In the past two decades, magnesium hydride (MgH₂) has attracted great interest due to its high hydrogen capacity [1]. However, the practical applications of MgH₂ are hindered by slow hydrogen sorption kinetics and poor cycle durability as well as bad hydrogen desorption thermodynamics [2,3]. Usually, nanosizing techniques have been applied to increase hydrogen sorption rate and decrease hydrogen desorption temperature of MgH₂ [4]. Among nanosizing methods, ball milling is a simple and effective route to obtain MgH₂ nanocrystallites [5,6]. Nevertheless, MgH₂/Mg nanocrystallites easily grow up during hydrogen absorption―desorption cycling [7], leading to deterioration of hydrogen storage properties [8]. The crystallite growth process is very complicated, which includes the size changes during the transitions and post-transitions between Mg and MgH₂. As one part of this fundamental research, therefore, it is necessary to clarify the growth characteristics of MgH₂ and Mg nanocrystallites.

Most recently, we reported the crystallite growth kinetics of Mg nanocrystallites, in which the crystallite growth exponent and activation energy of Mg nanocrystallites were determined to be n = 4 and Q =97.1 kJ/mol, respectively [9]. Minor Pr₃Al₁₁ nanoparticles introduced into Mg can inhibit the growth of Mg nanocrystallites [9,10]. However, the growth kinetics of MgH₂ nanocrystallites has been reported rarely, in spite of the fact that magnesium hydride is an important hydrogen storage material. The reason why the growth characteristics of MgH₂ nanocrystallites are relatively unexplored is probably because MgH₂ is susceptible to decomposition into Mg and H₂ upon heating above 300 °C. It was reported that the enthalpy and entropy changes for hydrogen desorption of MgH₂ nanoparticles are ΔH =71.22 kJ/mol H₂ and ΔS = 129.6 J/mol H₂/K, respectively [11]. Thus the equilibrium hydrogen pressure for hydrogen desorption of nano-sized MgH₂ is about 1.746 MPa at 400 °C. To avoid decomposition of MgH₂ during isothermal treatment process, the pressure of hydrogen atmosphere must be higher than the equilibrium pressure. Based on this idea, we have investigated the isothermal crystallite growth behavior of nanocrystalline MgH₂ under hydrogen atmosphere in this work. Furthermore, the effect of doped Pr₃Al₁₁ nanoparticles on growth kinetics of MgH₂ nanocrystallites has also been studied.

Commercial MgH₂ (98% purity) powder was purchased from Alfa Aesar and the nano-sized Pr₃Al₁₁ particles were prepared as described in Ref. [9]. To obtain MgH₂ nanocrystallites, pure MgH₂ and MgH₂―10 wt% Pr₃Al₁₁ samples were ball milled at 300 rpm for 100 h with a sample-to-ball weight ratio of 1:40. The ball milling was held under dry argon atmosphere. Finally, the ball milled samples were isothermally treated under a hydrogen pressure of 4 MPa at 300 °C, 350 °C and 400 °C for 1, 2, 5, 10 and 20 h. Although the ball milling led to slight sample contamination which might influence growth of nanocrystallites, the effect of contamination can be ignorable in this comparative investigation.

The powder X-ray diffraction (XRD) patterns of all samples were measured on a Rigaku D/Max 2500 V L/PC diffractometer using CuK_α radiation. The operating generator voltage and tube current were 50 kV and 200 mA, respectively. The sizes of MgH₂ nanocrystallites were determined by the Rietveld refinements of XRD data using the program RIETAN-2000 [12]. The detailed principle of calculation was described by Nakamura et al [13]. To confirm the results calculated from the Rietveld refinements of XRD data, transmission electron microscopy (TEM) images were observed on a FEI Tecnai F20 microscope. For preparation of TEM samples, the powder samples were dispersed in tetrahydrofuran by ultrasonic vibration and the suspensions were then deposited onto copper grids. Moreover, high-resolution TEM (HRTEM) images were also observed to reveal the growth feature of MgH₂ nanocrystallites.

Fig. 1 shows the Rietveld refinements of the XRD patterns for ball milled MgH₂ sample and MgH₂―10 wt% Pr₃Al₁₁ composite. It can be seen that MgH₂ neither decomposes into Mg and H₂ nor reacts with Pr₃Al₁₁ during the ball milling process. From the results of Rietveld refinements, the MgH₂ crystallite sizes in pure MgH₂ sample and MgH₂―10 wt% Pr₃Al₁₁ composite can be determined to be 13 and 8 nm, respectively. To confirm the sizes of MgH₂ nanocrystallites obtained by Rietveld refinements of XRD patterns, TEM observations were carried out as shown in Fig. 2(a) and (b). Based on the crystallite size distributions (see Fig. 2(c) and (d)), the average sizes of nanocrystalline MgH₂ in pure MgH₂ sample and MgH₂―10 wt% Pr₃Al₁₁ composite can be calculated to be 12.2 and 8.9 nm, respectively; which agree well with the results obtained by Rietveld refinements. Hence, in the following investigations all the sizes of MgH₂ nanocrystallites were determined from Rietveld refinements of XRD patterns. To ensure the computational accuracy, the maximum isothermal treatment time was selected as 20 hours so that the crystallite sizes would be no more than 100 nm.

Figs. S1-S6 in Supplementary Material display the Rietveld refinements of XRD patterns for the pure MgH₂ and MgH₂―10 wt% Pr₃Al₁₁ samples treated isothermally at 300 °C, 350 °C and 400 °C for different times. It can be seen that MgH₂ and Pr₃Al₁₁ exist stably in the heat treated samples, indicating that neither the decomposition of MgH₂ nor the reaction of MgH₂ with Pr₃Al₁₁ occurs during the isothermal treatment processes. The only change is that the widths of XRD peaks for MgH₂ gradually narrow with the increase of isothermal treatment temperature and prolongation of holding time. This implies that the MgH₂ nanocrystallites grow up during the isothermal treatments.

From the point of view of kinetics, there are several models proposed for crystallite growth [14]. Nevertheless, the crystallite growth kinetics of nano-sized Mg-based materials obeys the generalized parabolic growth law [15]. The relationship between crystallite size D and holding time t can be written as follows [16]:

where n is crystallite growth exponent, D₀ is initial crystallite size and k is a constant related to temperature. Fig. 3(a) and (b) shows the MgH₂ nanocrystallite sizes of isothermally treated MgH₂ and MgH₂―10 wt% Pr₃Al₁₁ samples, respectively. It can be seen that the average size of MgH₂ nanocrystallites increases with the rise of temperature and extension of time, which fit well with the generalized parabolic growth model. From Eq. (1), the crystallite growth rate dD/dt is expressed as follows [9]:

where dD/dt can be calculated from the curve tangents in Fig. 3.

Fig. 4 shows the relationships between ln(dD/dt) and lnD of pure MgH₂ and MgH₂―10 wt% Pr₃Al₁₁ samples, in which the slopes (1 ― n) are calculated to be ―4.3, ―4.0, ―3.6 for pure MgH₂ sample and ―5.4, ―5.1, ―4.7 for MgH₂―10 wt% Pr₃Al₁₁ composite isothermally treated at 300 °C, 350 °C and 400 °C, respectively. Therefore, the average growth exponents of MgH₂ nanocrystallites in pure MgH₂ and MgH₂―10 wt% Pr₃Al₁₁ samples are determined to be n = 5 and n = 6, respectively. As compared with the growth exponent of nanocrystalline Mg (n = 4) [9], nanocrystalline MgH₂ has a larger n value, meaning that the motion of MgH₂ crystallite boundaries is more difficult than that of Mg. It is well known that Mg and MgH₂ have different crystal structures. On the other hand, the crystallite growth of Mg is controlled by diffusion of Mg atoms. However, the crystallite growth of MgH₂ is dependent on both the H diffusion dominated by mobility of negatively charged interstitial H and the Mg diffusion dominated by mobility of Frenkel defects on Mg sites (interstitial Mg_i²⁺) [17,18]. Consequently MgH₂ nanocrystallites exhibit a larger growth exponent than Mg nanocrystallites, similar to magnesium oxide with n = 6 [19]. In MgH₂―10 wt% Pr₃Al₁₁ composite, the crystallite growth exponent increases further as compared with pure MgH₂. This is because the secondary phase has a pinning effect on growth of crystallites, identical to the situation in the Mg―Pr₃Al₁₁ composite [9].

Fig. 5 shows the linear relationships of ${{D}^{5}}-D_{0}^{5}$ vs. t for pure MgH₂ sample and ${{D}^{6}}-D_{0}^{6}$ vs. t for MgH₂―10 wt% Pr₃Al₁₁ composite at different temperatures. The slopes (k values) stand for growth rate constants of MgH₂ nanocrystallites, which can be described as [16]

where Q is activation energy of crystallite growth, R is the gas constant, T is isothermal treatment temperature and k₀ is a constant. With these k values, the Arrhenius relationships of ln(k) vs. 1000/T can be plotted in Fig. 6. Hence, the activation energies for crystallite growth of MgH₂ nanocrystallites in pure MgH₂ sample and MgH₂―10 wt% Pr₃Al₁₁ composite are determined to be 109.2 kJ/mol and 144.2 kJ/mol, respectively.

As reported previously [20], the crystallite growths in ball milled samples are very rapid within initial several minutes and then follow the generalized parabolic growth model during subsequent isothermal holding processes (as shown in Eq. (1)). The abnormal growth within initial several minutes of isothermal treatment was suggested to be related to the relaxation of lattice strain (see Fig. 3c and d) which was originated in ball milling process [21]. Nevertheless, the activation energies for crystallite growth obtained from the growth curves (see Fig. 3(a) and (b)) can be used to discuss growth mechanisms. It is generally accepted that a high activation energy for isothermal crystallite growth near the activation energy for lattice self-diffusion is related to grain-boundary migration mechanism, and a low value closer to the activation energy for grain-boundary diffusion corresponds to grain-boundary diffusion mechanism [20,22]. In many cases, however, grain-boundary migrations show activation energies closer to the corresponding values for grain-boundary diffusions [20,23]. Most probably grain-boundary diffusion mechanism and grain-boundary migration mechanism are concomitant and even competitive in the process of isothermal crystallite growth [[24], [25], [26], [27]]. For pure Mg sample, the activation energy for crystallite growth is 97.1 kJ/mol [9], which is smaller than the value (136 kJ/mol [28]) for lattice self-diffusion and larger than that (92 kJ/mol [29]) for grain-boundary diffusion. Hence both grain-boundary diffusion mechanism and grain-boundary migration mechanism may simultaneously occur during the crystallite growth process of Mg nanocrystallites. The pinning effect of the second phase Pr₃Al₁₁ can result in a further increase of activation energy for crystallite growth of Mg [9]. These mechanisms can be applied to explain the present result, in which the activation energy for crystallite growth of MgH₂ nanocrystallites in pure MgH₂ sample is 109.2 kJ/mol. This value is smaller than 142 kJ/mol (1.48 eV) for hydrogen self-diffusion and 274 kJ/mol (2.85 eV) for magnesium self-diffusion in MgH₂ [30]. Although no exact values for grain-boundary diffusions of hydrogen and magnesium in MgH₂ have been reported until now, it is possible that both mechanisms occur simultaneously in the growth process of MgH₂ nanocrystallites, similar to the situation of Mg nanocrystallites [9].

In the MgH₂―10 wt% Pr₃Al₁₁ composite, the activation energy for crystallite growth is 144.2 kJ/mol. This value is coincidental with the activation energy for hydrogen self-diffusion but still smaller than that for magnesium self-diffusion in MgH₂ [30]. The increase in activation energy for crystallite growth of MgH₂ is indeed attributed to the pinning effect of Pr₃Al₁₁ nanoparticles. Fig. 7 shows a HRTEM image of the MgH₂―10 wt% Pr₃Al₁₁ composite isothermally treated at 400 °C for 20 hours, revealing a Pr₃Al₁₁ nanoparticle at crystallite boundary of MgH₂. This indicates that Pr₃Al₁₁ has a pinning effect on growth of MgH₂ nanocrystallites. Such a result demonstrates the coexistence of both mechanisms in the crystallite growth process of MgH₂ from another side. To further evaluate the effect of crystallite size on dehydrogenation reaction rate, Fig. 8 compares the dehydrogenation curves of the MgH₂ with and without Pr₃Al₁₁ additive in different crystallite sizes. It can be seen that the finer MgH₂ has faster hydrogen desorption kinetics, which agrees with the previously reported results [[31], [32], [33]].

It is noteworthy that the present experiments were made under hydrogen atmosphere. If hydrogen pressure is lower than equilibrium pressure for hydrogen desorption of MgH₂, it will decomposes into Mg and H₂ in isothermal treatment process [[34], [35], [36]]. However, the crystallite growth kinetics of nanocrystalline MgH₂ would change when isothermal treatments are made under ultra-high hydrogen pressure (GPa-order) due to crystal structure modification of MgH₂ [37]. In spite of this, the present investigation can provide us with a deeply understanding of growth characteristics of MgH₂ nanocrystallites and a helpful guidance for developments of Mg-based hydrogen storage materials.

The growth characteristics of MgH₂ nanocrystallites in pure MgH₂ and MgH₂―10 wt% Pr₃Al₁₁ samples are comparatively investigated in the present work. The main conclusions can be drawn as follows:

(1) MgH₂ nanocrystallites in the pure MgH₂ sample prepared by ball milling has a growth exponent of n = 5. The activation energy for crystallite growth is determined to be Q =109.2 kJ/mol.

(2) In the ball milled MgH₂―10 wt% Pr₃Al₁₁ composite, the growth exponent of MgH₂ nanocrystallites increases to n = 6. Meanwhile, the activation energy for crystallite growth rises up to Q =144.2 kJ/mol.

(3) HRTEM images reveal the inhibition role of nano-sized Pr₃Al₁₁ phase in MgH₂ crystallite growth, leading to the increase of crystallite growth exponent and rise of activation energy for crystallite growth.

Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/ 10.1016/j.jmst.2020.01.063.