ABSTRACT This Project calculated the behavior of the FeC system under the effects of 120, 200 and 500 kOe magnetic fields. The phase diagram of FeC were generated for the previously mentioned magnetic fields using the ThermoCalc software. The lower portion of the diagram was pushed up while the lower portion moved down compressing the phase diagram of FeC.
Thermodynamic Calculations of FeC under Magnetic Field Eric Britt Florida State University
Results Figure 6: Graph of the location of P1 in the previous diagrams vs. magnetic field in kOe. Figure 7: Graph of the location of P2 in the previous diagrams vs. magnetic field in kOe. In conclusion, two eutectic points of the FeC diagram, P1 and P2, were tracked. Increasing magnetic field shiftd P1 up and P2 down compressing the center Austenite region of the FeC diagram.
References 1.TCS Public Binary Alloys TDB v1, for FeC this used, a. Din โAlan Dinsdale, SGTE Data for Pure Elements, NPL Report DMA(A)195, Rev August 1990 b. Gus P. Gustafson, Scan. J. Metall . Vol 14, (1985) p 259-267 TRITA 0237 (1984); C-Fe c. Din โAlan Dinsdale, SGTE Data for Pure Elements, NPL Report DMA(A)195, September 1989 d. Din โAlan Dinsdale, SGTE Data for Pure Elements, CALPHAD, Vol. 15, No. 4, pp. 317-425, (1991) 2. T. Kakeshita, T. Saburi, K. Kindo, S. Endo, Jpn. J. Appl. Phys. 36 1997. 7083. 3. B.D. Cullity, in: Introduction to Magnetic Materials, Addison Wesley, London, 1972, p. 117. 4. Joo, H., Kim, S., Shin, N., & Koo, Y. (2000). An effect of high magnetic field on phase transformation in FeโC system. Materials Letters, 43(5-6), 225-229. doi:10.1016/s0167-577x(99)00263-3 Note: To preserve the upward trend of the data from the above paper, which was taken to be correct, the signs of the susceptibilities for Cementite and Austenite and the signs of the Magnetic Gibbs Energy functions were reversed.
Phase Diagrams Figure 3: The Phase diagram of FeC at STP without any external magnetic field. For reference FCC is Austenite and BCC is Ferrite. Figure 4: Blowups around the lower eutectic point, labeled P1, showing the movement of that point with increasing magnetic field. Figure 5: Same as Fig. 2 for the upper eutectic point, P2.
P1
P2
P1 P1
P1
P1
P2 P2
P2
P2
Background
For chemical systems at constant temperature and pressure, the preferred
arrangement, phase, will minimize the Gibbs Free Energy, ๐บ, where
๐บ=๐ปโ๐๐
๐ป being Enthalpy, ๐ being Temperature, and ๐ being
Entropy. Equilibrium for a material can then be found by simply determining the phase of the material that has the least Gibbs Energy. If the Gibbs energy has such a large impact on a materials makeup, an interesting question is how to change G.
One way to externally change ๐บ is with magnetic field. The magnetic field
adds a term, the magnetic Gibbs Energy, โ๐บโ๐โ,
to the original Gibbs Energy, the thermal Gibbs Energy, ๐บโ๐กโ,
so that
๐บโ๐ก๐๐ก๐๐โ= ๐บโ๐กโ(๐, ๐)+โ๐บโ๐โ(๐, ๐ปโ๐โ)
where ๐ is the composition of the material, for this project Mass fraction C,
and ๐ปโ๐โ is the magnetic field strength.
The thermal Gibbs Energy functions for each phase of FeC were taken from the PBIN [1] library of ThermoCalc. For both Austenite, FCC, and Cementite the magnetic Gibbs energy was taken to be,
โ๐บโ๐โ(๐, ๐ปโ๐โ)= โ 1/2โ๐โ๐ โ๐ปโ๐โ2โ
Where Xs is the magnetic susceptibility. The susceptibilities for Austenite [2] and Cementite [3] are graphed vs. Temperature in K in Fig. 1 below using the ROOT software.
For Ferrite, BCC, the above formula is not accurate. โ๐บโ๐โ for Ferrite was calculates for 120, 200, and 500
kOe in the paper โAn effect of high magnetic field on phase transformation in FeโC systemโ. These functions were used in this work and are graphed vs. Temperature in K below using the ROOT software. The Curie Temperature of Ferrite, 1043 K, is marked.
Thanks The author would like to thank his supervisor, Dr. Ke Han, for all of the help and guidance on this project. This research was sponsored by DMR.
Austenite
Cementite
120 kOe
200 kOe
500 kOe