Ion-transport engineering of alkaline-earth hydrides for hydride

Article Cite This: Chem. Mater. 2018, 30, 5878−5885

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Ion-Transport Engineering of Alkaline-Earth Hydrides for Hydride Electrolyte Applications Andrew J. E. Rowberg,† Leigh Weston,†,‡ and Chris G. Van de Walle*,† †

Chem. Mater. 2018.30:5878-5885. Downloaded from pubs.acs.org by UNIV OF SUNDERLAND on 11/10/18. For personal use only.

Materials Department, University of CaliforniaSanta Barbara, Santa Barbara, California 93106-5050, United States ABSTRACT: The heavier alkaline-earth hydrides (AeH2; Ae = Ca, Sr, Ba) are promising materials for hydrogen energy applications, due to their excellent ionic conductivity and thermal stability. We use first-principles calculations to elucidate their defect chemistry and ion-transport mechanisms. On the basis of calculated formation energies, we find that hydrogen vacancies (VH) are present in large concentrations, and hence, transport is vacancy-mediated. The vacancy migration barrier depends strongly on the charge state of the vacancy, with V+H yielding the lowest barriers. The activation energy for ionic transport, which is the sum of the migration barrier and formation energy, can be further reduced by lowering the formation energy of the vacancies. This goal can be achieved by doping with acceptors, such as alkali-metal impurities, which induces larger concentrations of V+H. We show that, with optimized conditions for doping, ionic conductivities can be improved by several orders of magnitude; for BaH2, the conductivity is on par with proton conductivity in the best proton-conducting oxides. For BaH2, we find K to be the optimal dopant for enhancing conductivity, and for CaH2 and SrH2, we find Na to be optimal. The resulting large ionic conductivity of hydrogen makes the heavier alkaline-earth hydrides strong candidates for electrolytes in hydrogen fuel cells.

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INTRODUCTION Modern energy needs call for clean and efficient sources of electrochemical energy. Hydrogen, the most abundant element in the Universe, offers at least three times more chemical energy per mass than do most common chemical fuels, including natural gas.1 Metal hydrides are promising for hydrogen storage and transport applications, as they safely store hydrogen in the solid state while possessing fast hydrogen kinetics.2,3 The heavier alkaline-earth hydrides (AeH2; Ae = Ca, Sr, Ba), while not possessing high gravimetric densities of hydrogen, are among the best performers in terms of thermal stability, thermal reversibility, and ionic conductivity. Although low gravimetric hydrogen density may limit hydrogen storage efficiency in these metal hydrides, their fast hydrogen kinetics suggest that they may be effective solid-state electrolytes in hydrogen fuel cells. Recently, Verbraeken et al.4 showed that BaH2 exhibits hydride ionic conductivity rivaling that of the best-known proton conductors, which are generally considered the most promising ion conductors in the solid state. Many solid-state proton conductors, typically perovskite oxides, have drawbacks. Several have poor chemical stability, particularly in environments with acidic gases such as CO2 or SO3; many have poor thermodynamic stability relative to elemental or binary compounds; and some can exhibit structural instabilities leading to the growth of different phases at surfaces and interfaces.5 There are also few solid-state proton conductors that can operate effectively between 200 °C and 500 °C.6 However, CaH2, SrH2, and BaH2 are highly thermodynamically stable7 and operate under a wide range of temperature and pressure conditions. Unintended oxygen incorporation does not significantly affect their properties.4,8 © 2018 American Chemical Society

For these reasons, they may be attractive alternatives to proton-conducting oxides, especially if their ionic conductivity can be optimized. Improving ionic conductivity requires a thorough understanding of the diffusion process in CaH2, SrH2, and BaH2. The observed flow of negative ionic charge4 can be explained either by motion of an interstitial hydride ion (H−i ) or by a hydrogen vacancy-mediated mechanism. The experimental studies4,8,9 have surmised the latter based on large observed concentrations of hydrogen vacancies (VH). Here, we perform first-principles calculations based on density functional theory (DFT) to provide direct microscopic evidence for the dominant transport mechanism and to study the possible impact of cation vacancies as traps for mobile hydrogen species. We also investigate avenues for enhancing the ionic conductivity. The activation energy is the sum of the migration barrier and the formation energy of the responsible defect, and we systematically explore approaches for lowering the formation energy by adding dopants. It has been reported that Na doping impacts the ionic conductivity, particularly in SrH2.8 Our study provides clear explanations as well as guidelines for improving the hydride conductivity by doping. To our knowledge, the present investigations constitute the first DFT studies on defect chemistry and ionic conduction in CaH2, SrH2, and BaH2. We employ a hybrid functional, which significantly improves the description of electronic structure compared with traditional functionals.10 Consistent with Received: April 16, 2018 Revised: August 10, 2018 Published: August 13, 2018 5878

DOI: 10.1021/acs.chemmater.8b01593 Chem. Mater. 2018, 30, 5878−5885

Article

Chemistry of Materials

sets a lower bound on the H chemical potential, namely ΔμH = ΔHf(AeH2)/2, which we will call the hydrogen-poor limit. Similarly, we define a “hydrogen-rich” limit based on ΔμH = 0, corresponding to ΔμAe = ΔHf(AeH2). The calculated enthalpies of formation are listed in Table 1; these values are in reasonable agreement with other reports, both experimental and computational.23−25

experiment, we find that hydrogen vacancies (VH) can form in large concentrations, but unlike experiment, we can pinpoint the precise charge state of the vacancies. The charge state strongly impacts the migration barrier of VH, which can be as low as 0.16 eV for the positive charge state (V+H) but much higher (up to 0.95 eV) for the neutral and negative charge states. On the basis of our microscopic calculations, we offer a physical explanation for this trend. We find that the V+H defect is more mobile than in other metal hydrides.11−14 To lower the overall activation energy of hydride-ion diffusion, we also need to reduce the formation energy of V+H. We propose to accomplish this via doping with acceptor impurities such as alkali metals. We show that doping can significantly improve ionic conductivity, and in BaH2, the resultant conductivity is equivalent to proton conductivities in some of the best proton-conducting oxides. Our results thus provide a route toward improving hydride-ion conductivity in the heavy alkaline-earth hydrides, to the point of making them into compelling alternatives to more traditional solid-state proton conductors.

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Table 1. Calculated Enthalpies of Formation (in eV per Formula Unit) for Three Alkaline-Earth Hydrides (AeH2) and Four Alkali-Metal Hydrides (AH)

METHODOLOGY

∑ niμi + qEF + Δcorr

ΔμAe + 2ΔμH = ΔH (AeH 2 )

AH

ΔHf (eV)

CaH2 SrH2 BaH2

−1.84 −1.80 −1.69

NaH KH RbH CsH

−0.47 −0.44 −0.36 −0.27

ΔμA + ΔμH ≤ ΔH f (AH)

(3)

For the purposes of presenting our results, we choose the chemical potentials for the impurity species to correspond to this upper bound. Note that this choice represents the most favorable conditions for impurity incorporation and corresponds to the solubility limit. The calculated enthalpies of formation for the AH compounds are listed in Table 1.

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RESULTS AND DISCUSSION Bulk Properties. At room temperature and ambient pressure CaH2, SrH2, and BaH2 all crystallize in the cotunnite crystal structure, which has orthorhombic symmetry and is identified with the space group Pnma. This structure is shown in Figure 1 for the case of BaH2. There are two symmetrically

(1)

Here, E(Dq) represents the total energy of a supercell containing defect D in charge state q; Ebulk is the total energy of a supercell containing no defects; ni represents the number of atoms of species i added (ni < 0) or removed (ni > 0) from the system; μi is the chemical potential of species i in a theoretical external reservoir; EF is the Fermi level, which is a variable with values ranging from the valence-band maximum (VBM) to the conduction-band minimum (CBM); and Δcorr is a finite-size correction factor.21,22 The chemical potentials μi are variables in the calculation that must be carefully chosen so as to represent experimental conditions. For the AeH2 calculations in this work, μAe is referenced to the total energy of a single atom in the solid-phase Ae metal, and μH is referenced to the total energy of a H atom in a H2 molecule; we define ΔμAe and ΔμH with respect to these energies. Bounds can be placed on the Δμ values; the stability condition for AeH2 in thermodynamic equilibrium requires, f

ΔHf (eV)

We also define chemical potentials for impurity species that are used as dopants. The chemical potential of each alkali-metal dopant is referenced to the total energy of a single atom in the solid alkali-metal phase. An upper bound is placed on these chemical potentials of these impurities to prevent the formation of secondary alkali-metal hydride phases (AH),

Computational Details. Our calculations are based on DFT within the generalized Kohn−Sham scheme,15 as implemented in the Vienna Ab initio Simulation Package (VASP).16 We use the hybrid exchange-correlation functional of Heyd, Scuseria, and Ernzerhof (HSE),17 with 25% mixing of short-range Hartree−Fock exchange. Projector augmented wave (PAW) potentials18,19 are used with a plane-wave cutoff of 400 eV. The Ba 5s2 5p6 6s2, Sr 4s2 4p6 5s2, Ca 3s2 3p6 4s2, and H 1s2 electrons are treated explicitly as valence. For the bulk primitive cells, a 5 × 5 × 3 k-point grid is used to integrate over the Brillouin zone of the orthorhombic lattice; for the supercell calculations, a 2 × 2 × 2 grid is used. Calculations of migration barriers are based on the nudged elastic band (NEB) method with climbing images.20 Defect Calculations. To calculate defect properties, supercells are constructed with dimensions 3a × 2b × 2c, containing 12 primitive cells and 144 atoms in total. These supercells are used to simulate one of several point defects: H vacancies (VH), alkaline-earth cation vacancies (e.g., VBa), H interstitials (Hi), and substitution of one of four alkali metals (Na, K, Rb, and Cs) on cation sites (e.g., NaBa). The formation energy of a point defect D in charge state q, Ef(Dq), is calculated as follows:10

E f (Dq) = E(Dq) − E bulk +

AeH2

Figure 1. Cotunnite crystal structure of BaH2.

inequivalent sites for H atoms on the lattice that are arranged about the alkaline-earth atom in a distorted square pyramidal configuration. One of the sites, hereafter referred to as H1, is coordinated to nearby alkaline-earth atoms through shared corners of neighboring pyramids, while the other site, H2, is located on the remaining unshared vertex of the BaH5

(2)

where ΔH (AeH2) is the enthalpy of formation. An upper bound on the Ae chemical potential is determined by equilibrium with solidphase Ae metal, corresponding to ΔμAe = 0; combined with eq 2 this f

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formation energy (equal to 0.34 eV). The Fermi level can then be located anywhere in the range where V0H is the lowestenergy defect, and given its low energy, we expect this defect to form in large concentrations. Similar conclusions can be reached by inspecting the formation energy curves for SrH2 and BaH2 under H-poor conditions (Figure 2(b, c)); in both cases, the formation energy of V0H is 0.29 eV. In SrH2, V0H favors the H2 site, while V−H favors H1. In BaH2, V0H and V−H both favor H1. Under H-rich (Ca-poor) conditions, the formation energy of VH in CaH2 is increased, while the formation energy of VCa is decreased (Figure 2(d)). As a result, the intersection point of the formation-energy curves is shifted to lower values, namely 2.33 eV above the VBM, where the formation energy of V+H is 0.94 eV. In contrast to H-poor (Ca-rich) conditions, the formation energy of V0H now lies above this intersection, implying that charge neutrality can now be achieved with a + mixture of V+H and V−2 Ca . It should be noted that Hi has a very + similar formation energy as VH under these conditions. However, actual growth or operating conditions will tend to be below the H-rich limit, and therefore we do not expect H+i to be present in large concentrations in these materials. Again, the situation is very similar in SrH2 and BaH2. In SrH2, the formation energy of V+H is 0.97 eV, and in BaH2, it is 0.81 eV. We will return to the formation energies when discussing activation energies for hydrogen migration. Defect Migration. We now use the NEB method to determine the barriers for vacancy migration. By comparing several different migration pathways, we determined that the most energetically favorable path for vacancy migration involves hopping from a H1 site to a nearest neighbor H2 site, followed by a subsequent hop to the next-nearest neighbor H1 site, as shown in Figure 3(a) for BaH2; the general behavior is the same for CaH2 and SrH2. V+H has an energetic preference to reside on H1 (by 66 meV for CaH2, 29 meV for SrH2, and 60 meV for BaH2); thus, the barrier is slightly higher for vacancies migrating from the H1 site to H2 than from H2 to H1. We report the higher of the two barriers as the ratelimiting migration barrier. The potential energy pathway for migration between the H1 and H2 sites is shown in Figure 3(b).

pyramids. These sites are present in equal concentrations in the crystal. Our calculated bulk properties of orthorhombic CaH2, SrH2, and BaH2 are listed in Table 2, along with experimental data. Our calculated results are in good agreement with experimental values. Table 2 also summarizes our calculated band gap values for each material. Table 2. Calculated and Experimental Bulk Properties for CaH2, SrH2, and BaH2 material

method

a (Å)

b (Å)

c (Å)

band gap (eV)

CaH2

HSE exp.8 HSE exp.8 HSE exp.4

5.90 5.95 6.35 6.37 6.84 6.78

3.57 3.59 3.85 3.86 4.17 4.16

6.77 6.80 7.29 7.31 7.87 7.84

4.09

SrH2 BaH2

4.18 3.85

Defect Formation. We conducted a comprehensive study of point defects in CaH2, SrH2, and BaH2. The defect formation energies are plotted as a function of the Fermi level in Figure 2. Results are shown for chemical potentials representing H-rich (Ae-poor) and H-poor (Ae-rich) conditions. The lowest-energy defects are the ones that are most likely to be present in the material, but the formation energy depends on EF. In an actual material, EF is determined by the requirement of charge neutrality and is typically located near the crossing point of the formation-energy curves of the lowest-energy positively and negatively charged defects, where there are approximately equal concentrations of both species. Beginning with CaH2, we first consider the case of H-poor (Ca-rich) conditions (Figure 2(a)). It is clear that VH has a low formation energy, and this defect can be present as V+H, V0H, or V−H. The formation energies of the vacancies are very similar on the H1 and H2 sites, differing by less than 150 meV; we will indicate which site is favored by particular defects. V+H (on the H1 site) is the lowest energy positive defect, and V−2 Ca is the lowest energy negatively charged defect. Near the crossing point of their formation energies (at 3.25 eV above the VBM), a neutral defect (V0H, preferring the H2 site) has a lower

Figure 2. Defect formation energies for (a) CaH2, (b) SrH2, and (c) BaH2 under H-poor (Ae-rich) conditions, and (d) CaH2, (e) SrH2, and (f) BaH2 under H-rich (Ae-poor) conditions. The slopes of the line segments for each defect correspond to the charge state. 5880


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relax outward, making it easy for a neighboring H atom to move into the vacancy site: no Ba−Ba bonds need to be broken, and the Coulomb repulsion is reduced. The results in Table 3 clearly show the trend that migration barriers increase monotonically as the charge state changes from positive to negative for all three materials. In the case of H-rich (Ae-poor) conditions, for which charge compensation between V+H and V−2 Ae is predicted, the binding energy of these two defects becomes an important factor in determining the mobility of V+H. The binding energy between two defects, Ebind([D1D2]p+q), is defined as follows:

Figure 3. (a) Schematic pathway for VH migration between H1 and H2 sites in BaH2. (b) Potential energy change along the migration path for V0H or V+H in BaH2.

E bind([D1D2] p + q ) = E f (D1p) + E f (D2q) − E f ([D1D2] p + q )

Table 3 summarizes our calculated results for migration barriers for vacancies in charge states q = {−,0,+} for all three

(4)

Using this equation and the formation energies for V+H and −2 VAe , the binding energies are calculated as 0.23 eV for [VHVCa]−, 0.31 eV for [VHVSr]−, and 0.12 eV for [VHVBa]− (see Table 4). For any V+H that becomes trapped by a nearby V−2 Ae ,

Table 3. Migration Barriers Eb for Hydrogen Vacancies in CaH2, SrH2, and BaH2 material

Eb(V+H) (eV)

Eb(V0H) (eV)

Eb(V−H) (eV)

CaH2 SrH2 BaH2

0.16 0.16 0.18

0.70 0.72 0.53

0.95 0.87 0.66

Table 4. Binding Energies for Complexes between V+H and either Alkali-Metal Dopants or Cation Vacancies in CaH2, SrH2, and BaH2a

hydrides. The migration barriers for V0H are 0.70 eV in CaH2, 0.72 eV in SrH2, and 0.53 eV in BaH2, and for the negatively charged vacancy the barriers are even higher. In contrast, the migration barriers are much lower for the positively charged vacancy: 0.16 eV in CaH2 and SrH2, and 0.18 eV in BaH2. To the best of our knowledge, these migration barriers for V+H are lower than any other calculated values for VH migration in a metal hydride.11−14 The trend in the migration barrier for the various charge states can be explained by the occupation of the defect bonding state. For example, in BaH2, the formation of a hydrogen vacancy creates dangling bonds derived from Ba d states, which combine to form a localized bonding state in the band gap and antibonding states above the CBM. Figure 4

material

acceptor

Ebind (eV)

CaH2

V−2 Ca Na K Rb Cs V−2 Sr Na K Rb Cs V−2 Ba Na K Rb Cs

0.23 0.46 0.55 0.71 1.02 0.31 0.48 0.48 0.59 0.90 0.12 0.38 0.27 0.36 0.66

SrH2

BaH2

|rA−rAe| (Å) 0.06 0.41 0.51 0.60 −0.07 0.24 0.38 0.47 −0.23 0.08 0.22 0.31

a Differences in Ionic Radius between the Host Cation and each Dopant are also listed (from ref 26).

the binding energy must be overcome in order for VH+ migration to proceed. Therefore, hydride-ion transport under these conditions would be trap-limited. Ionic Conductivity. The ionic conductivity in the alkalineearth hydrides depends on both the migration barrier of VH and the vacancy concentration. The concentration, c, depends on the formation energy Ef through the following:

Figure 4. (a) Charge density isosurface showing the overlap of Ba d orbitals to form the occupied defect level of a V0H in BaH2. (b) Schematic showing the positions of the defect states relative to the VBM and CBM for the V0H defect. The bonding state is occupied by one electron in this case.

ij −E f yz zz c = Nsites expjjj j kBT zz (5) k { where Nsites is the concentration of sites per unit volume. The diffusivity, D, can be expressed as follows:

shows a charge density plot for the neutral defect alongside a schematic band diagram showing the relative positions of the CBM, VBM, and defect levels formed by creating a hydrogen vacancy. Due to the bonding nature of the gap state, populating it strengthens the bonds between these Ba atoms and makes it energetically difficult for a nearby H atom to move into the vacancy. The Ba−Ba bonding is even stronger in the case of V−H, where the defect state is doubly occupied. This explains why the migration barrier for the hydrogen vacancy is relatively high for V0H, and even higher for V−H. In the case of V+H, however, the gap state is unoccupied, and the Ba atoms

ij −E yz D(T ) = D0 expjjj b zzz j kBT z k { with D0 given by the following: ji ΔS zyz D0 ≈ ανa 2 expjjj z j kB zz k {

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(6)

(7) DOI: 10.1021/acs.chemmater.8b01593 Chem. Mater. 2018, 30, 5878−5885

Article


Figure 5. Formation energies of four alkali-metal dopants on the Ae site in the negative charge state, shown along with the formation energy of hydrogen vacancies, for (a) CaH2, (b) SrH2, and (c) BaH2 under H-poor (Ae-rich) conditions; and (d) CaH2, (e) SrH2, and (f) BaH2 under H-rich (Ae-poor) conditions.

where α is a geometry-related factor that is often close to unity; ν is a hopping frequency that can be approximated as 1013 s−1, close to a typical phonon frequency; a is the distance between sites; and ΔS is an entropy term.27 Our estimates below neglect this entropy term and thus constitute an underestimate of the diffusivity and conductivity. The ionic conductivity, σ, is then related to the defect concentration and the diffusivity via the Nernst−Einstein equation,28 σ=

ij −(E f + E b) yz D e 2N cDe 2 zzz = 0 sites expjjjj z kBT kBT k T B k {

dopants were derived from the calculated formation enthalpies of corresponding alkali-metal hydrides, listed in Table 1, using eq 3. The formation energies for the alkali-metal dopants are plotted in Figure 5. Only the negative charge states of the dopants are shown; neutral charge states are stable close to the VBM (within 0.5 eV or less) but do not affect our conclusions. The formation energies of the acceptors depend on the host material; we have identified the driving factor to be the size match between the dopant and the host atom, as discussed below. For CaH2 and SrH2, the acceptor dopant with the lowest formation energy is Na; for BaH2, the lowest-energy dopant is K. Hydrogen-poor (Ae-rich) conditions make it difficult for the dopant to incorporate on the Ae site, and hence lead to high formation energies. V0H remains the dominant defect for all three materials, as it is in the undoped case. In the H-rich (Aepoor) case, the formation energies of the dopants are shifted to lower values and intersect those for V+H at Fermi-level positions that are closer to the VBM than when charge compensation was provided by cation vacancies [Figure 2(d−f)]. With this shift, the formation energies for V+H are 0.67 eV for CaH2, 0.68 eV for SrH2, and 0.50 eV for BaH2. In CaH2 and SrH2, we note that these formation energies correspond to dopant concentrations on the order of 0.01 mol % at typical synthesis temperatures (600 °C); experiments observed up to 0.1 mol % dopant incorporation,8 in reasonable agreement with our calculations. Higher dopant concentrations will increase the hydrogen vacancy concentrations. Our calculated formation energies are distinctly lower than in the absence of dopants, and they directly translate into lower activation energies for ionic conductivity: 0.83 eV for CaH2, 0.84 eV for SrH2, and 0.68 eV for BaH2. We note that the activation energy for Kdoped BaH2 is comparable to the activation energies measured for proton conduction in the alkaline-earth zirconates, which range from 0.4 to 0.6 eV.29 The effect on conductivity at characteristic operating temperatures is summarized in Table 5. In each case, doping under H-rich conditions improves the conductivity relative to undoped materials (for which we assume charge compensation by V−2 Ae , and the lowest value of ΔμH that avoids formation of

(8)

where Ef + Eb = Ea is the activation energy. Clearly, conductivity is influenced equally by the formation energy and the migration barrier. Given that the lowest-energy charge state depends on the hydrogen chemical potential, and that the migration barriers strongly depend on the charge state, it is interesting to note how the activation energies change in different conditions. In the H-poor limit, V0H dominates, and Ea = Ef(V0H) + Eb(V0H) is 1.04 eV in CaH2, 1.01 eV in SrH2, and 0.82 eV in BaH2. Under H-rich conditions, V+H dominates; this defect has a lower migration barrier than V0H, but a higher formation energy, resulting in Ea values of 1.10 eV for CaH2, 1.13 eV for SrH2, and 0.99 eV for BaH2. These considerations make clear that, while it is desirable to take advantage of the lower migration barrier of V+H, a strategy is needed to lower its formation energy. Formation energy can be decreased by lowering the Fermi level; thus, we propose to move the Fermi level closer to the VBM by doping with impurities that act as acceptors. Conductivity Engineering through Alkali Metal Doping. The addition of impurities that act as acceptors will shift the defect equilibrium, such that charge neutrality is achieved by balancing V+H and negatively charged acceptors. This scheme will only work, of course, if the formation energy of the dopants is sufficiently low, something we can assess with our first-principles calculations. We consider four alkali metals as possible dopants: Na, K, Rb, and Cs. These elements have only one valence electron, compared with two for the alkalineearth cations, suggesting that they will act as acceptors when substituting at the cation site. Chemical potentials for these 5882


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Chemistry of Materials Table 5. Ionic Conductivities for V+H Migration in Doped AeH2 under H-Rich Conditions and in Undoped AeH2 under Conditions that Maximize V+H Formation, at a Typical Operating Temperature of 673 Ka

dopants are optimally incorporated under H-rich conditions (Figure 5). Unfortunately, the formation energy of V+H under H-rich conditions is high and serves to limit the activation energy. Under H-poor conditions, V+H has a significantly lower formation energy, but the formation energy of alkali metal acceptors is much larger. There is no reason, however, to insist that the chemical potential conditions for dopant incorporation need necessarily be the same as those for device operation. The two issues can be decoupled. Dopants are incorporated during synthesis of the material, which we can choose to perform under H-rich conditions to maximize the incorporation of the acceptor dopants [Figure 5(d−f)]. Once dopants are incorporated, the device can be operated under the conditions that are most favorable for hydrogen transport; namely, H-poor conditions, which favor VH formation [Figure 5(a−c)]. The underlying assumption here is that, once incorporated, the dopant impurities are not affected by the change in hydrogen chemical potential. That is actually a safe assumption. Synthesis is typically performed at higher temperatures than device operation. At the lower operating temperatures, the diffusivity of dopant atoms is very low, and they will essentially be locked into the lattice. In other words, under operating conditions, the mobility of hydrogen-related species vastly exceeds the mobility of the dopants. Moving to hydrogen-poor conditions during operation will increase hydrogen vacancy concentrations over and above the V+H concentration established by alkali-metal doping; however, charge neutrality still applies. Additional VH+ could be compensated by V−2 Ae , but such large point defects may not form readily at the temperatures used for device operation. Even if that is not a limitation, we estimate that only slight improvements in ionic conductivity (on the order of a few %) over the values listed in Table 5 can be obtained. While charged defects are necessary for electrolyte applications, V0H, which becomes the dominant defect under H-poor conditions, could actually benefit other applications such as hydrogen storage. In this case, the product of defect concentration and the diffusion coefficient is the relevant quantity to consider. Taking BaH2 as an example, the formation energy of V0H under H-poor conditions (0.29 eV) is 0.21 eV lower than that of V+H under H-rich conditions with K-doping (0.50 eV), leading to a concentration of V0H ≈ 40× greater than that of V+H. However, the migration barrier of V0H (0.53 eV) is 0.35 eV larger than that of V+H (0.18 eV), leading to a ∼400× decrease in the diffusion coefficient. Overall, incorporating additional VH0 under H-poor conditions will contribute to a 10% improvement in hydrogen transport in BaH2. While in this particular case the improvement is modest, we still consider it an important insight from our study that different choices of chemical potential conditions can and should be made for synthesis versus operation.

σ (S cm−1) CaH2 SrH2 BaH2

doped

undoped

4.73 × 10−4 3.72 × 10−4 5.85 × 10−3

4.50 × 10−6 2.51 × 10−6 2.79 × 10−5

a

The results for doped compounds are taken from the most energetically favored dopants: Na in CaH2 and SrH2, and K in BaH2.

V0H). The highest conductivity is obtained in doped BaH2, about 6 × 10−3 S cm−1 at T = 673 K; this conductivity is comparable to that of the best proton conducting oxides.29 In the following section, we will demonstrate that these conductivities can be optimized even further. While synthesis at the H-rich limit incorporates alkali-metal dopants and V+H in their highest concentrations, doping still proves advantageous even under less H-rich conditions. The hydrogen chemical potential should be limited to values that promote formation of V+H (as opposed to V0H), due to its low migration barrier. Taking BaH2 as an example, V+H will form through compensation with K−Ba for ΔμH ranging from 0 eV to −0.57 eV. At ΔμH = −0.57 eV, the formation energy of V+H is 0.56 eV. In the absence of doping, the formation energy of V+H has a minimum value of 0.81 eV. Thus, even quite far away from the H-rich limit, doping lowers the activation energy by 0.25 eV, which correlates to an increase in conductivity by almost two orders of magnitude at 673 K. Clearly, significant improvements in device performance can be realized through alkali-metal doping for a wide range of growth conditions. Just as we discussed in the case of compensation by cation vacancies, there will be an attractive interaction between V+H and the alkali metal acceptors. We have calculated complexes (in the neutral charge state) consisting of H vacancies and each of the four dopants. Binding energies evaluated using eq 4 are tabulated in Table 4. Interestingly, the lowest binding energies are obtained for those dopants that also exhibited the lowest formation energies (Figure 5). This result is promising, because trapping of the vacancy at the dopant would limit diffusion. Our results thus show that the dopants that are most easily incorporated (and hence have the largest impact on V+H concentrations) will do the least harm in terms of trapping. In Table 4, we list the difference in ionic radius between the dopants and the host cations. We observe a clear correlation between the binding energies and the size difference such that the most size-similar dopants lead to the smallest binding energies. The same correlation is evident for formation energies (Figure 5). For the optimal impurities (Na in CaH2 and SrH2, and K in BaH2) the ionic radius is within 0.1 Å of the ionic radius of the host cation. We therefore conclude that dopant size is an important consideration:30 the dopants that exhibit the best size match to the host cation have both the lowest formation energy and the lowest vacancy binding energy. Optimizing Hydrogen Transport in Doped Systems. The results discussed above clearly indicate that doping can lower the activation energy for hydride conductivity. However, there is room for further improvement by using optimal growth and operating conditions. We saw that alkali metal

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CONCLUSIONS We have used first-principles calculations to study hydride ion transport mechanisms in the alkaline-earth hydrides CaH2, SrH2, and BaH2. We showed that ionic transport is mediated by hydrogen vacancies; their low formation energy and small migration barrier results in a low overall activation energy for ionic conductivity. We propose that doping with alkali metals can lower the activation energy for ionic conductivity even further by lowering the formation energy of V+H, thereby increasing the 5883


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supported by the Office of Science of the U.S. DOE under Contract No. DE-AC02-05CH11231.

defect concentration in the material. We have found that the optimal dopants (in terms of formation energy and low trapping energies for V+H) are those closest in size to the host cations. The activation energy for hydride diffusion can be optimized by incorporating the dopants under H-rich conditions before switching over to H-poor conditions to take advantage of the low formation energy for hydrogen vacancies. Our results also allow us to compare these three hydrides and assess their prospects as hydride ion conductors. BaH2 emerges as the clear winner: the hydrogen vacancies that mediate diffusion have significantly lower formation energies (Figure 5) than in CaH2 and SrH2. In addition, these hydrogen vacancies have the lowest binding energies both to cation vacancies and to alkali metal dopants (Table 4), reducing the impact of trapping. Consideration of migration barriers for VH also favors BaH2 (Table 3): in the positive charge state, the barriers are comparable (and very low) in the three hydrides, while in the other charge states, BaH2 exhibits the lowest barriers. Combined with experimental reports showing its excellent thermal stability,4 we conclude that BaH2 is an especially attractive choice for applications requiring high hydride-ion conductivity, and we identify K as the optimal alkali-metal dopant. Doped CaH2 and SrH2 (with Na as the optimal dopant) may also have applicability in cases for which higher gravimetric densities of hydrogen are required. We find that optimal synthesis conditions can produce ionic conductivities for hydride conduction that are equivalent to proton conductivities in the best proton conducting oxides.29 Our results indicate that the alkaline-earth hydrides are promising candidates for hydrogen electrolytes, with the potential to match or surpass the performance of solid-state proton conductors. Their properties make them well-suited for energy applications in systems requiring fast hydrogen kinetics.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Andrew J. E. Rowberg: 0000-0002-2928-6917 Chris G. Van de Walle: 0000-0002-4212-5990 Present Address ‡

Energy Technologies Area, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, United States.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.J.E.R. was supported by the National Science Foundation (NSF) Graduate Research Fellowship Program under Grant No. 1650114. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF. L.W. and C.G.V.d.W. were supported by the Office of Science of the U.S. Department of Energy (DOE) (Grant No. DEFG02-07ER46434). Computational resources were provided by the Center for Scientific Computing at the California NanoSystems Institute and Materials Research Laboratory (an NSF MRSEC, Grant No. DMR-1720256) (NSF CNS0960316), and by the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility 5884


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Ion-transport engineering of alkaline-earth hydrides for hydride

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