Structural, elastic, and thermal properties of cementite (${\mathrm{Fe}}_{3}C$) calculated using a modified embedded atom method

Structural, elastic, and thermal properties of cementite (${\mathrm{Fe}}_{3}C$) were studied using a modified embedded atom method (MEAM) potential for iron-carbon (Fe-C) alloys. Previously developed Fe and C single-element potentials were used to develop a Fe-C alloy MEAM potential, using a statistics-based optimization scheme to reproduce structural and elastic properties of cementite, the interstitial energies of C in bcc Fe, and heat of formation of Fe-C alloys in L${}_{12}$ and B${}_1$ structures. The stability of cementite was investigated by molecular dynamics simulations at high temperatures. The nine single-crystal elastic constants for cementite were obtained by computing total energies for strained cells. Polycrystalline elastic moduli for cementite were calculated from the single-crystal elastic constants of cementite. The formation energies of (001), (010), and (100) surfaces of cementite were also calculated. The melting temperature and the variation of specific heat and volume with respect to temperature were investigated by performing a two-phase (solid/liquid) molecular dynamics simulation of cementite. The predictions of the potential are in good agreement with first-principles calculations and experiments.

Figure 1

Energy vs volume curves for Fe in bcc, fcc, and hcp crystal structures. The solid curve is constructed from experimental values in Table 2. For ease of comparison, the DFT curves are shifted vertically by a constant amount equal to the difference between experimental and DFT cohesive energies of Fe in bcc at equilibrium volumes.

Figure 2

Energy vs nearest-neighbor distance curves for C in diamond and graphite. The solid curve is constructed from experimental values in Table 2. For comparison, the DFT curve is shifted vertically to the experimental cohesive energy at the equilibrium nearest-neighbor distance.

Figure 3

Cohesive energy of graphite as a function of the $c/a$ ratio. Energy at zero is set to the minimum energy predicted by MEAM.

Figure 4

Comparison of energy vs volume curves for cementite. The dashed curve is constructed from experimental values of the cohesive energy, equilibrium volume, and polycrystalline bulk modulus of cementite. For comparison, the DFT curve is shifted vertically to the experimental cohesive energy at the equilibrium volume.

Figure 5

Comparison of the energy vs volume curves of the Fe-C alloy system in the $B_1$ structure. The DFT curve is shifted vertically to the MEAM-predicted cohesive energy at the equilibrium nearest-neighbor distance to aid the comparison with the MEAM curve.

Figure 6

Comparison of the energy vs volume curves of the Fe-C alloy system in the $L_{12}$ structure. The DFT curve is shifted vertically to the MEAM-predicted cohesive energy at the equilibrium nearest-neighbor distance to aid the comparison with the MEAM curve.

Figure 7

Snapshots of the two-phase MD simulation in the N-P-T ensemble with $T=1420$ K and $P=0$. Red spheres are Fe atoms, and blue spheres are C atoms. (a) Initial state of the simulation box, which contains both liquid and solid phases of cementite. (b) Intermediate state of the simulation box at 16 ns, as the solid phase propagates to the liquid phase. (c) Final state of the simulation box at 32 ns, when the entire system has turned into a solid phase.

Figure 8

Snapshots of the two-phase MD simulation in the N-P-T ensemble with $T=1430$ K and $P=0$. Red spheres are Fe atoms, and blue spheres are C atoms. (a) Initial state of the simulation box, which contains both liquid and solid phases of cementite. (b) Intermediate state of the simulation box at 20 ns, as the liquid phase propagates to the solid phase. (c) Final state of the simulation box at 30 ns, when the entire system has turned into a liquid phase.

Figure 9

Variation of properties of the two-phase system over the temperature. (a) Total energy of the system. (b) Volume of the system. The red curve is the first-principles data by Dick et al. [54]. (c) Specific heat of the system. The red curve is the first-principles data. (d) $dV/dT$ of the system.