Playing Hardball with Hydrogen: Metastable ... - ACS Publications

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Playing Hardball with Hydrogen: Metastable Mechanochemical Hydrogenation of Magnesium Nitride Uri Ash-Kurlander,† Gennady E. Shter,† Shifi Kababya,‡ Asher Schmidt,*,‡ and Gideon S. Grader*,† †

Department of Chemical Engineering and Grand Technion Energy Program and ‡Schulich Faculty of Chemistry and Russell Berrie Nanotechnology Institute, Technion − Israel Institute of Technology, Haifa 32000, Israel S Supporting Information *

ABSTRACT: Although thermodynamically unfavorable, magnesium nitride hydrogenation was realized by high-energy ball milling via the formation of hydride and amide or imide. Using a vibratory mill at room temperature, with initial H2 pressures of 40−80 bar, a constant-rate pressure decrease was observed throughout 200 h experiments, reflecting hydrogenation reaction progress. A combination of 1H and 15N solid-state magic-angle spinning (MAS) NMR techniques was used to identify unambiguously the reaction products as the metastable solid mixture of magnesium hydride and magnesium amide/imide. The NMR shows that the reaction products are disordered and of nonbulk, noncrystalline character. Our thermodynamic analysis shows that considerable pressure elevation and mechanical surface destabilization favor the hydrogenation reaction. We present an original model which suggests for the first time that the local gas pressure rises considerably in a confined zone of the fine powder impacted by colliding balls in the mill. This model describes a flow-restricted, short-term, nearly isothermal pressure elevation. The demonstrated ability to facilitate such thermodynamic unfavorable reactions and create a metastable hydrogen-rich product suggests a new concept for hydrogen storage and chemical conversion processes.

1. INTRODUCTION Hydrogenation of alkaline and alkaline-earth metal nitrides has received considerable attention in the past decade since Chen et al. described1 the reversible hydrogenation of lithium nitride (Li3N) to lithium amide (LiNH2) and hydride (LiH), as expressed in the following two-step reaction, involving the lithium imide (Li2NH) intermediate 4(0)

+1

−1

N−H system. The reaction between magnesium nitride (Mg3N2) and hydrogen gas (H2), the subject of this paper, although initially investigated in the first half of the 20th century is discussed only scarcely. Whitehouse reported on the direct reduction of magnesium nitride with H2 at 400−1000 °C and stated that ″no appreciable reduction took place″.23 Gmelins Handbuch Der Anorganischen Chemie24 cites contradicting results of different attempts of the discussed reaction. In fact, the apparent reactivity may be due to moisture in insufficiently pure hydrogen, as demonstrated in the 1930 report by Duparc et al.25 about ammonia emission. More recently, the reaction of Mg3N2 with hydrogen was investigated in analogy to the Li3N reaction with hydrogen (R1) and formulated in the following steps10

2(0)

Li3N + 2H 2 ⇄ Li 2NH + LiH + H 2 2(+1)

2(−1)

⇄ LiN H 2 + 2Li H

(R1)

The reversibility of the reaction above and its 10.4 wt % hydrogen capacity make the Li−N−H system a potential hydrogen storage medium. However, the high temperatures (>700 K)2 and high vacuum1,2 needed for complete desorption from the lithium imide−hydride mixture led to investigation of systems in which the lithium is partially substituted with other metals. Magnesium is the most widely investigated counterpart.3−18 Other Mg-containing metal−N−H systems where Li is replaced by heavier alkali metals, Na8,19 and K,20 or by an alkaline-earth (e.g., Ca) were investigated as well.21,22 The focus in these reports is on hydrogen desorption; however, the rehydrogenation needed for hydrogen storage was not always achieved.8 In spite of the aforementioned work on Mg-containing systems and the importance of metal-nitrides for hydrogenstorage, only limited data are available on reactions in the Mg− © 2012 American Chemical Society

Mg 3N2 + 2H ⇄ 2MgNH + MgH2

(R2)

2MgNH + MgH2 + 2H 2 ⇄ Mg(NH 2)2 + 2MgH2 (R3)

In the past decade, these reactions were conducted both by mechanochemistry21,26−28 via ball milling and by simple gas− solid reactions under heat,10,12,29 with focus on the reverse (hydrogen desorbing) reaction direction. Ball milling is commonly used to convey mechanical forces to solidsabrade, Received: November 4, 2012 Revised: December 20, 2012 Published: December 24, 2012 1237

dx.doi.org/10.1021/jp310903k | J. Phys. Chem. C 2013, 117, 1237−1246

The Journal of Physical Chemistry C

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motor. The reactor was connected to a pressure transmitter and a temperature probe. The reactor and vibrator were kept at ambient temperature. Three different initial nominal H2 (99.999%, Maxima) pressures were investigated: 40, 60, and 80 bar. Experiments were also carried out in deuterium (99.8%, H2O < 20 ppm, Specialty Gases of America) and blank N2 atmospheres at 40 bar. The reactor was left motionless for at least 48 h before reaction, and then the vibrator was turned on for 200 h. After the reaction, the reactor was kept idle for 48 h. 2.3. Solid-State MAS NMR. Solid-state 500.31 MHz 1H and 50.70 MHz 15N MAS NMR spectroscopy measurements were carried out on a 500 MHz AVANCE III (Bruker) solidstate NMR spectrometer equipped with triple-resonance probes using 4 mm (OD) Zirconia rotors. 1 H MAS NMR spectra were obtained with 2.5 μs π/2 and 5 μs π pulse widths, with an echo interval τ equal to the rotor period TR (66.6 μs); 36 transients were collected with a 960 s relaxation delay (rd). The sample was spinning at 15 000 ± 2 Hz. Phase-Modulated Lee−Goldberg (wPMLG5)42−46 homonuclear decoupling was employed to obtain better resolved 1H MAS NMR spectra. The experimental parameters of the optimized wPMLG5 cycle employed on-resonance 1 H irradiation with a 1.9 μs pulse width, 90 kHz rf level, 0.1 μs delay for phase setting, and an overall cycle time of 20 μs. The chemical shift scale was calibrated with respect to glycine: 2.6, 3.8(CH2), and 8.0(NH3) ppm. 15 N cross-polarization (CP) MAS echo experiments (indirect excitation) were carried out with 10.0 μs π pulse widths and an echo interval τ (200 μs) identical to the rotor period TR (rotor spinning at 5000 ± 2 Hz), with a 1H decoupling level of 100 kHz and 5.0 μs π/2 pulse. Hartmann−Hahn rf levels were matched at 50 kHz, with a 1 ms contact time. Relaxation delay was 3 s, and up to 66 000 transients were collected. 15N CPMAS with Interrupted Decoupling (CPid)47 experiment used a 74 μs interval without 1H decoupling; this interval is centered about the rotor-synchronized refocusing π-pulse. In all experiments, the data points of the free induction decay signals were left-shifted to the first rotational echo position prior to the Fourier transform. Deconvolution and peak areas were calculated by DMFIT.48 The chemical shifts of 1H and 15N are reported with respect to adamantane at 1.8 ppm and (15NH4)2SO4 (solid) at 0 ppm, respectively. MgH2 (Alfa Aesar, 98%) and Mg(OH)2 (Sigma Aldrich/ Fluka, 99%) were used as reference materials for 1H MAS NMR. 2.4. Other Measurements and Calculations. Specific Surface Area (SSA) was measured using a single-point BET on a Monosorb II analyzer (QuantaChrom). X-ray powder diffraction (XRD) spectra were collected with a Diffractometer D5000 (Siemens) with Cu Kα radiation. Powder was covered with PET film. HR-SEM images were taken on a Zeiss Ultra Plus microscope. Matlab was used for numerical Gibbs energy calculations. The integral in eq 2 was calculated using Matlab’s “quad” function, with one-Joule tolerance and 10 bar spacing. The integrand (molar volume) was evaluated by Matlab’s “fsolve” function with 10−5 cm3 mol−1 tolerance.

shear, and compress them repeatedly. Consequently, particles are broken and deformed, thereby exposing fresh and reactive surfaces. The resulting enhancement of chemical reactions is referred to as mechanochemical activation.30−33 Indeed, during ball milling of Mg-amide/Mg-hydride mixtures with molar ratios of 1:127 and 1:228 (as the product of reaction R3), hydrogen was desorbed, while an imide was formed in the solid phase. In the 1:2 milled mixture the imide was a transient phase, and by the end of the experiment only Mg3N2 was detected.28 In other words, reactions R2 and R3 have proceeded in the reverse direction, almost to completion. When the mixtures are heated without milling,10 the ingredients partially decompose, emitting NH3 and H2 and giving rise to Mg and Mg3N2. Interestingly, a short milling29 was sufficient to prevent decomposition and allow H2 desorption. Similar conclusions regarding the metastable nature of hydrogenated magnesium nitride can be established from the only two recent reports about direct Mg-nitride hydrogenation. Leng et al. have confirmed that even under 100 bar of hydrogen and at 200 °C reaction R2 does not advance.12 Kojima et al. ball milled Mg3N2 for 20 h under 10 bar of hydrogen and room temperature, but their results are inconclusive.26 However, based on enthalpy first-principles calculation only, and not on the Gibbs free energy, they claim that the hydrogenation may be impossible. Using previously published experimental thermodynamic data, we show below that the change of Gibbs free energy is highly positive for the discussed reactions, so the hydrogenation is indeed unfavorable. Nevertheless, we conclusively demonstrate that high-energy ball milling facilitates this thermodynamically unfavorable reaction, producing for the first time the metastable hydrogenated and deuterogenated magnesium nitride. Using a new mechanical model developed below, we show that a local, transient elevation of gas pressure during ball collision, not accounted for previously, can be considerable. This collision-induced local pressure rise and friction-induced surface activation establish a thermodynamic state that facilitates the otherwise metastable hydrogenation. Solid-state magic-angle spinning (MAS) NMR spectroscopy was used recently to investigate related systems.19,34−41 In this study, 1H and 15N solid-state MAS NMR experiments were employed to identify the hydrogenation products in the solid Mg−N−H system. In particular, the deuterogenated nitride yielded highly resolved residual hydrogen NMR spectra that made the assignment unambiguous.

2. EXPERIMENTAL SECTION 2.1. Materials and System. An amount of 5 ± 0.02 g of magnesium nitride (Alfa Aesar, 99.6% (metals basis)) was loaded into a 32 cm3 hardened-steel reactor with 12 tungsten heavy alloy balls (d = 10 mm), at a 1:22 powder/ball mass ratio. The reactor outer length is 10 cm and 7 cm OD. The inner dimensions are 7 cm in length and 2.5 cm in diameter with hemispherical ends. The hemisphere−cylinder−hemisphere design prevents powder accumulation in dead zones. The reactor is equipped with gas inlet and outlet valves on the cylinder face. 2.2. Reactions. The reactor was handled inside a glovebox (M. Brown) filled with N2 (99.99%, Maxima), with H2O < 0.1 ppm, where all materials and products were kept and prepared for reaction and analysis. High-energy mechanochemical reaction was performed by restraining the reactor to a vibration pot mill (Pilamec Megapot), equipped with a 750 W vibration 1238



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Figure 1. Pressure (black), temperature (red), and calculated gas content (blue) during experiments under 40 bar H2 (a) and (b) and N2 (c) and (d), from 2 days before vibration started and then 10.33 days under vibration (200 h) and 2 days after the vibration was stopped. See Supporting Information for detailed gas content calculations (Figure S1).

3. RESULTS

were corrected based on the N2 blank reference as shown in the Supporting Information. The measured specific surface area (SSA) of the 60 bar experiment product is 5.4 m2/g. This SSA enables the BET close-packed monolayer adsorption50 of only 3.42 × 10−4 mole hydrogen, about 3% of the eliminated gas. Therefore, the physical adsorption of hydrogen cannot be solely responsible for the observed hydrogen consumption. The decrease in hydrogen content reflects a reaction of 1.21 × 10−2 mole hydrogen, corresponding to a magnesium nitride conversion of 12.2% in reaction R2 or 6.1% in the successive reactions R2 and R3. It should be noted that the reaction does not slow down, and the experiments were limited to 200 h only for practical experimental reasons. Therefore, a plausible conclusion is that prolonged experiments will result in higher conversions. The resulting reaction rates were found to be pressure independent. Figure 2 describes the calculated gas content during 40 and 60 bar experiments for H2 and 40 bar for D2. While the pressure was raised by 50% from 40 to 60 bar, the gas consumption rate grew by only 5%. The H2 80 bar pressure (Figure S2, Supporting Information) presents a similar behavior. Preliminary experiments at lower pressures indicate that the reaction does not slow down below 40 bar. Moreover, when H2 is replaced by D2 we note (Figure 2) that the reaction rate has only marginally decreased (5%), suggesting that the reaction is isotope-effect independent. The possible significance of these phenomena to reaction kinetics investigation is discussed in Section 4.3 below. 3.2. Solid-State MAS NMR. A combination of straightforward 1H and 15N solid-state NMR measurements provides a demonstration of the hydrogen reactive incorporation into the magnesium nitride solid phase. Figure 3 shows the 1H MAS NMR spectra of the starting material, as-received Mg3N2 (Figure 3a), and the reaction products of the H2 and D2 40

3.1. Reaction Progress. The pressure change in the reactor during a typical experiment is shown in Figure 1a,c. The periodic (24 h) pressure oscillations seen in Figure 1 are caused by day−night temperature variations. As shown, the pressure decreased when the reactor was vibrated during all hydrogen experiments and remained constant when the reactor was at rest, i.e., before and after the experiment. Analogous blank experiment under N2 only (Figure 1c), showing a constant average pressure, proves that a hydrogen-specific interaction is responsible for gas elimination in the system. Figure 1a shows the pressure decrease from 41 to 37 bar during the 40 bar H2 experiment, while Figure 1b shows the calculated gas content (mol/L) profile in the system, derived from an appropriate virial EOS.49 The temperature shown in Figures 1a and 1c is higher than ambient while the vibration is turned on, due to the heat evolved from ball collisions, powder friction, and motor operation. The calculated hydrogen gas content, shown in Figure 1b, is less sensitive to the temperature oscillations and indeed shows the definite, constant-rate decrease of H2 concentration during vibration. The presence of a hydrogen-consuming reaction is further substantiated by the constant pressure observed when neither hydrogen nor deuterium are present in the vibrated reactor. Figures 1c and 1d show pressure, temperature, and calculated gas content for the N2 experiment (40 bar). Apart from temperature-related oscillations, both the pressure and nitrogen content remain constant. The calculated N2 molar concentration in Figure 1d decreases when vibration starts (and the temperature rises) and increases when it ends. A similar behavior is found in the H2 experiments, as shown in the raw calculated data in the Supporting Information (Figure S1). This sharp initial reduction and final elevation in the H2 content 1239



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with two main broad peaks: a ∼4.9 ppm peak associated with MgH2 nonbulk hydrogens (vide infra) and a ∼−1.4 ppm peak representing Mg(NH2)2 and/or MgNH.19,35−37 The pronounced peaks exhibited in this spectrum are a manifestation of the hydrogenation reaction products. The following NMR measurements further substantiate this determination. The 1H spectrum of the hydrogenation products exhibits broad peaks with limited resolution. This broadening is attributed to the overwhelming, long-range 1H−1H dipolar couplings among the abundant hydrogen nuclei. The D2 reaction, on the other hand, yields products in which the hydrogen atoms are diluted in a sea of deuterons. The residual hydrogen arises from the 0.2% H2 in the D2 gas and from the flushing gas (see Experimental Details in the Supporting Information). In these “dilute” hydrogen products, the dipolar 1 H−1H homonuclear interactions are therefore suppressed, giving rise to a much narrower and better-resolved 1H MAS NMR spectrum (Figure 3c). This spectrum clearly reproduces the main spectral features as seen for the H2 reaction products, showing a 4.4 ppm surface hydride peak and a ∼ −1.4 ppm amide/imide peak. We note that the spinning sidebands seen in the full spectra (insets of Figures 3b and 3c) arise from dipolar interactions. The reduced sideband intensities in the spectrum of the D2 products, compared to that of the H2 products, further confirm the suppression of the dipolar interactions as a result of the hydrogen dilution. Our working assumption is that under the current mechanochemical conditions the residual hydrogens are homogenized throughout all species. The 2H MAS NMR spectra of the D2 reaction products (not shown) represent the significant Mg3N2 deuterogenation in a manner analogous to the hydrogenation reaction, further confirming that the products of both reactions originate in the supplied D2 or H 2 gases. A detailed study that will address the determination of quadrupolar coupling parameters and their correlation with the products formed is underway and will be published separately. Enhanced resolution, similar to that of the “dilute” protons (D2 reaction products), is achieved for the H2 reaction products by the application of the 1H line narrowing technique (homonuclear decoupling) 42−46 as shown by the 1 H[wPMLG5] spectrum in Figure 3d. Both the hydrogen dilution by perdeuteration and the line narrowing approach give rise to comparable narrow spectral lines where the reaction products are identified unambiguously. The assignments are consistent with existing literature and are summarized in Table S1 (see Supporting Information). The reported 1H NMR chemical shifts may vary both due to the broad, characteristic 1H line width and due to variations in preparation of the reference materials. In this class of materials our (residual and linenarrowed) 1H NMR spectra exhibit the best resolved so far. We note that the 1H chemical shift of the pure (crystalline) MgH2 phase is 3.1−3.5 ppm,19,35,36 while the shift of our mechanochemical hydride product is 4.4−4.9 ppm (Table S1, Supporting Information). To account for this apparent difference, we measured 1H spectra of as-received MgH2. A short-T1 filtered 1H spectrum (rd = 5 s; see Supporting Information, Figure S3) shows a peak at ∼4.6 ppm attributed to surface or defect sites. The fully relaxed spectrum (rd = 960 s) shows a 3.3 ppm peak consistent with previous reports. This observation indicates that our magnesium hydride product has the characteristics of surface/defect species. This distinction is compatible with the nature of the mechanochemical process and the attained low partial conversion of the Mg3 N 2

Figure 2. Calculated gas content during H2 40 and 60 bar experiments and during D2 40 bar experiment, from 48 h before vibration started (at 2 days) and until 48 h after it stopped (at 10.33 days). The concentration was calculated using suitable compression factors and corrected based on the N2 blank. The uncorrected content profiles are shown in the Supporting Information (Figure S1b).

Figure 3. 500 MHz 1H MAS NMR spectra of the as-received Mg3N2 (a) and of the reaction products from high-energy ball-milling of Mg3N2 with 40 bar H2 (b, d) and D2 (c). Spectra (a−d) show the expanded centerband region; the b and c insets show full spectra with spinning sidebands marked by * (15 kHz spinning rate). Spectra (a) and (b) are normalized, accounting for number of scans and sample weight; the two spectra in the insets are also normalized.

bar experiments (Figure 3b and 3c). The spectrum of the asreceived starting Mg3N2 shows a negligible 1H content. The H2 experiment yields a partially resolved spectrum (Figure 3b) 1240



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at ∼26 ppm (27 ppm fwhm), while the D2 analogue shows none, reflecting the dilution of protonated species. In a different experimental NMR scheme, CPid,47 the CPMAS includes a short period without 1H decoupling (74 μs; interrupted decoupling). Peaks of nitrogen species with bound hydrogen atom(s) will be attenuated in this scheme. Its application to the H2 reaction products results in a substantially attenuated peak and therefore unambiguously identifies these as hydrogenbound nitrogen species. Moreover, the ∼26 ppm chemical shift of the cross-polarized nitrogen is in agreement with 15N MAS NMR of Mg(15NH2)2;53 in particular, the agreement is with the most downfield peak out of four different species. The extensive 15 N peak width (∼27 ppm) indicates high structural heterogeneity, hence attributing this peak to nonbulk species as discussed above for the MgH2. In the absence of Mg−15N− H data, we cannot delineate amide from imide and have to consider both as a mixture. The combination of the above NMR observations1H and 15 N chemical shifts, 15N{1H} CPMAS and CPidprovide unambiguous identification that the H2 reaction products are amide/imide species and hydride. Moreover, the 15N CPMAS and CPid observations reflect substantial 15N−1H dipolar interactions and therefore allow us to determine that the amide/imide hydrogen atoms are tightly bound. The NMR observations combined with the gas consumption measurements confirm that hydrogen was reactively incorporated into the magnesium nitride. Distinguishing the effects imparted by the occurrence of minute water contamination was demonstrated as well. The accumulated observations and their analysis provide novel insight into the hydrogenation process of Mg3N2. 3.3. Additional Analysis. HR-SEM images show that powder particle size was reduced considerably during the mechanochemical reaction, with many particles smaller than 100 nm. Figure 5a and 5b present the pristine Mg3N2 powder and the 200 h milled powder, respectively. Micron-sized pieces in the milled sample are aggregates of smaller particles. Mg3N2 is the only crystal structure identified in the product mixture using XRD. This result is expected since all new species may be amorphous under the reaction conditions. Furthermore, MgH2 and Mg(NH2)2 could not constitute more than 3.2% mass each (as deduced from reactant conversion), i.e., close to the detection limit of standard XRD. Indeed, this is corroborated by the 15N CPMAS and 1H MAS NMR that clearly show the heterogeneous, nonbulk characteristics of the products, hence suggesting they are dispersed within the bulk Mg3N2 particles and on their surface, rather than formed as discrete amorphous islands.

nanoparticles. In this process the reacted sites, originally surface, can end up buried and dispersed in the main componentthe bulk Mg3N2. These dispersed product species exhibit structural characteristics that differ from bulk MgH2 and are denoted nonbulk species. The 1H NMR spectrum of the D2 products (Figure 3c) resolves an additional peak, centered at ∼2.2 ppm and attributed to the presence of Mg(OH)2.51 Support to assigning this peak to the magnesium hydroxide is the fact that after six months storage of the sample (in the NMR rotor in the lab) the only observed spectral change is a small intensity increase of this peak (Figure S4, Supporting Information). The occurrence of Mg(OH)2 may arise due to minute humidity contamination in the process gases. The hydroxide peak is also noticeable, although not resolved (deconvolution not shown), in the spectrum of the H2 reaction products (Figure 3b). The 1 H[wPMLG5] spectrum (Figure 3d), given its limited S/N, is inconclusive regarding this peak. Additional components are identified in the 1H spectra of both the H2 and D2 reaction products. A small, narrow 4.3 ppm peak in the 1H NMR spectrum of the H2 products (Figure 3a) reports residual molecular H2 in the nanopowder, in accordance with previously reported metal hydrides40,41,52 (see Table S1, Supporting Information). Albeit the limited quantitative nature of the 1H MAS NMR spectra, it is noteworthy that the integrated intensities of the main two peaks, hydride vs amide/imide, are ∼1.1:1 for the H2 reaction products and ∼1.25:1 for the D2 reaction products. Their presence in similar quantities is in agreement with the 1:1 ratio predicted by the redox reactions, either R2 alone or the successive reactions R2 and R3. To further substantiate the identification of the amide/imide hydrogenation products as seen in the 1H spectra (Figure 3b− d), 15N{1H} CPMAS NMR spectra were acquired for the products of the H2 and D2 40 bar experiments as shown in Figure 4. In this technique, a 15N peak would appear only for immobile nitrogen species with neighboring hydrogen atom(s). We note that the 0.4% natural abundance of 15N and its low gyromagnetic constant severely limit the sensitivity of these measurements. The H2 reaction products show a peak centered

4. DISCUSSION The results above show that Mg3N2 was hydrogenated by mechanochemical reaction with hydrogen gas. As shown below, this result contradicts the expected reaction thermodynamics. However, this intriguing outcome can be explained by mechanochemical surface destabilization and the concept of transient, local gas-pressure elevation. 4.1. Physical Conditions during Collision. The system is reactive only during vibration. Hence, assessment of reaction thermodynamics should consider the physical conditions at the short time of ball collision and the nature of chemical species formed or present during collision. Because the reaction is gas− solid, the physical conditions of both phases should be

Figure 4. 50.7 MHz 15N{1H} CPMAS NMR spectra of the H2 and D2 40 bar experiment products. The red spectrum is a CPid (CPMAS with 74 μs interrupted decoupling) of the H2 reaction products, showing substantial attenuation due to dipolar coupling to the immediate, chemically bonded hydrogen atoms (15N−1H(2)). 1241



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and other parameters in our experiment. Only a head-on impact was considered. The preimpact relative velocity and the geometric and mechanical characteristics of the system are the only inputs needed. Unlike lower frequency systems,54−57 the high vibration frequency in our system (∼3000 rpm) does not allow the calculation of impact velocity. Hence, we will use ball velocities of 3.9, 6.0, and 18.7 m s−1 reported previously (see Supporting Information).54−57 Both ball−reactor and ball−ball collisions are considered. Using the system parameters in Table S2 (Supporting Information), the maximal impact pressure (Pmax), impact duration (2τ), and radius of the contacting surfaces (Hertz radius, rH) were calculated (see equations (S1)−(S5),54,60 Supporting Information) and are tabulated in Table 1. Table 1. Physical Conditions during Ball−Reactor and Ball− Ball Impact V [m s−1] 3.93 6 18.7

b−r b−b b−r b−b b−r b−b

Pmaxa−c [bar]

2τa−c [μs]

rHa−c [mm]

V̅ 0d [m s−1]

te [μs]

34 600 109 000 41 000 129 000 64 700 203 000

19 25 18 23 14 18

0.46 0.29 0.55 0.34 0.86 0.54

0.200 0.344 0.171 0.292 0.112 0.188

2300 835 3180 1170 7640 2860

a−c

Calculated by eqs (S3)−(S5) (Supporting Information), respectively. dCalculated by eq (S6) (Supporting Information). et = L/V̅ 0. b−r: ball−reactor; b−b: ball−ball.

The extreme pressures and short impact times represent an elastic collision of two spheres or ball and reactor wall without any powder between them. However, Maurice and Courtney54 showed that the work done on trapped (ductile) metal powder is a small fraction of the elastic collision energy (attributed to the pressure). We adopt this assumption and use Pmax as an estimation of the maximal pressure during ball collision-withpowder. The Hertz radius is used to estimate the range over which the powder experiences pressure elevation during ball impact, following such a postulation by Maurice and Courtney.54 In the following, we will show that the gas entrapped in the porous medium cannot fully escape in the very short time of impact, and hence its pressure must rise. To calculate the gas velocity, we used the Kozeny−Carman equation, also known as the Darcy equation61 (see Supporting Information, eq (S6)). Assuming a pressure drop of Pmax, taking rH as the length of the porous medium in the direction of flow, and considering powder particles with diameter of 50 nm (Figure 5), one obtains low gas velocities (Table 1). The characteristic time for gas flow, t, is the time it takes the gas to flow through the powder entrapped between two balls and escape the reactive impact zone. Because of the slow flow, t is more than twoorders-of-magnitude longer than 2τ. Hence, a significant amount of hydrogen gas is caught within the jammed powder; its volume decreases; and its pressure rises considerably, given the Pmax values. Calculating the exact extent of pressure elevation requires further refinement of the model. Under these conditions, the pressure is the governing degree of freedom (DOF) in the system. Hence, we will analyze the system’s thermodynamics in terms of the Gibbs free energy (see Section 4.2).

Figure 5. HR-SEM images of (a) pristine, as-received Mg3N2 and (b,c) reaction product powder at 20k and 50k magnifications, respectively, after 200 h milling under 40 bar H2. (a) is recorded with secondary electrons signal, while (b) and (c) are recorded with an In-Lens mixed signal.

considered. Significant theoretical and experimental work has been done in the past to model the short-term mechanical results of ball impact.54−59 Nevertheless, to the best of our knowledge, the gaseous phase pressure and temperature were not accounted for.54−59 In Section 4.1.1 we present a simplified model, showing that local gas-pressure increase during impact can be considerable. Its contribution to establish thermodynamic conditions that favor hydrogenation is evaluated in Section 4.2. Further calculations show that the experimental extent of reaction can be fully interpreted by this model (see Extent of Reaction in the Supporting Information). 4.1.1. Local Gas Pressure Elevation. The suggested gas− solid ball collision model extends the elastic Hertzian impact,60 taking into consideration local gas pressure elevation. The Hertzian model was implemented in detail for mechanical alloying by Maurice and Courtney.54 Using their assumptions and results, we estimated the maximal local pressure elevation 1242



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Under this condition, ΔG differs from ΔG° only by the change in Gibbs energy of the hydrogen due to pressure elevation

4.1.2. Temperature. For the Gibbs free energy to be the applicable thermodynamic potential, the temperature should also be regarded as a DOF. This demand is fulfilled since despite the fast pressure increase the compression is nearly isothermal rather than adiabatic. The nanosized powder dictates very short characteristic heat transfer times. The maximal temperature rise occurs in a thermally isolated solid−gas control volume. This isolation condition holds under the conservative assumption that heat conduction through the nitride powder and H2 gas out of the control volume is negligible. Then, the calculated maximal temperature rise during compression to 5000 bar is 10 °C. See Supporting Information for detailed calculations. Additional temperature elevation is caused by impact and shear of the solid nitride, yet the fine nanostructure of the gas− solid system ensures a uniform temperature. However, since heat conduction through the solid network is not negligible, the gas−solid system is not adiabatic, and the temperature should be regarded as an additional DOF. Hence, Gibbs free energy is the suitable thermodynamic potential for the discussed gas− solid system. 4.2. Thermodynamic Considerations. As mentioned above, the Gibbs free energy determines the system thermodynamics. ΔG°, the change in standard Gibbs energy for the successive reactions R2 and R3, is given as a function of temperature ◦ ◦ ΔG◦ = ΔH298K − T ΔS298K

ΔG(P) = ΔG◦ − n H2

∫P

P

0

V ̃ dP *

(2)

where nH2 = 4 is the number of moles of hydrogen per reaction formulation; P0 is the standard pressure (1 atm); P is the reaction pressure; Ṽ is hydrogen’s molar volume; and P* is an integration variable. The molar volume was obtained numerically from the hydrogen-modified van der Waals equation of state, formulated by Hemmes et al.68 The integral being positive, hydrogen pressure elevation makes ΔG more negative. Figure 6 shows that hydrogen pressure elevation makes ΔG negative above 3870 bar, hence favoring reactions R2 and R3. This pressure is only 2−10% of Pmax.

(1)

Using the values in Table 2, ΔG298K ° = 105.6 kJ/mol. This large positive value means that the hydrogenation reactions R2 Table 2. Enthalpy and Entropy Valuesa for Species in Reactions R2 and R3 Mg3N2 H2 Mg(NH2)2 MgH2 a

ΔH°f,298K [kJ mol−1]

ΔS°298K [J mol−1 K−1]

−461.1 0 −351.0b −76.2

87.7 130.7 52c 31.0

Figure 6. 298 K isotherm of ΔG, the change of Gibbs energy, for successive reactions R2 and R3, as a function of reaction pressure. At 3870 bar, ΔG = 0.

Ref 62. bRefs 28 and 63. cRef 64.

Another result of the above calculation is that the system pressure of 40−80 bar makes the reaction thermodynamics significantly more favorable. For example, ΔG is ∼70 kJ/mol at 40 bar and ∼62 kJ at 80 bar compared to ΔG of ∼106 kJ at 1 bar. 4.2.2. Mechanochemical Surface Destabilization. Mechanochemistry causes various defects at the solid surface and consequently increases the surface free energy.69 For example, the mechanochemical friction of MgO and the consequent “structural disorder”69 were reported by Butyagin and colleagues70−73 to enhance the surface free energy by ∼100 kJ/mol.71,73 If the extent of surface destabilization in the case of the hydrogenation of Mg3N2 is of that order, it would suffice alone to make ΔG negative and the reaction favorable. Although such a mechanism is straightforward, to the best of our knowledge this concept of surface destabilization was not invoked so far to interpret or pursue unfavorable mechanochemical gas−solid reactions. Mechanochemistry of thermodynamically favorable gas−solid reactions was routinely considered only to enhance their rate.30 This enhancement induces only a kinetic effect and is referred to as mechanochemical activation. It partially stems from the same structural disordering that leads to thermodynamic surface destabilization69 and drives the unfavorable reactions described herein.

and R3 are thermodynamically unfavorable and that hydrogenated magnesium nitride is metastable at standard conditions. The change of standard entropy is negative, ΔS°298K = −496 J K−1 mol−1, reflecting the fact that the standard reactions are limited by hydrogen entropy which is largely diminished when the solid amide and hydride phases are formed. Additional Gibbs-related data were calculated by Michel et al.65 using first principles. They obtained cryogenic equilibrium temperatures for reactions R2 and R3, in line with T calculation from eq 1 with ΔG° = 0. Although MgNH enthalpy and entropy are not explicitly reported,65 the extremely low temperature of R2 reversibility means it is very unfavorable at room temperature as well. The above analysis explains the reported hydrogen inertness of Mg3N2,12 which increases with temperature. 4.2.1. Pressure Dependence. To quantify the thermodynamic significance of pressure elevation predicted by the above model, we evaluated ΔG for the successive reactions R2 and R3 as a function of pressure. It is assumed that the pressure66 and particle size67 have negligible influence on the thermodynamic properties of the solids (nitride, amide/imide, and hydride). 1243



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term local pressure elevation is pursued to explain the mechanochemical hydrogen reactivity of magnesium nitride. The experimental results, combined with the pressure elevation model prediction and surface destabilization, demonstrate a route to facilitate thermodynamically unfavorable reactions, allowing formation of metastable hydrogen-rich products. This can initiate the exploration of a new concept of gas−solid chemical conversion processes.

The chemical mechanisms that allowed surface destabilization of MgO71,72 were not yet studied in Mg3N2, and therefore their energetic contribution cannot be estimated. Nevertheless, we argue that the basic disordering mechanism is valid in our case as well and contributes in concert with the pressure increase to establish negative ΔG. 4.3. Apparent Reaction Rate−Pressure Dependence and Isotope Effect. The lack of dependence of the apparent reaction rate on pressure and on hydrogen-to-deuterium substitution is directly interpreted by fast adsorptionmuch faster than the time interval between two collisions; even at lower pressures, all active centers in the nitride have to be populated by either H2 or D2, to account for the observed rate independence. The fast adsorption is consistent with the findings of Butyagin and colleagues.71 The lack of isotope effect suggests that the rate-determining step (RDS) does not involve H2 or D2. However, based on our experimental data, reaching a definitive confirmation of the reaction mechanism is currently impossible and is beyond the scope of this publication. 4.4. Brief Comparative Analysis of Previous Reports. There are few examples of metastable mechanochemical products of solid−gas reactions in the literature. Unlike our case, in these studies the gas−solid reaction is favorable; however, the solid product is formed in a metastable phase,74,75 and the reaction can take place without mechanochemical impact. The only example of an unfavorable gas−solid reaction that depends on mechanochemistry to form a metastable product is the oxidation of gold by carbon dioxide,76 in which the thermodynamics and mechanism are fundamentally different. The comprehensive reaction model described herein offers possible explanations to the seemingly contradicting results of Hu et al., mentioned in the Introduction.27,28 In that work Mg(NH2)2 and MgH2 are favorably consumed during milling, while in our case they are formed. According to our model the reason may be the planetary ball mill Hu and co-workers used, which offers low gas-pressure rise. Maurice and Courtney54 show that impact velocities in similar mills are about 3% of the velocities discussed herein, and therefore the expected gas pressure is 2 orders of magnitude lower. However, the reverse reactions are easily realized, where a close solid−solid contact may be enough to trigger the favorable reaction. The maximum local H2 pressure in the experiments by Hu and colleagues27,28 is limited by low H2 partial pressure since initially a pure argon atmosphere was used. Hence the local pressure rise is significantly limited compared to our system and is insufficient to facilitate the reaction discovered here.

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ASSOCIATED CONTENT

S Supporting Information *

Experimental Details; Calculation of hydrogen gas content and related blank-subtraction with exemplifying figures; Additional resultspressure during H2 80 bar experiment; Additional NMR resultsMgH2 and Mg(OH)2 spectra, spectra of reaction products stored for 6 months in NMR rotor, and spectra from repeated measurements; Gas−Solid Collision Modelequations and calculations; Calculation of Temperature Rise during Compression and Heat transfer coefficient; Extent of Reaction; References. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Prof. Gideon S. Garder. Tel.: 972-4-8292008. Fax: 972-48295099. E-mail: [email protected]. Prof. Asher Schmidt. Tel.: 972-4-8292583. Fax: 972-4-8295703. E-mail: chrschm@tx. technion.ac.il. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the generous help of Robert C. Bowman, Jr., CEO in RCB Hydrides LLC, OH, who shared with us his wide expertise in NMR of complex metal hydrides; Dr. G. M. Reisner (Technion) for prolonged XRD measurements and analysis; and Victor Halperin (Technion) for fruitful scientific discussions. G. Grader was supported by Arturo Gruenbaum Chair in Material Engineering. G. Shter was supported by a joint grant from the Ministry of Absorption and the Council for Higher Education of Israel under the framework of the Kamea Program. We thank the Grand Technion Energy Program and The Ed Satell Family for financial support.

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REFERENCES

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5. CONCLUSIONS The hydrogenation of magnesium nitride was shown to be unfavorable under standard conditions, requiring an extreme pressure of ∼4000 bar to be realized. Nevertheless, we have shown experimentally for the first time that this reaction is feasible, by compounding magnesium nitride with hydrogen in a vibratory mill. The reaction progress was evidenced by the pressure decrease during the 200 h experiment. The metastable reaction products, magnesium hydride and magnesium amide/ imide, were unambiguously identified using 1H and 15N MAS NMR spectroscopy. We propose that gas pressure rises considerably during milling within a confined zone between colliding balls and walls. A new concept of flow-restricted short1244



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