Chinese Journal of Chemical Physics  2016, Vol. 29 Issue (5): 545-548

#### The article information

Wan Zhen-zhen, Wang Zhong-min, Wang Dian-hui, Zhong Yan, Deng Jian-qiu, Zhou Huai-ying, Hu Chao-hao

Alloying Effect Study on Thermodynamic Stability of MgH2 by First-principles Calculation

Chinese Journal of Chemical Physics, 2016, 29(5): 545-548

http://dx.doi.org/10.1063/1674-0068/29/cjcp1602036

### Article history

Received on: February 29, 2016
Accepted on: May 12, 2016
Alloying Effect Study on Thermodynamic Stability of MgH2 by First-principles Calculation
Wan Zhen-zhena, Wang Zhong-mina,b, Wang Dian-huia, Zhong Yana,b, Deng Jian-qiua, Zhou Huai-yinga, Hu Chao-haoa
Dated: Received on February 29, 2016; Accepted on May 12, 2016
a. School of Materials Science and Engineering, Guilin University of Electronic Technology, Guilin 541004, China;
b. Guangxi Experiment Center of Information Science, Guilin 541004, China
Abstract: First-principles calculations based on density functional theory were performed to study the effect of alloying on the thermodynamic stability of MgH2 hydride (rutile and fluorite structures) with transitional metals (TM=Sc, Ti, Y) and group IIA elements (M=Ca, Sr, Ba). The results indicate that fluorite structure of these hydrides are more stable than its relative rutile structure at low alloying content (less 20%), structural destabilization of MgH2 appears in the alloying cases of Ti, Sr and Ba respectively. The structure-transition point from rutile structure to fluorite structure is at around 20% for MgH2-TM, and about 40% for MgH2-M. The formation enthalpy of fluorite Mg0.5Ba0.5H2 is about 0.3 eV and higher than that of fluorite MgH2, indicating that its hydrogen-desorption temperature at atmospheric pressure will be much lower than that of pure MgH2. Good consistency between experimental and calculated data suggests that above-adopted method is useful to predict structural transition and properties of MgH2 based hydrides for hydrogen storage.
Key words: MgH2     First-principles study     Alloying     Destabilization     Structural transition
I. INTRODUCTION

As one of the most promising hydrogen storage materials, magnesium hydride (MgH$_2$) has attracted huge interest in hydrogen storage field due to its abundant resource, low cost and high hydrogen-storage capacity of 7.6 wt%. However, its application in hydrogen-storage is limited because of its poor hydrogen absorption and desorption performance. In practice it often takes several hours for (de)hydrogenation at a relatively higher temperature about 623 K [1-3].

To improve the hydrogenation kinetics of Mg hydride, a large number of experimental and theoretical investigations have been performed extensively in the last decades. These studies have shown that doping the third foreign elements into MgH$_2$ is an efficient way to decrease dehydrogenation temperature and expedite kinetics of MgH$_2$ [4-6]. Kelkar and co-authors have found that the Mg-H bond in Al-doped MgH$_2$ is more susceptible to dissociation and thus the thermodynamic stability of MgH$_2$ is decreased [7, 8]. The TMs (Ti, Mn, and Ni) doping influence on (110) surface of MgH$_2$ has been investigated by Dai et al. [9, 10]. They have found that Ti atoms prefer to occupy both substitutional [9] and interstitial sites [10], while Mn and Ni tend to occupy the interstitial sites near the surface of MgH$_2$. An investigation performed by Er et al. [11] has shown that for TM (TM = Sc, Ti, V, and Cr) concentration approaching $x$=0.2 in Mg$_x$TM$_{1-x}$H$_2$, the fluorite structure with cubic H environment becomes more stable than the rutile one. Mamula et al. have investigated electronic structure and charge distribution topology of MgH$_2$ doped with 3d transition metals using the full potential (linearized) augmented plane waves method with addition of local orbitals (FP-LAPW+LO and APW+LO), and found that along the 3d series TMs accomplish different kinds of bonding with the nearest and next-nearest neighbor hydrogen atoms that in general weaken related Mg-H bonds and destabilize the surrounding MgH$_2$ matrix [12].

A major improvement in discharge kinetics resulting from alloying Mg with Sc has been reported by Notten et al [13]. Up to 80% of Mg contents, the reversible capacity exceeded 5 wt% and the corresponding desorption properties were still excellent. The Mg-Sc system has been extensively studied by using several diffraction techniques, and it was found that the ternary hydride retains the fluorite-type structure of pure ScH$_2$ [14]. This structure contains large empty octahedral interstitials, which facilitate rapid hydrogen diffusion. This has recently been confirmed by Conradi et al. [15]. NMR measurements have shown that the hopping rates of hydrogen between different hydrogen sites in ScH$_2$ and Mg$_{0.65}$Sc$_{0.35}$H$_2$ are about seven and eight orders of magnitude more rapid than that in MgH$_2$, respectively. Recently, based on the theoretical considerations presented by Vajeeston et al. [16] and their experimental finding [17], Pauw and co-authors [18] have further concluded that for MgH$_2$ the transformation from a rutile-type structure to a fluorite-type structure could be accelerated by alloying with transition metals.

In this work, based on two crystallographic modifications of MgH$_2$ (rutile-type and fluorite-type), a theoretical investigation based on density functional theory (DFT) of MgH$_2$-transitional metals (TM=Sc, Ti, Y) and MgH$_2$-group IIA elements (M=Ca, Sr, Ba) was carried out. The destabilizing mechanism of MgH$_2$ alloying with TM/M for hydrogen storage performance was also discussed via analyzing the change in the calculated enthalpy of formation, lattice parameters, and electron density of states (DOS).

II. COMPUTATIONAL DETAILS

All DFT calculations were performed using the Vienna $ab$ $initio$ Simulation Package [19]. The interactions between core and valence electrons were described with the projector augmented wave method [20]. Perdew-Burke-Ernzerhof implemented generalized gradient approximation [21] was used to treat the exchange and correlation energies. The plane-wave energy cutoff was set to 400 eV and the $k$-point mesh in the Brillouin zone was about 0.03$\times$2$\pi$ Å$^{-1}$ in all calculations. During structure optimization the lattice parameters, volume and atom positions were allowed to relax fully within symmetry restrictions. The convergence criterion for total energy was set to 10$^{-5}$ eV during the self-consistent calculations.

Two types of crystal structure of MgH$_2$ which are the rutile structure (tetragonal, P42/mnm) and fluorite structure (cubic, Fm-3m) are generally considered. In this work, the super cell models containing 8 metal atoms (seen in Fig. 1) were established in order to consider the effect from different alloying contents on the formation enthalpy of the two structural modifications.

In general, the stability of any compound can be evaluated by its formation enthalpy. The formation enthalpy of MgH$_2$ based hydrides can be defined as:

 (1)

where $E_{\mathrm{Mg}_{1-x}\mathrm{M}_x\mathrm{H}_2}$, $E_\mathrm{Mg}$ and $E_\mathrm{M}$ are the calculated total energies of Mg$_{1-x}$M$_x$H$_2$, Mg, and M bulk materials, and $E_{\mathrm{H}_2}$ is the energy of isolated H$_2$ molecule.

 FIG. 1 1$\times$1$\times$4 cell of the rutile structure (left, tetragonal, P42/mnm) and 1$\times$1$\times$2 cell of the fluorite structure (right, cubic, Fm-3m). The big spheres are Mg atoms, and the small spheres are H atoms.
III. RESULTS AND DISCUSSION A. MgH2-TM system hydrides

Calculated formation enthalpies of MgH$_2$-TM (TM=Sc, Ti, Y) hydrides are shown in Fig. 2. The calculated formation enthalpy of rutile MgH$_2$ is -0.64 eV (or -61.8 kJ/mol), which has about 20% difference compared with the literature value (-77 kJ/mol) [22], but agrees well with the theoretical results (-0.66 eV) [13, 16-18]. Considering that the experiment was carried out under 673 K, so these calculated values at ground state are acceptable.

In the case of MgH$_2$ with rutile structure, the formation enthalpies decrease with the increase of alloying content of Sc and Y, indicating that rutile structure of MgH$_2$ is stabilized by alloying with Sc or Y. While an apparent increase of formation enthalpy is obtained when alloying with Ti in the range of 0-37.5%, Mg$_{0.625}$Ti$_{0.375}$H$_2$ has a higher formation enthalpy value of -0.45 eV, which is 0.19 eV higher than that of pure MgH$_2$, but the formation enthalpy will decrease when the alloying content of Ti is above 37.5%.

In the case of MgH$_2$ with fluorite structure, the structure of pure MgH$_2$ is less stable than the rutile structure of MgH$_2$. But the fluorite structure becomes more stable than the rutile structure when Sc, Ti or Y atoms doping content reaches 20%, which indicates that Mg$_{0.8}$TM$_{0.2}$H$_2$ energetically prefers to a cubic fluorite structure. This is consistent with the experimental findings suggested by X-ray diffraction [13, 14]. It also agrees well with the results of electrochemical experiments, which has reported that alloying with 20% of transitional metal can greatly improve the hydrogen desorption kinetic performance [23].

Figure 2 shows an important point, 20% of alloying content is a structure transition point from rutile structure to fluorite structure, the formation enthalpy of fluorite structure of MgH$_2$ becomes more negative than that with rutile structure when $x$ is above 0.2. As to Mg$_{1-x}$Ti$_x$H$_2$ calculation, the rutile structure is destabilized by 0.17 eV when $x$=0.25. The most unstable status is around $x$=0.375, the formation enthalpy of Mg$_{0.5}$Ti$_{0.5}$H$_2$ is -0.39 eV, which is 0.24 eV more positive than that of pure MgH$_2$. However, the fluorite structure still becomes the most stable one at $x$=0.2, similar to Mg-Sc system. These results are in accordance with the results reported by Pauw et al. [18]. MgH$_2$-TM system hydrides have the structure-transition tendency from rutile structure to fluorite structure at a specific point of alloying content, the transition point is about 20% for transition metals.

 FIG. 2 Formation enthalpy of Mg-TM hydrides.
B. MgH2-M system hydrides

Calculated formation enthalpies of Mg$_{1-x}$M$_x$H$_2$ (M=Mg, Ca, Sr) are shown in Fig. 3. It can be clearly found from Fig. 3 that alloying with Ca will result in the increase of thermodynamic stabilities of Mg$_{1-x}$Ca$_x$H$_2$ hydride since the calculated formation enthalpies of the rutile and fluorite structure always decrease with the increase of alloying content. However, the alloying treatment with Sr can induce a slight decrease in the thermodynamic stabilities of rutile Mg$_{1-x}$Sr$_x$H$_2$, since the enthalpy of Mg$_{0.625}$Sr$_{0.375}$H$_2$ is 0.06 eV higher than that of MgH$_2$. Figure 3 also clearly indicates that the most obvious decrease in structural stability of both rutile and fluorite structure is from the alloying treatment with Ba. It can be observed that the enthalpy of rutile Mg$_{0.5}$Ba$_{0.5}$H$_2$ is 0.33 eV higher than that of MgH$_2$. In addition, the structural transition point from the rutile to fluorite structure is around 40% for Mg$_{1-x}$M$_x$H$_2$, which has a big delay compared with that of Mg$_{1-x}$TM$_x$H$_2$ hydrides (about 20%). At this point, its theoretical hydrogen-storage capacity is 3.1 wt%.

 FIG. 3 Formation enthalpy of Mg-M hydrides.
C. Electronic properties of Mg0:5Ba0:5H2

As mentioned above, alloying with Ba will lead to an obvious decrease in the thermodynamic stability of Mg$_{1-x}$M$_x$H$_2$ and the fluorite Mg$_{0.5}$Ba$_{0.5}$H$_2$ has a high formation enthalpy, so here Mg$_{0.5}$Ba$_{0.5}$H$_2$ has been selected to make a comparison with pure MgH$_2$. After structure optimization, the cubic fluorite structure of Ba doped MgH$_2$ is distorted, and the unit cell volume is obviously increased by 39.9%. The interatomic distance between Mg and H atoms also significantly increased from 1.94 Å to 2.24 Å. So the interaction between Mg and H will be weakened. Calculated DOS of rutile MgH$_2$ is shown in Fig. 4. There is a wide band gap (about 2.73 eV) between the conduction band and valence band, revealing its insulating nature. The partial DOS of MgH$_2$ suggests that its valence bands are mainly contributed by H 1s states, while the contribution from the Mg 3s and 2p orbitals is not so much. The involvement of 2p electrons in the valence band is an evidence of hybridization of Mg 3s and 2p orbitals. The DOS of Ba-doped MgH$_2$ (Mg$_{0.5}$Ba$_{0.5}$H$_2$) is presented in Fig. 5. With Ba-doping, the Ba 5p and 4d orbitals make a distinct contribution to the valence band. While a peak within the energy range from -10 eV to -15 eV is mainly ascribed to the hybridization of H 1s and Ba 5p orbitals, indicating that there exists a strong bonding between Ba and H atoms. Although Mg$_{0.5}$Ba$_{0.5}$H$_2$ still keeps its non-metallic nature, its metallization is obviously improved as suggested from the relative decrease of band gap.

 FIG. 4 Calculated DOS of rutile MgH$_2$.
 FIG. 5 Calculated DOS of fluorite Mg$_{0.5}$Ba$_{0.5}$H$_2$.
IV. CONCLUSION

Based on two crystallographic modifications of MgH$_2$ (rutile-type and fluorite-type), the relative thermodynamic stabilities of MgH$_2$-TM and MgH$_2$-M (TM=Sc, Ti, Y, M=Ca, Sr, Ba) have been studied by first-principles calculations. Rutile structure of MgH$_2$ will transform into fluorite structure when alloying with these elements. For MgH$_2$-TM hydrides, the structure-transition point from rutile structure to fluorite structure is at around 20% substitution, which agrees very well with both experimental and previous calculated data. For MgH$_2$-M hydrides, this structural transition point is at around 40% substitution. Furthermore, Ti Sr, and Ba substitution not only cause the structure transition, but also reduce its thermodynamic stabilities, especially in the case of Ba substitution. The formation enthalpy of fluorite Mg$_{0.5}$Ba$_{0.5}$H$_2$ is 0.33 eV higher than that of pure rutile MgH$_2$, suggesting that its hydrogen-desorption temperature at atmospheric pressure will be much lower compared to pure MgH$_2$. Mg$_{0.5}$Ba$_{0.5}$H$_2$ also has a reasonable theoretical hydrogen-storage capacity of about 3.1 wt%, which indicates that it would be a potential candidate of hydrogen storage materials.

V. ACKNOWLEDGMENTS

This work is supported by the National Natural Foundations of China (No.51261003, No.51471055, No.51401060, and No.11464008), the Natural Foundations of Guangxi Province (No.2016GXNSFGA380001 and No.2014GXNSFGA118001), and Guangxi Experiment Center of Information Science (No.20130113 and No.YB1512).

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a. 桂林电子科技大学材料科学与工程学院, 桂林 541004;
b. 广西信息科学实验中心, 桂林 541004