# DFT Calculations of the Structural, Mechanical, and Electronic Properties of TiV Alloy Under High Pressure

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{43.5}V

_{49.0}Fe

_{7.5}, and the hydrogen capacity reached up to 3.90 wt% (H/M = 1.90) at 253 K. Meanwhile, Seo et al. [8] reported that the V

_{0.68}Ti

_{0.20}Fe

_{0.12}alloy showed the largest hydrogen capacity of 3.6 wt%, and heat treatment can effectively improve hydrogen capacity, such as that in the V

_{0.375}Ti

_{0.20}Cr

_{0.30}Mn

_{0.075}alloy with a hydrogen capacity of 2.2 wt%. Therefore, as the new hydrogen storage materials, TiV-based alloys have been greatly investigated [4,9,10,11]. However, the structural, mechanical, and electronic properties of TiV alloys remain unrevealed under high pressure due to the complexity of calculations, thereby limiting the applications of TiV alloys under high pressure.

## 2. Methodology

^{2}3p

^{6}3d

^{2}) and V (4s

^{2}3p

^{6}3d

^{3}) are the valence electrons, and the Vanderbilt-type ultrasoft pseudopotentials were applied to address the ion–electron interactions [16]. On the basis of a precise convergence test, the plane–wave cutoff energy was optimized as 400 eV, and the Brillouin-zone k-point grid [17] was selected as 13 × 13 × 13 in the electronic calculations of the TiV alloy. The space group of the TiV alloy belongs to Im-3m, and the symmetric crystal structure of the TiV alloy is shown in Figure 1, and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm [18] was applied in the process of structural geometry optimization with respect to the applied pressures ranging from –10 to 50 GPa. The energy convergence criterion was set at 1.0 × 10

^{−6}eV/atom in self-consistent calculations, and the Hellmann–Feynman force of each atom was lower than 0.01 eV/Å.

## 3. Results and Discussion

#### 3.1. Structural Properties and Stability

#### 3.2. Mechanical Properties

#### 3.3. Anisotropy

#### 3.4. Electronic Properties

## 4. Conclusions

- (1)
- The critical pressure of the structural phase transition for the TiV alloy is 42.05 GPa, and the symmetric crystal structure of the TiV alloy produces structural phase transition when the applied pressure exceeds 42.05 GPa.
- (2)
- The high pressure can improve resistance to volume change, but the biggest resistances to elastic and shear deformation occur under $P=5\text{}\mathrm{GPa}$ for the TiV alloy.
- (3)
- The results of Pugh’s $B/G$ ratio suggest that the TiV alloy is essentially characterized by excellent ductility, and high pressure can enhance the ductility of the TiV alloy.
- (4)
- The $\left(110\right)\left[1\overline{1}0\right]$ direction has stronger resistance to shear deformation than the $\left(100\right)\left[010\right]$ direction, and high pressure improves resistance to elastic deformation in the $\langle 100\rangle $ direction. Cauchy pressure reveals that the atomic bonding of the TiV alloy is mainly the metallic bond, and high pressure leads to strong atomic bonding.
- (5)
- DOS results indicate that the TiV alloy presents metallicity, and high pressure disrupts the structural stability of the TiV alloy, thereby inducing structural phase transition.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Dependencies of dimensionless ratios $a/{a}_{0}$ and $V/{V}_{0}$ on the applied pressure for the TiV alloy.

**Figure 4.**Dependencies of the elastic constants ${C}_{ij}$ on the applied pressure for the TiV alloy.

**Figure 5.**Dependencies of shear modulus $G$, Young’s modulus $E$, and bulk modulus $B$ on the applied pressure for the TiV alloy.

**Figure 12.**Schematic of isosurface contours of charge density for the TiV alloy under different pressures. The isosurface levels are set as 0.0406 ${r}_{0}^{-3}$ (${r}_{0}$: Bohr radius).

TiV Alloy | This Work | Others |
---|---|---|

Lattice constant $a$ (Å) | 3.107 | 3.156 [10], 3.163 [20], 3.165 [21] 3.120 [22], 3.159 [23], 3.140 [24] 3.280 [25] |

**Table 2.**Comparisons of the calculated results with the work of Ikehata et al. [25] at $P=0$ and $T=0$.

TiV Alloy | This Work | Ikehata et al. [25] |
---|---|---|

${C}_{11}$ (GPa) | 178.16 | 169.6 |

${C}_{12}$ (GPa) | 126.92 | 122.3 |

${C}_{44}$ (GPa) | 21.52 | 33.6 |

${C}_{44}$ (GPa) | 144.00 | 138.07 |

Young’s modulus $E$ (GPa) | 65.71 | 81.81 |

Shear modulus $G$ (GPa) | 23.07 | 29.19 |

Poisson’s ratio $\sigma $ | 0.42 | 0.40 |

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**MDPI and ACS Style**

Yu, F.; Liu, Y.
DFT Calculations of the Structural, Mechanical, and Electronic Properties of TiV Alloy Under High Pressure. *Symmetry* **2019**, *11*, 972.
https://doi.org/10.3390/sym11080972

**AMA Style**

Yu F, Liu Y.
DFT Calculations of the Structural, Mechanical, and Electronic Properties of TiV Alloy Under High Pressure. *Symmetry*. 2019; 11(8):972.
https://doi.org/10.3390/sym11080972

**Chicago/Turabian Style**

Yu, Fang, and Yu Liu.
2019. "DFT Calculations of the Structural, Mechanical, and Electronic Properties of TiV Alloy Under High Pressure" *Symmetry* 11, no. 8: 972.
https://doi.org/10.3390/sym11080972