Optimization and properties of BCC Fe and ηFe2C crystal structures using MAPS Abinit plugin

In this case study, Abinit plugin within MAPS was used to optimize the crystal structures of both BCC Fe and ηFe2C. Then different properties such as the density, cell parameter or bulk modulus were calculated and compared with previous experimental and theoretical calculations.
 
1. Parameters convergence for BCC Fe. 

The BCC Fe crystal structure was loaded from MAPS structure database. The structure of ηFe2C was found in literature and directly loaded into MAPS. This material is orthorhombic (space group Pnmm) with 4 Fe and 2 C atoms. The positions of the different atoms are (x, 0.25, 0) for Fe and (0, 0, 0) for the C atoms. The experimentally measure lattice parameters a = 4.704 Å, b = 4.318 Å and c = 2.830 Å were used. This structure was built using MAPS crystal builder. The two crystal structures are represented in Figure 1-a and c.
 
Several single point calculations were performed using Abinit plugin with in MAPS Platform in order to study the evolution of the energy as a function of the k-point grid and energy cutoff. For these calculations the GGA DFT, functional PBE was used together with ultrasoft PAW pseudopotentials. A smearing function together with a smearing temperature of 0.01 Ha were used.
 
As shown in The Table 1 the k-point grid appears to be converged for a 6x6x6 k-point grid and the energy cutoff for a Ecut = 20 Ha. The same parameters were used for ηFe2C system.
 

Table 1: Evolution of the cell energy (in Ha) as a function of the k-point grid and the energy cutoff.
Table 1: Evolution of the cell energy (in Ha) as a function of the k-point grid and the energy cutoff.

2. Geometry optimization of Fe and ηFe2C
 
The optimized BCC Fe and ηFe2C crystal structures are represented in Figure 1-a and c. for both structures the convergence was rapidly achieved.
 

Figure 1: Optimized structure for Fe (a) and ηFe2C (b) and energy evolution along the geometry optimization (b and d respectively)
Figure 1: Optimized structure for Fe (a) and ηFe2C (b) and energy evolution along the geometry optimization (b and d respectively)

The optimized lattice parameters are exposed in Table 2. The results obtained are in very good agreement with experimental one. The error made on the lattice density or parameters are of about 1% or less validating the selected parameters.
 

Table 2: Experimental and calculated attice parameters and density for Fe and ηFe2C crystal structures
Table 2: Experimental and calculated attice parameters and density for Fe and ηFe2C crystal structures

The Figure 2 shows the density of states for up and down spins for both Fe and ηFe2C. The up and down spin density of states were calculated for both Fe and ηFe2C. In these two crystal structures, the density of states of the two spin clearly show a dissymmetry characteristic of a magnetic material.
 

Figure 2: Density of state for α (blue) and β (green) spin from Fe (a-) and ηFe2C (b-) crystal structures.
Figure 2: Density of state for α (blue) and β (green) spin from Fe (a-) and ηFe2C (b-) crystal structures.

3. Bulk modulus of Fe and ηFe2C
 
In order to understand the effect of carbon atoms on the elastic properties of iron when forming ηFe2C iron carbide, the bulk moduli of BCC Fe and ηFe2C were calculated. Figure 3 shows the evolution of the lattice energy when changing the lattice volume. The Bulk Moduli were extracted from the Murnhagan equations: BFe = 168 GPa and BηFe2C = 238 GPa. Both results are in very good agreement with previous experimental and theoretical results: 170 GPa for Fe and 243 GPa, 223 GPa2 and 226 GPa for ηFe2C). The increase of the Bulk Modulus shows that the addition of carbon atoms within iron crystal increases its resistance to external mechanic pressure.
 

Figure 3: Calculated energy as a function of BCC Fe (a-) and ηFe2C (b-) unit cell volume.
Figure 3: Calculated energy as a function of BCC Fe (a-) and ηFe2C (b-) unit cell volume.

We presented here a study of the bulk properties BCC iron and ηFe2C iron carbide using Abinit plugin within MAPS platform. The structural, magnetic and mechanic aspects of these two materials were studied and compared experimental data showing that periodic DFT calculations can be used as an efficient and reliable tool to study, understand and predict the properties of new materials.
 
References:

  1. http://scienomics.com/products/abinit
  2. Oila A., Lung C., Bull S., Journal of Materials Science, DOI:10.1007/s10853-013-7942-0.
  3. http://scienomics.com/products/molecular-modeling-platform
  4. P. Hohenberg and W. Kohn, Phys. Rev. 136B, 864 (1964).
  5. W. Kohn and L. J. Sham, Phys. Rev. 140A, 1133 (1965).
  6. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
  7. K. Laasonen, A. Pasquarello, R. Car, C. Lee, D. Vanderbilt, Phys. Rev. B 47, 10142 (1993). DOI 10.1103/PhysRevB.47.10142.
  8. P. E. Blöchl, Phys. Rev. B 50, 17953 (1994).
  9. F. Murnaghan, Proc Natl Acad Sci U. S. A. 30(9), 244 (1944).
  10. http://periodictable.com/Elements/026/data.html
  11. H. Faraoun, Y. Zhang, C. Esling, H. Aourag, Journal of Applied Physics 99(9), 093508 (2006). DOI 10.1063/1.2194118.
  12. Z. Lv, S. Sun, P. Jiang, B. Wang, W. Fu, Computational Materials Science 42(4), 692 (2008). DOI 10.1016/j.commatsci.2007.10.007.