In this review, I examine the influence of nanoscale materials features on the hydrogen-metal interaction. The small system size, the abundance of surfaces/interfaces, and the spatial distribution of phases are the key factors to understand the hydrogen sorption properties of nanomaterials. In order to describe nanoscale-specific thermodynamic changes, I present a composition and atomic quantitative model applicable to every hydride-forming material, independently on its structure. The effects

more »

... f surface free energy, interface free energy, and elastic constraint, are included in a general expression for the thermodynamical bias. In the frame of this model, I critically survey theoretical and experimental results hinting at possible changes of thermodynamic parameters, and in particular, enthalpy and entropy of hydride formation, in nanostructured Mg-based metallic compounds as compared to their coarse-grained bulk counterparts. I discuss the still open controversies, such as destabilization of ultra-small clusters and enthalpy-entropy compensation. I also highlight the frequently missed points in experiments and data interpretation, such as the importance of recording full hydrogen absorption and desorption isotherms and of measuring the hysteresis. Finally, I try to address the open questions that may inspire future research, with the ambition of tailoring the properties of hydride nanomaterials through a deeper understanding of their thermodynamics. Crystals 2018, 8, 106 2 of 28 abundance (0.13 wt% in sea water and 2.76 wt% in the earth crust [12]), low cost, environmental compatibility, and of course lightness. MgH 2 has moderately high gravimetric and volumetric hydrogen density of ρ m = 7.6 wt% H and ρ V = 110 kg H/m 3 . The formation of MgH 2 from Mg and H is an exothermic process with enthalpy ∆H 0 ∼ = −74 kJ/mol H 2 and entropy ∆S 0 ∼ = −133 J/K mol H 2 [13, 14] . From the point of view of reversible hydrogen storage, these figures reveal that MgH 2 is far too stable to allow hydrogen desorption at p(H 2 ) = 1 bar below 100 • C, as it would be necessary to feed a proton exchange membrane fuel cell [15] . In fact, using the van 't Hoff equation (see Section 2.1), it can easily be calculated that the decomposition temperature at p(H 2 ) = 1 bar is about 283 • C. Conversely, the strongly negative formation enthalpy makes Mg and Mg-based compounds appealing for heat storage applications, e.g., in concentrated solar power plants [6, 12] . MgH 2 is an insulator with a band gap of about 4.2 eV and therefore the metal-hydride transformation in Mg films induces a remarkable optical change from reflective to transparent. This behavior can be exploited to study H-sorption in thin films and nanostructures [16] , where the sensitivity of bulk techniques based on pressure or mass changes would be insufficient. The hydrogen sorption properties of a material can be modified in two ways. The more obvious is the change of its composition, typically playing with elements that have different bonding strengths with hydrogen. This approach may yield either solid solutions or compounds with a new crystalline structure, and has pushed the development of successful ternary hydrides such as LaNi 5 H 6 and FeTiH 2 [17] . The other approach exploits the unique features of nanostructured materials and takes advantage of the continuous development in synthesis techniques and in high-resolution structural characterization methods [18] . Nanostructured materials, the building blocks of which are smaller than ≈100 nm in at least one spatial direction, constitute a bridge between the molecular world and bulk solids at the true thermodynamic limit. Their equilibrium and transport properties may depart significantly from those of bulk counterparts with the same chemical composition. The new physics and chemistry at the nanoscale stem essentially from two peculiar features, namely the small size and the high volume fraction occupied by surfaces/interfaces. These two fingerprints of all nanomaterials are intimately connected because the volume fraction of surfaces/interfaces scales inversely with the system size. The "small size" condition is defined via a comparison to a characteristic length of the material, like for instance the mean free path of particles or excitations (electrons, phonons and magnons) that carry of energy, charge and spin. Alternatively, it could be the length of a magnetic interaction or the Bohr radius of a bound exciton. The spatial extensions of microstructural defects provide other examples of characteristic lengths, e.g., the width of magnetic domain walls, the width of antiphase boundaries, and the critical size of Frank-Read dislocation sources. New properties can be expected whenever the systems size L, in at least one spatial direction, is similar to or smaller than one of these intrinsic length scales. If such a condition applies, one speaks of a confinement effect on the material's properties. At the same time, the de Broglie wavelength λ dB of the aforementioned carriers can be similar to L. By analogy with the quantized energy levels of plane waves confined in a box of width L, we can guess that the separation ∆E between two levels will scale inversely with some power of L. Therefore, with decreasing L, one enters a new world in which the condition ∆E > k B T holds, meaning that adjacent energy levels are no longer mixed up by thermal excitations and that a quantization effect can emerge on properties, which are normally continuous in bulk materials. One of the most enlightening cases of confinement and quantization is the quantized electrical conductance at a quantum point contact of a 2-dimensional electron gas (2DEG) [19] . The abundance of interfacial regions in nanomaterials implies that the local environment of a macroscopically relevant fraction of constituent atoms differs significantly from the ideal crystalline structure. In fact, for atoms located at interfaces and surfaces, the number and the chemical species of neighboring atoms, as well as the bond lengths and bond angles, are not the same as for inner atoms. This structural difference brings about significant changes in many properties, often in opposite directions. For instance, at surfaces/interfaces the mass transport is faster than in the bulk due Crystals 2018, 8, 106 3 of 28 to their less dense atomic packing [20] , whereas the electrical conductivity drops due to scattering of charge carriers. The abundance of surface atoms with diverse local environment is particularly relevant in the field of heterogeneous catalysis, where both the activity and selectivity towards a given reaction product depend on very specific surface sites [21] . Surfaces/interfaces are characterized by an excess enthalpy due to missing or weakened interatomic bonds and by an excess entropy arising both from enhanced structural disorder and from soft modes in the vibrational density of states [22] . Enthalpy and entropy bring opposite contributions to the Gibbs free energy and therefore compete in the stabilization of the microstructure. However, the enthalpy term usually overwhelms the entropic one so that nanoscale materials are prone to coarsening phenomena when exposed to high homologous temperatures. The spatial distribution of elements within a multi-component nanoscale object offers a new degree of freedom for its thermodynamic description. The classical distinction between random mixing, short-range-order and clustering, so successful in bulk binary alloys, must be extended to encompass various spatial arrangements in the case of nanoalloys. As an example, different clustering patterns in a binary NP may result in various morphologies such as Janus-like, surface-segregated or onion-like structures [23] . The interplay between these variants enriches the corresponding phase diagram by mapping new temperature-composition regions where one specific morphology is the most stable. This review is organized as follows: in Section 2, I address the influence of system size, abundance of surfaces/interfaces, and spatial distribution of phases, on the hydrogen sorption properties of nanoscale materials. I specifically discuss the effects of surfaces, interfaces, elastic constraint and alloying. I present a quantitative model to predict and explain thermodynamic changes and discuss general ideas applicable to every hydride-forming material, independently on its composition and atomic structure. In Section 3, I critically examine selected experimental results on Mg-based nanostructures, starting with pure Mg in Section 3.1 and moving to Mg alloys and compounds in Sections 3.2-3.5. In the Conclusions, I summarize the major findings and share some ideas for future research directions. I note that excellent reviews both on size effects [24, 25] and on the synthesis of nanostructured Mg-based hydrides [11, 26] have been published. The peculiarity of the present work is the critical comparison between theory/modeling and experimental results. I put great care in assessing the reliability of the thermodynamic parameters extracted from the analysis of experimental data. After about 20 years of intense worldwide research on nanostructured hydrides, often characterized by sensational claims and contrasting reports, I hope to clarify some still open controversies, to draw the reader's attention to frequently missed points in the interpretation of hydrogen sorption data, and to stimulate future research activities.