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 ‘Alan 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 ‘Alan Dinsdale, SGTE Data for Pure Elements, NPL Report DMA(A)195, September 1989 d. Din ‘Alan 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 Fe–C 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, 𝐺, where

𝐺=𝐻−𝑇𝑆

𝐻 being Enthalpy, 𝑇 being Temperature, and 𝑆 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 𝐺 is with magnetic field. The magnetic field

adds a term, the magnetic Gibbs Energy, ∆𝐺↓𝑚 ,

to the original Gibbs Energy, the thermal Gibbs Energy, 𝐺↓𝑡 ,

so that

𝐺↓𝑡𝑜𝑡𝑎𝑙 = 𝐺↓𝑡 (𝑇,  𝑋)+∆𝐺↓𝑚 (𝑇,   𝐻↓𝑚 )

where 𝑋 is the composition of the material, for this project Mass fraction C,

and 𝐻↓𝑚  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,

∆𝐺↓𝑚 (𝑇,   𝐻↓𝑚 )=  − 1/2 𝑋↓𝑠 𝐻↓𝑚↑2 

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. ∆𝐺↓𝑚  for Ferrite was calculates for 120, 200, and 500

kOe in the paper “An effect of high magnetic field on phase transformation in Fe–C system”. 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