Large-Scale Computational Screening of Binary Intermetallics for

Article pubs.acs.org/JPCC

Large-Scale Computational Screening of Binary Intermetallics for Membrane-Based Hydrogen Separation Nita Chandrasekhar† and David S. Sholl* School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100, United States S Supporting Information *

ABSTRACT: Hydrogen separation using metal membranes offers significant energetic, technological, and economic advantages over conventional separation processes, resulting in extensive efforts to develop favorable membrane materials. Intermetallics are stoichiometric compounds of two or more metals that form an ordered structure. This work exhibits a systematic search for intermetallic membrane materials for hydrogen separation from potential candidates using density functional theory (DFT)-based methods to quantitatively predict solubility, diffusivity, and permeability. Geometric correlations were used to significantly decrease the number of calculations performed without compromising on the accuracy of the predictions. In this work, 1001 intermetallic structures were screened, and eight materials, MnTi, MgZn2, PtTl2, FeHf2, HfTa, NiTi, TiV, and Fe2Y, were identified as potential candidates for hydrogen separation membranes based on the calculated hydrogen permeability. This work, in addition to identifying novel membrane materials, highlights the significance of computational tools for screening large libraries of materials for specific applications.

1. INTRODUCTION Industrial-scale production of hydrogen entails H2 separation from syngas components using energy-intensive and costly methods such as pressure swing adsorption and cryogenic distillation.1 Metal membranes offer significant advantages over these conventional processes due to their high-temperature stability and perfect selectivity for hydrogen over other gas species.2−4 Different types of metal membranes such as pure metals, alloys, and amorphous metals have been studied for H2 separation, and their performance and properties have been extensively reviewed in the literature.5−13 Palladium and palladium-based membranes show favorable hydrogen permeabilities but are expensive and sensitive to sulfur poisoning, motivating the identification of new membrane materials with comparable hydrogen permeabilities and increased resistance to sulfur poisoning.1,4 Intermetallics are ordered compounds of two or more metals. It has been speculated that they may have the potential to demonstrate improved resistance to sulfur poisoning due to their increased thermodynamic stability relative to disordered solid solutions.14,15 Previous work examined palladium-based binary intermetallics as potential candidates for hydrogen separation.14 However, palladium-based binary intermetallics represent a fraction of the total intermetallics that exist, and it would therefore be useful to examine the large number of intermetallics not considered previously for use in hydrogen separations.16 Purely computational approaches for predicting material properties have been developed that enable screening of dense materials for this application faster than is possible © 2015 American Chemical Society

experimentally. Elaborate density functional theory (DFT)based lattice models exist that can predict hydrogen permeability in excellent quantitative agreement with experiments and require few inputs from experimental data.2,4,17 However, these methods are limited in their scope for screening large libraries of materials since these methods are computationally intensive and often require human intervention. In this work, DFT-based methods are used to evaluate hydrogen solubility and diffusivity of hundreds of intermetallics at a fraction of the computational cost incurred using previously developed models.2,17 Geometric correlations were used to reduce constraints on the number of calculations without compromising accuracy. A systematic screening procedure is implemented that is divided into three stages: sorting based on space groups, solubility-based screening, and activation barrier based screening. This approach is illustrated schematically in Figure S1 in the Supporting Information. The models used to predict hydrogen solubility and diffusivity of intermetallics are similar to those validated previously and provide sufficient accuracy to eliminate unfavorable candidates.

2. MATERIALS SELECTION AND COMPUTATIONAL METHODS 2.1. Materials Selection. Our algorithm for H solubility and diffusivity prediction in hundreds of intermetallic structures uses the binary intermetallic structures listed in the Inorganic Received: September 1, 2015 Revised: October 28, 2015 Published: October 29, 2015 26319

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calculated using DFT within the harmonic approximation with the assumption that the vibrations of interstitial H are decoupled from lattice phonons. Using the total and zeropoint energy, the binding energy of H in each interstitial site is calculated and used to calculate the solubility using Sieverts’ law.2 Plane-wave DFT calculations were performed using the Vienna ab initio simulation package (VASP).20−23 DFT calculations were performed with the PW91 generalized gradient approximation functional using the projector augmented wave method.24−27 A cutoff energy value of 250 eV was used, and geometries were relaxed using a conjugate gradient method until the forces on all atoms were less than 0.03 eV/Å. Geometric relaxation to obtain the lattice parameters was performed using a 10 × 10 × 10 k-point mesh to sample the reciprocal space and relaxing the lattice constants and all internal coordinates. Under the assumption that bulk diffusion is rate-limiting, the concentration of hydrogen atoms in the metal, θH, are in equilibrium with the ambient hydrogen pressure.2 At dilute hydrogen loadings, i.e., H/M < 0.1, θH is given by Sieverts’ law. The dilute loading assumption was found to be valid for a wide range of T and P for Pd and Pd alloys.2 Hence, this assumption was used to calculate the solubility of the intermetallics considered in this work. To identify H binding sites in an intermetallic, we adapted an automated method developed previously for amorphous materials by Hao and Sholl.28 This method initially places hydrogen atoms on a grid inside the metal lattice and then computes the positions of hydrogen where the potential energy of the H atom is at a minimum using empirical Lennard-Jones potentials. This calculation gives an estimate of the location of the binding sites in the material. These initial estimates were used as the starting configurations for DFT calculations that minimized the system’s energy while allowing all atoms (metal and H) to relax. The unit cell volume was held fixed in these calculations. This approach assumes that lattice expansion caused by the interstitial hydrogen is minimal, a reasonable assumption for materials in which the loading of interstitial H is low. The highest H concentration used in these calculations was one H in a supercell of 32 metal atoms. For materials with more than 32 metal atoms in the crystal unit cell, binding energies were calculated with one H atom in the unit cell. The vibrational frequencies and zero-point energies of interstitial H were calculated by making small displacements of the H around the local minima at the binding sites with the assumption that the vibration of the interstitial H atom is decoupled from the phonons of the metal lattice.29 These calculations were performed using displacements for H atom of 0.18 Å, a value chosen such that the assumption of harmonic potential is reasonable. Once the binding energy of each interstitial site and the zero-point energies were available, the net solubility of H was calculated using the method defined by Kamakoti and Sholl,2 which includes the effects of the multiple vibrational energy levels available to interstitial H atoms. If the locations of H binding sites inside the material are known a priori, the number of calculations involved in computing the solubility of H in each materials decreases significantly. This is because the methods used in our earlier work to identify potential H binding sites results in the generation of hundreds of candidate binding sites. The identification of actual binding sites from this list involves hundreds of DFT calculations for each material. Adopting the

Crystal Structure Database (ICSD) as a starting point for the screening process.16 The materials in the database that are unsuitable for membrane purposes due to factors such as insufficient thermal stability, very high or low pressure phase occurrence, or lack of direct experimental evidence (i.e., purely computational entries) were removed from further consideration. Additional details of this screening procedure are provided in Table S2 in the Supporting Information. The remaining intermetallics were sorted according to their space groups, and the space groups were ranked based on the number of candidate structures of each type within each space group. A plot encompassing all the materials sorted by their space groups is shown in Figure S2. The 15 most populated space groups were selected for the next steps in the screening process since a substantial proportion of structures (64%) belong to these space groups. This filtering process yielded 981 distinct materials. A total of 169 of these candidate structures obtained from ICSD had partial occupancies or incomplete structures and could not be directly used as an input for DFT calculations. For these structures, the positions of the atoms were obtained from prototype structures and the lattice constants listed in the ICSD were used to manually construct a unit cell. To rapidly identify favorable candidates from the 981 materials using a limited number of DFT calculations, a representative structure was chosen randomly from each space group. Other materials in each space group were examined with the assumption that the geometric locations of the unique H binding sites in the representative structure is common between crystal structures within the same space group. This assumption is supported by data from previous calculations for different Fm3̅m (fcc) structures.14,17 Although the locations of binding sites are the same in similar materials, the binding energy of H in each material depends on the material’s constituent elements. This can mean, for example, that the kind of site that defines the lowest energy site (i.e., the global minimum energy) for H may differ between two materials with the same space group. 2.2. Computational Methods. Hydrogen permeation through metal membranes is a multistep process consisting of dissociative chemisorption of H2, diffusion through the membrane, and recombinative desorption at the permeate side. We follow extensive earlier work modeling dense metal membranes under practical operating conditions.2,14 When interstitial hydrogen concentrations are low, the net solubility of hydrogen can be described using Sieverts’ law and diffusion can be described by the self-diffusivity of interstitial H.2,18 The calculations in this work assume bulk diffusion as the ratelimiting step and do not consider surface effects, which can influence membrane performance under low-temperature conditions.19 In this regime, the net permeability of a membrane can be obtained once the solubility and diffusivity of interstitial H in the membrane material are known. Below, we describe the computational methods used to predict each of these quantities separately. The solubility of interstitial H in the representative structure for each space group was calculated by locating all possible H binding sites in the crystal structure and performing firstprinciples DFT calculations that minimized the system’s energy while allowing all atoms (metal and H) to relax. This approach assumes that lattice expansion caused by the interstitial hydrogen is minimal, a reasonable assumption for materials in which the loading of interstitial H is low. The vibrational frequencies and zero-point energies of interstitial H were also 26320

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The Journal of Physical Chemistry C H binding site positions obtained from one structure across crystal structures within a space group makes this screening process on an average more than 20 times faster than performing independent calculations for every material. It is important to note that the structure of each binding site in each material is still fully optimized using DFT in our calculations; the only assumption in these calculations is that the approximate location of interstitial H in the energy minima determined in each representative crystal structure also defines (subject to local optimization) the complete set of energy minima in other intermetallics with the same crystal structure. The efficiency in the approach just described lies in the reduction of the number of these DFT calculations that must be performed. To calculate the binding energies of H in all the structures, pymatgen was used.30,31 After H solubility was predicted in a large collection of intermetallics, DFT-based methods were used to predict the diffusivity of H in a selected subset of these materials. The rationale for selecting these materials is described in section 3.1, and the methods used for calculating the diffusivities of interstitial H are described in section 3.2.

Figure 1. Computed H solubility in hydrogen per metal atom (H/M) at 1 atm H2 and 600 K for materials from the Cmcm space group. For the materials with multiple phases, solubility was calculated using the structure stable at 600 K. Eight of the 29 structures were selected to have diffusion characterized based on having solubility between the limits defined by the horizontal lines in the figure.

3. RESULTS The lattice constants of the structures obtained from ICSD were compared with those obtained from DFT. The crystal structures obtained from ICSD were used as input in geometric relaxation calculations performed using DFT. In a majority of cases, DFT results were in excellent agreement with the ICSD structures (see Supporting Information). In cases where there was significant variation between the structures, the DFToptimized structures were used as a starting point for the next steps in the screening process. 3.1. H Solubility. Our earlier work on palladium-containing intermetallics showed that an initial screening based solely on H solubility is a useful way to narrow the list of candidate materials.14 To select potential favorable candidates using solubility as a screening criterion, the H solubility in hydrogen per metal atom (H/M) at 1 atm H2 and 600 K was plotted as a function of the volume/metal atom (Å3) for each space group. An example of this data for the Cmcm space group is shown in Figure 1. Similar plots were generated for the remaining 14 space groups (see Supporting Information). A solubility range of 10−1−10−5 H/M was used to identify potentially favorable candidates as was used for palladium-based intermetallics.14 As discussed in our earlier work, materials with solubility higher than this range are not able to give the low interstitial H concentrations that are desirable for membranes at typical operating conditions and materials with solubility below this range are not able to yield high net permeabilities regardless of how fast interstitial H can diffuse in them. The materials that have solubility in this range were chosen for diffusivity calculations. Among the 15 space groups studied, 161 candidates were found to have solubilities that justified analysis of H diffusion. The binding energies of these materials selected are described in Table S5 in the Supporting Information. The results indicate that H solubility and atomic volume are uncorrelated, as observed previously in palladium-based intermetallics.14 There is no obvious trend among the element combinations of the materials that have solubilities in the favorable range as shown in Figure 1. A large number of the materials have one element that forms favorable hydrides, i.e., binds hydrogen very favorably. These elements include Mg, Sc, Y, Ti, Zr, and Hf.32,33 Out of 161 favorable materials chosen

using solubility as the screening criteria, 113 (70%) have at least one element that is among the five elements listed above that form very stable hydrides. However, this trend is not predictive in nature since there are intermetallics that include a strong hydride former but have solubility lower than 10−5 H/M. Pt8Ti is an example of such an intermetallic, with a computed solubility of 5.4 × 10−7 H/M at 600 K and 1 atm H2 (Figure S3 (I4/mmm) in the Supporting Information). Figure 2 summarizes the H binding energies in the full set of 981 intermetallics. For membrane applications, binding

Figure 2. Histogram of the binding energy distribution of the 981 intermetallics studied. For each material, the lowest binding energy, i.e., the energy of the most H favorable binding site, is shown in the figure. The red star represents the binding energy of H in pure Pd (Eb = −0.12 eV). A total of 62% of the structures have binding energies that lie between 0.1 and 0.8 eV. For all of these materials, the existence of interstitial H is energetically unfavorable. The lowest binding energy encountered in our calculations is for Ti7Zr3, Eb = −4.78 eV. Both metals in this intermetallic form very stable hydrides. 26321

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after removal of the duplicates reduces the number of calculations by up to 50% in many space groups. Further details are provided in the Computational Methods section. Once a complete set of transition states had been determined for a representative structure from a space group, the total and zero-point energies for this set of transition states were computed for every material of interest with the same space group. Full relaxation of the interstitial H and metal atoms was allowed in these calculations.4,35 The resulting set of local activation barriers was used to estimate the net energy barrier to H diffusion through each material. The potential energy surface was mapped, and the paths from one of the most favorable binding energy sites to another similar site were mapped. The minimum energy difference that must be overcome for hydrogen to hop between the most favorable sites was taken as an estimate of the net activation energy barrier. The variation in this net energy barrier among the 161 materials we considered is shown in Figure 3. It is notable that almost all of the materials have larger diffusion activation energies than pure Pd.

energies similar to that of pure Pd that give dilute interstitial H concentrations are desirable. Only 117 materials have computed H solubilities more favorable than pure Pd (binding energies 0.1 H/M. These results are in agreement with previous literature where FeHf2 has H/M of 1.03 at 3 atm

4. SUMMARY In conclusion, we have used DFT-based methods to systematically examine hydrogen solubility, diffusivity, and permeation through 981 binary intermetallics. These calculations required no experimental input apart from the structure of the materials and are useful for identifying suitable materials for hydrogen separation. Solubility was shown to be an effective initial screening parameter for finding materials for hydrogen separation. The set of materials for which diffusivity calculations were performed was substantially reduced based on initial calculations predicting H solubility. Our screening methods have greatly reduced the computational effort required to screen such a large set of materials compared to earlier computational approaches without compromising on the quality of resulting predictions.2,4,11,28 Eight materials were identified that have predicted permeabilities higher or similar to that of pure Pd. The constituent elements of a majority of these eight intermetallics are inexpensive in comparison to pure Pd. With the exception of Pt, Y, and Hf, the remaining eight elements (Zn, Mg, Mn, Ti, Ni, Fe, Ta, Tl) are extremely inexpensive compared Pd. For one material, MnTi, we computationally examined the possibility of phase segregation to form TiH2, finding that this undesirable process is thermodynamically unfavorable under at least some operating conditions of interest. Nevertheless, for implementation of these materials as membranes, experimental testing needs to be performed to examine possible issues such as slow H2 dissociation on the surface, phase separation, and poisoning due to gas-phase impurities.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b08536. Details of the screening algorithm, hydrogen binding energies, hydrogen solubilities, and additional figures (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Phone: +1 404 894-2822. E-mail: [email protected]. edu. Present Address †

N.C.: Praxair, Inc., 175 East Park Dr., Tonawanda, NY 14209.

Notes

The authors declare no competing financial interest. 26324

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