Destabilization of the Mg-H system through elastic constraints

We tune the thermodynamics of hydrogen absorption in Mg by means of elastic clamping. The loading isotherms measured by hydrogenography show that Mg films covered with Mg-alloy-forming elements, such as Pd and Ni, have hydrogen plateau pressures more than two orders of magnitude higher than bulk Mg at the same temperature. An elastic model allows us to interpret the Mg thickness dependence of the hydrogen plateau pressure. Our results provide the basis for the development of new hydrogen storage materials with excellent thermodynamic properties.

Hydrogen is an attractive energy carrier for a future sustainable energy system. Compact hydrogen storage is however still a scientific and technological challenge [1]. Storage of molecular hydrogen, both gaseous and liquid, requires high pressures or very low temperatures and is thus not energy efficient. An alternative is to store atomic hydrogen in metal or complex hydrides. Storage in metal-hydrides allows, in principle, to achieve high volumetric and gravimetric densities and to reversibly operate at room temperature and atmospheric pressure. However there are thermodynamic and kinetic limitations associated with the chemical reactions involved in hydrogen absorption and desorption.
An optimal metal-hydride system has a hydrogen equilibrium pressure of 1 bar at room temperature. Due to weight constraints the interest of the scientific community has turned to lightweight hydride-forming elements such as Li, B, Na, Mg and Al. Mg can store up to 7.6 mass% of hydrogen, forming the ionic MgH 2 compound, but shows poor kinetics of hydrogen absorption/desorption and a hydrogen equilibrium pressure of 1 bar at the far too high temperature of 573 K. The absorption and desorption kinetics can be enhanced by reducing the size of the Mg grains via ball milling [2] hence shortening the hydrogen diffusion length, or by addition of proper catalysts [3]. Many efforts are currently dedicated to modifying the thermodynamics of the Mg-H system in order to promote hydrogen dissociation at lower temperatures. Some destabilization has been observed upon reduction of particle size [4] and alloying of Mg with other elements [5,6], although this generally implies a reduction in the total hydrogen storage capacity. Theoretical works suggest the possibility to reduce the hydrogen desorption temperature in both MgH 2 nanoparticles with grain size smaller than ∼1.3 nm [7] and in MgH 2 layers with thicknesses below few unit cells [8].
In this letter we show that the thermodynamic stability of the Mg-H system can be drastically modified via elastic constraints. This is a direct consequence of the long range H-H interaction in metals [9,10]. In a metal with free surfaces two hydrogen atoms feel an attractive interaction, while in a perfectly clamped sample the interaction becomes repulsive.
Clamping can thus be used to tune the equilibrium hydrogen pressure to the levels required for specific applications. To prove the validity of our approach we prepared two series of capped Mg thin films: 1) to explore the role of chemical binding we deposited Mg thin films capped with different transition metals: Ni, Pd, Ti, Nb and V; 2) in order to study the thickness dependence of the elastic effect we prepared a series of Pd-capped Mg films of different thicknesses. The effect of clamping is strongly dependent on the chemical nature of the transition metal used as a cap-layer and will be interpreted with a simple elastic model. By choosing the appropriate sample geometry we are able to increase the hydrogen plateau pressure more than 200 times with respect to bulk Mg. Hydrogen absorption in our samples is measured by means of optical spectroscopy and Hydrogenography [6], a novel technique that allows to measure Pressure-Optical Transmission-Isotherms (PTI's). In a PTI the amount of light transmitted by a thin film is measured as a function of increasing pressure at constant temperature: when the metallic Mg films load with hydrogen the Mg-MgH 2 metal-insulator transition leads to an abrupt increase in the amount of transmitted light. From the Beer-Lambert law, ln(T /T M ) ∝ c H d, the logarithm of the optical transmission, T , normalized for the transmission of the film in its metallic state, T M , is proportional to the hydrogen concentration in the film, c H and to the film thickness, d. Measuring PTI's is therefore in all respects equivalent to measure standard Pressure-Composition-Isotherms [11]. The films used in this study are deposited in a UHV chamber (p < 10 −6 Pa) by RF/DC magnetron sputtering on glass and quartz substrates. All films are covered with Pd to prevent oxidation and catalyze hydrogen absorption. Optical reflection spectra are measured in a PerkinElmer Lambda 900 diffraction grating spectrometer, with energy range between 0.5 and 6.5 eV, during (de)hydrogenation at room temperature and H 2 pressures up to 10 5 Pa. PTI's are recorded in an optical cell that allows to vary the hydrogen pressure from 10 −1 to 10 6 Pa at constant temperatures, between 313 and 573 K. Further details on the hydrogenography experimental setup can be found in Ref. [6]. In Fig. 1  In the inset a cartoon of the sample geometry: glasssubstrate/Ti/Mg/Ti/Mg/Pd. and Ni do not load with hydrogen. Ti, Nb and V layers on the contrary load at the beginning of the pressure ramp but, due to the metallic nature of their hydrides, produce very small optical effects compared to Mg. The observed plateaus are therefore only due to the formation of MgH 2 upon hydrogen absorption. The isotherm shown in Fig. 1 exhibits two clear and distinct plateaus of similar width. Since the width of the plateau is proportional to the thickness of the material the two plateaus must originate from the two distinct Mg layers. Furthermore, to obtain such a well defined double-plateau we have to assume that the two Mg layers are elastically disconnected [12] and have different site energies for hydrogen absorption. To prove these hypotheses we measure the optical reflection of the 2x[Ti(10nm)Mg(20nm)]Pd(20nm) sample deposited on quartz, while slowly increasing the hydrogen pressure. Optical spectra are measured through the transparent quartz substrate at near-normal incidence. In Fig. 2a the measured spectra are shown for three different steps of loading: 1) as-deposited metallic sample, 2) at intermediate loading and 3) fully loaded sample. The calculated spectra shown in Fig. 2b are generated with SCOUT [13] by taking into account the volume expansion occurring upon hydrogenation of Mg and Ti and including a rough interface between the quartz substrate and the first Ti layer. In the simulation the intermediate step is due to the complete loading of one of the two Mg layers while the other remains metallic. Comparison with the experimental spectra shows unambiguously that the Mg layer sandwiched between two Ti layers absorbs hydrogen at a lower pressure than the one capped with Pd. This is rather counterintuitive since the "Ti-sandwiched Mg" lies on the bottom of the sample and hydrogen has to dif-  [14], [15], [16], [17] and [14] respectively. fuse through the top Mg layer, which remains in the diluted α phase, in order to reach the bottom one. For this mechanism to take place the two Mg layers have to differ with respect to their thermodynamic properties and they must be elastically disconnected by the presence of a Ti layer in between.  Mg and the substrate we can assume that the only clamping effect is due to the top capping layer. Clearly two behaviors are distinguishable: 1) Mg alloy forming elements such as Ni and Pd have a strong effect on the thermodynamic properties of Mg, leading to a much higher plateau pressure than the one measured for Mg films of equal thickness capped with Ti, Nb and V; 2) the latter elements, which are immiscible with Mg, effectively behave like "scissors" and lead to "quasi-free" Mg layers with elastically disconnected interfaces. Assuming that the origin of the destabilization observed is only elastic in nature, we can build a simple model consisting of two layersa Mg and a cap-layer -glued to each other as shown in the inset in Fig. 3. Hydrogen atoms absorbed by the Mg layer isotropically expand the lattice of the metallic host, while the Mg feels a compressive stress in the x and y directions due to the cap layer. In the z direction there is no stress built up by the clamping but we have to take into account the strain along the z direction due to the Poisson's ratio, ν. The two layers are in vacuum and no effect of the substrate is taken into account, basically assuming that the bottom Ti layer is a perfect scissor. By taking into account only elastic constraints we can calculate the effective volume expansion of the Mg layer upon hydrogen absorption. Furthermore, the enthalpy of hydride formation has a simple volume dependence through the bulk modulus, B [19]: d∆H/d ln V = −B Mg V H , where V H is the partial molar volume of hydrogen in Mg. We can then derive an expression for the plateau pressure of the capped magnesium layer, Mg * , with respect to free bulk magnesium, Mg 0 : According to the model the equilibrium pressure for the capped Mg has a straightforward dependence on the thickness of the Mg layer, d Mg . Fig. 4 shows visible: a) the width of the plateau, w, is proportional to d Mg as expected from the Beer-Lambert law, b) the plateau pressure decreases with increasing Mg thickness as predicted by the model. A 10 nm thick Mg film has an equilibrium hydrogen pressure of 2.8·10 3 Pa at 333 K, more than 200 times higher than bulk Mg at the same temperature (p 0 333 K = 12 Pa [18]). The plateau width is measured by dividing each isotherm into three regions: the solid solution (α phase) before the plateau, the coexistence region (α + β phases) and the fully hydrogenated region (β phase) after the plateau and fitting each part with a straight line: the width is then given by the distance, in units of ln(T /T M ), between the intersection points. With the same geometrical construction we obtain the equilibrium pressure, as the pressure in the middle of the plateau. Ideally one would expect w → 0 for d Mg → 0, however, although the plateau width is found to be proportional to the Mg thickness, a linear fit shows a relation of the type w = A(d Mg − d 0 ), with d 0 = 6 nm. The presence of an intercept indicates that the total amount of Mg undergoing a phase transition to MgH 2 is thiner than expected and that we can assume for all samples that ∼6 nm of Mg are "lost" due to alloying with the top Pd layer. In the comparison with the model we will therefore take into account an effective Mg thickness d = d Mg − d 0 . The formation of an interfacial Mg-Pd alloy is directly responsible for the strong clamping effect observed and is consistent with the difference in width observed in the two plateaus of Fig. 1, corresponding exactly to 6 nm. The inset in Fig. 4 shows the thickness dependence of the plateau pressure of Pd-capped Mg layers: plotting [ln(p * /p 0 )] −1 versus the effective Mg thickness we find a linear dependence as predicted by the model, with intercept I = 0.16 and slope S = 7.6 · 10 −3 nm −1 . Substituting into equations 2 the literature values for the structural parameters of Mg, Pd and H (V H = 2.24 cm 3 /mol, V Mg = 13.97 cm 3 /mol, ν Mg = 0.29, ν Pd = 0.39, E Mg = 45.2 GPa, E Pd = 126 GPa) and taking T = 333 K and d Pd = 40 nm, we obtain the theoretical values I th = 0.27 and S th = 2.1 · 10 −3 nm −1 . The agreement between experiment and theory is surprising when considering the strong approximations made in the model: no substrate is taken into account, the only interaction is elastic, hence neglecting surface energy contributions, and the layers are assumed to behave as perfect elastic bodies. The rather large S value obtained from the fit can be explained considering the alloying effect taking place at the Mg/Pd interface and assuming that only a fraction of ∼10 out of 40 nm of Pd has a significant clamping effect on the Mg underneath. The discrepancy in the I values could reflect the fact that we consider the Young's modulus of metallic Mg: taking into account MgH 2 , which is stiffer than Mg, would lead to a closer agreement between experiment and theory. The elastic model developed for a double-layer can be easily extended to 3D Mg nanoparticles embedded in a skin of hard material. Assuming Mg particles of 10 nm of diameter and a skin of 2 nm thickness, the model predicts an increase in hydrogen equilibrium pressure of more than 2000 times with respect to bulk Mg at the same temperature. The effect of clamping described in the present work is not only important in the perspective of hydrogen storage applications, but it is crucial in understanding the thermodynamics of all hydrogen-absorbing capped thin films, from switchable mirrors [20] to electrode materials for batteries [21], hydrogen detectors [22] multilayers and superlattices [23].
In conclusion we have shown the possibility to tailor the thermodynamics of a metal-hydrogen system by means of elastic constraints. Thin films of Mg are used as a model metal-hydrogen system. Elements immiscible with Mg behave like scissors, while Mg-alloy-forming elements exert a clamping effect that leads to huge increases in hydrogen equilibrium pressures. Clamping arises as a consequence of alloying between Mg and the capping layer and its effects can be understood on the basis of a simple elastic model. The possibility to tune the thermodynamics of a metal-hydrogen system by elastic means offers attractive new possibilities for compact hydrogen storage. This work is supported by the Technologiestichting STW, the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) through the Sustainable Hydrogen Programme of Advanced Chemical Technologies for Sustainability (ACTS) and the Marie Curie Actions through the project Complex Solid State Reactions for Energy Efficient Hydrogen Storage (COSY:RTN035366).