[Paper Review] Ab initio investigations of point and complex defect structures in B2-FeAl

Halil İbrahim Sözen, Tilmann Hickel+1 more|arXiv (Cornell University)|Jan 15, 2021

Intermetallics and Advanced Alloy Properties12 references4 citations

TL;DR

This study uses ab initio density functional theory (DFT) to systematically investigate point and complex defect structures in B2-FeAl, addressing inconsistencies in prior defect formation energy calculations. It identifies the single Fe vacancy as the dominant defect near stoichiometry (up to 1.6% at 1450 K), with double Fe antisites and double Al antisites dominating in Fe-rich and Al-rich regions, respectively, and demonstrates that chemical potential, supercell convergence, and magnetic treatment critically influence defect energetics.

ABSTRACT

In this work we have studied the defect structure and corresponding defect concentration investigations through the theoretical, experimental and computational works on B2-type Fe-Al alloys. We have used ab initio framework in order to investigate the defect structure. To have a proper explanation for high defect concentration in B2-FeAl, we did not confine with point defect, but extend the work on defect complexes. The possible defect formation energies were calculated with the dependence of chemical potential and carefully investigated against supercell size and the effect of magnetism. The calculations revealed that the double Fe antisite at Fe rich condition, the single Fe vacancy at intermediate region (i.e in the stoichiometry) and the double Al antisite is the dominant defect close to Al rich condition, where mainly Al rich region was unstable. From the obtained defect formation energies, defect concentrations were calculated at different temperatures with respect to Al concentration for B2-FeAl. It has been found that increasing Al content and temperature gradually leads to increase in the vacancy content. It has also seen that the dominant defect for all temperature ranges was the single Fe vacancy at the exact stoichiometry and the highest single Fe vacancy content detected with 1.6 % at 1450 K.

Motivation & Objective

• To resolve long-standing discrepancies in reported defect formation energies for B2-FeAl, particularly for Al and Fe vacancies.
• To investigate the role of supercell convergence, non-magnetic Fe approximations, and chemical potential dependence in defect energy calculations.
• To determine the dominant point and complex defect types across varying Al concentrations and temperatures.
• To calculate defect concentrations using consistent thermodynamic models and compare them with experimental data.
• To provide a foundation for future studies on defect kinetics and diffusion mechanisms in B2-FeAl.

Proposed method

• Employed plane-wave DFT within the VASP code using the PAW method and PBE-GGA exchange-correlation functional.
• Conducted calculations with both non-magnetic and ferromagnetic Fe to assess magnetic effects on defect formation energies.
• Used supercells of varying sizes (up to 128 atoms) to ensure convergence of defect formation energies.
• Calculated defect formation energies as a function of chemical potential for Fe and Al to model non-stoichiometric conditions.
• Applied the grand canonical ensemble approach to compute defect concentrations using the standard thermodynamic relation for defect equilibria.
• Validated results against experimental lattice parameters, bulk modulus, and cohesive energy from literature.

Experimental results

Research questions

• RQ1 Why do previous defect formation energy calculations for B2-FeAl show such a wide range of values, especially for Al vacancies?
• RQ2 How do supercell size, magnetic state of Fe, and chemical potential dependence affect the calculated defect formation energies?
• RQ3 Which point and complex defects dominate in Fe-rich, stoichiometric, and Al-rich B2-FeAl under high-temperature conditions?
• RQ4 What is the predicted defect concentration profile across varying Al content and temperature (1000 K and 1450 K)?
• RQ5 To what extent does the B2 structure remain stable in Al-rich conditions, and what defects drive its instability?

Key findings

• The single Fe vacancy is the dominant defect at stoichiometric composition, reaching a maximum concentration of 1.6% at 1450 K.
• In Fe-rich conditions, the double Fe antisite is the dominant defect, with calculated concentrations of ~3.8% at 1000 K and ~5% at 1450 K, showing good agreement with experimental data.
• In Al-rich conditions, the double Al antisite becomes dominant, and the B2 structure is predicted to be unstable beyond ~50.5 at.% Al due to negative formation energy for this complex defect.
• The Al vacancy has the highest formation energy (orders of magnitude higher than other defects), resulting in negligible concentrations across all conditions.
• Defect formation energies are highly sensitive to chemical potential, supercell size, and the treatment of Fe magnetism, which explains much of the variability in prior literature.
• The single Fe vacancy remains dominant from stoichiometry up to ~52 at.% Al at 1000 K and up to ~57 at.% Al at 1450 K, indicating a broad stability window for this defect type.