# A DFT Study of Hydrogen Storage in High-Entropy Alloy TiZrHfScMo

^{1}

^{2}

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^{†}

## Abstract

**:**

## 1. Introduction

_{3}TiNi

_{2}[4], and Zr(Cr

_{0.5}Ni

_{0.5})

_{2}[5] have been taken as promising materials for hydrogen storage due to their high volume density, safety, and reversibility [6]. In particular, high-entropy alloys (HEAs) with a body-centered cubic (BCC) structure have become one of the most developed groups of new materials [7].

^{−1}mol

^{−1}and the atomic radius differences (θ) should be smaller than 6.6%. Here, θ is defined as:

_{i}is the atomic radius of element i, C

_{i}is the percentage of each component of the alloy, and $\overline{r}\left({\sum}_{i=1}^{n}{C}_{i}\xb7{r}_{i}\right)$ is the average atomic radius. The large lattice distorsion for high θ value (>6.6%) may lead to the formation of intermetallic precipitations, such as Laves phases [10,11].

_{2}) at 299 °C and the maximum measured hydrogen storage capacity is 2.7 wt.%. Karlsson et al. [14] studied the hydrogenation mechanism of the TiZrHfVNb HEA under different pressure and temperature conditions, and found that the large lattice distortions caused by atomic radius difference in the HEA are favorable for absorption in both octahedral and tetrahedral sites.

_{mix}), and the entropy of mixing (ΔS

_{mix}) for TiZrHfScMo alloy were 4.87%, 2.24 KJ/mol, and 13.4 J/(K·mol), respectively, satisfying the criteria for HEA proposed by Zhang et al. [11]. It is expected that this HEA could favor efficient hydrogen storage. A density functional theory (DFT) method was used to investigate the structural and electronic properties of hydrogenated TiZrHfScMo with different hydrogen concentrations and evaluate its potential as a hydrogen storage material. The present study may open up new possibilities for hydrogen storage based on this HEA and promote further theoretical and experimental investigations of the related topic.

## 2. Computational and Experimental Details

^{3}4s

^{1}for Ti, 4s

^{2}4p

^{6}4d

^{3}5s

^{1}for Zr, 5d

^{3}6s

^{1}for Hf, 3d

^{2}4s

^{1}for Sc, 4d

^{5}5s

^{1}for Mo, and 1s

^{1}for H. The cutoff energy of the plane waves is 650 eV and the Brillouin zone integration is performed by the Monkhorst–Pack scheme with a 2 × 2 × 2 k-point mesh. For the BCC TiZrHfScMo HEA, we employ a 5 × 5 × 2 supercell containing 100 atoms. Eleven compositions are considered for hydrogenated HEA (i.e., TiZrHfScMo-H

_{x}), with x varying from 0.25 to 10. For each composition, we generate 100 different configurations using the Python program and determine the most energetically stable configuration by structural optimization. In the total energy calculations, the energy and force convergence limits are 1 × 10

^{−4}eV/atom and −1 × 10

^{−3}eV/Å, respectively.

^{2}in the Zeiss Auriga workstation (Jena, Germany). The samples for EBSD measurements are carefully prepared by mechanical grinding using diamond abrasive paper and subsequent final polishing using a vibratory polisher.

## 3. Results and Discussion

#### 3.1. The Structural Parameters of the TiZrHfScMo HEA before and after Hydrogenation

_{0.20}Zr

_{0.18}Hf

_{0.21}Sc

_{0.21}Mo

_{0.20}, which is consistent with the designed equiatomic TiZrHfScMo alloy. Figure 1b shows the EBSD map of TiZrHfScMo alloy, and the grain size of this alloy is measured as 104.2 ± 52.3 um, indicating that the TiZrHfScMo alloy has a great crystallinity. The above results indicate that a single phase of TiZrHfScMo high-entropy alloy is synthesized successfully.

_{x}. As seen in Figure 2, the displacement of alloy elements is more significant with the increasing hydrogen content. Note that no intermetallic compounds are formed in the TiZrHfScMo hydrides. The calculated lattice constants are summarized in Table 1, along with the available experimental results for comparison. The variation of the lattice constant for TiZrHfScMo-H

_{x}is illustrated in Figure 3. The lattice constant increased with the increasing hydrogen content, which results in volume expansion varying from 0.18% to 7.07%.

#### 3.2. The Energetic Properties of the TiZrHfScMo HEA and Its Hydrides

_{form}), defined as the energy difference between the final compound and initial constituents, is calculated. The H

_{form}is calculated by the following equation [20]:

_{2}molecule, and $E\left(Ti\right)$, $E\left(Zr\right)$, $E\left(Hf\right)$, $E\left(Sc\right)$ and $E\left(Mo\right)$ are the single atomic energies of the pure elements in their respective stable solid states. The calculated H

_{form}is summarized in Table 2 and plotted in Figure 4. As shown in Table 2, the H

_{form}of the TiZrHfScMo-H

_{x}are all negative, suggesting that the process of hydrogenation is an exothermic process and the hydrides with H concentration varying from 0.05 wt.% to 2.14 wt.% are all energetically stable [20]. These results indicate that the TiZrHfScMo HEA has great potential to be a hydrogen storage material [21]. As shown in Figure 4, the H

_{form}decreases significantly when the H content increases to 1.72 wt.% and then the formation enthalpy started to increase, suggesting that the hydride formation becomes relatively more difficult when the H content reached a certain level. The decreased formation enthalpy may be due to the lattice expansion, which leads to an increasing volume of the HEA TiZrHfScMo and makes it easier for hydrogen atoms to occupy the sites [22].

_{B}) is defined as [23,24]:

_{x}with hydrogen content. Note that the E

_{B}is large enough, suggesting that the process of hydrogen absorption is chemical sorption, and there may be covalent bonding between the hydrogen and metal elements [2]. Furthermore, the decline of E

_{B}indicates that the stability of the system is gradually decreasing [23]. Therefore, if the concentration of hydrogen reaches a certain level, the hydride will not exist stably any more.

#### 3.3. Electronic Structures and Mulliken Population Analysis of TiZrHfScMo-H_{x}

_{0.25}, TiZrHfScMo-H

_{1.5}, and TiZrHfScMo-H

_{3}for comparison, which are presented in Figure 6. It is shown that all the structures behaved with metallic characters [5].

_{0.25}, TiZrHfScMo-H

_{1.5}, and TiZrHfScMo-H

_{3}, the H 1s orbitals mainly interact with the s orbitals of alloy elements in the energy range of −8 to −4.5 eV, indicative of strong bonding between the H and the metal elements. Especially, the hybridization between the H–s and Hf–s is the most significant, meaning that the <H–Hf> interaction may be stronger than the interaction between the H and other metal elements. These results suggest that the structural stability of hydrides may be influenced by the different bonding between H and metal elements.

^{2}4s

^{2}for Ti, 4d

^{2}5s

^{2}for Zr, 5d

^{2}6s

^{2}for Hf, 3d

^{1}4s

^{2}for Sc, 4d

^{5}5s

^{1}for Mo, and 1s

^{1}for H. If the average value of the Mulliken charge is positive, it means that there must be electron loss for this element after bonding, while a negative value implies electron gain [20]. The larger the negative (or positive) value of the charge for an element, the stronger the ability to gain (or lose) electrons. As can be seen from Figure 7a, the Ti and Sc atoms in all cases lose electrons, while the H and Mo atoms gain electrons in all the considered hydrides. The Mo has a stronger ability to gain electrons, and with the increasing of the hydrogen content, the charge values of H and Mo get closer. A possible explanation is that the electronegativity of Mo is the strongest among all the metal elements in the investigated system and is similar to the electronegativity of H [27]. The overlap population is another way to investigate the charge distribution on the chemical bond. A higher positive population indicates a higher covalent nature in the chemical bonding, and a negative value of overlap population is responsible for the antibonding states in the chemical bonding [28]. The average values of the overlap population between the hydrogen and metal elements are listed in Table 4 and plotted in Figure 7b. As shown in Figure 7b, the overlap population between H and metal elements is always positive, indicative of covalent bonding interaction between them [29]. Furthermore, with increase of the hydrogen concentration, the <Ti–H> bonding is weakening, and the <Hf–H> and <Mo–H> bonding become stronger, indicative of different roles of metal atoms during the absorption and desorption processes of hydrogen storage.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Illustration of schematic views of (

**a**) the HEA TiZrHfScMo; (

**b**–

**l**) TiZrHrScMo-H

_{x}, where x is the number of hydrogen atoms per formula unit. The yellow, red, green, purple, and pink spheres represent Hf, Mo, Sc, Ti, and Zr atoms, respectively. The hydrogen atoms are represented by the smaller wine-colored spheres.

**Figure 3.**The variation of lattice parameters for the TiZrHfScMo hydrides with increasing hydrogen content.

**Figure 4.**The calculated formation enthalpy and binding energy for the TiZrHfScMo hydrides with different hydrogen content.

**Figure 6.**The projected density of state (PDOS) of (

**a**) TiZrHfScMo-H

_{0.25}, (

**b**) TiZrHfScMo-H

_{1.5}, and (

**c**) TiZrHfScMo-H

_{3}. The Fermi level was set to zero.

**Figure 7.**(

**a**) The average charge distribution of different elements in the TiZrHfScMo hydrides with increase of the hydrogen content. (

**b**) The average overlap population between hydrogen and metal elements in the hydrides of HEA TiZrHfScMo with increase of the hydrogen content.

**Table 1.**The calculated and experimental lattice constants for M–H

_{x}(M = TiZrHfScMo, x is the number of hydrogen atoms per formula unit).

Config. | Lattice Constant (Å) |
---|---|

Exp. | 3.444 |

M | 3.325 |

M–H_{0.25} | 3.331 |

M–H_{0.5} | 3.337 |

M–H | 3.350 |

M–H_{1.5} | 3.367 |

M–H_{2} | 3.383 |

M–H_{2.5} | 3.400 |

M–H_{3} | 3.420 |

M–H_{5} | 3.46 |

M–H_{6} | 3.492 |

M–H_{8} | 3.526 |

M–H_{10} | 3.56 |

**Table 2.**The calculated formation enthalpy and binding energy of the M-H

_{x}(M = TiZrHfScMo, where x is the number of hydrogen atoms per formula unit).

Config. | Formation Enthalpy (eV/Atom) | Binding Energy (eV/Atom) |
---|---|---|

M–H_{0.25} | −0.0147 | 0.97 |

M–H_{0.5} | −0.0531 | 0.91 |

M–H | −0.1174 | 0.87 |

M–H_{1.5} | −0.1704 | 0.85 |

M–H_{2} | −0.2161 | 0.84 |

M–H_{2.5} | −0.2599 | 0.85 |

M–H_{3} | −0.3008 | 0.86 |

M–H_{5} | −0.3894 | 0.81 |

M–H_{6} | −0.4359 | 0.83 |

M–H_{8} | −0.477 | 0.8 |

M–H_{10} | −0.4478 | 0.69 |

**Table 3.**The average charge (

**e**) of different elements in M–H

_{x}(M = TiZrHfScMo, x = 0.25, 0.5, 1, 1.5, 2, 2.5, and 3).

Config. | H | Ti | Zr | Hf | Sc | Mo |
---|---|---|---|---|---|---|

M–H_{0.25} | −0.093 | 0.175 | −0.002 | −0.042 | 0.059 | −0.166 |

M–H_{0.5} | −0.092 | 0.176 | 0.008 | −0.036 | 0.062 | −0.164 |

M–H | −0.095 | 0.182 | 0.013 | −0.013 | 0.070 | −0.157 |

M–H_{1.5} | −0.103 | 0.193 | 0.026 | 0.010 | 0.077 | −0.151 |

M–H_{2} | −0.103 | 0.189 | 0.049 | 0.030 | 0.081 | −0.144 |

M–H_{2.5} | −0.106 | 0.185 | 0.053 | 0.060 | 0.086 | −0.119 |

M–H_{3} | −0.113 | 0.179 | 0.076 | 0.083 | 0.109 | −0.107 |

**Table 4.**The overlap population between hydrogen and metal elements in M–H

_{x}(M = TiZrHfScMo, x = 0.25, 0.5, 1, 1.5, 2, 2.5, and 3).

Config. | Ti–H | Zr–H | Hf–H | Sc–H | Mo–H |
---|---|---|---|---|---|

M–H_{0.25} | 0.1520 | 0.0640 | 0.0382 | 0.0888 | 0.0262 |

M–H_{0.5} | 0.1159 | 0.0865 | 0.0692 | 0.0875 | 0.0269 |

M–H | 0.0771 | 0.0711 | 0.0706 | 0.1112 | 0.0357 |

M–H_{1.5} | 0.0917 | 0.0716 | 0.0685 | 0.0915 | 0.0477 |

M–H_{2} | 0.0793 | 0.0865 | 0.0835 | 0.0768 | 0.0585 |

M–H_{2.5} | 0.0683 | 0.0839 | 0.0851 | 0.0784 | 0.0793 |

M–H_{3} | 0.0666 | 0.0874 | 0.0853 | 0.0838 | 0.0742 |

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**MDPI and ACS Style**

Hu, J.; Shen, H.; Jiang, M.; Gong, H.; Xiao, H.; Liu, Z.; Sun, G.; Zu, X.
A DFT Study of Hydrogen Storage in High-Entropy Alloy TiZrHfScMo. *Nanomaterials* **2019**, *9*, 461.
https://doi.org/10.3390/nano9030461

**AMA Style**

Hu J, Shen H, Jiang M, Gong H, Xiao H, Liu Z, Sun G, Zu X.
A DFT Study of Hydrogen Storage in High-Entropy Alloy TiZrHfScMo. *Nanomaterials*. 2019; 9(3):461.
https://doi.org/10.3390/nano9030461

**Chicago/Turabian Style**

Hu, Jutao, Huahai Shen, Ming Jiang, Hengfeng Gong, Haiyan Xiao, Zijiang Liu, Guangai Sun, and Xiaotao Zu.
2019. "A DFT Study of Hydrogen Storage in High-Entropy Alloy TiZrHfScMo" *Nanomaterials* 9, no. 3: 461.
https://doi.org/10.3390/nano9030461