ARTICLE pubs.acs.org/JPCC
Extended Solubility Limits and Nanograin Refinement in Ti/Zr Fluoride-Catalyzed MgH2 Fokko M. Mulder,* Sarita Singh, Sabine Bolhuis, and Stephan W. H. Eijt Fundamental Aspects of Materials and Energy, Department of Radiation, Radionuclides and Reactors, Faculty of Applied Sciences, Delft University of Technology, Mekelweg 15, 2629JB Delft, The Netherlands
bS Supporting Information ABSTRACT: Catalyzing magnesium hydride by 5 mol % titanium fluoride is observed to have a pronounced impact on the materials nanoscaling and the thermodynamics of H sorption. Surprisingly small ∼30 nm MgH2 crystallites result after hydrogen uptake, which are apparently stabilized by abundant interface interactions, arresting Ostwald ripening. Rapid hydrogen uptake is observed from temperatures as low as 10 °C, with for the first time large quantities of H inserted into the hexagonal Mg metal phase before formation of the tetragonal hydride phase. Temperature dependent equilibrium pressure measurements at different overall H compositions reveal strongly reduced enthalpy and entropy changes upon hydride formation for the most reactive part of the sample, with a close to perfect linear correlation between them. It is argued that the origin of this effect is in the abundant hydrogen dissolved in the α-phase and abundant vacancies present in the β-phase due to the interaction between α- and β-phase domains in the nanograins, i.e., strongly altered solubility limits. The titanium/zirconium fluoride additives are converted to respectively titanium/zirconium dihydride and MgF2, which apparently stabilize by their closely matching lattices respectively the Mg metal and hydride phase at their interfaces. Being nanodispersed, this leads in addition to nanoscale grain refinement. The formation of a new stable [Mg, T]2TH6 (T = Ti or Zr) phase with a large cubic unit cell is observed after prolonged cycling and annealing times.
’ INTRODUCTION Magnesium hydride is attractive for hydrogen storage because of its high hydrogen weight fraction (7.6 wt %). However, Mg suffers from poor kinetics and high ab- and desorption temperatures, which makes it inappropriate for practical application. The addition of suitable catalysts and/or tailoring of small crystallite (particle) sizes is known to improve the sorption kinetics.16 However, without catalyst these crystallites are known to grow by spontaneous annealing and Ostwald ripening during the hightemperature hydrogen cycling to micrometer sizes. In the presence of catalysts like Nb and V, the crystallite growth is largely arrested on nanoscales, but depending on the amount added, these still become as large as 150 nm.7,8 However, maintaining the crystallite sizes at such nanoscale dimensions throughout the sorption reactions, i.e., counteracting the spontaneous growth to micrometer sizes, appears important. Furthermore, a recent study9 has shown that also for Ti- or TiCl3-catalyzed NaAlH4 materials reported by Bogdanovic et al.,10,11 nanostructured desorption products NaH and Al occur that have high sorption reversibility, while strong, largely irreversible, growth of the crystallites sizes occurs during sorption for uncatalyzed NaAlH4. The catalyst products TiAl∼3 and NaCl were indicated as nucleation centers of respectively the isostructural Al and NaH phases.9 The analogy with TiCl3-catalyzed NaAlH4 prompted us to study TiF3-catalyzed MgH2 because of the anticipated formation of MgF2 (isostructural to MgH2, while MgCl2 has a different crystal structure). The assumption is that MgF2 can therefore act r 2011 American Chemical Society
as seeding crystals for MgH2 because it shares the same crystallographic structure and has a very good lattice matching. When finely dispersed throughout the material, the abundant MgF2 nucleation centers for MgH2 will cause each individual MgH2 crystallite to grow only on a limited scale. A number of studies were recently published12,13 that indeed show superior catalytic activity of TiF3 and the formation of MgF2. The addition of Ti itself as a catalyst using ultrahigh energy ball milling14 and the possible catalytic activity of Ti/TiH2 has recently attracted renewed interest in using pure Ti. Mg and Ti form no intermetallic compounds or alloys, which may mean that this catalyst could possibly be less prone to side reactions. The MgTiH system is studied intensively in thin film produced on substrates1522 revealing a direct interplay between structural features, layer thickness, and hydrogen uptake characteristics. Also a pronounced alteration of thermodynamic parameters20 due to interfacial strains propagating throughout the material was observed. In addition, research has been performed on MgTiH powders prepared via ball milling,14,2325 which showed that the addition of Ti has a beneficial effect on the sorption properties, albeit by far not as strong as the TiF3 addition reported previously and in the present study. No direct proof was presented of the form the Ti catalyst takes in the powder samples, while in the thin film samples a cubic fluorite Received: May 4, 2011 Revised: December 14, 2011 Published: December 19, 2011 2001
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Figure 3. Amount of Mg that is present in the α-Mg or β-MgD2 phase as a function of the amount of D2 loaded in the sample, determined from the volumetric gas load recording and pressure changes. The maximum load of 100% corresponds with full conversion to MgD2. The temperature is 150 °C. The absolute amount of Mg in the α- and β-phase combined remains constant throughout cycling (normalized to 100% at full D2 load).
Figure 1. In situ neutron diffraction measurements performed during deuterium loading and unloading in TiF3-catalyzed Mg. The applied timetemperature profile is given in Figure 5.
Figure 4. D occupancy in the β-magnesium deuteride during loading and unloading of D as extracted from Rietveld refinements. The correction is described in the text.
absorption and desorption experiments in combination with X-ray diffraction. Figure 2. Neutron diffraction patterns of TiF3-catalyzed Mg during absorption of D2 from 0% to 28% (corresponding to MgD0.56) at 150 °C during the first cycle of the in situ neutron measurements. A large amount of D is loaded, but the α-Mg shows only small peak intensity changes. The strongest peak of the β-MgD2 phase is at 2.2 Å and shows very little intensity at 28% loading.
MgTiH phase was reported,16 having domains that are Tirich or Mg-rich with coherent lattices. These coherent lattices were not observed in the powders,25 however. The latter indicates that the nonequilibrium deposition of thin films involving atomic-scale intermixing is a relevant method for the formation of the (metastable) cubic MgTiH phase and can lead to extreme effects on hydrogen sorption. In situ neutron diffraction measurements were performed on TiF3-catalyzed MgH2, facilitating the observation of hydrogen densities, particle sizes, and other structural features of the crystalline phases during the sorption reactions. The thermodynamic properties were studied via van't Hoff plots of the equilibrium pressure versus 1/T for various overall hydrogen contents in the samples. Long-term hydrogen loading and temperature effects on the structures were observed using
’ RESULTS In Situ Neutron Diffraction and X-ray Diffraction. Neutron diffraction patterns of the TiF3-catalyzed sample are shown in Figures 1 and 2 after and during various stages of the experiments, together with several neutron diffraction patterns during in situ deuterium loading and unloading. The Rietveld refinements on the diffraction patterns collected in the in situ neutron measurements yield the phase fractions, deuterium contents, and observed particle sizes as plotted in Figure 35. Full loading of deuterium and subsequent complete desorption was performed in two different cycles, the second one starting at 50 °C by putting 10 bar D2 in the fixed volume of the sample container and tubing toward it. Immediately, a very fast decrease of the pressure was observed leading to a pressure of 1 bar in less than 1 min and to below 0.1 bar in 2 min. At the same time, the temperature of the sample rose from 50 °C to a maximum of 105 °C as determined at the outside of the quartz tube used (1 mm wall thickness). This directly shows the surprisingly rapid and strongly exothermic reaction of the hydrogen uptake reaction in this catalyzed sample at low temperatures. From the known volume and pressure drop, we deduced that this first load of deuterium was enough to load up to an average composition of MgD∼0.4. 2002
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Table 1. Structural Parameters and Anisotropic Temperature Factors of α-Mg Metal Inserted with D up to MgD0.47 at 150 °C, wRp = 0.04 atom
Wyck.
x/a, y/b, z/c
P63/mmc
Mg
2d
1/3, 2/3, 1/4
1.00
a = 3.2196 (9) Å
D
2a
0, 0, 0
0.25 ( 0.03
c = 5.2279(9) Å
D
4f
1/3, 2/3, 0.95
0.11 ( 0.03
phase
fraction
atom U11 [Å2] U12 [Å2] U13 [Å2] U22 [Å2] U23 [Å2] U33 [Å2]
Figure 5. Observed crystallite sizes of α-Mg and β-MgD2 during various stages of the loading and unloading of D2 and the temperatures of the sample. The error can be judged from the scatter in the data. The arrow indicates the spontaneous heating to above 100 °C directly during the first loading of D2 starting at 50 °C (the two small bumps later show additional heating after further loading steps).
Most remarkably, no MgD2 β-phase is detected yet in the recorded neutron diffraction patterns, but there are small changes in the peak intensity of the Mg α-phase. The remarkable conclusion has to be that, unlike normal bulk Mg that accepts only a density of ∼104 in its lattice at these temperatures before forming MgH2, the solubility of hydrogen in the α-phase is increased by orders of magnitude (Figure 3). There is no room for a significant amorphous fraction in the data since the amount of Mg summed over the α- and β-phase remains constant and the full capacity is reached at the highest hydrogen loading. In the corresponding diffraction patterns, however, there is only little change in the peak intensities of the Mg spectra (Figure 2). A detailed Rietveld analysis of the Mg phase in the neutron diffraction patterns was started introducing D on the octahedral (2a) and tetrahedral (4f) sites. In previous density functional theory simulations,26 it was shown that hydrogen preferably diffuses through Mg metal using these sites. The Rietveld analysis indeed yields a high occupation of D on the 2a site and a lower occupation on 4f, with fairly large anisotropic temperature factors indicating motional or static disorder (Table 1). The density of D in the Mg α-phase appears to be as large as MgD∼0.3 on the basis of the refinements, which comes close to the volumetrically determined load of D. The surprising result that substantial amounts of H dissolve in the Mg α-phase prompted us to reanalyze previously obtained data on Nb- and V-catalyzed MgH2 reported earlier7 in order to see if such a large H (D) fraction in the Mg α-phase could be observed. This was not the case: at most a fraction of MgD∼0.03 could be justified from these data. This indicates that in the current materials the Mg α-phase is modified by the presence of the Ti fluoride catalyst in a way that either the uptake of hydrogen in the modified α-phase has become energetically more favorable or the uptake in β-MgH2 has become less favorable energetically. Stabilization of the Mg-α phase might be possible by a small solubility of F in α-Mg, by stabilization of the surface of the Mg crystallites by incorporation of F,27 by an interaction of Mg with the TiH2 that is present even after desorption, or by a combination of these factors. The solubility data of F in (bulk) Mg are not known in detail; however, Ma et al. reported that two different forms of F ions are observed in F 1s photoelectron spectroscopy28
Mg D 2a
0.0179 0.67
D 4f
0.35
0.0020 0.38
0.0 0.0
0.0179 0.67
0.0 0.0
0.0202 0.65
0.17
0.0
0.35
0.0
0.8
in TiF3-catalyzed MgH2. One form is the MgF2 also observed here in the XRD patterns, while the other form is attributed to F in which the F valence electron is transferred to the F ions more completely. Such effect seems possible for F dissolved in Mg as there is relatively much less F present in the strongly electropositive Mg than is the case in MgF2. In our diffraction data we cannot discriminate between D and F in the Mg phase because these elements have a similar coherent neutron scattering length of 6.7 and 5.7 fm for D, F respectively. However, before the D loading at 50 °C one can already observe a small ∼2% occupancy close to the 2a site in the neutron data, which then has to be attributed to F. Also, in the X-ray data of a desorbed sample a 2% occupation of the 2a site with coordinates (0, 0, 0.083) can be consistently observed. Such a site occupation is similar to occupation of the 2a site (0, 0, 0) having an anisotropic atomic displacement or temperature factor along the c-axis. We conclude that the Mg α-phase appears to be taking up large amounts of D before it converts to the rutile β-phase of MgH2 and that the Mg α-phase indeed seems to be stabilized by having a small amount of F dissolved in it. Clearly, the error bars for observing such low amounts of dissolved F are comparable to the occupation value fitted. For this reason 19F NMR is currently being performed. Such F solubility in the α-Mg phase does not need to be the only reason for increased stability of the α-phase; also titanium hydride may play a role here as a crystallite that stabilizes the α-Mg surface as described below. From the results presented above, we see that the most rapid part of the hydrogen uptake corresponds to the uptake in the α-phase. Further hydrogen absorption involves the formation of the β-phase, but the rate of uptake remains fast. At a temperature of 150 °C, the uptake speed starts to reduce from the point onward when no α-phase is present anymore. Figure 4 clearly shows that the MgD2x phase is pronouncedly off-stoichiometric, as was previously also reported in ref 7. During the initial desorption, the higher stability of titanium hydride compared to that of magnesium hydride causes the titanium hydride to remain. During the first subsequent loading cycle at 150 °C of D2 the unexpected presence of the hydrogen remaining in the 5 mol % TiH2 phase after desorption caused that a correction for the difference in neutron scattering length of hydrogen and deuterium had to be made (Figure 4). The applied correction is based on the fact that the 5% H still present in the sample rapidly exchanges with D of the MgDx phase formed during loading with deuterium, since it is known that TiH2 contains highly mobile H, and as soon as it can exchange with D it will also appear in the MgD2x. During this first sorption cycle we assumed that the constant amount of H present in the sample is mixed homogeneously with the absorbed D. At the 2003
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Figure 6. Model for the grain refinement by the MgF2 nucleation centers and a TiH2 film located on the surface of a ∼120 nm α-Mg grain. Upon hydrogen loading the β-phase MgH2 nucleates on the ∼12 nm MgF2 grains and starts growing inward, the α-Mg becomes smaller and smaller, and the β-MgH2 cannot grow much larger than ∼30 nm. The TiH2 is also present near the Mg/MgH2 and may serve as a stabilizer for the surface of the α-Mg.
highest loading fraction reached after ∼200 min, the corrected (D + H) site occupancy in MgD2 then is very close to 1 (figure 4), which shows that the correction is properly performed. For the second loading, such correction was not necessary because the H was largely removed together with the D (95% diluted, and therefore only a small fraction 1H remaining in the titanium hydride) during desorption in the first sorption cycle. This can also be observed from the corresponding disappearance of the incoherent background in Figure 1. The appearance of the vacancies in the MgD2x is a consequence of the nanoscale size of the particles. The basic underlying mechanism involves the presence of interface energies upon phase separation that result from tensions between the α- and β-phase and local composition gradients. This causes that the formation of such interfaces within a single grain need to be prevented, leading to different solubility limits. Such effects were first described in ref 7. More recently similar effects have been found in two-phase Li insertion reactions involving nanoparticles,29,30 and a theoretical framework was elaborated for such reactions in nanoparticles.2931 The presence of vacancies in MgH2x during loading and unloading is important for the uptake and release speed of hydrogen, since hydrogen vacancies may greatly facilitate the mobility of hydrogen in metal hydrides.3234 At the highest pressures used during the loading, the defect density reduces to less than 2% and basically the full storage capacity is reached, in close agreement with the amount of gas added and the sample weight. Role of MgF2 as a Grain Refiner. The neutron diffraction results clearly show that the MgD2x crystallites have remarkably small dimensions throughout the D2 cycle (Figure 5). The coherent domains of MgD2x become as small as ∼30 nm judging from line broadening and using the large d-spacing range available to judge the type of line broadening (size or strain). This is an indication that the fluoride indeed works better as a grain refiner than previously applied catalysts. For similar amounts (in mol %) of catalyst, the MgH2 particle sizes then ranged up to ∼150 nm in the cases of V or Nb as the catalyst. In the present study the Mg metal grains also develop small sizes, starting from about 150 nm, reducing to ∼50 nm during loading. The fact that the particle size of Mg reduces upon D2 absorption indicates that individual Mg grains lose material to the MgD2 phase and that in this case therefore phase boundaries are going to be present inside such grains.35 This is a difference with the case of Nb/V as a catalyst7 since there both the α- and β-phase had sizes of 150 nm. An explanation may be that the small MgF2 particles
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Figure 7. Seen from two directions, a possible orientation of the TiH2 phase on the α-Mg metal phase is shown, which consists of continuous lattice planes of the different metal ions as indicated, i.e., corresponding to a relatively strain-free interface. Green, Mg; gray, Ti; white, H. The indicated planes are left, [2, 2, 0] TiH2 and [1, 1, 0] Mg; right, [1, 1, 1] TiH2 and [0, 0, 2] Mg.
(∼12 nm from the diffraction line broadening) that act as seed crystals lower the surface energy of the MgH2 attached to it so much that the energy related to the strain-full interface with the α-phase is compensated. Many interfaces between different MgH2 grains will also be introduced, since the MgH2 domains are smaller than the original Mg crystallites. In a recent paper, Danaie et al.36 showed that abundant twinning of MgH2 can occur with limited impact on the thermodynamic properties, i.e., the lattice energy penalty for such twinning, which leads to reduced sizes of the coherent structural domains, is not very large. It is thus reasonable that abundant MgH2MgH2 interfaces can be present, yielding the observed small overall crystallite sizes in Figure 5. In Figure 6 a possible model of the development of the morphology is presented. The small MgF2 crystallites on the surface of the larger Mg grains may act as nucleation centers from which differently oriented magnesium hydride crystallites start growing. As a consequence the Mg domain then reduces while the MgH2 domains can only grow to a much smaller size than the initial Mg grain. The role of the TiH2 phase on the surface is described below. One may wonder what happens with fluorine that is dissolved in the Mg. The simplest possibility is that it just dissolves into the MgD2, sitting on the hydrogen site. Since the neutron cross sections of D and F are similar such low % substitution will be hardly visible. Upon desorption it would then be dissolved in Mg again. The Fate of Ti and Zr. In order to gain a better insight into the fate of Ti upon hydrogen cycling, X-ray diffraction studies were performed on similarly prepared samples. Further, ZrF4catalyzed MgH2 samples were studied for comparison. The X-ray diffraction pattern of the MgH2 + 0.05ZrF4 sample in Figure 8 shows the presence of ZrH2 and MgF2 after prolonged cycling and final desorption at 280 °C. This indicates that the following reaction has taken place for a part of the sample: 2MgH2 + ZrF4 f 2MgF2 + ZrH2 + H2. The Zr scatters strongly, which causes clear diffraction peaks of the ZrH2—although they are very broad— to be present. In analogy, during hydrogen desorption from the initial ball-milled MgH2 + 0.05TiF3 sample the following reaction takes place: 3MgH2 + 2TiF3 f 3MgF2 + 2TiH2 + H2 for part of the sample since both MgF2 and TiH2 are present in the Rietveld refinements. The TiF3 on the other hand has disappeared after desorption, while it was still present directly after ball milling. The TiH2 has very broad X-ray diffraction lines similar to the ZrH2. Note that the presence of TiH2 or ZrH2 in samples in which the MgH2 is desorbed is justified by the lower enthalpy of formation of TiH2 (118 kJ/mol H237,38) and ZrH2 (162 kJ/ mol H239,40) compared to that of MgH2 (74.4 H2 kJ/mol41). Although a much weaker neutron coherent scatterer, the TiH2 is 2004
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MgyTi1yH2, albeit that pure alloys are not formed.21,22 Also first-principles DFT calculations42 indicate the meta-stability of the cubic TiH2 phase upon Mg substitution to similarly high concentrations, albeit that a band gap signature typical for MgH2 develops in calculated electron energy density-of-states, which may point to a loss of metallic character. The character of the cubic Ti/ZrH2 with possible Mg in it is currently investigated further using solid state NMR. In our materials the results of the X-ray diffraction of a Ti- or Zr-containing sample which has undergone extensive loading and unloading reactions over prolonged times show a number of distinct additional diffraction peaks at 2θ = 24.2, 28.1, 40.1, and 72.9°. These peaks could be indexed and refined as a Mg2TiH6 and Mg2ZrH6 type structure respectively of the known cubic K2PtCl6 type, with space group Fm3m, and a = 6.3511 and 6.3503 Å for respectively Ti and Zr. The intensity of the peaks at 2θ = 24.2° and 40.1° are very sensitive to the transition metal at the Mg site; it appears that the compounds are not stoichiometric but that the Mg content is lowered significantly by Ti/Zr substitution on the Mg site (Table 2). This structure type is already known for Mg2FeH6 (with a = 6.4469 Å) and Mg2CoH6;43,44 however, as far as we know it has not been reported before for Ti and Zr. The presence of these peaks is detected in samples that have been under hydrogen gas at temperatures of ∼200 °C for at least several days to weeks, which may indicate that the crystallites only then have grown to sufficiently large sizes to enable detection by XRD. The fact that such [Mg, T]2TH6 structure can form shows that the Mg and Ti/Zr are close enough together to react over prolonged times; i.e., the phase separation which occurs in pure Ti/Zr and Mg mixtures is at least incomplete in the hydrided material. We considered also the presence of Mg2TiF6 or MgTF6 (T = Ti, Zr) type compounds that could be isostructural with MgCrF6;45 however, such phases were not found in diffraction. The [Mg, Ti]2TiH6 phase reported here is a new ternary MgTiH compound. Previously Kyoi et al. investigated the high-pressure synthesis of another new MgTiH phase with composition Mg7TiHx, showing promising hydrogen uptake properties.46 In Mg1yTiyH2 thin films reports show a different single coherent crystal lattice which remains of the cubic fluorite type even up to a composition of Mg0.87Ti0.13H2. There the films show a complex nanoscale structure in which a partial chemical segregation of the Mg and Ti occurs, but only on length scales well below 10 nm, as evidenced from X-ray diffraction, EXAFS, and positron annihilation studies.21,22 Equilibrium Pressure Measurements. The results of equilibrium pressure measurements at different temperatures at a fixed overall composition for the example of MgH0.14 are shown in Figure 9. During the measurements the temperature was increased stepwise, and the pressures were recorded until equilibrium was reached. The same temperatures were measured going down in temperature. The differences between the equilibrium pressures determined in the rising and lowering temperature
also present in the neutron diffraction as a diffuse, incoherent scattering background stemming from the H that is still present during the first set of spectra obtained during loading D2 in the sample. Only after subsequently unloading the D2 as far as possible at 300 °C, the H is largely removed by exchange and flushing with D. The present investigation cannot exclude the presence of Mg in the TiH2 or ZrH2; based on Miedema’s rule of reversed stability, such Ti/Zr MgHx compound would have a higher stability than pure Ti/ZrH2 due to the instability of the Ti/ZrMg alloy. In X-ray diffraction a Ti/ZrHx compound with random substituted Mg on the Ti/Zr position would be indistinguishable (except a small effect on lattice parameters), while in our neutron diffraction the contrast would be reduced since the positive scattering length of Mg (+5.38 fm) would partly compensate that of Ti (3.44 fm). In experimental results in thin films of hydrided TiMg, it was observed18 that Mg can substitute Ti in the cubic TiH2 phase up to large fractions y < 0.87 in
Figure 8. Top: X-ray diffraction on a long-term cycled and desorbed MgH20.05TiF3 sample. The spectra below give the contributions of respectively TiH2, [Mg,Ti]2TiH6, MgF2, and MgO, the remainder being Mg. Bottom: idem for MgH20.05ZrF4. The broad features of the ZrH2 and TiH2 are clearly visible. The insets show distinct peaks of the [Mg,Ti/Zr]2Ti/ZrH6, MgF2, and MgO phases indicated by *, +, and O, respectively.
Table 2. Structural Parameters of [Mg, T]2TH6 with T = Ti, Zra atom
Wyck.
x/a, y/b, z/c
fraction
Uiso [Å2]
Fm3m
Mg/Ti or
8c
1/4, 1/4, 1/4
0.51/0.49 ( 0.02
0.025
a = 6.3511(5) Å (Ti)
Mg/Zr
0.16/0.84 ( 0.02
0.025
a = 6.3503(5) Å (Zr)
Ti/Zr H
1 1
0.025 0.025
phase
a
4a 4f
0, 0, 0 0.26, 0, 0
The refined overall compositions are Mg0.99Ti2.01H6 and Mg0.32Zr2.68H6, respectively, from refinements with wRp = 0.038. 2005
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Figure 9. Equilibrium pressures measured for stepwise increasing and decreasing temperatures for the TiF3-catalyzed material with overall H composition corresponding to MgH0.14. The bulk equilibrium pressures calculated from ΔH = 74.5 kJ/mol H2 and ΔS= 135.1 J/Kmol H2 of Stampfer et al.41 are shown for comparison.
runs are only very limited, indicating that equilibrium pressure values can be accurately determined and that hysteretic effects are small. Although the sample reacts rapidly under large applied overpressures, reaching a real pressure equilibrium still takes significant time, especially at the lower temperatures used. However, for an uncatalyzed sample measuring such lowtemperature equilibrium pressures is impossible altogether. It should be noted that this method induces only very small changes in the overall hydrogen content of the samples because of the very small volume available for the gas phase in the experimental setup. The T induced pressure changes correspond to maximum overall H concentration differences of ∼104 H/Mg. The small amount of H exchanged will mean that essentially the most reactive or most unstable fraction of the sample is probed, which is especially interesting for the catalytic process. The experimental method used is different from the often applied method using temperature dependent pressurecomposition graphs where the composition is changed over a whole range, but where normally only the midpoint of H concentrations is considered (MgHc∼1) to construct a van't Hoff plot. In our case the point closest to this midpoint gives a result closest to the normal MgMgH2 bulk value. Currently it is also investigated what the pressure composition graphs would yield in these samples. Another issue with understanding the results is the fact that the overall compositions used span from a composition where there is possibly only a solid solution of H in the α-Mg phase, up to a composition in which clearly two metal hydride phases have to be present (based on the neutron diffraction). As will be discussed below, in a single grain the diffuse interface model31 describes the presence of both the α- and β-phases where the amounts of each phase can be varied by moving the interface through the grain. For this reason we will use in this instance that the gas is in equilibrium with two phases in each grain for the overall H contents used in Figures 9 and 10. In such case the enthalpy of formation dH and the entropy change dS0 for a reference pressure p0 obey the relationship 1 p dH dS0 ln ¼ 2 p0 RT 2R
ð1Þ
where dH is the heat of the reaction of the process MgHcα + 1/2(c β c α )H 2 f MgHcβ, where c α and c β are the total amounts of H present in the α- or β-phase respectively before and after the addition of hydrogen. As is described in ref 47 for a
Figure 10. Values of ΔH and ΔS plotted against each other for bulk MgH2 (black squares), TiF3-catalyzed MgH2 (blue diamonds), and ZrF4-catalyzed MgH2 (red circles) for various compositions MgHc. The error bars were determined from the difference between the values extracted from the van't Hoff plots for rising and for lowering temperatures. The open square refers to values observed in Mg0.9Ti0.1 hydride from.14.
two-phase system dS0 ¼
Sβ Sα 1 0 dS cβ cα 2 H2
ð2Þ
includes a term associated with the change in entropy at a standard pressure p0 (e.g., 1 bar) for the α-phase going to the β-phase in the reaction MgHcα + 1/2(cβ cα)H2 f MgHcβ. Equations 1 and 2 can also be applied for a single-phase reaction between hydrogen and the metal, but then cα and cβ do not represent fixed concentrations but they are the varying concentrations x before and after the dissolution of more hydrogen in the single-phase MgHx. In conventional lattice gas models for H dissolution in a two-phase metal system47 dS0 reduces to dS0 = 1/2dS0H2. However, in these nanostructured materials strains and interfaces strongly influence the local compositions, phase behavior, and solubility limits in α- and β-domains that are connected through an interface. This results in the varying D contents fitted here and in previous work on Li and D storage materials;7,48 i.e., the Sβ Sα as well as cβ cα will vary as a function of the overall H content of the material; first there is a single phase, and after establishing of two phases still there is a mutual influence between the α- and β-phase unlike in bulk materials. The enthalpies of formation dH and the change in entropy dS0 (where p0 is 1 bar) involved in the hydrogen absorption are deduced from the equilibrium pressure data using eq 1 and plotted against each other in Figure 10 as a function of the overall hydrogen content c. Several striking results emerge: first of all dH for the fraction of the material measured is strongly increased (less negative) with respect to the bulk value for MgH2 for a small overall hydrogen content c. Such strong deviation from the bulk has not been observed before, although significant deviations were reported,14 as also indicated in Figure 10. The same holds for dS0. Second, there is a strong correlation between the change in the numeric values of dH and dS0. The dashed line drawn in Figure 10 goes almost perfectly through the data points obtained at various concentrations c in MgHc0.04TiF3, and the same line also goes through the point for the ZrF4-catalyzed sample and the bulk MgH2 value. Notably the line extends continuously from 2006
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The Journal of Physical Chemistry C small overall concentrations, where there in principle could be only a nanostructure imposed solid solution α-MgHcα, to the concentrations where the in situ neutron diffraction shows there are two phases α-MgHcα and β-MgHcβ. Such enthalpyentropy correlations are reminiscent of “compensation effects” that are reported in other systems.49 The origin of such correlation is generally poorly understood, but a general mechanism seems to consists of a weakening of intermolecular bonds (related to the enthalpy) which leads to an increase of the configurational freedom and hence a smaller degree of ordering in the system (related to the entropy).49 The continuous and correlated changes in dH and dS0, as observed here in the dH dS0 diagram of Figure 10, therefore may well arise because the hydrogenation reactions of the fraction of the material probed, though closely related, vary continuously with hydrogen concentration as the hydrogen actually binds at a varying bond strength to the gradually changing material. A simple qualitative rationale for such a correlated variation of dH and dS0 in our system consists of the following. From the diffraction experiment, insights are gained about the change in dS0: significant hydrogen vacancy densities are present in the β-MgH2 phase, and on the other hand significant hydrogen densities are dissolved in the α-Mg phase. Furthermore, there are abundant interfaces introduced. The configurational entropy related to the presence of abundant vacancies on the one hand and the abundant dissolved hydrogen in Mg on the other hand will be substantial, much more than in bulk Mg/MgH2 which has virtually no H dissolved in Mg (concentrations of the order of 104) nor vacancies in MgH2. This considerable entropy present in the solid state will make the entropy difference dS0 in going from the gas phase to the solid state lower; i.e., this can thus explain the observed reduced dS0 for the catalyzed nanosamples. Also, the clear dependence on the overall hydrogen content follows from this mechanism because the vacancy density changes monotonously with the overall composition. On the other hand, a number of contributions to the free energy lead to the detected less negative values for H found in the solid state nanostructured and catalyzed material. The reduced number of chemical bonds present in a hydrogen deficient β-MgH2x will lead to less strong bonding of the hydrogen and, consequently, to a less negative H and a smaller dH difference with the enthalpy of the hydrogen in the gas phase. For the α-MgHy metal phase, the free energy is less negative to start with, while the enthalpy at infinite dilution in bulk Mg ΔH∞ is positive.50 Additional factors in the free energy are the surface energies of the particles and the distance of the hydrogen with respect to the surfaces, the interface energies between the different phases, and the influence of strain and deformation on phase volumes.51 In nanocrystalline materials such interface and surface energies become prominent factors in the total free energy7,29,31 because of the largely increased surface(interface)-to-volume ratios, and these energies can influence the phase behavior in a fundamental way. In general the change of dH and dS0 can be discussed in the framework of the Gibbs free energy G, which is minimized to yield the phase behavior of a system; this should also hold for small variations of the hydrogen content. The chemical potential of hydrogen absorption in the metal hydride system, μ, follows from dG = μ dc for constant T and P with c the overall concentration of hydrogen in the hydride system which is controlled externally. On the other hand, for a certain overall concentration c in the material the number of H atoms Nα and Nβ in the α- and β-phase respectively follow from the equilibrium condition
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0 = (dG/dNα )p=p0 = dH/dNα T dS0/dNα, which leads to dH = T dS0 for any experimental temperature T and a certain reference pressure p0. In itself, this does indicate that a relation between dH and dS0 as in Figure 10 may be expected; however, it does not explain what causes the change in dH and dS0. The line in Figure 10 corresponds to dH ∼ 5.1 102 K dS0, which indicates here a proportionality constant T0 ∼ 510 K. In a normal bulk two-phase MgMgH2 material such changes do not occur, first of all since the plateau pressures are constant over the width of the plateau and therefore no variation in dH and dS0 with overall concentration is present. Second, such variations cannot be measured at the low temperatures used here since there is no such reactive fraction of the material present. For single-phase, solid solution type metal hydrides the material continuously changes upon H insertion. In the so-called lattice gas model for a single-phase solid solution metal hydride, we would approximate dH = E + acα 1/2 dHH2 and dS0 is given by eq 2 and equals dS0 = R ln(cα /(1 cα)) 1/2 dS0H2 . The variation with cα results from d(dH)/dcα = a and d(dS0)/ dcα = R/(cα(1 cα)) . The variation of d(dH)/d(dS0) = a(cα(1 cα))/R over the applied concentration range 0.14 < cα < 0.48, in which a single phase was present in the neutron diffraction, is not large (factor 2). This may indeed indicate that a correlation between dH and dS0 is to be expected. The ∼0.48 is about the maximum concentration that may be present in an α-phase, judging from the dynamically measured neutron data; however, in practice the sample during the equilibrium pressure measurements may already contain some β-phase as well, which would lower the effective cα. It is, however, striking that the correlation between dH and dS0 that is present in this most reactive part of the material is not only in the α-phase concentration region but also extends to high overall concentrations (in fact the bulk point is also positioned on the same line). Then the presence of both phases and their mutual influencing due to the nanostructuring should be taken into account. An approach to incorporate this may be as follows. In the recent work of Burch et al.,31 a model of the effect of nanostructuring on insertion compounds is given which attributes an energy penalty for a gradient in inserted ion densities near phase boundaries. This energy penalty comes in addition to the homogeneous free energy of mixing which would lead to solid solution behavior outside the coexistence range and spontaneous phase separation in between the solubility limits. Such description of an additional interface energy term is similar to what was argued in refs 7 and 29. In order to quantify the energy terms in the description of Burch et al.,31 a regular solution model for the mixing of two hydride phases is used, with in addition a term that results from the gradients in composition near the interface: Z 1 ghom ðcÞ þ ð∇cÞ 3 K 3 ð∇cÞ F dV Gmix ¼ V 2 Here c represents the Li concentration, V the volume, and F the density of hydrogen sites per volume unit. K is the gradient energy penalty tensor, assuming it is constant independent of the concentration c and the spatial position. Without the contribution to the energy of mixing of the concentration gradient, K = 0, the solubility limits follow from the equilibrium conditions leading to the common tangent construction. With the concentration gradient term, regions in which the local concentrations (strongly) deviate from the bulk concentrations can occur in 2007
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The Journal of Physical Chemistry C nanostructured materials. In such regions the (homogeneous) free energy is then given by ghom(c) = ac(1 c) + kBT [c log c + (1 c) log(1 c)], where the first and second terms represent respectively the homogeneous enthalpy and entropy term. Here c = 0 corresponds to Mg and c = 1 to MgH2. If we now assume that varying the H concentration by a small amount (ΔH/Mg ∼ 104) will not change the gradient of the phase boundary (the position may change), then only the ghom term changes and dH/ dc = a(1 2c) and dS0/dc = kB [log c log(1 c) ]. When comparing the concentration dependence of 1/kBT dH/dc and 1/kB dS0/dc for a = 2kBT, the two curves practically coincide for 0.2 < c < 0.8 (see Supporting Information); i.e., for this value of a, the change in T dS0 and dH with concentration c are identical and also for other values of a they are linearly dependent. From the experimental data we require that for the fraction of the material that is actively participating in the equilibrium pressure measurements dH = 5.1 102 K dS0, which corresponds to a value T0 = 5.1 102 K and a = 10.2 102 kB. Besides their correlation the other observation is that dH and dS0 show relatively high values (less negative) for this most reactive fraction of the material at low overall concentration c. From the in situ neutron diffraction, we can deduce that at low c there is predominantly α-Mg with large amounts of H dissolved in it and only low amounts of β-MgH2x. Inside a grain one can imagine that phase boundaries are either still absent or they are in a corner of the particle where the β-phase just nucleated. The hydrogen coming from the gas phase will thus predominantly interact with α-Mg that has a high H content and a fully stressed phase boundary and β-phase fraction. This should explain the relatively high dH and dS0. In ref 31 a criterion for the stability of the solid solution region is given as
2a 1 þ > π2 λ2 =L2 kB T c0 ð1 c0 Þ
where c0 is a particular concentration, L is the size of the particle, and λ is the length of the interphasial width of the interface, i.e., the thickness of the phase boundary over which the concentration varies from the H-poor to the H-rich value. Phase separation occurs in between the solubility limits c0( with vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 u 1 1 c0( ¼ ( u 2 t2 2a π2 λ2 =L2 kB T Based on the solubility limits determined from our in situ neutron diffraction experiment of approximately c0 = 0.25 and c0+ = 0.75, this leads to {(1/2) [1/((2a)/(kBT) (π2λ2/L2))]}1/2 = 1/4 and 16/7 = (2a)/(kBT) (π2λ2/L2). Since the correlation between entropy and enthalpy leads to an estimation of a = 2kBT for the parameter a, one obtains π2λ2/L2 = 12/7, i.e., λ/L = ((12/7)/π2)1/2 = 0.42. In our case of crystallite sizes of less than 100 nm for α-Mg and of ∼30 nm for β-MgH2, this indicates that λ should have a value of 12 nm or more to obtain a consistent description of the size-dependent solubility limits and the observed correlation between entropy and enthalpy based on the effect of a diffuse interface alone. In view of the large lattice mismatch, and the strong volume expansion upon hydrogen uptake to MgH2, such length scale for a phase boundary seems reasonable. In the electron microscopy work of Isobe et al.52 on a niobium oxide catalyzed magnesium hydride sample an MgMgH2 interface with an approximate thickness of ∼9 nm is deduced,
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Figure 11. Free energy of bulk MgHc as a function of overall composition c (red curves). The green curves represent the free energy of TiF3catalyzed MgHc that results from interface and surface energy contributions occurring in the nanoparticles growing on grain-refining seed crystals. The alteration of the solubility limits cα and cβ is indicated by the arrows.
judging from the number of Mg(101) lattice spacings that fit in the interface area. Such a 9 nm interface thickness is indeed not far from the 12 nm deduced above, which supports that the most reactive fraction of the material involves that fraction of the material in which such diffusive interface description can be utilized. At lower overall H concentration apparently the most reactive materials fraction which contributes consists of those particles in which an interface is being established, while pure α- and pure β-phase particles are less reactive. The conclusion is that the entropyenthalpy correlation for the most reactive fraction of the material is to be expected in grains in which a homogeneous mixing of hydrogen into the metal phase is accompanied by vacancies in the hydride phase over an extended range of compositions c, leading to a continuous variation of the binding of hydrogen in the material. Since in our system the solubility limits are observed to be strongly altered compared to bulk, leading to narrowing of the miscibility gap, there are indeed widely extended ranges of c for which the local composition gradually changes in both the α- and β-phases. Such solubility limits that vary inside the miscibility gap while varying the overall hydrogen composition were also observed in ref 7. They were recently also observed in detail and associated with the diffuse interface model in Li-ion storage materials.48 The order of magnitude of the change in ΔH (increase of ∼25 kJ/mol H2, or ∼130 meV/H) is similar to what is observed in the change of the insertion voltages of up to several 100 meV near the changed solubility limits of ∼40 nm Li-ion storage material LiFePO4.53 Free Energy and Phase Behavior of Nanocrystallites Grown on Grain-Refining Seed Crystallites. From the above experimental results, the inferred grain-refining action of the added seed crystals and the presence of abundant interfaces introduced in these nanomaterials, we propose a behavior of the free energy of insertion of hydrogen in the TiF3-catalyzed Mg as sketched in Figure 11. A sketch of the main surfaces and interfaces that appear to play a role for TiF3- (or ZrF4-) catalyzed and nanostructured Mg and MgHx materials is given in Figure 12. Several interface and surface contributions are involved upon transformation of the TiF3-catalyzed Mg to MgH2. First, there is the surface free energy of the α- and of the β-phase, which leads to a surface free energy term54 3Ωσ r 2008
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Figure 12. Indicative phase behavior in (catalyzed and) nanostructured Mg upon hydrogen uptake, and the surface (σ) and interface (γ) energies that will play a role. Top: when only surface energies of the α-Mg and β-MgH2 are present (no catalysts on the surface) the lowest free energy can be reached by having α-particles (dark gray) next to β-particles54 (light gray). The solubility limits will depend on the relative surface energies σα and σβ. Bottom: in the case of the TiF3-catalyzed Mg the interfaces between Mg, MgH2 and TiH2 (blue), and MgF2 (red) occur, i.e., interface energies29 γα/β,T/F. The good lattice matching between α-Mg and TiH2 and between MgH2 and MgF2 makes it favorable to maintain coexisting α- and β-phases inside one particle at the expense of an αβ interface energy γαβ. The β-phase actually consists of many smaller domains (Figure 6, here omitted for clarity), leading to γββ.
where Ω is the volume per Mg or MgHx unit and σ the surface free energy of a particle with radius r. For free isolated Mg and MgH2 nanoparticles, one would have a σα and σβ (Figure 12). The formation of an interface between α and β would be prevented54 as is observed experimentally in the Nb- and V-catalyzed materials.7 Depending on the relative values of σα and σβ, the system will prefer the transition to the β-phase for lower or higher H concentrations inside the nanoparticles.54 In the present case of TiF3-catalyzed Mg, we assume that the surface free energy is modified because of the presence of grain-refining seed crystals, which will lower the surface free energy compared to a free isolated nanocrystal. In fact, one may rather speak of the interface energies γ of the fluoride (F) and titanium hydride (T) phases with the α- and β-phases (i.e., γαT, γβT, γαF, γβF as indicated in Figure 12) than of pure surface energies. For α-Mg we assume that these free energy contributions are negative, resulting in a free energy lower than that of bulk α-Mg. Such negative contribution may result from the interface interaction γαT with the TiH2 phase indicated in Figures 6 and 7. Such an interface will have a thickness that depends on enthalpy and entropy factors as described in ref 31 and above. Apart from these interface effects, a small fraction of F dissolved in the Mg may also lower the free energy of the α-phase. In Figure 11, the green curve at c = 0 is therefore lowered with respect to the red bulk curve. This is consistent with the low pressures required to load hydrogen in the α-phase during the in situ neutron diffraction measurements. The free energy of the β-phase could also be lowered by the interface interaction γβF with the MgF2 seed crystallites, which show very close lattice matching with the β-MgH2 phase. Further, the presence of small MgH2 domains is observed, indicating the presence of many MgH2 twinning planes, resulting from the many different MgF2 seeding crystallites present that fix the orientation of the growing MgH2 phase domains. For simplicity there is only one MgH2 domain sketched in the lower part of Figure 12. In reality, however, there will be
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Figure 13. Lattice parameters of the bulk α-Mg phase with varying amounts of H inserted at the interstitial 2a and 4f sites as obtained from DFT calculations (VASP) and from the experiment at 150 °C where no β-phase is present yet. The experimental error bar is comparable to the symbol size, and the DFT error in lattice parameters is larger ∼0.07 Å, judging from the scatter.
many different domains (Figure 6) having interfaces and their associated energy term γββ. The γββ contributions will effectively increase the free energy for large overall concentrations of H in the system when the different oriented β phase domains touch each other. For this reason the green β phase curve has a minimum shifted to the left of x = 2, leading to a further alteration of the solubility limit. The increasing pressure required to fill the β-phase from x ∼ 1.5 to x ∼ 2 is consistent with the increasing free energy toward x = 2, keeping in mind that ΔG = kBT(1/2)(ln(P/P0)). As described above, the main reason for a reduced solubility gap stems from the occurrence of interfaces between α-Mg and β-MgH2 in combination with the presence of TiH2 and MgF2. Using the dependence of interface energies on the overall composition as introduced in ref 29, we can apply a construction for determining the free energy penalty due to the αβ interface free energy given by the gray line in Figure 11. The solubility limits cα and cβ determined by the vertical dash-dotted lines then result. The sketch is made for values for the solubility limits close to the values of cα ∼ 0.5 and cβ ∼ 1.5 observed in the in situ neutron diffraction, i.e., determined from the hydrogen contents of the sample just before the formation of the first β-phase fraction and just after the last α-phase fraction has disappeared, respectively (Figure 3). Effect of H Dissolved in α-Mg from DFT Calculations. The in situ neutron diffraction data of Figure 2 provide the surprising observation of a large H concentration dissolved in the α-phase of Mg while there are hardly any lattice parameter changes visible. In order to explore if this is also to be expected theoretically, firstprinciples DFT calculations using VASP were employed on a number of structure models where H was inserted in the α-Mg hcp structure. H was inserted at the 4f (1/3, 2/3, ∼0.08) and 2a (0, 0, 0) sites with varying densities, and the unit cell parameters were allowed to relax freely. In Figure 13 the lattice parameters are plotted as a function of the amount of H inserted in the model. It appears that up to the experimentally observed H concentrations of MgH∼0.4 only very limited changes in the lattice parameters are expected indeed, which agrees with the experimental neutron data in Figures 2 and 13. If in addition there is a stabilizing effect from interface interactions from matching lattices of TiH2, the effect could even be lower. The small effect on lattice parameters is related to the relatively open structure of 2009
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The Journal of Physical Chemistry C hcp α-Mg, enabling absorption of relatively large fractions of hydrogen atoms in the open space between the Mg atoms without substantial lattice expansion.
’ MATERIALS AND METHODS The powders MgH2 (purity of 98%, obtained from ABCR GmbH & Co. KG) and 5 mol % TiF3 or ZrF4 (>99.9%, Alfa Aesar) were milled under Ar atmosphere in a Fritsch Pulverisette 6 planetary monomill with a ball-to-powder ratio of close to 50:1 (32 4 g balls: 2.67 g of initial weight of total powder) for a period of 60 min with a rotational speed of 400 rpm. A pause of 15 min was taken after every 15 min rotation interval. The handling of all powders was done in a glovebox containing argon as a working gas with O2 and H2O contents of e0.1 ppm. Catalyst powders and equipment such as balls, bowl, and spatula, etc., were baked out in a vacuum oven at around 80 °C for a few hours before bringing them into the glovebox. The sizes of asreceived MgH2 and ball-milled MgH2 were found to be 150 and 30 nm, respectively. These sizes were extracted from the Rietveld fitting on X-ray diffraction (XRD) patterns, which were obtained using Cu K-α radiation on a PANalytical Type X’Pert Pro diffractometer. The XRD pattern of the freshly ball-milled sample showed the presence of β-MgH2, γ-MgH2, TiF3, and traces of MgO. After the milling, the sample was desorbed in the glovebox using temperatures ranging from 25 to 280 °C. A significant amount of 35% of the total desorbed hydrogen was released already at
