Theoretical Study of Nitrogen Absorption in MetalsKyoungjin Lee,† Simona Liguori,‡ Peter Psarras,‡ and Jennifer Wilcox*,‡

†Department of Energy Resources Engineering, Stanford University, 367 Panama Street, Stanford, California 94305, United States‡Department of Chemical and Biological Engineering, Colorado School of Mines 1613 Illinois Street, Golden, Colorado 80401,United States

*S Supporting Information

ABSTRACT: Nitrogen binding in open structure body-centered-cubic (bcc) metals wasstudied to understand atomic nitrogen absorption in these systems in order to assess theirfeasibility as membrane materials for nitrogen separation and subsequent reactivity forammonia production. For a metallic membrane to be feasible for this application, it mustexhibit adequate solubility that allows for sufficient permeability. Using first-principlecalculations it was demonstrated that nitrogen is too soluble in pure vanadium due to itsstrong binding in this metal (i.e., binding energy of −2.80 eV/atom), but throughalloying, the binding energy may be tuned to mimic the weaker hydrogen bindingexhibited in Group V metals, leading to high permeability. In particular, alloys of Ru andMo were investigated. The Bader charge and density of states analyses showed thatnitrogen binding in pure V is enhanced by the electrostatic and covalent interactionbetween nitrogen and surrounding V atoms, whereas repulsive interaction with analloying component, Ru or Mo, with nitrogen resulted in the less stable binding ofnitrogen in the alloys. Reduced binding energies were observed in both alloys (e.g., −1.64 eV/atom for both V53Ru and V15Moalloys). In particular, Mo13V3 alloy showed a nitrogen BE of −0.041 eV, which is very similar to the BE of H in Pd. The nitrogensolubility in Mo was estimated based upon a thermodynamic equilibrium assumption with systematic corrections to thecalculated vibrational frequencies, showing agreement to the experimental solubility. Using the same correction scheme, nitrogensolubility in V−Mo was estimated to be 4 orders of magnitude higher at 1000 K for a 25 at. % V alloy composition compared topure Mo. This theoretical study provides useful guidance for the discovery of promising materials for metallic membranes forammonia synthesis.

1. INTRODUCTIONThe nitrogen cycle is one of the most significant biogeochem-ical cycles on Earth, as nitrogen is an essential nutrient for allforms of life. Although nitrogen is freely available in theatmosphere as dinitrogen (N2), nitrogen conversion processesfrom a gaseous to a fixed form are very limited in nature (e.g.,occurring through plant growth). Today, industrial ammoniasynthesis for fertilizer production, known as the Haber-Boschprocess, requires intensive energy associated with hightemperature (400−500 °C) and high pressure (up to 30MPa) during the synthesis.1 These harsh operating conditionsare necessary due to the high affinity of dissociated nitrogenatoms toward the catalyst surface in addition to the highactivation barrier associated with N2 dissociation.

2 The overallprocess consists of continuous flow and frequent recovery ofunreacted gases, resulting in a method capable of producinglarge amounts of ammonia. Approximately 141 million tonnesof ammonia were produced worldwide in 2015 through thisindustrial processes, and domestically, 88% of ammoniaconsumption was for fertilizer production. Given the highdemand of ammonia and the high production capacity of plantsthat synthesize it, this process is considered the second-mostenergy-intensive chemical manufacturing process in the U.S.and worldwide,3 accounting for 2% of total global energy use4

and about 1% of total global greenhouse gas emissions.5 For

these reasons, the need for advanced catalytic methods for thereduction of N2 to ammonia remains a requirement forsustainability in the food, energy, and water systems cycle. Thecurrent study explores the potentiality of metallic membranesfor N2 separation with the final intent to find an alternate routeto producing ammonia.In a metallic membrane reactor for ammonia synthesis, a

metallic membrane provides reaction sites for ammoniasynthesis as well as separates nitrogen. In specific, a densemetallic layer permeable to nitrogen allows for high-purityatomic nitrogen stream to readily react with hydrogen availableon a catalyst to produce ammonia. The feasibility of thisapproach depends on the nitrogen flux through the membrane,which follows the equation:6

δ= × −J P

p p( )n n

NN ,ret N ,per

2

2 2

(1)

where JN2is the nitrogen permeating flux through the

membrane, P is the permeability, pN2,retn and pN2

,pern are thepartial pressures of nitrogen in the retentate and the permeate

Received: May 31, 2017Revised: July 10, 2017Published: July 11, 2017

Article

pubs.acs.org/JPCC

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sides of the membrane, respectively, and δ is the membranethickness. n is an exponent of pressures, which is empiricallydetermined. The permeating flux is inversely proportional tothe membrane thickness and directly proportional to thenitrogen permeability, which is the product of solubility, S, anddiffusivity, D, in the metal. The current study focusesspecifically on evaluating atomic nitrogen solubility in open-structured body-centered-cubic (bcc) metals to screen goodcandidates for the metallic membrane reactors for ammoniasynthesis.The solubility and diffusivity of nitrogen in metals have been

reported in previous studies, but none of these previous studieshave considered for the application to the nitrogen-selectivemembranes. Since permeability is the product of those twoterms, nitrogen permeability can be estimated from theliterature. Table 1 lists nitrogen solubility and diffusivity in

various bcc metals reported in the literature. It is shown that Fehas much higher permeability than other metals, and V has alsorelatively high permeability. Note that the dominating factor isdifferent in those two metals; V has a large solubility, whereasFe has extremely high diffusivity. Group 5 metals (V, Nb, andTa) have relatively high permeability than group 6 metals (Cr,Mo, and W) at the same temperature. Since the nitrogenpermeability values of Mo and W at 500 °C are significantlylower than those of group 5 metals at 500 °C, the values at 800°C are given for Mo and W to practically compare. Vanadiumand Cr may be directly compared as a representative of groups5 and 6, respectively. The nitrogen solubility is higher in V thanin Cr, whereas the diffusivity is higher in Cr than in V. Thepermeability, in turn, is higher in V than in chromium. Thesetrends imply that there might be a trade-off between themagnitudes of solubility and diffusivity; hence, a moderatelyhigh solubility and diffusivity may offer the highest perme-ability.If metals with different permeabilities form alloys, the

permeability of those alloys may vary between the values ofthe pure metal components. In this way, the transport propertyof metallic membrane can be tuned in future studies. For thenitrogen-selective membranes to be feasible, a target perme-ability could be the value close to the hydrogen permeability inPd,7−10 which has been commercialized for decades. Comparedto Pd, pure V has higher solubility but much lower diffusivity,resulting in the low permeability. In bulk V, nitrogen wasshown to bind strongly in the interstitial sites. The nitrogenbinding in the O-site (−2.55 eV/atom) was shown to be more

stable than that in the T-site (−1.31 eV/atom). The stablebinding energy of nitrogen in the bulk V was approximately anorder of magnitude stronger compared to H binding in Pd (i.e.,−0.12 eV/H in the O-site).11 On the other hand, the nitrogenbinding energy in Fe reported in the literature was 0.02 eV/atom,12−13 which is very close to the binding energy of H in Pd.Note that nitrogen diffusivity in Fe is considerably higher thanthat in any other bcc metals (Table 1), inferring that thebinding energy close to zero may be an indicator of enhanceddiffusion in metals with moderate solubility.Nitrogen binding in the bcc metals and their alloys has been

widely reported both theoretically and experimentally. In theliterature, multiple experiments to measure nitrogen bindingand diffusion have been performed for various metals (e.g.,V,14,15−20 Nb,17,18 Ta,14,17,21,22 Cr,23−28 Mo,23,26−28 andFe).29,30 Also, theoretical studies focusing on nitrogen in thebulk metals have supported the O-site binding of nitrogen inV,31 W,32 and Fe.33,34 Lattice expansion often occurs due to thelarge atomic size of nitrogen compared to the size of interstitialsites.14,33,34 When other defect sites, such as vacancies, grainboundaries, and dislocations, exist in metal structures, thosesites tend to exhibit stronger binding of nitrogen.23,35,36

However, only limited number of nitrogen binds to thosesites since the defect concentrations are limited, and themobility of defects decreases with nitrogen binding. Introduc-ing nitrogen to metals is often referred to as “nitriding.” In steelmanufacture, nitriding is a metal strengthening process toenhance mechanical properties of steels. In this study, nitridingoccurs at the initial step of nitrogen permeation, and metalsurface may transform into nonbcc nitrides as suggested bymany metal−nitrogen phase diagrams. The goal for thenitrogen-selective metallic membranes is to maintain a dilutesolid solution phase, in which the mobility of interstitialnitrogen is relatively high.In this study, nitrogen binding characteristics in metal and

metal alloys are investigated using first-principles calculations.Nitrogen binding energies associated with optimized geometryare demonstrated, and the electronic structure effect on thenitrogen binding in metals is analyzed. Pure V system withnitrogen interaction will be first discussed, followed by V−Ruand V−Mo alloy system discussion to expand possibleselections of membrane materials beyond pure metals.Ruthenium (Ru) alloy was chosen because Ru is well-knownas a catalyst for ammonia synthesis, implying that thedissociation of molecular nitrogen may easily proceed on Rusurfaces. The effect of Ru as an alloy component in a V−Rualloy on the nitrogen binding energy as well as the charge andelectronic structure will be discussed. Another V-based alloychosen in this study is the Mo−V alloy. Molybdenum has a bccstructure in its pure state and is known to form bcc alloys withV in any composition, which may be helpful to diffuse atomicnitrogen in the bulk phase. At elevated temperatures, Mo mayform nitrides, which are known to be good catalysts forammonia synthesis. Since ammonia synthesis might occursimultaneously during the membrane operation with in situnitride formation, testing Mo as an alloy component mayprovide insights into the development of nitrogen-selectivemembranes for ammonia synthesis. Various compositions ofV−Mo alloys were studied with the aim of searching formembrane materials with sufficient nitrogen permeability.

Table 1. Nitrogen Solubility, Diffusivity, and EstimatedPermeability in Various bcc Metals

metalT

[°C]solubility[at.%]

diffusivity[10−15 m2/s]

permeability [10−15

mol/m.s.Pa0.5] ref

V 500 2.66 0.32 1.6 3718

Nb 500 0.15 0.09 0.020 18Ta 500 1.7 0.01 0.025 22

37Cr 500 0.02 4.0 0.19 38

39Mo 800 − − 0.63 27W 800 − − 0.0020 27Fe 500 0.2 1400 600 29

30

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2. COMPUTATIONAL METHODOLOGY

2.1. DFT Calculation Parameters. First-principles calcu-lations based on DFT40,41 were performed using the Vienna abinitio Simulation Package (VASP, v5.2.12)42−45 with theprojector augmented wave (PAW) method46,47 to describenucleus-electron interactions. Electron exchange-correlationfunctionals were represented with the generalized gradientapproximation (GGA) using the model of Perdew, Burke, andErnzerhof (PBE).48,49 For V and V−Ru alloy studies, planewaves with a kinetic energy cutoff of 550 eV were used todescribe electronic wave functions, while an energy cutoff of400 eV was used for V−Mo alloy study. While the electronicenergy in the self-consistent field was converged below 10−6 eV,the total energy convergence to within 1 meV/atom wasachieved with respect to the energy cutoff and k-pointparameters. The first-order Methfessel and Paxton smearingmethod50 with a width of 0.1 eV was used for the Fermi-levelintegration.Geometry optimization was performed with a 3 × 3 × 3

conventional bcc supercell (54 atoms) in V and V−Ru alloystudies, and a 2 × 2 × 2 conventional bcc supercell (16 atoms)was used for V−Mo alloy study. The Monkhorst−Packscheme51 was applied for the sampling of k-points in each ofthose supercells with k-spaces of 4 × 4 × 4 and 12 × 12 × 12,respectively. Both the lattice (shape and volume) and atomicpositions were allowed for relaxation. The ionic positions wererelaxed using the conjugate-gradient algorithm so that theabsolute values of the forces on unconstrained atoms becameless than 0.01 eV/Å or the total free energy change betweenionic optimization steps became smaller than 10−5 eV.The energy of the N2 molecule in the gas phase was

calculated by placing one N2 in a 20 × 20 × 20 Å3 cubic boxand choosing the Γ-point. The binding energy (BE) of atomicnitrogen in an interstitial binding site with respect to gaseousN2 was calculated by taking the total free energy differencebetween the initial (pure V and the nitrogen molecule in thegas phase) and the final state (one nitrogen bound in aninterstitial site of the V structure):

= − −E E E E12i VN V Ni 2 (2)

such that EVNi, EV, and EN2

are the total energies of V with aninterstitial nitrogen, the bulk V, and nitrogen in the gas phase,respectively. Note that, in this definition, a negative value of BEimplies a thermodynamically favored binding state of theinterstitial nitrogen.Vibrational frequencies of the binding nitrogen were

calculated for a few stable O-sites in V and V alloys. Thenormal-mode vibrational frequencies of the nitrogen atom werecalculated by a finite displacement method with a displacementsize of 0.015 Å. The free energy and the vibrational frequencyof a N2 molecule in the gas phase were calculated by placingone N2 in a 20 × 20 × 20 Å3 cubic box and choosing the Γ-point.The charge and electronic properties upon nitrogen

absorption in V were investigated by carrying out a Badercharge analysis52−54 and a projected density of states (PDOS)analysis. The Bader charge analysis provided a consistent wayto partition the charge distribution calculated from theintegrated electronic density in the DFT calculations and toassign charge values to individual atoms. This method is helpfulin interpreting the redox reactions among adjacent chemical

species. For example, the differences in the partitioned chargebetween pure metal and the metal with nitrogen absorptionindicate the charge transfer between bulk metal and nitrogen,thereby identifying the charge interaction in the absorptionprocess. In the Bader analysis on the bulk material because theatoms are located at very short distances to each other,counting the electron transfer is possibly inaccurate due to thepresence of core charges. Therefore, both core and valenceelectrons were considered in the Bader charge calculations,although the core electrons did not participate in any chemicalinteractions. The PDOS analysis demonstrates the electronicenergy states of each chemical species with respect to the Fermilevel. These energy states of different species may overlap eachother, which indicates potential hybridization of the statesleading to covalent bonding between those species. Thechanges in the chemical environment may shift the DOS, andparticularly, the shift in metal d-bands can be correlated to thereactivity of the metal.55 Thus, to quantitatively compare the d-band shift, the center of the metal d-bands was calculated.

3. RESULTS AND DISCUSSION3.1. Nitrogen Absorption in Pure Vanadium. 3.1.1. Ge-

ometry of Nitrogen Binding in Vanadium. The geometry ofan O-site in pure bcc metals is not a regular octahedron, buttwo vertices are closer to the center than the other four. Afternitrogen binding in the O-site, the geometry of the binding sitebecame elongated along the short vertices thereby forming amore regular octahedral shape. That is, only the two of the sixmetal atoms were displaced farther apart, but the rest of theatoms merely changed their positions or were slightlycontracted to each other. In the literature, a similar deformationof the O-site has been reported for carbon and nitrogen bindingin other bcc metals.21,22,24,25 Such deformation can be explainedby energy minimization. The increased free energy due tolattice expansion upon nitrogen binding would be over-compensated by the lowered energy from the stabilizedinteraction between nitrogen and V in a deformed O-site.The expansion of the T-site would be more energetically costlycompared to that of the O-site because all of the four metalatoms consisting of the T-site need to be displaced. Therefore,the T-site binding was less stable than the O-site binding afterthe optimization of the metal lattices. The O-site preference ofnitrogen binding in the bcc metals observed in this study agreeswell with previous experimental and theoretical studies.26−28

The BEs of calculated in this study are −2.80 and −1.38 eV/Nfor the O-site and T-site binding, respectively. The difference inthe BEs from the previous study is due to the size of supercellused in the calculations, as discussed in Section S2.

3.1.2. Multiple Nitrogen Binding in Vanadium. For singlenitrogen binding discussed in the previous section, an evendistribution of nitrogen atoms was assumed for an equilibriumstate. In practice, however, this assumption may become invalidas nitrogen concentration increases or when a dynamic processis considered for atomic nitrogen diffusion through bulk metals.For instance, two nitrogen atoms may stay nearby if attractiveinteraction exists, or there might be a threshold distancebetween two nitrogen atoms if repulsive interaction dominates.To test these hypotheses, various nitrogen configurations weretested by placing two nitrogen atoms at various distances in theO-sites and optimizing the geometry to determine theminimized free energy for each configuration.The results of the first-principles calculations on each

configuration are presented in Table 2, including an optimized

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N−N distance, an average BE per nitrogen atom, and thepercentage of volume expansion. The N−N distances listedhere are the shortest N−N distance measured in the optimizedstructure. The values in Table 2 are summarized in Figure 1.

In a few cases where the initial N−N distance between twoO-sites was extremely short, the T-site binding was found to bethe local minimum. In Figure 1, those cases were shown on aregime of high binding energy and high volume expansion.Although the T-site binding is generally unstable compared tothe O-site binding, when two nitrogen atoms were forced tostay linearly along the neighboring O-sites, one or two nitrogenatoms moved to the T-site to avoid extremely high stressesassociated with the shared V atom of the O-sites. Similar straineffect of nitrogen binding in the bcc metals has been reportedin the literature.33,36

Two trends are demonstrated in Figure 1. First, the final N−N distance was barely correlated to the magnitude of the BE.Second, the % volume expansion with respect to pure Vseemed to have a strong correlation with the BE. These trendscan be explained by the same mechanism suggested in the casesof single-nitrogen binding. The N−N interaction was not dueto the direct interaction between nitrogen atoms but due to thestrain effect caused by nitrogen binding. The empiricalcorrelation shown in Figure 1 between the BE and the volumeexpansion for each N−N configuration implies that the weakbinding is mostly due to the high free energy caused by thestrain associated with the volume expansion.The BE for the strongest nitrogen binding site in the

presence of another nitrogen nearby was shown to beapproximately −2.7 to −2.8 eV/atom, which was close to theBE of a single nitrogen in V. A common feature in the geometry

of the strong-binding cases was that the two O-sites did notshare any metal atoms. This distinctive binding structureimplies that nitrogen binding in a neighboring O-site is highlyunlikely. In the case of hydrogen, a similar trend has beenreported; the hydrogen binding in the presence of anotherhydrogen within 2.1 Å is energetically prohibited. Thethreshold distance for nitrogen neighboring is slightly largerthan that of hydrogen due to the large size of the nitrogenatom.

3.1.3. Electronic Structure of Nitrogen in Vanadium. Theresults of the Bader charge analysis are shown in Figure 2,

which shows the charge distribution on individual atoms of Vand nitrogen for both the O-site (Figure 2a) and T-site (Figure2b) occupations. The electrons were donated mostly from Vatoms surrounding nitrogen and transferred to the nitrogenatom. This donor−acceptor relationship can be also predictedby the electronegativity of individual elements. According toPauling’s scale of electronegativity, the values of nitrogen and Vare 3.04 and 1.63, respectively. Thus, nitrogen has a strongertendency to pull more electrons (negative charge) than V. Thenitrogen atom in the interstitial sites of V gained a charge of−1.61e (O-site) and −1.54e (T-site). Note that the charge gainon nitrogen atoms in the O- and T-sites were quite similar,despite their significantly different BEs. The absolute chargegain on nitrogen, therefore, does not seem to correlate with thestrength of nitrogen binding in V.It is noteworthy that the quantitative charge distribution on

V atoms in those two binding sites appeared to be quitedifferent. At the O-site, the two V atoms at the shortest vertices(dN−V = 1.89 Å) from the octahedral center donated 14.6% ofthe charge, whereas the four second-nearest V atoms (dN−V =

Table 2. Binding Energy, Atomic Distance, and Volume Expansion of V Containing Two Nitrogen Atomsa

Config. no. BE per N [eV] final N−N dist. [Å] lattice a [Å] lattice b [Å] lattice c [Å] vol exp (%)

1 −1.42 2.54 3.00 3.03 3.03 2.272 −2.33 2.47 3.03 2.99 3.03 1.853 −2.71 2.78 2.99 2.99 3.07 1.694 −1.74 3.58 3.14 2.96 2.96 2.465 −2.82 3.52 3.02 3.03 2.99 1.746 −2.77 3.65 2.99 3.03 3.03 1.687 −2.78 4.15 2.99 2.99 3.07 1.658 −2.66 4.61 3.03 2.99 3.03 1.809 −2.82 5.31 2.99 2.99 3.06 1.74

aVanadium lattice constant = 3.02. N−N bond length = 1.25 [Å].

Figure 1. Nitrogen BEs calculated from DFT and the associatedoptimized geometry in V54N2 system. Volume expansion (%) wascalculated by comparing to the volume of pure vanadium.

Figure 2. Bader charge analysis on nitrogen in V (a) O-site and (b) T-site. Colors surrounding the atoms are not proportional to the chargebut are used as a guide.

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2.04 Å) donated 69.7% of the charge that nitrogen gained,thereby, in total, 84% of the charge coming from the metalatoms forming the octahedral shell. In the T-site, on the otherhand, the four V atoms at the tetrahedral vertices (dN−V = 1.90Å) donated 52.2% of the charge that nitrogen gained. Note thatopposite charges would be electrostatically stabilized, and theirdistance would be inversely proportional to the electricpotential energy. Thus, the “negatively-charged” nitrogenatom would be better stabilized by nearby “positively-charged”V atoms. In the O-site binding, a greater number of V atomswere present close to the nitrogen atom compared to the caseof the T-site binding, implying that the high charge density onthe O-site V atoms may have contributed to the stable bindingof nitrogen in the O-site.A similar Bader analysis was conducted for the system

consisting of two nitrogen atoms in a V54 supercell, as shown inFigure 3. The binding configurations shown in Figure 3 (panels

a and b) correspond to the configuration nos. 2 and 5,respectively, as listed in Table 2. In the vicinity of the twonitrogen atoms, the V atoms donated more electrons thanthose far from nitrogen. The trend of the charge distribution inthe O-site was similar to that observed in the single-nitrogensystem: the four V atoms at farther vertices donated the most,and the other two atoms at closer vertices donatedapproximately half less. In configuration 2, there were three Vatoms shared in the two O-sites, which donated −0.5e, − 0.5e,and −0.36e. Those at the far vertices donated −0.3e each, andthose at the close vertices donated −0.16e each. Inconfiguration 5, only one V atom was shared within the twoO-sites. This shared V atom donated the most (−0.57e),

followed by those at the far vertices (−0.3e each) and those atthe close vertices (−0.12e each). As a greater number of Vatoms participated in the charge donation in configuration 5than in configuration 2, slightly more charge was pulled tonitrogen in configuration 5, enhancing the electrostaticattractive interaction between V and nitrogen. Also, therepulsive electrostatic interaction between two “negatively-charged” nitrogen atoms was much weaker in configuration 5than in configuration 2 because of the longer N−N distance.These electrostatic interactions explain why the nitrogenbinding in configuration 5 is more stable than in configuration2. The calculated BEs of configurations 2 and 5 are different by0.5 eV/atom.The DOS analysis shows the chemical bonding nature of

nitrogen in the O- and T-sites in V. In Figure 4, the peaksassociated with V atoms near both the O- and T-sitesoverlapped with the energy states of the nitrogen atom,whereas no overlap was observed in the DOS of pure V. Theoverlapping peaks indicate that covalent character existsbetween nitrogen and V in the bulk binding site. Thesecovalent interactions imply strong bonding between nitrogenand surrounding V atoms, agreeing with the highly negativeBEs. In the literature, similar band hybridization betweeninterstitial nitrogen and neighboring Fe atoms in the bcc Fe hasbeen reported.36

In addition, the shift of the vanadium DOS peaks toward lowenergy levels before and after nitrogen absorption is clearlyseen in the region of the nitrogen 1π state. In the O-site, theDOS of the V atom nearest to the nitrogen atom shows a shiftslightly lower than that of second-nearest V atom. Since it isdifficult to determine the relevance of such a subtle shift, the d-band center was calculated as a representative measure of the d-band shift. The d-band centers of various V atoms in the O-siteand T-site are shown in Figure 4 (panels a and b, respectively),in addition to being listed in Table 3. The d-band center of the

V atom nearest to the nitrogen atom in the O-site wasdetermined to be −0.57 eV, whereas that of pure V appeared tobe −0.25 eV, which agrees with the visual observation of the d-band shift. The shift in the d-band center of the second-nearest

Figure 3. Bader charge analysis on two nitrogen atoms in the O-sitesin V. The corresponding configurations are shown in Table 2: (a)configuration 2 and (b) configuration 5.

Figure 4. Partial DOS of vanadium d-bands in the presence of nitrogen binding in (a) O-site and (b) T-site.

Table 3. D-Band Centers for V Atoms in the Presence ofNitrogen Binding

purebulk

O-site,nearest

O-site, 2ndnear

T-site,nearest

d-band center (eV) −0.25 −0.57 −0.28 −0.46distance to nitrogen(Å)

N/A 1.89 2.06 1.90

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V atom in the O-site was rather subtle with a d-band center of−0.28 eV. The V atom nearest to nitrogen in the T-site showedits d-band center at −0.46 eV, which shifted slightly less thanthat in the O-site. The O-site geometry seemed to allow for amore extensive overlap of the orbitals than the T-site geometry,leading to the larger shift in the V d-band for the O-site. The d-band shift to a lower energy indicates an increasing chance offilling antibonding states, inferring the reduced reactivity of themetal toward nitrogen. That is, V atoms neighboring tonitrogen would be not as reactive as pure V to incorporateanother nitrogen. This conclusion supports the binding energyresults showing less stable binding of nitrogen in the vicinity ofanother nitrogen atom.3.2. Nitrogen Absorption in Vanadium−Ruthenium

Alloys. 3.2.1. Geometry and Binding Energy of Nitrogen inV53Ru Alloy. The optimized geometry of the V53Ru alloy wascompared to the pure V supercell in Figure 5a. The Ru atom

has a slightly larger atomic diameter (1.50 Å) than a V atom(1.43 Å). Thus, compared to the pure V54 supercell with alattice constant of 3.00 Å, the lattice size including the Ru atomincreased to 3.04 Å, whereas the size of the lattice without Ruslightly decreased to 2.99 Å, as shown in Figure 5a. The Vlattice size far from the Ru atom remained similar to that ofpure V.Figure 5b shows the case where a nitrogen atom was added

to the optimized V53Ru supercell. The local geometry of themetal in this case was different from the case of nitrogen inpure V. The shortest distance between V and nitrogen in pureV supercell was 1.89 Å. On the other hand, in V53Ru, the V−Ndistance was shortened to 1.86 Å, while the Ru−N distanceincreased to 1.95 Å. Upon nitrogen absorption, the size of theV53Ru lattice increased by 25% (i.e., from 3.04 to 3.81 Å). It isnoted that the strain caused by nitrogen in pure V54 was 26%.The lattice size perpendicular to the maximum strain wasmeasured to be 2.89 Å, which corresponds to 3.6% of the latticereduction due to the Poisson effect. For nitrogen binding inpure V54, the Poisson contraction was 4.0%. Thus, themechanical stresses caused by nitrogen binding in pure V andthat in the V−Ru alloy do not differ greatly.The effect of Ru on the stability of nitrogen atom in the V−

Ru alloy can be assessed by comparing the binding energies ofnitrogen in various sites in the alloy. Table 4 lists the bindingenergies of nitrogen and the distances of nitrogen to Ru beforeand after structure optimization. The same results were alsoplotted in Figure 6. The binding of nitrogen near Ru (<3 Å) in

the alloy appeared to be weaker than that in pure V. When thedistance between Ru and N exceeded approximately 3 Å, thebinding energy was not significantly affected by the presence ofRu. Note that the distance is nearly the size of a V lattice. If Ruis present in every other lattice, a nitrogen atom would not beaffected by the presence of Ru. This simple approximationindicates that a Ru composition of at least 25 at. % in the V−Rualloy would be needed to significantly impact nitrogen binding.If the concentration of Ru is below 25 at. %, there would be Ru-free binding sites available for stronger nitrogen binding. As aresult, the average binding energy of nitrogen in the alloyswould become similar to that in pure V despite the Ru content.Since Ru is an expensive metal, the V−Ru alloy with a high Rucontent of over 25 at. % may not be economically feasible. Also,alloys with a Ru content over 25 at. % are known to form anonbcc structure,31 which may decrease nitrogen permeationthrough the alloys.

3.2.2. Electronic Structure of Nitrogen in V53Ru Alloy. Thecharge distribution trend between V and Ru can be explainedby their electronegativity. According to Pauling’s scale onelectronegativity, the values of V and Ru are 1.63 and 2.20,respectively, indicating that Ru pulls electrons from V. Figure 7(panels a and b) shows the Bader charge distribution in theV53Ru alloy with and without nitrogen, respectively. In V53Ru,Ru gained −1.55e in total from surrounding V atoms. Thenearest neighbors donated −0.15e each, while the second-nearneighbors donated −0.05e each. When nitrogen was bound inthe O-site nearest to Ru, both Ru and nitrogen pull electronsfrom V. Since the electronegativity of nitrogen (3.04) is higherthan that of Ru, slightly more negative charge was pulledtoward nitrogen from Ru. Note that the values of the negativecharge pulled to nitrogen were very similar in a differentenvironment, as shown in Table 5: −1.61e in pure V, −1.51e in

Figure 5. Optimized geometries of (a) V53Ru and (b) V53Ru withnitrogen binding to an O-site.

Table 4. Nitrogen Binding Energies in Various O-sites inV53Ru

config.no.

initial Ru−N(Å)

optimized Ru−N(Å)

binding energy(eV/atom)

10 1.50 1.95 −1.6411 2.12 2.20 −2.0112 3.35 3.38 −2.6013 3.67 3.74 −2.6514 4.50 4.49 −2.7015 4.50 4.50 −2.5016 4.74 4.75 −2.7117 5.41 5.42 −2.70

Figure 6. Nitrogen binding energy in V53Ru alloy with respect to thedistance of nitrogen to Ru.

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the vicinity of the Ru atom in V53Ru, and −1.61e in the casewhere the Ru atom was far away in the V53Ru alloy. On theother hand, the charge gain on Ru varied significantly by thepresence of nitrogen. In the vicinity of nitrogen, Ru pulledmuch fewer electrons than in the absence of nitrogen. At a fardistance from nitrogen, Ru pulled more electrons withoutcompeting with nitrogen.While the attractive forces between nitrogen and V due to

electrostatic interaction were similar to those in the pure Vsystem, significant repulsion occurred between nitrogen andRu, as they both were “negatively charged.” Although themagnitude of the charge gain on Ru was much smaller at ashort Ru−N distance, the overall repulsion was affected moreby the short distance between the point charges. As thedistance between Ru and nitrogen became far, the repulsionbarely affected the potential energy of the nitrogen-bound alloy,thereby maintaining the binding energy to the same level ofthat in pure V. On the basis of the binding energy and chargedistribution in configuration 12, the repulsive charge effectbetween Ru and N was determined to fade beyond 3 Å, as alsoshown in Figure 6.The charge transfer between nitrogen and metals has also

been reported in the literature. Due to the high electro-negativity of nitrogen, charge transfer usually occurs from themetal to nitrogen. Compared to carbon, which has been studiedmore extensively, nitrogen involves more charge transfer,thereby a stronger electrostatic interaction with metals.56 Forinterstitial carbon in Fe-based metal alloys, the alloy componentinfluenced the binding energy of carbon (1) via the largeatomic size of the alloy, resulting in repulsive interactions and(2) via magnetic couplings among Fe, alloy and carbon,showing attractive interaction in limited alloys.57 In this study,however, nitrogen interaction with the alloy componentthrough the charge transfer well explains the trend in the

binding energies rather than the geometric and magneticcoupling effect.The PDOS analysis on the V53Ru alloy was compared to

pure V in Figure 8. The PDOS of Ru in V53Ru exhibited a

strong overlap with those of nearby V atoms at −3.4 eV,whereas no peaks appeared in the PDOS of pure V at the sameregion. This overlap occurred in a low-energy region of the d-band structure, indicating that the bonding interaction betweenRu and V would likely exist. In addition to the overlap in thelow-energy region, the PDOS of the V atom nearest to Rushowed a partial overlap at 1−2 eV. These high-energy stateswere potentially antibonding states, or conduction bands, andsince these states were empty (as they were above the Fermilevel), the bonding interaction was regarded as stable. Overall,the d-band center of V53Ru was slightly shifted by 0.03 eV to alower energy level due to the presence of the low-energy statesof Ru. Since Ru has its d-band at a much lower energy levelthan V, the local interaction for nitrogen binding would bemore favored with V than Ru.The PDOS trend indicating the V−Ru−N interaction varies

with different binding sites in V53Ru. In Figure 9, the PDOS ofnitrogen, Ru, and V in four different binding sites of V53Ru areshown. In the legend, “V, NN” and “V, NNN” represent the Vatoms that are the nearest neighbor and the next nearestneighbor, respectively, to nitrogen. The peak(s) associated withnitrogen appeared between −7 and −5 eV. At a short Ru−Ndistance (e.g., 1.95 Å) (Figure 9a), a sharp nitrogen peakshowed a significant amount of overlap with the Ru and Vpeaks, indicating covalent character between nitrogen and thesurrounding metal atoms. Also, the PDOS of Ru at a shortdistance to nitrogen was located at a lower energy level thanthose at a long distance to nitrogen. The d-band center of Ru inthis case also showed a significant low-energy shift, as shown inTable 6. This lower-energy shift of the nitrogen-coupled Rustates implies that there would be a high chance of filling theRu’s antibonding states compared to the unshifted bands;therefore, the binding of nitrogen in the presence of Ru may beweaker than that in the absence of Ru. The weakened bindingenergy of nitrogen near Ru may be partially attributed to thisband-shift effect. At a slightly longer Ru−N distance (e.g., 2.20Å) (Figure 9b), the overlapping regions of the PDOS betweenRu and nitrogen were still present, and there might be a slightband-shift effect, which destabilized the nitrogen binding in thisconfiguration. Beyond a Ru−N distance of 3 Å, the PDOS ofRu did not show a significant overlap with that of nitrogen(Figure 9, panels c and d); therefore, no substantial interactionbetween Ru and nitrogen was anticipated, as supported by thebinding energy comparison.

Figure 7. Bader charge distribution in (a) V53Ru and (b) V53Ru withnearest N. Colors surrounding the atoms are not proportional to thecharge used as a guide.

Table 5. Bader Charge on Ru and N in Various NitrogenBinding Configurations in V53Ru Alloy

config.no.

binding energy(eV/atom)

bader charge on Ru(e)

bader charge on N(e)

10 −1.64 −1.12 −1.5111 −2.01 −1.15 −1.5512 −2.60 −1.53 −1.6117 −2.70 −1.53 −1.61

Figure 8. PDOS analysis on Ru and V atoms in the V53Ru alloy.

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3.2.3. Nitrogen Binding in V54‑xRux (x = 2−6) Alloys. Toexamine nitrogen binding within octahedral shells of varying Rucomposition, octahedral V NN and NNN sites were system-atically replaced with Ru to create 14 unique octahedral bindingsites, with the total number of Ru atoms in NN and NNNpositions ranging from 2 to 6 (see Figure S1 forconfigurations). Due to the noted weakening of nitrogenbinding proximal to Ru in the V53Ru structure, it wasanticipated that increased Ru presence relative to nitrogenwould serve to further destabilize interstitial binding. Whencompared to nitrogen binding in the V53Ru structure (−1.64 eVat an Ru−N separation of 1.95 Å), configurations with two Ruatoms in the octahedral shell surrounding nitrogen resulted inbinding energies ranging from −1.24 to −0.43 eV, where thegreatest reduction in binding energy was observed for theconfiguration with two axially oriented Ru atoms (Table 7).Interestingly, moving the two Ru atoms from axial to equatorialpositions stabilized the nitrogen binding energy by ca. 0.80 eV.This is likely due to the greater proximity of Ru−N in the axialconfiguration (1.95 Å) when compared to the equatorial case(2.16−2.19 Å). Three unique configurations can be achievedwith the substitution of three Ru atoms into NN and NNNpositions, yielding nitrogen binding energies on the order of

−0.58 to −0.03 eV. Here, as before, the weakest binding energycorresponds with the configuration where Ru occupies bothaxial positions. This case produces a result most similar to thebenchmark H binding in V (−0.06 eV).All octahedral shell configurations with a Ru:V ratio greater

than unity resulted in positive binding energies, where nitrogenbinding in the full Ru octahedral shell (n = 6) was shown to beleast stable of all configurations (+1.33 eV). The Ru−Rudistance (axial) of 3.88 Å is not sterically accommodating forinterstitial nitrogen binding, and nitrogen is not likely to beobserved in these higher at. % Ru configurations in the absenceof extreme partial pressure N2. The Bader charge on nitrogenbecame less negative with increasing Ru substitution, owing tothe stronger Pauling electronegativity value of Ru whencompared to V. Generally, the nitrogen binding energy wasstrongly correlated to qN (r2 = 0.93). Thus, though Badercharge was shown to be ineffective at comparing relative O- andT-site binding, it may be viewed as a predictor of nitrogenbinding strength in different O-sites.

3.3. Nitrogen Absorption in Vanadium−MolybdenumAlloys. 3.3.1. Geometry Optimization of V−Mo Alloys. Thestructures of six different binary alloy compositions of the Mo−V alloys, in addition to pure metals, were optimized, as shownin Figure 10. The lattice constants of the optimized structuresare listed in Table 8. The calculated lattice constants agree wellwith the theoretically estimated values based on Vegard’s law.

Figure 9. PDOS of V53Ru with nitrogen binding in various sites.

Table 6. D-Band Centers of Ru, VNN, and VNNN in V53Ru inthe Presence of Nitrogen

config. no. Ru (eV) VNN (eV) VNNN (eV)

10 −2.18 −0.64 −0.2711 −1.73 −0.57 −0.2612 −1.70 −0.60 −0.2817 −1.75 −0.60 −0.28

Table 7. Binding Energy and Bader Charge for Nitrogen inOctahedral Shells of Varying V/Ru Composition

system Ru:Va nitrogen BE (eV) Bader charge (e)

a 1:2 −1.10 −1.45b 1:2 −1.18 −1.46c 1:2 −1.24 −1.45d 1:2 −0.43 −1.43e 1:1 −0.49 −1.37f 1:1 −0.58 −1.38g 1:1 −0.03 −1.35h 2:1 0.33 −1.22i 2:1 0.11 −1.25j 2:1 0.34 −1.21k 2:1 0.41 −1.27l 5:1 0.82 −1.19m 5:1 0.82 −1.18n ∞ 1.33 −1.08

aRatio of Ru atoms to V atoms in the 6-atom octahedral shellsurrounding interstitially bound nitrogen.

Figure 10. Mo−V alloys of various compositions (atomic ratio) testedin this study.

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Note that these ideal alloy structures were created assumingthat the Mo−V mixtures were close to equilibrium. In actualalloy structures, local disorder may exist due to dynamicequilibrium of the alloys.In each of the optimized alloy structures, one nitrogen atom

was introduced in the available O-site, and the entire structurewas further optimized. All of the possible O-sites were tested ineach alloy structure, considering the symmetry of the structure.After nitrogen introduction and optimization, one of the latticeaxes was expanded by 3−7%, along which the O-site expansionoccurs. Exemplary results of the optimized nitrogen-bindingstructures in Mo15V are shown in Figure 11.

3.3.2. Binding Energy and Vibrational Frequency ofNitrogen in V−Mo Alloys. The calculated binding energies ofnitrogen in the various O-sites and the vibrational frequenciesat the most stable binding sites are listed in Table 9. As the Vcontent in the alloys increased, the nitrogen binding becamestronger, which is clearly shown in Figure 12. The change inbinding energy with varying alloy compositions implies that thebinding energy can be tuned to give a proper level of solubilityand diffusivity of nitrogen, thereby providing a high nitrogenpermeability. It is noticeable that the BE of nitrogen in Mo12V4(25 at. % V) is close to the value of hydrogen BE in Pd. Unlikethe binding energy trend, the vibrational frequencies remainrather constant throughout the alloy compositions.3.4. Nitrogen Solubility in Metals Mo and Mo−V

Alloys. A related study was previously carried out by theauthors on hydrogen solubility in a number of transitionmetals58 and a different trend of hydrogen solubility with therespective temperature was found for the different investigatedmetals. Specifically, hydrogen solubilities in V, Nb, Ta, and Pd

decreased with increasing temperature, whereas those in W, Ni,Pt, Cu, Ag, and Au increased with increasing temperature.These opposite trends may in part be correlated to the sign ofthe binding energy since the binding energy is equivalent to theenthalpy of dissolution or absorption. However, compared tohydrogen, the estimation of nitrogen solubility in metals usingthis same method may be limited mainly because of the twosignificant differences between hydrogen−metal and nitrogen−metal systems: (1) a strong molecular bond of nitrogen gas and(2) the large atomic size of nitrogen. These differencesultimately lead to a high chance of a phase transition associatedwith nitride formation, for which the assumption of dilute solid-solution would no longer be valid.Specifically, the high stability of the nitrogen molecule owing

to its strong binding implies that once the atomic species areformed after bond-breaking, they will be very unstable andhighly reactive to metals. In addition, to break such a strong

Table 8. Optimized Lattice Constants of Mo, V, and VariousMo−V Alloys

compositionlattice constant (Å)

calculatedlattice constant (Å) Vegard’s

law

Mo16 3.169 −Mo15V1 3.158 3.158Mo14V2 3.148 3.148Mo13V3 3.136 3.137Mo12V4 3.124 3.126Mo8V8 3.072 3.084Mo1V15 3.002 3.009V16 2.998 −

Figure 11. Nitrogen binding in the various O-sites of the Mo15V alloy.

Table 9. Binding Energies and Vibrational Frequencies ofNitrogen in the Various O-Sites of the Mo−V Alloys

metal/alloy label O-site %binding energy

(eV)vibrational frequencies

(cm−1)

pure Mo O-site

100 0.835 831.4 357.9 357.7

Mo15V1 O1 12.5 0.004 791.1 404.5 404.5O2 25 0.744 − − −O3 25 0.787 − − −O4 25 0.842 − − −O5 12.5 0.845 − − −

Mo14V2 O1 25 −0.010 804.4 399.2 399.1O2 50 0.667 − − −O3 25 0.823 − − −

Mo13V3 O1 37.5 −0.041 806.9 425.9 425.9O2 25 0.61 − − −O3 25 0.551 − − −O4 12.5 0.822 − − −

Mo12V4 O1 50 −0.116 817.2 428.9 428.8O2 50 0.431 − − −

Mo8V8 O1 50 −1.423 − − −O2 50 −0.289 889.9 382.7 382.7

Mo1V15 O1 12.5 −2.485 798 491.8 478.2O2 25 −2.464 − − −O3 25 −2.448 − − −O4 25 −2.307 − − −O5 12.5 −1.638 − − −

pure V O-site

100 −2.550 776.9 428.9 428.8

Figure 12. Nitrogen binding energy as a function of V molar fractionin Mo−V alloys.

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bond, high temperature is usually required. As a result, in thepresence of atomic nitrogen at high temperature, metal nitridemay become more stable than the strained metal with the large-sized interstitial nitrogen. Then, metal nitrides may start togrow, with nitrogen being stuck in the metal lattice structure,and with only little able to penetrate through the metal. Thisscenario likely happens in the case of metals with a strongaffinity to nitrogen, such as V.On the other hand, for less reactive metals, such as Mo, the

nitrogen concentration may remain dilute, and thus, the phasetransition will be less likely. In this case, the nitrogen solubilitymay be estimated by the same scheme used for hydrogensolubility in metals. However, the permeability of nitrogenthrough metals would be much lower compared to that ofhydrogen because of the high energy barrier associated withnitrogen diffusion.The low permeability renders accurate experimental

measurements to be much more difficult, as well as deterioratesthe reliability of the experimental data. Therefore, theoreticalmethods to estimate nitrogen solubility, diffusivity, andpermeability become greatly valuable in searching for potentialmembrane materials. This study focuses specifically on thenitrogen solubility estimation for less-reactive metals, in whichdilute solid-solution assumption remains valid.First, the solubility of nitrogen in pure Mo was estimated by

combining the first-principles calculation results and theequations of thermodynamic equilibrium. Figure 13 shows

the estimated solubility compared to the experimental solubilityreported in the literature as a function of temperature (Figure13a) and inverse temperature (Figure 13b).21,59 The solubilitydata were drawn on the log scale, as a function of temperatureand inverse temperature. Since the binding energy was positive,the nitrogen absorption was endothermic, and, thus, thesolubility increases with temperature increase.Note that the absolute values of the slope of the linear plots

in Figure 13b represent the enthalpy of dissolution, ΔH. Thesolubility follows the Arrhenius equation as follows:

= × − Δ⎛⎝⎜

⎞⎠⎟S S

Hk T

exp0B (3)

= − Δ⎛⎝⎜

⎞⎠⎟S S

Hk T

ln ln1

0B (4)

such that S is solubility, S0 is the maximum solubility given forinfinite temperature, kB is Boltzmann’s constant, and T istemperature in Kelvin. The calculated slopes are listed in Table10. The enthalpy of dissolution derived from the calculatedsolubility showed a very similar value to those reported in theexperimental literature,21,59 whereas the S0 values calculatedshowed a significant discrepancy from the literature.To enhance the accuracy of the solubility estimation, the

calculated solubility was corrected to match the experimentalsolubility by systematic adjustment of the two variables: bindingenergy and vibrational frequency. The sensitivity of thesolubility estimation was analyzed upon changing the bindingenergy and vibrational frequency, as shown in Figure 14 (panelsa and b, respectively). The decrease in binding energy led to theincrease in solubility, and more importantly, both the slope andthe magnitude of the plots changed in Figure 14b when thebinding energy was varied. On the other hand, when thevibrational frequency values were adjusted, the plots in Figure14 (panels c and d) were shifted in parallel to each other, withthe slope remaining constant. These observations provide ascheme for how to systematically correct the calculatedsolubility. Note that the calculated solubility showed nearlythe same slope as that of experimentally reported solubility.Thus, the binding energy value was fixed, but the vibrationalfrequency was adjusted to match the experimental solubility.Another reason for correcting vibrational frequency but not thebinding energy is because solid state phonon calculations wereconsidered less accurate in general compared to the energycalculations. As demonstrated in Figure 14d, the vibrationalfrequency of 18% of the originally calculated frequenciesprovided the best match. Since no direct experimental resultshave been reported in the literature regarding nitrogenvibrational frequencies in Mo, it is unsure whether thecorrected vibrational frequency is close to a real physical value.Using the correction factor of 18% on the vibrational

frequencies, further solubility calculations were conducted forMo−V alloys with high Mo content. As shown in Figure 15, theeffect of a small concentration of V added to Mo wasnoticeable. The Mo−V alloy of 6.25 at. % vanadium showed thesolubility enhanced by three-orders of magnitude at 1000 K,and that of 25 at. % vanadium showed enhancement of four-orders of magnitude. The enhancement in solubility with thesame V content was more significant at lower temperature. InMo−V alloys, the temperature dependence of the nitrogensolubility became much lower compared to that in pure Mosince the absolute value of the average binding energy in thealloys was close to zero. No experimental solubility values arecurrently available for comparison, but the estimating protocolwas corroborated in pure metal systems with hydrogen and

Figure 13. Calculated and experimental nitrogen solubility in log scaleas a function of (a) temperature and (b) inverse temperature.

Table 10. Slope of the plots in Figure 14b and Calculated ΔH

slope − ΔH/10000/kB intercept ln S0 R2 ΔH [eV] S0

EXP131 −1.029 −2.978 1.0000 0.887 0.0509EXP232 −0.9284 −3.121 0.99992 0.800 0.0441calculated −1.031 −8.157 0.99969 0.888 0.0003

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nitrogen. These theoretical predictions may guide the upperlimit of nitrogen solubility in those alloys.

4. CONCLUSIONSIn this study, nitrogen binding characteristics of V, V−Ru, V−Mo, and Mo were investigated by first-principles calculations.The nitrogen binding in the bcc metals was most stable in theO-site with the displacement of nearby metal atoms. Due to thedisplacement and the subsequent distortion of the lattice, theoccupation of additional nitrogen was not favored in the nearbyinterstitial sites. Nitrogen binding in V was very strong with anapproximate binding energy of −2.55 eV/atom, which wasenhanced by the electrostatic and covalent interaction betweennitrogen and surrounding metal atoms. Due to this strongbinding, the formation of a dilute solid solution in V seemed

unlikely, potentially leading to nitride formation. To improvenitrogen permeability in these metals, it was hypothesized thatweaker binding may be favorable thereby leading to enhancednitrogen diffusivity in the dilute solid solution. Thus, V-basedalloys with weak binding energies including V−Ru and V−Mowere chosen for testing nitrogen binding characteristics.Reduced binding energies were observed in both alloyscontaining Ru or Mo (e.g., −1.64 eV/atom for both V53Ruand V15Mo alloys). In particular, Mo13V3 alloy showed anitrogen BE of −0.041 eV, which is very similar to the BE of Hin Pd. The nitrogen solubility in Mo was estimated bythermodynamic equilibrium assumption with systematiccorrections to the calculated vibrational frequencies, showingagreement to the experimental solubility. Using the samecorrection scheme, the nitrogen solubility in V−Mo wasestimated to be 4 orders of magnitude higher at 1000 K for 25at. % V alloy composition compared to pure Mo. Thistheoretical study has the potential to provide useful guidance tothe discovery of promising materials for metallic membranesapplied to ammonia synthesis.

■ ASSOCIATED CONTENT

*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpcc.7b05315.

The effect of various relaxation modes and supercell size.In addition, the 14 unique configurations involving theO-site occupation of nitrogen in alloys of VRu (FigureS1), as well as the details associated with the nitrogensolubility estimations (PDF)

Figure 14. Solubility on the log scale as a function of temperature or inverse temperature with varying binding energies (in eV) and vibrationalfrequencies (in % of the original calculations). Plots in (a and b) show the effect of binding energy, and those in (c and d) show the effect ofvibrational frequency.

Figure 15. Nitrogen solubility estimated in this study using first-principles calculation with vibrational frequency correction (scalefactor of 18%) and thermodynamic equilibrium in dilute solidsolutions.

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■ AUTHOR INFORMATION

Corresponding Author*E-mail: wilcox@mines.edu. Tel: (303) 273-3885. Fax: (303)273-3730.

ORCIDPeter Psarras: 0000-0002-5302-3412Jennifer Wilcox: 0000-0001-8241-727XNotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

We would like to acknowledge the Texas Advanced ComputingCenter (TACC) at the University of Texas at Austin forproviding HPC resources that have contributed to the researchresults reported within this paper: URL: http://www.tacc.utexas.edu. In addition, we acknowledge the Air Force Office ofScientific Research, Grant FA9550-16-1-0357, for supportingthis work.

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The Journal of Physical Chemistry C Article

DOI: 10.1021/acs.jpcc.7b05315J. Phys. Chem. C 2017, 121, 17016−17028

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