room temperature,
6
3
2
23
17
2
but some compounds are unstable at low temperature in the literature . The presently calculated liquidus
[112]
and solidus in Figure 11(B) agree with the experimental data [106-108] . Table 8 compares the calculated results
of invariant reactions together with the experimental results. The temperatures and compositions of two
eutectic reactions, L ↔ Fe Er + Fe Er and L ↔ Fe Er + hcp-Er, are calculated to be 1,601.8 K and 18.2 at.%
17
23
6
2
2
Er and 1,185.6 K and 66.9 at.% Er, respectively. A congruent reaction of Fe Er (L ↔ Fe Er) happens at
2
2
1640.4 K, and those of four peritectic reactions (L + bcc-Fe ↔ fcc-Fe, L + fcc-Fe ↔ Fe Er , L + Fe Er ↔ Fe 23
2
17
3
Er , and L + Fe Er ↔ Fe Er) are calculated to be 1,663.2 K, 1,625.1 K, 1,601.8 K, and 1,615.0 K, respectively,
2
3
6
agreeing well with the results [106-108] .