# Impact of Nano-Scale Distribution of Atoms on Electronic and Magnetic Properties of Phases in Fe-Al Nanocomposites: An Ab Initio Study

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## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Results for Individual Phases

## 4. Results for Nanocomposites

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Atomic positions (expressed as fractions of supercell dimensions) within the computational supercells shown in Figure 1. Aluminium positions are the first six rows in the case of Fe-Al variants and the first eight rows in the case of Fe${}_{3}$Al.

Fe-Al SQS | Fe-Al SQS no 1NN | Fe-Al SQS no 1&2NN | Fe${}_{3}$Al | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | $\sqrt{\mathbf{2}}$/2 | 1 | 1 | $\sqrt{\mathbf{2}}$/2 | 1 | 1 | $\sqrt{\mathbf{2}}$/2 | 1 | 1 | $\sqrt{\mathbf{2}}$/2 |

0.75 | 0.75 | 0.50 | 0.50 | 0.75 | 0.25 | 0.25 | 0.00 | 0.75 | 0.25 | 0.00 | 0.75 |

0.25 | 0.00 | 0.75 | 0.75 | 0.00 | 0.75 | 0.25 | 0.50 | 0.75 | 0.75 | 0.00 | 0.75 |

0.50 | 0.75 | 0.75 | 0.25 | 0.00 | 0.25 | 0.00 | 0.25 | 0.25 | 0.25 | 0.50 | 0.75 |

0.00 | 0.75 | 0.75 | 0.25 | 0.50 | 0.25 | 0.00 | 0.75 | 0.25 | 0.75 | 0.50 | 0.75 |

0.25 | 0.50 | 0.25 | 0.50 | 0.25 | 0.25 | 0.50 | 0.25 | 0.25 | 0.00 | 0.25 | 0.25 |

0.50 | 0.50 | 0.50 | 0.50 | 0.25 | 0.75 | 0.50 | 0.75 | 0.25 | 0.00 | 0.75 | 0.25 |

0.50 | 0.25 | 0.25 | 0.75 | 0.50 | 0.75 | 0.75 | 0.50 | 0.75 | 0.50 | 0.25 | 0.25 |

0.75 | 0.50 | 0.25 | 0.00 | 0.75 | 0.75 | 0.75 | 0.00 | 0.75 | 0.50 | 0.75 | 0.25 |

0.00 | 0.25 | 0.75 | 0.50 | 0.75 | 0.75 | 0.00 | 0.25 | 0.75 | 0.00 | 0.25 | 0.75 |

0.00 | 0.75 | 0.25 | 0.00 | 0.75 | 0.25 | 0.00 | 0.75 | 0.75 | 0.00 | 0.75 | 0.75 |

0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.25 | 0.50 | 0.25 | 0.75 | 0.50 | 0.25 | 0.75 |

0.00 | 0.25 | 0.25 | 0.75 | 0.00 | 0.25 | 0.50 | 0.75 | 0.75 | 0.50 | 0.75 | 0.75 |

0.25 | 0.00 | 0.25 | 0.25 | 0.50 | 0.75 | 0.25 | 0.00 | 0.25 | 0.25 | 0.00 | 0.25 |

0.50 | 0.75 | 0.25 | 0.75 | 0.50 | 0.25 | 0.75 | 0.00 | 0.25 | 0.75 | 0.00 | 0.25 |

0.75 | 0.75 | 0.00 | 0.25 | 0.00 | 0.75 | 0.25 | 0.50 | 0.25 | 0.25 | 0.50 | 0.25 |

0.25 | 0.50 | 0.75 | 0.00 | 0.25 | 0.75 | 0.75 | 0.50 | 0.25 | 0.75 | 0.50 | 0.25 |

0.75 | 0.50 | 0.75 | 0.75 | 0.75 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

0.00 | 0.50 | 0.00 | 0.50 | 0.50 | 0.50 | 0.50 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 |

0.50 | 0.25 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.50 | 0.00 |

0.75 | 0.00 | 0.25 | 0.75 | 0.75 | 0.00 | 0.50 | 0.50 | 0.00 | 0.50 | 0.50 | 0.00 |

0.25 | 0.25 | 0.50 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.50 |

0.50 | 0.00 | 0.50 | 0.25 | 0.25 | 0.50 | 0.50 | 0.00 | 0.50 | 0.50 | 0.00 | 0.50 |

0.00 | 0.00 | 0.50 | 0.50 | 0.00 | 0.50 | 0.00 | 0.50 | 0.50 | 0.00 | 0.50 | 0.50 |

0.50 | 0.50 | 0.00 | 0.00 | 0.00 | 0.50 | 0.50 | 0.50 | 0.50 | 0.50 | 0.50 | 0.50 |

0.25 | 0.25 | 0.00 | 0.50 | 0.50 | 0.00 | 0.25 | 0.25 | 0.00 | 0.25 | 0.25 | 0.00 |

0.75 | 0.25 | 0.00 | 0.25 | 0.25 | 0.00 | 0.75 | 0.25 | 0.00 | 0.75 | 0.25 | 0.00 |

0.25 | 0.75 | 0.00 | 0.75 | 0.25 | 0.00 | 0.25 | 0.75 | 0.00 | 0.25 | 0.75 | 0.00 |

0.75 | 0.00 | 0.75 | 0.25 | 0.75 | 0.00 | 0.75 | 0.75 | 0.00 | 0.75 | 0.75 | 0.00 |

0.50 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.25 | 0.25 | 0.50 | 0.25 | 0.25 | 0.50 |

0.75 | 0.25 | 0.50 | 0.75 | 0.25 | 0.50 | 0.75 | 0.25 | 0.50 | 0.75 | 0.25 | 0.50 |

0.25 | 0.75 | 0.50 | 0.25 | 0.75 | 0.50 | 0.25 | 0.75 | 0.50 | 0.25 | 0.75 | 0.50 |

0.00 | 0.50 | 0.50 | 0.00 | 0.50 | 0.50 | 0.75 | 0.75 | 0.50 | 0.75 | 0.75 | 0.50 |

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**Figure 1.**Schematic visualization of the 32-atom supercells used in our calculations: (

**a**) a general special quasi-random structure (SQS) model for the Fe-Al phase (with 18.75 at.% Al), (

**b**) an SQS model for the Fe-Al phase without any 1st nearest-neighbor (NN) Al-Al pairs, (

**c**) an SQS model for the Fe-Al phase without the 1st and 2nd NN Al-Al pairs and (

**d**) a 32-atom supercell of the Fe${}_{3}$Al intermetallics. The unrelaxed atomic positions are listed in Table A1 in the Appendix.

**Figure 2.**Schematic visualization of local atomic magnetic moments calculated for individual phases (see Figure 1): (

**a**–

**c**) are SQS models for the Fe-Al phase with different atomic arrangements and (

**d**) for the Fe${}_{3}$Al. The moments are visualized so that the diameters of the spheres reflect the magnitudes of the local magnetic moments (a few examples are in parts (

**b**,

**d**) in ${\mathsf{\mu}}_{\mathrm{B}}$). Magnetic moments of Al atoms are so small, less than 0.05 ${\mathsf{\mu}}_{\mathrm{B}}$, that they are shown only as blue dots.

**Figure 3.**Dependences of local magnetic moments of Fe atoms in all studied phases (shown in Figure 1) as functions of concentration of Al atoms in the 1st (

**a**) and the 2nd (

**b**) coordination shell, respectively.

**Figure 4.**Calculated dependences of the density of states (DOS) of the Fe atoms at the Fermi level ${E}_{\mathrm{F}}$ in the case of NM states as a function of the Al concentration in the 1st (

**a**) and the 2nd (

**b**) coordination shell, respectively. Part (

**c**) shows the DOS of the Fe atoms at the ${E}_{\mathrm{F}}$ in the case of NM states as a function of their local magnetic moments in the case of FM states.

**Figure 5.**The dependences of local magnetic moments of Fe atoms on the density of states of these atoms (A and B represent coefficients in a linear fit $y=A$ × $x+B$ and ${r}^{2}$ is the coefficient of determination): (

**a**) a general Fe-Al SQS, (

**b**) an SQS without the first NN Al-Al pairs, (

**c**) Fe-rich Fe${}_{3}$Al without the first and the second nearest neighbour Al-Al pairs, and (

**d**) Fe${}_{3}$Al.

**Figure 6.**Calculated total densities of states (TDOS) in the case of the 32-atom supercells as models for individual phases: figures (

**a**–

**c**) are SQS models for the Fe-Al phase with different atomic arrangements and figure (

**d**) for the Fe${}_{3}$Al intermetallic compound.

**Figure 7.**Visualization of nanocomposite supercells for the (001) interface plane. The figures show how the Fe${}_{3}$Al intermetallic compound is combined with different models of the Fe-Al phase with 18.75 at.% Al, in particular the general SQS (A2-like) model (

**a**), the SQS model without the 1st NN Al-Al pairs, B2-like, (

**b**) and the SQS without the 1st and 2nd NN Al-Al pairs, D0${}_{3}$-like (

**c**).

**Figure 8.**The same as in Figure 7 but for nanocomposite supercells with the (110) interface plane.

**Figure 9.**Differences in the magnitude of local magnetic moments of Fe atoms induced by the interfaces within the nanocomposites. They are visualized by the diameter of spheres representing individual Fe atoms (two are listed in subfigure (

**h**)). Gold (black) color of the spheres indicate positive (negative) changes. The sub-figures (

**a**,

**d**,

**g**) correspond to the nanocomposites shown in Figure 7a–c, respectively, the sub-figures (

**b**,

**e**,

**h**) to those in Figure 8a–c, respectively, and the sub-figures (

**c**,

**f**,

**i**) corresponds to the nanocomposites with the (1$\overline{1}$0) orientation of the interfaces (not shown). Please note that due to the fact that the differences are rather small, the scaling connecting the value of the difference and the diameter of the spheres is three times bigger than the scaling applied in Figure 2.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Miháliková, I.; Friák, M.; Jirásková, Y.; Holec, D.; Koutná, N.; Šob, M.
Impact of Nano-Scale Distribution of Atoms on Electronic and Magnetic Properties of Phases in Fe-Al Nanocomposites: An Ab Initio Study. *Nanomaterials* **2018**, *8*, 1059.
https://doi.org/10.3390/nano8121059

**AMA Style**

Miháliková I, Friák M, Jirásková Y, Holec D, Koutná N, Šob M.
Impact of Nano-Scale Distribution of Atoms on Electronic and Magnetic Properties of Phases in Fe-Al Nanocomposites: An Ab Initio Study. *Nanomaterials*. 2018; 8(12):1059.
https://doi.org/10.3390/nano8121059

**Chicago/Turabian Style**

Miháliková, Ivana, Martin Friák, Yvonna Jirásková, David Holec, Nikola Koutná, and Mojmír Šob.
2018. "Impact of Nano-Scale Distribution of Atoms on Electronic and Magnetic Properties of Phases in Fe-Al Nanocomposites: An Ab Initio Study" *Nanomaterials* 8, no. 12: 1059.
https://doi.org/10.3390/nano8121059