Solid-state hydrogen desorption of 2 MgH2 + LiBH4 nano-mixture: A kinetics mechanism study

Accepted Manuscript Solid-state hydrogen desorption of 2 MgH2 + LiBH4 nano-mixture: A kinetics mechanism study Zhao Ding, Pingkeng Wu, Leon Shaw PII:

S0925-8388(19)32733-1

DOI:

https://doi.org/10.1016/j.jallcom.2019.07.218

Reference:

JALCOM 51506

To appear in:

Journal of Alloys and Compounds

Received Date: 17 April 2019 Revised Date:

19 June 2019

Accepted Date: 18 July 2019

Please cite this article as: Z. Ding, P. Wu, L. Shaw, Solid-state hydrogen desorption of 2 MgH2 + LiBH4 nano-mixture: A kinetics mechanism study, Journal of Alloys and Compounds (2019), doi: https:// doi.org/10.1016/j.jallcom.2019.07.218. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Graphical Abstract

ACCEPTED MANUSCRIPT Submitted to “Journal of Alloys and Compounds”, April 2019 Solid-State Hydrogen Desorption of 2 MgH2 + LiBH4 Nano-Mixture: A Kinetics Mechanism Study Zhao Ding, a Pingkeng Wu, b Leon Shaw a,* Department of Mechanical, Materials and Aerospace Engineering Illinois Institute of Technology, Chicago, USA b McKetta Department of Chemical Engineering, The University of Texas at Austin, Austin, USA

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Abstract

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a

The dehydrogenation reaction pathway and rate-limiting step of a nano-LiBH4 +

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nano-MgH2 mixture with a 0.5:1 molar ratio, which has been shown to have the ability to reversibly release and absorb ~5.7 wt.% H2 at 265 oC, have been investigated in detail. The study reveals that the solid-state dehydrogenation kinetics of the MgH2 + 0.5 LiBH4 mixture at 265 oC is nucleation-and-growth controlled. The rate-limiting step for dehydrogenation via the two parallel reaction pathways has been identified through examination of the elementary

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reactions as the nucleation and growth of reaction products LiH and MgB2. The interfacial area between MgH2 and LiBH4 plays a critical role in the nucleation and growth of LiH and MgB2, and thus influence the dehydrogenation kinetics and H2 storage capacity of the MgH2

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+ 0.5 LiBH4 mixture. X-ray diffraction, SEM analysis and specific surface area measurements reveal that the evolution of the powder characteristics before and after isothermal hydrogen uptake/release cycles is consistent with the kinetics observation and

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analysis. This study indicates that to further improve the dehydrogenation kinetics of the MgH2 + LiBH4 mixture, the nucleation and growth rates of LiH and/or MgB2 should be enhanced in the future, while the interfacial area between MgH2 and LiBH4 should be increased and maintained to be as large as possible during hydrogen uptake/release cycles.

Keywords: Hydrogen Storage Materials; Kinetics; LiBH4; MgH2; High-Energy Ball Milling; Nano-engineering * Corresponding author: [email protected] 1

ACCEPTED MANUSCRIPT I. Introduction

The research about reversible hydrogen storage materials has attracted more and more attention in the past two decades [1-8]. Currently, researchers all over the world have shown

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their extreme interests in LiBH4 due to its high gravimetric and volumetric hydrogen densities of 18.5 wt.% and 121 kg H2/m3, respectively [9]. However, its unfavorable thermodynamics and sluggish kinetics for dehydrogenation have limited its potential application for on-board application of fuel cell vehicles [10]. Under such background,

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studies on lowering the temperature of hydrogen release have become popular.

Currently, there are four major approaches that have been tried to modify the

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thermodynamics and/or kinetics of dehydrogenation from LiBH4. These include: (i) seeking novel catalysts to enhance hydrogen release kinetics [11], (ii) Employment of nanoengineering, either using mesoporous scaffolds to confine LiBH4 in nanoscales or mixing nanotubes and mesoporous gels with LiBH4 [12], (iii) thermodynamic destabilization of LiBH4 via the partial substitution of Li+ cations by other cations with larger

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electronegativity [13], and (iv) introduction of additives to stabilize the dehydrogenated state, thereby thermodynamically destabilizing LiBH4 [14,15]. Among these four approaches, the last one shows great promise because it not only tunes the thermodynamics, but also

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improves the kinetics. It is worth noting that similar approach called ball-milling process assisted by dielectric-barrier discharge plasma has already shown the dual-tuning effects of the thermodynamics and kinetics for Mg-based hydrogen storage materials [16-18]. It has

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been shown that introduction of additive(s) to LiBH4 has the potential to store and release hydrogen with a theoretical capacity of 11.45 wt.% H2 at a relative lower temperature through the reaction shown below [19].

2LiBH4 (s) + MgH2 (s) =2 LiH (s) + MgB2 (s) + 4H2 (g)

(1)

Recently, our group has shown that the nano-MgH2 + nano-LiBH4 mixture with molar ration of 2:1 produced from a novel process, termed as ball milling with aerosol spraying 2

ACCEPTED MANUSCRIPT (BMAS), has the ability to release and absorb ~5.7 wt.% H2 at 265 oC [20], which is the highest reversible H2 storage capacity ever reported for the LiBH4 + MgH2 system in solid state [19, 21-23], since the melting point of LiBH4 is 265 oC. This BMAS-processed powder contains 25 at.% LiBH4 in the mixture for the stoichiometric reaction of Eq. (1), and thus will

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be denoted as the BMAS powder with 25% LiBH4 hereafter. It is found that the unusually high reversible hydrogen storage exhibited by the BMAS powder with 25% LiBH4 is accomplished through two parallel reaction pathways. One is nano-MgH2 decomposes to form Mg and H2 first, and then Mg reacts with LiBH4 to form MgB2, LiH and H2, as shown

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in reactions (2) and (3) [19].

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MgH2 (s) = Mg (s) + H2 (g)

2LiBH4 (s) + Mg(s) = 2LiH (s) + MgB2 (s) + 3 H2 (g)

(2) (3)

The other reaction pathway is that nano-LiBH4 decomposes to form Li2B12H12 and H2 first and then Li2B12H12 reacts with MgH2 to form MgB2, LiH and H2, as shown in reactions (4)

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and (5) [24, 25].

12 LiBH4 (s) = Li2B12H12 (s) + 10 LiH (s) + 13 H2 (g)

(5)

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Li2B12H12 (s) + 6 MgH2 (s) = 6 MgB2 (s) + 2 LiH (s) + 11 H2 (g)

(4)

Note that Reactions (4) and (5) have been shown to take place in situ during high-energy ball milling of MgH2 at ambient temperature along with aerosol spraying of LiBH4 dissolved in

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tetrahydrofuran (THF) solution [24]. Furthermore, these reactions can be utilized for hydrogen storage and release applications, as demonstrated lately [19, 21, 22]. Given the significantly improved hydrogen storage capacity for the LiBH4 + MgH2

system obtained via BMAS, investigation on the reaction kinetics of dehydriding reactions from the BMAS powder with 25% LiBH4 is of great theoretic interest and technological importance. Thus, the dehydrogenation kinetics of the BMAS powder with 25% LiBH4 is analyzed for the first time in this study. In addition, the kinetics effects of all of the four elementary reactions for the two parallel dehydriding reaction pathways, i.e., reactions (2) 3

ACCEPTED MANUSCRIPT and (3) and reactions (4) and (5), are included in the quantitative analysis. Furthermore, the powder characteristics before and after dehydriding and re-hydriding cycles are considered in order to provide additional insights into the kinetics mechanisms for the enhanced storage properties and the degradation in cycling performance. The understanding developed from

nano-MgH2 mixture in the future.

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II. Materials and Procedure

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this study will shed light on how to increase the dehydrogenation rate of the nano-LiBH4 +

The experimental raw materials includes MgH2 + C mixture and LiBH4/THF solution.

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MgH2 + C mixture was prepared by mixing MgH2 with hydrogen storage-grade (98%) + 5 vol.% pre-milled C (synthetic graphite) [26-31] and 2.0 M LiBH4 in THF solution was purchased from Sigma-Aldrich.

The elementary diagram of the homemade automated BMAS device, together with its on-and-off program of ball milling, aerosol spraying and vacuuming, is shown in Figure 1.

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The parameters used in experiments have been discussed in Ref. [20]. Note that the BMAS powder prepared for the subsequent characterizations is free from THF residue. This is achieved by vacuum (10-4 MPa) drying the BMAS powder at ambient temperature for 36 h.

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Because THF is a volatile solvent (see Figure S1 in Supplemental Material), 20-minute holding at room temperature will lead to the complete evaporation of THF solution.

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The Sieverts’-type pressure-composition-temperature (PCT) unit from Advanced Materials Corporation is employed to conduct dehydrogenation and re-hydrogenation cycles. The PANalytical Empyrean diffractometer equipped with an incident-beam focusing mirror and an X’Celerator detector with MoKα radiation is employed for the X-ray diffraction (XRD) analysis. The JEOL JSM 5900-LV scanning electron microscope (SEM) is used for observing the particle morphology. Detailed experimental conditions for PCT, XRD and SEM data collection can be found elsewhere [20]. It is worth noting that the leakage of the PCT chamber is very small (see Figure S2) and had taken into account when calculating and reporting the hydrogen contents of the BMAS powder in dehydrogenation and 4

ACCEPTED MANUSCRIPT re-hydrogenation. The two-channel Nova Quantachrome 2200e surface area & pore size analyzer is used to determine the specific surface area (SSA) of samples at different processing stages based on the Brunauer–Emmett–Teller (BET) method.

3.1 Kinetics of the Solid-State Hydrogen Release

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III. Results and Discussion

Dehydrogenation and re-hydrogenation behaviors of the BMAS mixture as a function

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of time and temperature are shown in Figure 2. It is clear that the mixture has a rapid hydrogen absorption rate and slow desorption rate. Take the first cycle for an example. The

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release curve appears not completed yet after 10-hour’s holding at 265 oC. In contrast, 96.9% H2 has already been absorbed in the first two hours during the heating process to 265 oC. Since dehydrogenation process is much slower than the hydrogenation process, this study focuses on the slower one so that guidelines can be provided to improve the slower process. In analyzing the H2 release kinetics, one should note that the 5.7 wt.% H2 released and

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absorbed in the first cycle is about two thirds of the theoretical storage capacity for the BMAS powder with 25% LiBH4 which is calculated to be about 9.1 wt.% H2. Second, most of the H2 is released in the isothermal (265 °C) and isobaric (265 °C) conditions. Thus, the

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analysis is performed with the assumption of isothermal and isobaric conditions. Finally, the shrinking-core model [33], which has been widely employed to investigate the kinetics of gas/solid reactions, has been utilized to analyze the possibilities of various kinetics

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mechanisms. The suitability of using this model will be discussed later. In using the shrinking-core model, several possible rate-limiting steps that can control

the reaction kinetics, which include (i) diffusion of a diffusing species through the product layer, (ii) movement of the reactant/product interface at a constant speed, (iii) nucleation and growth of the product, and (iv) desorption or adsorption of the gaseous phase at the surface of the solid particle, have been considered. The corresponding equations for these rate-limiting steps have been derived previously and are listed below [32,33]. These equations are based on examining the fraction reacted,

, as a function of holding time, t [34, 35]. 5

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/

(1 − )

= 1 −

/



= 1 −

= 1 −

(−

=

/

diffusion-controlled reactions

(6)

moving-interface controlled reactions

(7)

nucleation-and-growth controlled reactions

(8)

gas-desorption controlled reactions

(9)

)



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(1 − )

where r is the average particle size of the BMAS particles, k1, k2, k3 and k4 are the rate

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constants for their respective kinetics mechanisms, and m is the mechanism constant the value of which depends on the detail of nucleation and growth of the product (to be discussed

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in detail later). To evaluate the dehydriding kinetics at 265 °C shown in Figure 2, the incomplete dehydrogenation at the end of each isothermal dehydrogenation should be taken into account. For example, equation (6) would be modified to be (1 − ′ ⋅ ) where

/

= 1 −



/

(10)

′ is the proportion of H2 desorption at the end of the release segment of the

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theoretical hydrogen storage capacity of the BMAS powder with 25% LiBH4, which is 9.1 wt.% as mentioned previously. Thus,

=1 at the end of each release segment, whereas ′=1

only if the H2 released at the end of the release segment equals the theoretical hydrogen ′ is smaller than 1. Similarly,

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storage capacity of the system (i.e., 9.1 wt.%). Otherwise,

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equations (7) - (9) should also be modified, respectively, to be equations (11) - (13):

(1 − ′ ⋅ ) ′⋅

/

= 1− ′⋅

=

= 1 − (−

)



(11) (12) (13)

Note that the determination of k3 and m constant can be done easily by re-arranging equation (12) to the following form



! " =



+ $

(14) 6

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Thus, a linear relationship will be present if experimental data is plotted in



! " %&.

and the dehydrogenation kinetics is controlled by nucleation and

growth processes. Under these conditions the slope of the line is equal to m, while the

! " axis gives rise to ln k3.

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interception of the line with the

Table 1 summarizes the fitting equations through the least-squares method obtained from all of the dehydrogenation curves, i.e., 1R, 2R, 3R, 4R, 5R and 6R curves, shown in

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Figure 2 with the assumption that the dehydrogenation kinetics is diffusion controlled. Similarly, the fitting equations for all of the dehydrogenation curves shown in Figure 2 have

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been obtained for moving-interface controlled reactions, nucleation-and-growth controlled reactions and gas-desorption controlled reactions, and these fitting equations are listed in Tables 2, 3 and 4, respectively.

By examining the R-square values for each possible rate-controlling mechanism shown in Tables 1, 2, 3 and 4, it is very clear that the experimental data fits the

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nucleation/growth-controlled model better than the other models. This conclusion can also be easily obtained by examining Figures 3(a), (b), (c) & (d) where the experimental data of the 5R curve in Figure 2 is compared with the fitting equations based on the assumptions of diffusion controlled, moving-interface controlled, nucleation-and-growth controlled and

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gas-desorption controlled reactions, respectively. These figures show visually that nucleation-and-growth controlled reactions provide the best fit to the experimental data of the

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5R curve, consistent with the R-square value analysis. The same conclusion can be attained for 1R, 2R, 3R, 4R and 4R data. Therefore, it is concluded that the dehydrogenation kinetics of the BMAS powder with 25% LiBH4 is controlled by nucleation and growth of the dehydrogenation products.

To support the conclusion above, the details of the nucleation-and-growth controlled reactions are considered further. It is known that nucleation and three-dimensional growth controlled reactions are well-described by the Johnson-Mehl-Avrami (JMA) equation [36]. Since the smallest m obtained from the curve fitting is 3.27 (5R sample in Table 3), the growth of nuclei should be three-dimensional. 7

ACCEPTED MANUSCRIPT t

− ln(1 − f ' f ) = (4π / 3) ϒ 3 ∫ I (t − τ ) 3 d τ

(15)

0

where ϒ is the growth rate, I is the nucleation rate per unit volume, and

τ

is a finite

time interval. The growth rate ϒ is typically treated as a constant during an isothermal

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reaction, while the nucleation rate I is also considered as unchanged in many literatures [37-39]. However, for a more general case we relax this limitation and allow I to be a function of holding time and cycle numbers because powder characteristics change with

pre-existing at time t = 0, − ln(1 − f ' f ) = (4π / 3) ϒ

t

3

∫ ct

x

(t − τ ) 3 d τ

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0

after integration,

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holding time and particularly with cycle numbers. Assume I = ct x and there are N0 nuclei

−ln(1− f ' f ) = (π / 3)ϒ3 (N0t3 + ct 4+x ) let

k = (π /3)ϒ3 , then we have

1 ] = ln k + ln( N0t3 + ct 4+x ) ln(1− f ' f )

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ln[

(17)

(18)

1 ] = ln k + m ln t , which is used for the ln(1− f ' f )

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Comparing Eq. (18) with Eq. (14), i.e., ln[

(16)

data regression, the following qualitative arguments can be obtained.

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(i) when x = 0, the nucleation rate is constant as I = c . In this case t 4 + x = t 4 over rules t 3 and thus ln[

1 ] ≈ ln k + ln(ct 4+ x ) = ln k + ln c + (4 + x)ln t , m= 4 ; ln(1− f ' f )

(ii) when x > 0 , the nucleation rate increases with time as I = ct x . Similar to earlier case, t 4 + x dominates t 3 and thus, m = 4 + x . In this particular case, m will be larger than 4;

(iii) when −1 < x < 0 , the nucleation rate I = cx

and diminished with time. t 4 + x leads t 3

t

and thus, m = 4 + x , lies in between 3 and 4; (iv) when x ≤ − 1 , the nucleation vanishes faster than the last case. However, here the leading order is t 3 and thus, m = 3 . 8

ACCEPTED MANUSCRIPT Summarizing the above four cases with all the scenarios included, we can conclude that the value of m is determined by the dependence of the nucleation rate on the reaction time. There are three regimes of the m value. Between 3 and 4 (not include 4), the nucleation rate decrease as reaction continues. At m = 4, the nucleation rate is constant. Values larger

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than 4 indicate accelerating nucleation as reaction goes on. Similar results can be found in Ref. [40].

Applying the aforementioned physical meaning of m to the data in Table 3, the following trends can be established. For the first two dehydrogenation processes, the m

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values are slightly larger than 4, indicating an increased nucleation rate with time. Furthermore, the larger departure from 4 for m in the first dehydrogenation corresponds to the

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faster nucleation rate, suggesting that the nucleation rate for the first dehydrogenation (m = 4.165) is faster than that of the second one (m = 4.077). Starting from the third cycle, m becomes smaller than 4, implying the vanishing nucleation as reaction proceeds. It can also be seen that the fitted m values as well as the k values gradually go down with increasing cycles of dehydrogenation, suggesting the degradation of the kinetics performance. In

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addition, it appears that the degradation has stopped after 5 cycles of dehydrogenation and re-hydrogenation because both m and k values in Table 3 have little change from 5R to 6R samples. The mechanism(s) responsible for the degradation of the kinetics performance is

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discussed below.

A note should be given that in our case, the nucleation involves two solid phases and takes place at the solid-solid interface. Therefore, the nucleation rate is closely related to the

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area of the interface, rather than the volume from the JMA equation (15). In the beginning of the experiment, the interface area is quite large because of the relatively small solid particles due to the nature of the BMAS process. As a result, the nucleation rate is fast in the first and second dehydrogenation processes. As dehydrogenation cycles increase, the solid particles grow in size and the interface area decreases in the reactants. This reasonably explains the degradation of the reaction kinetics, and more details will be discussed in Section 3.3. Previously, our group has demonstrated that the rate-limiting step for solid-state dehydrogenation of the ball-milled LiBH4 + MgH2 mixture is diffusion controlled [38]. 9

ACCEPTED MANUSCRIPT However, the curve fitting of the diffusion-controlled model for the BMAS powder with 25% LiBH4 has excluded this possibility based on the following reasons. First, the R-squared values for diffusion-controlled reactions are the smallest (Table 1) among all the four mechanisms investigated. Second, the first constant on the right side of the equation from the

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diffusion-controlled reaction is 20% to 39% deviated from 1 (i.e., 1.197 – 1.386) when compared with Eq. (10), whereas that constant for the moving-interface-controlled reaction is only 8% to 15% (1.075 – 1.147) deviated from 1 when compared with Eq. (11). This constant is required to be equal to 1 for both diffusion-controlled and moving-interface-controlled

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reactions. Otherwise, the models have no physical meaning. The larger departure from 1 for the diffusion-controlled reaction, combining with its unsatisfactory R-square values, helps us

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to rule out the possibility of the diffusion-control reaction. Therefore, it can be concluded that the rate-limiting step for dehydrogenation has changed from the diffusion-controlled reaction for the ball-milled LiBH4 + MgH2 mixture to the nucleation/growth-controlled reaction for the BMAS powder with 25% LiBH4. Such a change can be attributed to the much smaller LiBH4 particles generated from the aerosol sprayed LiBH4/THF solution for the BMAS

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mixture than the LiBH4 obtained from hydrogenation of the bill-milled LiH + MgB2 powders [38]. The substantially reduced particle sizes of the BMAS powder lead to a greatly decreased diffusion time. As a result, the nucleation and subsequent growth of LiH and MgB2

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products at the MgH2/LiBH4 interface have become the slowest reaction step. What we should note here is that the perquisite of aforementioned kinetics analysis is assuming that all the involving particles are monodisperse, which is not possible for the real

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experimental system. Nevertheless, it is proposed [41] that for the dehydrogenation and re-hydrogenation kinetics, the distribution of particle size has little influence if the reacted fraction,

, is smaller than 60%. Even when

is higher than 60%, the deviation from the

behavior of monodisperse particles is still no more than 5% [41]. Therefore, the present conclusion obtained based on the assumption of monodisperse particles is valid for the BMAS powder with 25% LiBH4 because the largest fractions reacted in the first dehydrogenation is only 63%.

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ACCEPTED MANUSCRIPT 3.2 Reaction Pathways and Kinetics of Elementary Reactions As established previously in Ref. [20], the unusually high reversible hydrogen storage for the BMAS powder with 25% LiBH4 is accomplished through two parallel reaction pathways. One is the MgH2-Mg pathway, i.e., nano-MgH2 decomposes to form Mg and H2

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first via reaction (2) and then Mg reacts with LiBH4 to form MgB2, LiH and H2 via reaction (3). The other is the LiBH4-Li2B12H12 pathway, i.e., nano-LiBH4 decomposes to form Li2B12H12 and H2 first via reaction (4) and then Li2B12H12 reacts with MgH2 to form MgB2, LiH and H2 via reaction (5). These reaction pathways become possible because of the

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presence of nano-MgH2 and nano-LiBH4 and their intimate mixing, enabled by the BMAS process [20]. For more detailed analysis and establishment of the two parallel reaction

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pathways, please refer to Ref. 20. However, it should be emphasized that both reaction pathways require reactions between two solid reactants. Specifically, reaction between LiBH4 and Mg, i.e. reaction (3), is required for the MgH2-Mg pathway, whereas reaction between Li2B12H12 and MgH2, i.e. reaction (5), is a must for the LiBH4-Li2B12H12 pathway. Because of these solid state reactions (3) and (5), the areas of interfaces between solid reactants are

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critical for the overall reaction rates. The finer the particles and the more uniform mixing of the reactants, the larger interfacial areas between the reactants and thus the faster reaction kinetics.

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Since we have proven in Section 3.1 that the overall solid-state dehydriding reaction for the BMAS powder with 25% LiBH4 is nucleation/growth-controlled, it is invaluable to consider the kinetics effects of the four possible elementary reactions, getting more insights

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into the kinetics nature of each elementary reaction. Such analysis is described below. Dehydrogenation via the MgH2-Mg Pathway: The analysis of the dehydriding

curves of the ball-milled (640 min) and hand-mixed MgH2 + 5 vol.% C mixtures with the aid of Eq. (10), is shown in Figure 4. Clearly, whether with or without ball milling, the dehydrogenation of MgH2 + 5 vol. % mixture can be represented as a diffusion-controlled reaction.

By

comparison,

analyses

of

these

two

processes

using

the

moving-interface-controlled reaction model (Figure S3a), nucleation/growth controlled reaction model (Figure S3b) and gas-desorption-controlled reaction model (Figure S3c) do 11

ACCEPTED MANUSCRIPT not result in satisfactory results. The linear fitting equations obtained from the diffusion-controlled reaction model, corresponding to the ball-milled and hand-milled

(1 − ′ ⋅ )

/

= 1.012 − 0.0003

(1 − ′ ⋅ )

/

= 1.005 − 0.00007

/

R2 = 0.9918

(19)

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mixtures respectively, are shown in Eqs. (19) and (20) below.

(20)

with /

with

R2 = 0.9364

Since the particle size reduction of MgH2 in the BMAS powder with 25% LiBH4 is

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also achieved through ball milling, it is reasonable to conclude that the rate-controlling step of reaction (2) for the BMAS powder with 25% LiBH4 is also the H2 diffusion through a Mg

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product layer (Fig. 5a). The driving force of the diffusion has been attributed to the density gradient of greater H2 concentration at the interfacial areas between MgH2 and Mg when compared with the H2 concentration at the Mg surface. Whether the Mg product layer generated during the decomposition of MgH2 is porous or not is analyzed through the theory of Pilling–Bedworth (P-B) ratio [42]. The Pilling–Bedworth ratio (RPB) for the common

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oxidizing reaction (21) is shown in Eq. (22). RPB has been employed to determine whether the metal can form protective oxides on the metal surface during oxidation since 1923 [42, 43].

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. -(&) + /2 0 (1) → -3 04 (&) 567 =

89: ;< 89

=9: ;< ∙ ?9

= 3 ∙ =

9 ∙ ?9: ;<

(21)

(22)

where VMx Oy and VM stand for the molar volumes of the oxide film and the metal reacted, respectively; MMx Oy and MM are the molecular masses of the oxide and metal, respectively; and ρM

x Oy

and ρM are the densities of the oxide and metal, respectively. It is

generally agreed that when RPB is smaller than 1, a porous and adherent oxide film would be generated. When RPB is between 1 and 2, the oxide coating is passivating and provides a 12

ACCEPTED MANUSCRIPT protecting effect against further surface oxidation. However, the oxide film would crack and chip off if RPB is larger than 2. Since VMgH2 and VMg are 18.15 cm3 mol-1 and 13.98 cm3 mol-1, respectively, RPB for reaction (2) is calculated to be 0.77, which suggested that the obtained Mg product layer here should be porous and also adherent. H2 is required to diffuse

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through this layer before its desorption from the Mg surface to ensure the continuous decomposition of MgH2.

Based on the discussion above, reaction (2) can be described in three elementary

MgH → Mg + H ●

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H ● → H ○

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steps, as expressed in Eq. (23) – (25) below and schematically shown in Figure 5(a).

H ○ → H + ○

(23) (24) (25)

Here, Eq. (23) represents decomposition of MgH2 into Mg at the interface between MgH2 and Mg, accompanying with the formation and absorption of H2 at an active interfacial site, ●.

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Eq. (24) describes the process that H2 diffuses from an active interfacial site, ●, to an active Mg surface site, ○. Finally, Eq. (25) presents H2 desorbs from the active Mg surface site (see Figure 5a).

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Since Section 3.1 has established that the overall dehydrogenation of the BMAS powder with 25% LiBH4 is nucleation-and-growth controlled and the analysis of this section (Figure 4) has proven that reaction (2) is diffusion-controlled, it is then reasonable to deduce

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that reaction (3) is nucleation-and-growth controlled. This nucleation-and-growth controlled reaction can be described in three elementary steps as expressed by Eqs. (26) to (28) and schematically shown in Figure 5(b).

Mg + LiBH → Mg + ◆ + LiBH Mg + ◆ + 2 LiBH → 2 LiH + MgB + 3 H ◆ H ◆ → H + ◆

(26) (27) (28) 13

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Here, Eq. (26) represents the contact of Mg with LiBH4 to form an active Mg/LiBH4 interface site, ◆ , and Eq. (27) stands for Mg reacting with LiBH4 to form LiH and MgB2, accompanied by H2 absorption at the active Mg/LiBH4 interface. Finally, Eq. (28) describes

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desorption of H2 from the Mg/LiBH4 interface, leaving behind an active interface site. Based on these elementary steps, it can be concluded that large interfacial areas between Mg and LiBH4 nanoparticles are needed for reaction (3) to occur. In addition, the rate-limiting step for this reaction is the nucleation and growth of LiH and MgB2 particles. Furthermore, this is

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also the slowest step for reactions (2) and (3), leading to the overall dehydrogenation of the BMAS powder with 25% LiBH4 exhibiting the nucleation-and-growth controlled kinetics.

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Dehydrogenation via the LiBH4-Li2B12H12 Pathway: A previous study [44] on the dehydrogenation properties from nanoscale LiBH4 obtained from the LiBH4/THF solution has shown that the slowest reaction step for reaction (4), i.e., the decomposition of nano-LiBH4 at 265 °C, is H2 desorption on the surface. Since the nano-LiBH4 in the BMAS powder with 25% LiBH4 is also produced through aerosol spraying of the LiBH4/THF solution, it is

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reasonable to conclude that reaction (4) is gas-desorption controlled. Considering the solid products of reaction (4), Li2B12H12 + 10 LiH, as a whole, the RPB value of reaction (4) could be calculated to be 0.63 because the molar volume of LiBH4 is 32.71 cm3 mol-1 and the molar

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volume of (Li2B12H12 + 10 LiH) is 248.26 cm3 mol-1. Here the density value of Li2B12H12 is taken to be 1.029 g cm-3, calculated from ICSD using POWD-12 based on the proposed

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structure [45]. Thus, the (Li2B12H12 + 10 LiH) product layer from reaction (4), if present on the surface of the LiBH4 core, would also be adherent and porous. Based on the discussion above, reaction (4) can be schematically shown in Figure 6(a) and expressed by Eqs. (29) to (31) with the following three elementary steps.

12 LiBH → ( Li B H + 10 LiH ) + 13 H █

(29)

13 H █ → 13 H □

(30)

13 H □ → 13 H + 13 □

(31)

14

ACCEPTED MANUSCRIPT Here, Eq. (29) represents decomposition of LiBH4 to (Li2B12H12 + 10 LiH) at the interface between LiBH4 and (Li2B12H12 + 10 LiH), accompanying with the formation and absorption of H2 at an active interfacial site, ■, whereas Eq. (30) describes the process that, H2 diffuses from an active interfacial site, ■, to an active (Li2B12H12 + 10 LiH) surface site, □. Finally,

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Eq. (31) presents H2 desorbs from the active (Li2B12H12 + 10 LiH) surface site (see Figure 6a).

Since the overall dehydrogenation of the BMAS powder with 25% LiBH4 is nucleation/growth controlled and the rate-limiting step for reaction (4) is gas desorption, it

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can then be deduced that reaction (5), i.e., the reaction between MgH2 and Li2B12H12 to form MgB2, LiH and H2, is a nucleation/growth controlled reaction. Furthermore, the nucleation

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and growth of the reaction products is the slowest step if the dehydrogenation of the BMAS powder with 25% LiBH4 proceeds through the LiBH4-Li2B12H12 pathway. The elementary steps for reaction (5) can be described by Eqs. (32) to (34) and schematically shown in Figure 6(b).

+ MgH → Li B H ◇ MgH

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Li B H

Li B H ◇ 6 MgH → 2 LiH + 6 MgB + 11 H ◇

(33) (34)

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11 H ◇ → 11 H + 11 ◇

(32)

Here, Eq. (32) represents Li2B12H12 contact with MgH2 to form an active Li2B12H12/MgH2

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interface site, ◇, while Eq. (33) stands for Li2B12H12 reacting with MgH2 to form LiH and MgB2, accompanied by H2 absorption at the active Li2B12H12/MgH2 interface. Eq. (34) describes desorption of H2 from the Li2B12H12/MgH2 interface, leaving behind an active interface site.

It is interesting to note that the rate-limiting step for both the MgH2-Mg and LiBH4-Li2B12H12 dehydrogenation pathways are associated with the nucleation and growth of the reaction products LiH and MgB2, enabled by large interfacial areas between the reactants LiBH4 and Mg for reaction (3) and Li2B12H12 and MgH2 for reaction (5). These results indicate that nucleation and growth of LiH and/or MgB2 are slow. Thus, in order to have fast 15

ACCEPTED MANUSCRIPT nucleation and growth of LiH and MgB2, one needs to generate nano-LiBH4 + nano-MgH2 with the small particle sizes before cycles of dehydrogenation and re-hydrogenation at 265 o

C. The ultrafine LiBH4 and MgH2 particles and their intimate mixing can offer large

interfacial areas between reactants to form LiH and MgB2 through reactions (3) and (5). Finer

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particle sizes could be readily achieved by extending the ball milling time. To suppress particle growth during dehydrogenation and re-hydrogenation cycles, the crystal growth inhibitor can be added during ball milling. Various additives, such as TiH2 [46], TiC [47], Mg~6Ni [48], Ni@rGO nanocomposite [49], Fe clusters@ grapheme [50] and

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TiB2@grapheme nanosheets [51], are all proved to act as not only a grain refiner during ball milling but also a crystal growth inhibitor for Mg during cycling of hydrogen release and

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uptake. It is also worth noting that Ostwald ripening phenomenon that would bring about larger particle growth at the expense of smaller particles has been effectively suppressed for the LiNH2 + LiH system after substantial high-energy ball milling [52]. This becomes possible because long-time ball milling results in uniform particle sizes. As a result, there is little or no driving force for a particular particle to grow at the expense of other particles.

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Therefore, extensive high-energy ball milling with the addition of crystal growth inhibitors should be the simplest and most effective method to improve the dehydrogenation kinetics and cycle stability. The effects of large interfacial areas and other powder characteristics on

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characterizations.

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the dehydrogenation kinetics are further discussed below with the aid of various powder

3.3 Powder Characteristics of the BMAS Mixture The investigation of powder characteristics before and after dehydrogenation and

cycling can provide additional insights into the kinetics and mechanisms for the dehydrogenation of the BMAS powder with 25% LiBH4. XRD patterns of the BMAS powder under various conditions are shown in Figure S7. Based on Figure S7, the crystallite size of MgH2 has been calculated using the Scherrer formula [29] and summarized in Table 1 through which the gradual growth of the crystallites of MgH2 particles has been noticed as the number of dehydrogenation and re-hydrogenation cycles increase. 16

ACCEPTED MANUSCRIPT The crystallite sizes of LiBH4 cannot be identified from XRD due to its amorphous state. Thus, we have sprayed LiBH4/THF solution to a porous PTFE membrane and examined the morphology and size of the particles trapped by the PTFE membrane using SEM. The result indicates that aerosol sprayed LiBH4 particles are indeed in the range of 20 to 100 nm

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(see Figure S4). Thus, when sprayed into a ball milling canister during the BMAS process, these LiBH4 nanoparticles are expected to be occluded into MgH2 nanoparticles because of repeated fracture and cold welding of MgH2 during ball milling, thereby creating a uniform mixture of MgH2 and LiBH4 at nanoscales. Given that the isothermal dehydrogenation

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temperature (265 °C) is 96% of LiBH4’s melting temperature (275 °C) and the holding time is 20 h per dehydrogenation/re-hydrogenation cycle, both crystallite and particle growth of

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LiBH4 should be expected [54].

The evidence for particle growth can be obtained through SEM imaging and BET surface area measurements. The specific surface areas (SSA) of the BMAS powder with 25% LiBH4 at various conditions, determined using the BET method, are summarized in Table 5. Several interesting trends are noted from this set of data. First, the hand mixed MgH2 + C

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mixture has the highest SSA because the SSA of the hand mixed MgH2 + 5 vol.% C mixture before BMAS is dominated by the pre-milled graphite with a very large SSA (~630 m2/g) [55]. Second, due to the occlusion of graphite particles by MgH2 and LiBH4 during the

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BMAS process, the SSA of the BMAS mixture has reduced from 67.7 to 13.4 m2 g-1. Third, the subsequent thermal exposure during dehydrogenation and re-hydrogenation cycles has reduced the SSA further from 13.4 to approximately 0.7 – 1.4 m2 g-1. Since the decrease in

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the SSA can only be caused by the following three phenomenon: (i) particle growth, (ii) agglomeration of multiple particles, or (iii) both [39], it can be concluded that particle growth and/or agglomeration of multiple particles have taken place during cycling. To further reinforce this conclusion, SEM examination was performed. By comparison of Figure 7(a) and (b), the particle sizes of the BMAS powder with 25% LiBH4 have been decreased to ~100 nm, which is much smaller than that of the hand-mixed MgH2 + 5 vol.% C mixture (~1 µm). However, some of the particles have been discovered to be ~500 nm (Figure 7e), after the sixth dehydrogenation. These evidences unambiguously indicate that gradual particle 17

ACCEPTED MANUSCRIPT growth and agglomeration have taken place during dehydrogenation and hydrogenation cycles, consistent with the conclusion derived from the SSA analysis. As discussed in Section 3.2, the dehydrogenation and re-hydrogenation of the BMAS powder are through two parallel reaction pathways, i.e., the MgH2-Mg pathway with

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reactions (2) and (3) and the LiBH4-Li2B12H12 pathway with reactions (4) and (5). MgH2 with nanosize is necessary for reactions (2) and (3), whereas, LiBH4 with nanosize is indispensable for reactions (4) and (5). The onset temperature would be higher than 265 oC for reactions (2) and (4), if the particles sizes of MgH2 and LiBH4 reactant are larger than

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nano-scale [24, 44]. In addition, large interfacial area is the prerequisite for reactions (3) and (5) to take place, which have also been proven to be the rate-limiting step, happening at 265 o

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C [55, 56]. Thus, the powder characterization results discussed above can provide the

reasons why the H2 storage capacity of the BMAS powder with 25% LiBH4 gradually decreases as the number of cycles increases, as observed in Figure 2. Since the growth of crystallite and particle sizes and the reduction in the interfacial area will lead to the gradual decay of dehydrogenation kinetics, future work should aim at preventing crystallite and

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particle growth as well as minimizing gradual loss of interfacial areas.

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IV. Concluding Remarks

The present study provides detailed investigation of the dehydrogenation kinetics of a nano-LiBH4 + nano-MgH2 mixture in a 0.5:1 molar ratio (the BMAS powder with 25%

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LiBH4 mixture). The intimate mixing of nano-LiBH4 and nano-MgH2 is achieved through an automated BMAS process with high-energy ball milling time of 640 min and 56 BMAS cycles. The major conclusions drawn from this study are follows. 1) BMAS is effective in producing nano-LiBH4 + nano-MgH2 mixture with intimate mixing. As a result, the rate-limiting step has been altered from H2 diffusion for the ball-milled nano-LiBH4 + nano-MgH2 mixture [38] to nucleation/growth-controlled dehydrogenation for the BMAS powder with 25% LiBH4 mixture.

18

ACCEPTED MANUSCRIPT 2) The rate-limiting step for the BMAS powder with 25% LiBH4 mixture is identified to be the nucleation and growth of LiH and MgB2 at the interfacial area between nano-LiBH4 and nano-MgH2. 3) The kinetics performance of the BMAS powder with 25% LiBH4 mixture during

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isothermal cycling at 265 oC degrades gradually. The nucleation rates increase with time for the first two dehydrogenation cycles. However, the vanishing nucleation is discovered in the subsequent cycles.

4) The MgH2-Mg reaction pathway proceeds in two major steps: (i) decomposition of

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MgH2 which is rate-limited by the diffusion of H2 through the porous Mg product layer outside the MgH2 shrinking core and (ii) reaction between Mg and LiBH4 the rate of which

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is controlled by the nucleation and growth of LiH and MgB2 at the Mg/LiBH4 interface. 5) The LiBH4-Li2B12H12 reaction pathway proceeds in two major steps: (i) decomposition of nano-LiBH4 the rate of which is controlled by H2 gas desorption on the surface of the (Li2B12H12 + 10LiH) product layer outside the LiBH4 shrinking core and (ii) reaction between Li2B12H12 and MgH2 which is rate-limited by the nucleation and growth of LiH and

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MgB2 at the Li2B12H12/MgH2 interface.

6) The degradation of the kinetics performance and gradual decay in the reversible hydrogen storage capacity of the BMAS powder with 25% LiBH4 can be associated with

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gradual increases in the crystallite and particle sizes and a decrease in the interfacial area

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during hydrogenation and dehydrogenation cycles.

Acknowledgements – This work was supported under the U.S. National Science Foundation (NSF) with the Award No. CMMI-1261782. The assistance in collecting the SSA data by Mr. Maziar Ashuri at Illinois Institute of Technology is greatly appreciated.

References

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ACCEPTED MANUSCRIPT [18] L. Ouyang, Z. Cao, H. Wang, J. Liu, D. Sun, Q. Zhang, M. Zhu, Enhanced dehydriding thermodynamics and kinetics in Mg (In)–MgF2 composite directly synthesized by plasma milling, J. Alloys Compd. , 586 (2014) 113-117. [19] J.J. Vajo, S.L. Skeith, F. Mertens, Reversible storage of hydrogen in destabilized LiBH4, The Journal of Physical Chemistry B, 109 (2005) 3719-3722. [20] Z. Ding, Y. Lu, L. Li, L.L. Shaw, High Reversible Capacity Hydrogen Storage through Nano-LiBH 4 + Nano-MgH 2 System, Energy Storage Materials, (2019) In Press. Li–Mg–B–H systems, J. Alloys Compd. , 446 (2007) 306-309.

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[21] T. Nakagawa, T. Ichikawa, N. Hanada, Y. Kojima, H. Fujii, Thermal analysis on the [22] F.E. Pinkerton, M.S. Meyer, G.P. Meisner, M.P. Balogh, J.J. Vajo, Phase boundaries and reversibility of LiBH4/MgH2 hydrogen storage material, J. Phys. Chem. C, 111 (2007) 12881-12885.

[23] J. Yang, A. Sudik, C. Wolverton, Destabilizing LiBH4 with a metal (M= Mg, Al, Ti, 19134-19140.

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V, Cr, or Sc) or metal hydride (MH2= MgH2, TiH2, or CaH2), J. Phys. Chem. C, 111 (2007) [24] Z. Ding, X. Zhao, L.L. Shaw, Reaction between LiBH 4 and MgH 2 induced by high-energy

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ball milling, J. Power Sources 293 (2015) 236-245.

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[27] M. Güvendiren, E. Baybörü, T. Öztürk, Effects of additives on mechanical milling

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and hydrogenation of magnesium powders, Int. J. Hydrogen Energy 29 (2004) 491-496. [28] C. Wu, P. Wang, X. Yao, C. Liu, D. Chen, G. Lu, H. Cheng, Hydrogen storage properties of MgH2/SWNT composite prepared by ball milling, J. Alloys Compd. , 420 (2006) 278-282. [29] A. Zaluska, L. Zaluski, J. Ström-Olsen, Structure, catalysis and atomic reactions on the nano-scale: a systematic approach to metal hydrides for hydrogen storage, Appl.

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Phys. A 72 (2001) 157-165.

[30] J. Huot, G. Liang, R. Schulz, Mechanically alloyed metal hydride systems, Appl. Phys. A 72 (2001) 187-195.

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[31] Z. Huang, Z. Guo, A. Calka, D. Wexler, J. Wu, P. Notten, H. Liu, Noticeable improvement

in

the

desorption

temperature

from

graphite

in

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MgH2/graphite composite, Mater. Sci. Eng. A, 447 (2007) 180-185. [32] L.L. Shaw, R. Ren, T. Markmaitree, W. Osborn, Effects of mechanical activation on dehydrogenation of the lithium amide and lithium hydride system, J. Alloys Compd. , 448 (2008) 263-271.

[33] L. Dinh, C. Cecala, J. Leckey, M. Balooch, The effects of moisture on LiD single crystals studied by temperature-programmed decomposition, J. Nucl. Mater. , 295 (2001) 193-204. [34] G. Welsch, P.D. Desai, Oxidation and Corrosion of Intermetallic Alloys, in, METALS INFORMATION ANALYSIS CENTER WEST LAFAYETTE IN, 1996.

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ACCEPTED MANUSCRIPT [35] T. Markmaitree, R. Ren, L.L. Shaw, Enhancement of lithium amide to lithium imide transition via mechanical activation, The Journal of Physical Chemistry B, 110 (2006) 20710-20718. [36] M. Avrami, Kinetics of phase change. I General theory, J Chem Phys., 7 (1939) 1103-1112. [37] J.W. Christian, The theory of transformations in metals and alloys, Newnes, 2002. [38] X. Wan, T. Markmaitree, W. Osborn, L.L. Shaw, Nanoengineering-enabled solid-state

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hydrogen uptake and release in the LiBH4 plus MgH2 system, J. Phys. Chem. C, 112 (2008) 18232-18243.

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[41] M.H. Mintz, Y. Zeiri, Hydriding kinetics of powders, J. Alloys Compd. , 216 (1995) 159-175. 529-582.

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[42] N. Pilling, The oxidation of metals at high temperature, J. Inst. Met., 29 (1923) [43] H. Rode, D. Orlicki, V. Hlavacek, Noncatalytic gas‐solid reactions and mechanical stress generation, AlChE J. , 41 (1995) 1235-1250.

[44] X. Wan, L.L. Shaw, Novel dehydrogenation properties derived from nanoscale LiBH4, Acta Mater. , 59 (2011) 4606-4615.

[45] M. Paskevicius, M.P. Pitt, D.H. Brown, D.A. Sheppard, S. Chumphongphan, C.E. Buckley, First-order phase transition in the Li 2 B 12 H 12 system, PCCP 15 (2013)

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15825-15828.

[46] M. Ponthieu, M. Calizzi, L. Pasquini, J. Fernández, F. Cuevas, Synthesis by reactive ball milling and cycling properties of MgH2–TiH2 nanocomposites: Kinetics and isotopic effects, Int. J. Hydrogen Energy 39 (2014) 9918-9923. [47] M.S. El-Eskandarany, E. Shaban, A.A. Alsairafi, Synergistic dosing effect of nanocatalysts

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nanocrystalline MgH2 powders, Energy, 104 (2016) 158-170. [48] A. Teresiak, M. Uhlemann, J. Thomas, A. Gebert, The metastable Mg∼ 6Ni

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ACCEPTED MANUSCRIPT [52] W. Osborn, T. Markmaitree, L.L. Shaw, The long-term hydriding and dehydriding stability of the nanoscale LiNH2+ LiH hydrogen storage system, Nanotechnology, 20 (2009) 204028. [53] H.P. Klug, L.E. Alexander, X-ray diffraction procedures: for polycrystalline and amorphous materials, X-Ray Diffraction Procedures: For Polycrystalline and Amorphous Materials, 2nd Edition, by Harold P. Klug, Leroy E. Alexander, pp. 992. ISBN 0-471-49369-4. Wiley-VCH, May 1974., (1974) 992.

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[54] R.M. German, Powder metallurgy science, Metal Powder Industries Federation, 105 College Rd. E, Princeton, N. J. 08540, U. S. A, 1984. 279, (1984).

[55] K. Crosby, L.L. Shaw, Dehydriding and re-hydriding properties of high-energy ball milled LiBH4+ MgH2 mixtures, Int. J. Hydrogen Energy 35 (2010) 7519-7529.

[56] Y. Zhong, X. Wan, Z. Ding, L.L. Shaw, New dehydrogenation pathway of LiBH 4+ MgH

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2 mixtures enabled by nanoscale LiBH 4, Int. J. Hydrogen Energy 41 (2016) 22104-22117.

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Tables

Table 1. The linear equations obtained from curve fitting of the dehydrogenation data in Figure 2 with the aid of Eq. (10) through the least-squares method

(1-f’f)1/3 =1.386 - 0.0032 t1/2

2R

(1-f’f)1/3 =1.298 - 0.0024 t1/2

3R

(1-f’f)1/3 =1.279 - 0.0023 t1/2

4R

(1-f’f)1/3 =1.250 - 0.0021 t1/2

5R

(1-f’f)1/3 =1.219 - 0.0019 t1/2

6R

(1-f’f)1/3 =1.197 - 0.0017 t1/2

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1R

R-square 0.9393 0.9175 0.9390

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Linear Equations

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Sample ID

0.9403 0.9443 0.9383

1R

Linear Equations

R-square

(1-f’f)1/3 =1.147 – 0.000010 t

0.9500

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Sample ID

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Table 2. The linear equations obtained from curve fitting of the dehydrogenation data in Figure 2 with the aid of Eq. (11) through the least-squares method

(1-f’f)1/3 =1.120 - 0.000008 t

0.9576

(1-f’f)1/3 =1.108 - 0.000008 t

0.9704

4R

(1-f’f)1/3 =1.096 - 0.000007 t

0.9734

5R

(1-f’f)1/3 =1.083 - 0.000006 t

0.9771

6R

(1-f’f)1/3 =1.075 - 0.000005 t

0.9743

2R

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3R

1

ACCEPTED MANUSCRIPT

Sample ID

Linear Equations

R-square

1R

In{In[1/(1-f’f)]} = -43.797 + 4.165 In t

0.9596

2R

In{In[1/(1-f’f)]} = -46.393 + 4.077 In t

3R

In{In[1/(1-f’f)]} = -41.585 + 3.917 In t

4R

In{In[1/(1-f’f)]} = -38.132 + 3.576 In t

5R

In{In[1/(1-f’f)]} = -35.031 + 3.268 In t

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Table 3. The linear equations obtained from curve fitting of the dehydrogenation data in Figure 2 with the aid of Eq. (14) through the least-squares method

6R

In{In[1/(1-f’f)]} = -35.773 + 3.327 In t

0.9792

0.9750 0.9808

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0.9834

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0.9801

Table 4. The linear equations obtained from curve fitting of the dehydrogenation data in Figure 2 with the aid of Eq. (13) through the least-squares method

2R 3R 4R

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5R 6R

R-square

f’f = -0.318 - 0.000024 t1/2

0.9543

f’f = -0.282 - 0.000019 t1/2

0.9664

f’f = -0.254 - 0.000018 t1/2

0.9719

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1R

Linear Equations

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Sample ID

f’f = -0.230 - 0.000017 t1/2

0.9799

f’f = -0.201 - 0.000015 t1/2

0.9744

f’f = -0.186 - 0.000014 t1/2

0.9735

2

ACCEPTED MANUSCRIPT Table 5. XRD-determined crystallite sizes of MgH2 and the measured specific surface areas of various mixtures indicated Crystallite size of MgH2 (nm)

Specific surface area (m-2/g)

Hand mixed MgH2 + C

64.88

67.741

BMAS

28.64

13.426

1R

∗N/D

1S

48.84

6R

65.70

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Sample ID

1.358

1.332

0.725

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∗ N/D stands for “not detectable”. After dehydrogenation, the MgH2 peak is too small (almost

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disappear) to quantify the MgH2 crystallite size.

3

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Figure 1. (a) Schematic of the automated BMAS device and (b) its operation flow-chart where “1” means “on” and “0” means “off” on the Y axis. Note that the three functions of the automated BMAS machine, i.e., ball milling (BM), aerosol spraying (AS) and vacuuming, are controlled independently by Eaton EASY 512-AC-RC programmable control relay module.

1

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Figure 2. Comparisons in dehydrogenation and re-hydrogenation behaviors of the BMAS powder with 25% LiBH4: (a) the first dehydrogenation (1R), (b) the second dehydrogenation (2R), (c) the third dehydrogenation (3R), (d) the forth dehydrogenation (4R), (e) the fifth dehydrogenation (5R), and (f) the sixth dehydrogenation (6R) as a function of time. Note that (g) represents the temperature ramp as a function of time, while (a’), (b’), (c’), (d’) and (e’) are the corresponding re-hydrogenation processes for (a), (b), (c), (d) and (e) processes, respectively.

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Figure 3. Comparison between the experimental data of the 5R curve in Figure 2 with the fitting equation indicated above, plotted in (a) (1 − ′ ⋅ ) / . / as defined as defined by Eq. (11); (c) by Eq. (10); (b) (1 − ′ ⋅ ) / . .

as defined by Eq. (14); (d)

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as defined by Eq.

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Figure 4. The amount of H2 released from the hand-mixed and ball-milled MgH2 + 5 vol.% C mixture, plotted in (1 − ′ ⋅ ) / / as defined by Eq. (10).

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Figure 5. Schematic of the dehydrogenation via the MgH2-Mg pathway: (a) Mg product from reaction (2) forms a continuous shell outside the MgH2 shrinking core, leading to a reaction rate controlled by H2 diffusion through the Mg product layer, and (b) reaction (3) takes place at the Mg/LiBH4 interface, leading to the nucleation and growth of MgB2 + LiH products (shown inside the dashed box), accompanied by H2 release.

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Figure 6. Schematic of the dehydrogenation via the LiBH4-Li2B12H12 pathway: (a) the (Li2B12H12 + 10 LiH) products from reaction (4) form a continuous shell outside the LiBH4 shrinking core, leading to a reaction rate controlled by H2 gas desorption at the surface of the (Li2B12H12 + 10 LiH) product layer, and (b) reaction (5) takes place at the Li2B12H12/MgH2 interface, leading to the nucleation and growth of MgB2 + LiH products (shown inside the dashed box), accompanied by H2 release.

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Figure 7. FESEM images: (a) hand-mixed MgH2 + 5 vol.% C mixture, (b) BMAS sample, (c) 1R sample, (d) 1S sample, and (e) 6R sample.

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Highlights The solid-state dehydrogenation kinetics of the MgH2 + LiBH4 mixture is nucleation-and-growth controlled.

reaction products LiH and MgB2.

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The rate-limiting step for dehydrogenation is the nucleation and growth of

The interfacial area between MgH2 and LiBH4 plays a critical role in the nucleation and growth of LiH and MgB2.

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the interfacial area between reactants.

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Decay in the reaction kinetics is associated with particle growth and decrease in