#
Influence of Chemical Substitution and Light Element Insertion on the Magnetic Properties of Nanocrystalline Pr_{2}Co_{7} Compound

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## Abstract

**:**

_{3}/mmc) into an orthorhombic (Pbcn) and monoclinic (C2/c) structure during hydrogenation. The absorption of H by the Pr${}_{2}$Co${}_{7}$ compound led to an increase in the T${}_{C}$ value from 600 K at x = 0 to 691 K at x = 3.75. The Pr${}_{2}$Co${}_{7}$H${}_{0.25}$ hydride had optimal magnetic properties: H${}_{c}$ = 6.1 KOe, (BH)${}_{\mathrm{max}}$ = 5.8 MGOe, and T${}_{C}$ = 607 K. We tailored the mean field theory (MFT) and random magnetic anisotropy (RMA) methods to investigate the magnetic moments, exchange interactions, and magnetic anisotropy properties. The relationship between the microstructure and magnetic properties is discussed. The obtained results provide a fundamental reference for adapting the magnetic properties of the Pr${}_{2}$Co${}_{7}$, Pr${}_{2}$Co${}_{6.5}$Fe${}_{0.5}$, Pr${}_{2}$Co${}_{7}$C${}_{0.25}$, and Pr${}_{2}$Co${}_{7}$H${}_{0.25}$ compounds for potential permanent nanomagnets, high-density magnetic recording, and magnetic refrigeration applications.

## 1. Introduction

## 2. Synthesis Methods of Pr${}_{\mathbf{2}}$Co${}_{\mathbf{7}}$, Pr${}_{\mathbf{2}}$Co${}_{\mathbf{7}-\mathbf{x}}$Fe${}_{\mathbf{x}}$, Pr${}_{\mathbf{2}}$Co${}_{\mathbf{x}}$C${}_{\mathbf{x}}$, and Pr${}_{\mathbf{2}}$Co${}_{\mathbf{x}}$H${}_{\mathbf{x}}$ Samples

## 3. Structural, Microstructural, and Magnetic Characterizations of the Samples

## 4. Structural Properties

#### 4.1. Nanocrystalline Pr${}_{2}$Co${}_{7}$ Compound

#### 4.2. Nanocrystalline Pr${}_{2}$Co${}_{7-x}$Fe${}_{x}$ (x = 0, 0.25, 0.5, 0.75, and 1) Compounds

#### 4.3. Structural Analysis of Nanocrystalline Pr${}_{2}$Co${}_{7-x}$Fe${}_{x}$ Compounds with EXAFS

#### 4.4. Nanocrystalline Pr${}_{2}$Co${}_{7}$C${}_{x}$ (x = 0–1) Compounds

#### 4.5. Nanocrystalline Pr${}_{2}$Co${}_{7}$H${}_{x}$ (x = 0–10.8) Compounds

## 5. Intrinsic Magnetic Properties

#### 5.1. Nanocrystalline Pr${}_{2}$Co${}_{7-x}$Fe${}_{x}$ (x = 0, 0.25, 0.5, 0.75, and 1) Compounds

#### 5.2. Nanocrystalline Pr${}_{2}$Co${}_{7}$C${}_{x}$ (x = 0–1) Compounds

#### 5.3. Nanocrystalline Pr${}_{2}$Co${}_{7}$H${}_{x}$ (x = 0–10.8) Hydrides

#### 5.4. Mean Field Theory (MFT) and Random Magnetic Anisotropy (RMA) Analysis

#### 5.4.1. Nanocrystalline Pr${}_{2}$Co${}_{7}$C${}_{x}$ (x = 0–1) Compounds

#### 5.4.2. Nanocrystalline Pr${}_{2}$Co${}_{7}$H${}_{x}$ (x = 0–10.8) Hydrides

#### 5.5. Magnetocaloric Effect of the Nanocrystalline Pr${}_{2}$Co${}_{7}$ Compound

## 6. Extrinsic Magnetic Properties

#### 6.1. Nanocrystalline Pr${}_{2}$Co${}_{7-x}$Fe${}_{x}$ (x = 0, 0.25, 0.5, 0.75, and 1) Compounds

#### 6.2. Nanocrystalline Pr${}_{2}$Co${}_{7}$C${}_{x}$ (x = 0–1) Compounds

#### 6.3. Nanocrystalline Pr${}_{2}$Co${}_{7}$H${}_{x}$ (x = 0–10.8) Hydrides

## 7. Conclusions

_{3}/mmc) structure to an orthorhombic (Pbcn) and monoclinic (C2/c) structure during hydrogenation. The absorption of hydrogen by the Pr${}_{2}$Co${}_{7}$ compound led to an increase in T${}_{C}$ from 600 K at x = 0 to 691 K at x = 3.75. The Pr${}_{2}$Co${}_{7}$H${}_{0.25}$ hydride had the best magnetic properties: H${}_{c}$ = 6.1 KOe, (BH)${}_{\mathrm{max}}$ = 5.8 MGOe, M${}_{r}$ = 40 emu/g, and T${}_{C}$ = 607 K. We adapted the MFT and RMA methods to investigate the magnetic moments, exchange interactions, and magnetic anisotropy properties. The correlations between microstructure and magnetic properties were discussed. The obtained results could provide a reference for tailoring the magnetic properties of the Pr${}_{2}$Co${}_{7}$, Pr${}_{2}$Co${}_{6.5}$Fe${}_{0.5}$, Pr${}_{2}$Co${}_{7}$C${}_{25}$, and Pr${}_{2}$Co${}_{7}$H${}_{0.25}$ compounds for potential permanent nanomagnets, high-density magnetic media, magnetic refrigeration applications, and hydrogen storage.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

EDS | Energy-Dispersive X-ray Spectroscopy |

EXAFS | Extended X-Ray Absorption Fine Structure |

${H}_{c}$ | Coercive Field |

HRTEM | High-Resolution Transmission Electron Microscopy |

${M}_{r}$ | Remanent Magnetization |

STEM | Scanning Transmission Electron Microscopy |

${T}_{C}$ | Curie Temperature |

MFT | Mean Field Theory |

RMA | Random Magnetic Anisotropy |

RCP | Relative Cooling Power |

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**Figure 1.**Bright-field micrography of the Pr${}_{2}$Co${}_{6.25}$Fe${}_{0.75}$ compound (

**a**). The grain size distribution is shown in the inset (

**b**).

**Figure 2.**HRTEM images (the selected area of electron diffraction is shown in the inset): (

**a**) Pr${}_{2}$Co${}_{6.25}$Fe${}_{0.75}$ and (

**b**) Pr${}_{2}$Co${}_{6}$Fe${}_{1}$ compounds annealed at 1023 K. Elemental mapping of Pr${}_{2}$Co${}_{6.25}$Fe${}_{0.75}$: (

**c**) Pr, (

**d**) Co and (

**e**) Fe.

**Figure 3.**Experimental EXAFS spectra in k space of the imaginary part of the Fourier transforms of the Pr${}_{2}$Co${}_{6.5}$Fe${}_{0.5}$ compound, adjusted using Models 1 and 4. Black and red lines show the experimental signal and theoretical curves, respectively.

**Figure 4.**Bright-field micrographs of Pr${}_{2}$Co${}_{7}$C${}_{0.75}$ (

**a**). The grain size distribution is shown in the inset (

**b**).

**Figure 5.**(

**a**) Bright-field TEM image of the nanocrystalline Pr${}_{2}$Co${}_{7}$C${}_{0.75}$ compound. (

**b**) High-resolution image of the area in between grains shown in the green square in (

**a**). (

**c**) The EDS line profile presented as a function of the distance d from point A.

**Figure 7.**Position of the Co${}_{1}$ atom in the orthorhombic ($Pbcn$) and monoclinic ($C2/c$) structures projected in the ≺1 0 1≻ direction.

**Figure 9.**(

**a**) Calculated change in the magnetic moments (M${}_{Pr}$(T), M${}_{Co}$(T)) and magnetization (M(T)) of the nanocrystalline Pr${}_{2}$Co${}_{7}$C${}_{0.25}$ compound. (

**b**) The solid lines are the M(T) of nanocrystalline Pr${}_{2}$Co${}_{7}$C${}_{x}$ found calculated in the MFT analysis. The symbols show the experimental data.

**Figure 10.**The magnetization curves M(H) of the nanocrystalline Pr${}_{2}$Co${}_{7}$C${}_{x}$ compounds (x = 0, 0.25, 0.5, 0.75, and 1). The solid lines show the fit to the experimental data (symbols).

**Figure 11.**The experimental data on the coercivity H${}_{c}$ as a function of $\xi $ = ${\left(A{K}_{1}\right)}^{1/2}$.

**Figure 12.**Magnetic entropy $\Delta {S}_{M}$(T) around the Curie temperature T${}_{C}$ for the 2:7 H structure.

**Figure 13.**Magnetic entropy $\Delta {S}_{M}$(T) around the Curie temperature T${}_{C}$ for the 2:7 R structure.

**Figure 14.**Hysteresis loops of the Pr${}_{2}$Co${}_{7}$, Pr${}_{2}$Co${}_{7}$C${}_{0.25}$, and Pr${}_{2}$Co${}_{7}$C${}_{0.75}$ compounds, measured at 293 K.

**Figure 15.**(

**a**) The evolution of the coercivity H${}_{c}$ as a function of annealing temperature T${}_{a}$ of the Pr${}_{2}$Co${}_{7}$C${}_{x}$ compounds ($x=0,0.25$). (

**b**) The grain size as a function of C content x is shown in the inset.

**Table 1.**Structural data from the Rietveld analysis of nanocrystalline Pr${}_{2}$Co${}_{7-x}$Fe${}_{x}$ compounds.

x | 0.0 | 0.25 | 0.5 | 0.75 | 1 |
---|---|---|---|---|---|

a (Å) | 5.068(3) | 5.068(2) | 5.076(3) | 5.078(1) | 5.102(2) |

c (Å) | 24.458(2) | 24.462(4) | 24.473(5) | 24.474(3) | 24.475(4) |

c/a | 4.826 | 4.827 | 4.822 | 4.826 | 4.785 |

V(Å${}^{3}$) | 544.02 | 544.08 | 546.09 | 546.56 | 550.18 |

${R}_{B}$ | 3.2 | 2.7 | 1.7 | 2.865 | 2.437 |

${\chi}^{2}$ | 3.80 | 3.72 | 3.58 | 3.52 | 3.68 |

**Table 2.**The interatomic distance (R) and coordination number (N) found with the FEFF6 software package for different possible positions of Fe for the Pr${}_{2}$Co${}_{6.5}$Fe${}_{0.5}$ compound.

Number | Shell | N | R(Å) |
---|---|---|---|

Fe in-12k | |||

1 | Fe-Co | 7 | 2.50 |

2 | Fe-Pr | 3 | 2.91 |

3 | Fe-Pr | 2 | 3.29 |

Fe in 6h-site | |||

1 | Fe-Co | 8 | 2.49 |

2 | Fe-Pr | 4 | 3.17 |

**Table 3.**EXAFS adjustment parameters for Pr${}_{2}$Co${}_{7-x}$Fe${}_{x}$ (x = 0.5, 0.75, and 1): interatomic distances (R), quality factor (QF), and Debye–Waller factor (${\sigma}^{2}$).

x = 0.5 | x = 0.75 | x = 1 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

N | ${\mathit{\sigma}}^{2}$(Å${}^{2}$) | R(Å) | QF | N | ${\mathit{\sigma}}^{2}$(Å${}^{2}$) | R(Å) | QF | N | ${\mathit{\sigma}}^{2}$(Å${}^{2}$) | R(Å) | QF | |

Model 1 (12) | ||||||||||||

Fe-Co | 7 | 0.008(1) | 2.48(1) | 0.71 | 7 | 0.010(1) | 2.49(1) | 1.13 | 7 | 0.011(1) | 2.50(1) | 1.21 |

Fe-Pr | 3 | 0.010(1) | 2.96(2) | 3 | 0.011(3) | 2.95(2) | 3 | 0.012(4) | 2.94(3) | |||

Fe-Pr | 2 | 0.010(1) | 3.21(4) | 2 | 0.011(3) | 3.18(5) | 2 | 0.012(4) | 3.14(4) | |||

Model 4 (6h) | ||||||||||||

Fe-Co | 8 | 0.010(1) | 2.49(1) | 2.43 | 8 | 0.012(1) | 2.49(1) | 2.65 | 8 | 0.012(1) | 2.49(1) | 3.90 |

Fe-Pr | 4 | 0.017(6) | 3.01(4) | 4 | 0.016(4) | 3.02(3) | 4 | 0.024(3) | 3.04(4) |

($\mathit{\rho}\%/{\mathbf{QF}}_{\mathit{R}}$) | ($\mathit{\rho}\%/{\mathbf{QF}}_{2.3\u20133.5}$) | |
---|---|---|

Model 1 | 1.2/4.9 | 0.18/2.3 |

Model 4 | 2.91/12.3 | 5.8 / 70.1 |

**Table 5.**Structural data obtained by the Rietveld analysis of Pr${}_{2}$Co${}_{7}$C${}_{x}$ (x = 0.25, 0.50, 0.75, 1) compounds.

x | 0.0 | 0.25 | 0.5 | 0.75 | 1 |
---|---|---|---|---|---|

a (Å) | 5.068(1) | 5.070(3) | 5.076(1) | 5.079(11) | 5.080(2) |

c (Å) | 24.456(2) | 24.509(5) | 25.009(3) | 25.576(4) | 26.981(2) |

c/a | 4.825 | 4.832 | 4.841 | 5.035 | 5.311 |

V(Å${}^{3}$) | 544.02 | 547 | 555 | 567.4 | 598.9 |

${R}_{B}$ | 3.1 | 2.43 | 1.31 | 2.76 | 2.42 |

${\chi}^{2}$ | 3.80 | 3.28 | 3.60 | 3.38 | 3.36 |

**Table 6.**The values of M${}_{s}$, the factors $\sigma $ and $\rho $, the field H${}_{a}$(kOe), H${}_{u}$(kOe), H${}_{ex}$(kOe), ${A}_{ex}$, and d${}_{c}$ (nm) for the nanocrystalline Pr${}_{2}$Co${}_{7}$C${}_{x}$ (x = 0, 0.25, 0.5, 0.75, 1) compounds, measured at 293 K.

$\mathit{\delta}$ | M${}_{\mathit{S}}$ | $\mathit{\sigma}$ | $\mathit{\rho}$ | H${}_{\mathit{a}}$ | H${}_{\mathit{u}}$ | H${}_{\mathbf{ex}}$ | ${\mathit{A}}_{\mathbf{ex}}$ | d${}_{\mathit{c}}$ |
---|---|---|---|---|---|---|---|---|

0 | 55 | 3450 | 12.5 | 227.48 | −37.12 | 42.39 | 1.15 | 15 |

0.25 | 60 | 3000 | 9 | 212.13 | −43.38 | 48.07 | 1.81 | 22 |

0.50 | 65 | 2600 | 8 | 197.48 | −44.17 | 47.27 | 2.05 | 35 |

0.75 | 70 | 2300 | 7 | 185.74 | −45.25 | 47.61 | 2.57 | 60 |

1 | 73 | 1900 | 5 | 168.81 | −51.41 | 52.46 | 3.04 | 134 |

**Table 7.**The saturation magnetization M${}_{s}$, factors $\sigma $ and $\rho $, magnetic anisotropy field H${}_{a}$(kOe), coherent anisotropy field H${}_{u}$(kOe), exchange field H${}_{ex}$(kOe), exchange constant ${A}_{ex}$, and distance d${}_{c}$ (nm) values for the nanocrystalline Pr${}_{2}$Co${}_{7}$H${}_{x}$ hydrides, measured at 293 K.

$\mathit{\delta}$ | M${}_{\mathit{S}}$ | $\mathit{\sigma}$ | $\mathit{\rho}$ | H${}_{\mathit{a}}$ | H${}_{\mathit{u}}$ | H${}_{\mathbf{ex}}$ | ${\mathit{A}}_{\mathbf{ex}}$ | d${}_{\mathit{c}}$ |
---|---|---|---|---|---|---|---|---|

0 | 55 | 3450 | 12.5 | 227.48 | −3.712 | 42.39 | 1.15 | 15 |

0.25 | 65 | 2500 | 9 | 212.13 | −4.009 | 48.07 | 1.45 | 21 |

2.50 | 77 | 3100 | 8.92 | 197.48 | −4.817 | 47.27 | 2.04 | 31 |

3.75 | 74 | 2200 | 6.91 | 197.48 | −5.122 | 47.27 | 2.05 | 33 |

6.10 | 70.63 | 2108 | 6.02 | 185.74 | −5.253 | 47.61 | 2.56 | 56 |

10.8 | 56.57 | 1957 | 5.23 | 168.81 | −5.495 | 52.46 | 3.07 | 112 |

**Table 8.**Extrinsic magnetic properties of Pr${}_{2}$Co${}_{7-x}$Fe${}_{x}$ at T = 293 K: H${}_{c}$ (kOe), M${}_{r}$ (emu/g), and (BH)${}_{\mathrm{max}}$ (MGOe).

x | H${}_{\mathit{c}}$ | M${}_{\mathit{r}}$ | (BH)${}_{\mathbf{max}}$ |
---|---|---|---|

0.25 | 12 | 48 | 9.1 |

0.5 | 11.5 | 43 | 9 |

0.75 | 6.5 | 41 | 5.5 |

1.00 | 2 | 40 | 1.3 |

x | 0 | 0.25 | 0.50 | 0.75 | 1 |
---|---|---|---|---|---|

${H}_{c}$ (kOe) | 11 | 17.5 | 6.1 | 1.5 | 0.95 |

${M}_{r}$ (emu/g) | 36 | 43 | 41 | 41 | 40 |

(BH)${}_{\mathrm{max}}$ (MGOe) | 11.8 | 12.5 | 5.3 | 3.1 | 1.1 |

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**MDPI and ACS Style**

Fersi, R.; Mliki, N.; Bessais, L.
Influence of Chemical Substitution and Light Element Insertion on the Magnetic Properties of Nanocrystalline Pr_{2}Co_{7} Compound. *Magnetochemistry* **2022**, *8*, 20.
https://doi.org/10.3390/magnetochemistry8020020

**AMA Style**

Fersi R, Mliki N, Bessais L.
Influence of Chemical Substitution and Light Element Insertion on the Magnetic Properties of Nanocrystalline Pr_{2}Co_{7} Compound. *Magnetochemistry*. 2022; 8(2):20.
https://doi.org/10.3390/magnetochemistry8020020

**Chicago/Turabian Style**

Fersi, Riadh, Najeh Mliki, and Lotfi Bessais.
2022. "Influence of Chemical Substitution and Light Element Insertion on the Magnetic Properties of Nanocrystalline Pr_{2}Co_{7} Compound" *Magnetochemistry* 8, no. 2: 20.
https://doi.org/10.3390/magnetochemistry8020020