#
Impact of Disorder on Properties of Vacancies: A Case Study of B2 and A2 Polymorphs of Non-Stoichiometric Fe_{2}CoAl

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## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Schematic visualizations of our computational supercells representing the B2 phase (

**a**) and A2 phase (

**b**) of Fe${}_{2}$CoAl (some atoms, such as those in the vertices, are shown with their periodic images). The B2 phase exhibits two sublattices—one occupied by an equal amount of Fe and Co, while the other by equal amounts of Fe and Al.

**Figure 2.**Computed directional dependences of Young’s modulus for both the B2 phase (

**a**) and A2 phase (

**b**) illustrating single-crystal elastic properties. Please mind different ranges of values corresponding to the same color scale.

**Figure 3.**Calculated directional dependence of the minimum and maximum value of Poisson ratio of the A2 phase (

**a**) together with a cut in the x-z plane (

**b**). The negative values, indicating auxetic properties, are visualized using red color and a few examples are pointed at by red arrows.

**Figure 4.**Schematic visualizations of local magnetic moments for the B2 (

**a**) and A2 (

**b**) phase. The magnitudes of local magnetic moments are indicated by the diameter of the spheres representing the atoms with an example of the scaling shown for one particular Fe atom (2.5 ${\mu}_{\mathrm{B}}$) in part (

**a**).

**Figure 5.**Computed formation energies of Fe vacancies in the B2 (

**a**) and A2 (

**b**) phase together with the changes of the total magnetic moment of the whole supercell of the B2 (

**c**) and A2 (

**d**) phase (compared with a hypothetical reduction by the magnetic moment of one FM bcc Fe atom, 2.2 ${\mu}_{\mathrm{B}}$, see the horizontal dashed line) and the vacancy-induced volumetric change for both the B2 (

**e**) and A2 (

**f**) phase.

**Figure 6.**Calculated formation energies of Co vacancies in the B2 (

**a**) and A2 (

**b**) phase together with the changes of the total magnetic moment of the whole supercell of the B2 (

**c**) and A2 (

**d**) phase of Fe${}_{2}$CoAl (compared with a hypothetical reduction by the magnetic moment of one FM hcp Co atom, 1.5 ${\mu}_{\mathrm{B}}$, see the horizontal dashed line) and the vacancy-induced volumetric change for both the B2 (

**e**) and A2 (

**f**) phase.

**Figure 7.**Computed formation energies of Al vacancies in the B2 (

**a**) and A2 (

**b**) phase together with the changes of the total magnetic moment of the whole supercell representing the B2 (

**c**) and A2 (

**d**) phase and the vacancy-induced volumetric changes for both the B2 (

**e**) and A2 (

**f**) phase.

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## Share and Cite

**MDPI and ACS Style**

Friák, M.; Pavlů, J.; Šob, M. Impact of Disorder on Properties of Vacancies: A Case Study of B2 and A2 Polymorphs of Non-Stoichiometric Fe_{2}CoAl. *Crystals* **2021**, *11*, 1207.
https://doi.org/10.3390/cryst11101207

**AMA Style**

Friák M, Pavlů J, Šob M. Impact of Disorder on Properties of Vacancies: A Case Study of B2 and A2 Polymorphs of Non-Stoichiometric Fe_{2}CoAl. *Crystals*. 2021; 11(10):1207.
https://doi.org/10.3390/cryst11101207

**Chicago/Turabian Style**

Friák, Martin, Jana Pavlů, and Mojmír Šob. 2021. "Impact of Disorder on Properties of Vacancies: A Case Study of B2 and A2 Polymorphs of Non-Stoichiometric Fe_{2}CoAl" *Crystals* 11, no. 10: 1207.
https://doi.org/10.3390/cryst11101207