Theoretical Study of Nitrogen Absorption in Metals - ACS Publications

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Theoretical Study of Nitrogen Absorption in Metals Kyoungjin Lee, Simona Liguori, Peter Psarras, and Jennifer Wilcox J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b05315 • Publication Date (Web): 11 Jul 2017 Downloaded from http://pubs.acs.org on July 18, 2017

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The Journal of Physical Chemistry

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

Department of Energy Resources Engineering, Stanford University, 367 Panama Street,

Stanford CA 94305, USA; ‡

Department of Chemical and Biological Engineering, Colorado School of Mines, 1613 Illinois

Street, Golden CO 80401. USA

KEYWORDS: Density functional theory, Nitrogen absorption, Nitrogen solubility, Group V metals, Nitrogen-selective membrane, Catalytic metallic membrane ABSTRACT: Nitrogen binding in open structure body-centered-cubic (bcc) metals was studied to understand atomic nitrogen absorption in these systems in order to assess their feasibility as membrane materials for nitrogen separation and subsequent reactivity for ammonia production. For a metallic membrane to be feasible for this application, it must exhibit adequate solubility that allows for sufficient permeability. Using first-principle calculations it was demonstrated that nitrogen is too soluble in pure vanadium due to its strong binding in this metal (i.e., binding energy of −2.80 eV/atom), but through alloying, the binding energy may be tuned to mimic the weaker hydrogen binding exhibited in Group V metals, leading to high permeability. In particular, alloys of Ru and Mo were investigated. The Bader charge and density of states analyses showed that nitrogen binding in pure V is enhanced by the electrostatic and covalent interaction between nitrogen and surrounding V atoms, whereas repulsive interaction with an alloying component, Ru or Mo, with nitrogen resulted in the less stable binding of nitrogen in the alloys. Reduced binding energies were observed in both alloys, e.g., −1.64 eV/atom for both V53Ru and V15Mo alloys. In particular, Mo13V3 alloy showed a nitrogen BE of −0.041 eV, which is very similar to the BE of H in Pd. The nitrogen solubility in Mo was estimated based upon a thermodynamic equilibrium assumption with systematic corrections to the calculated vibrational frequencies, showing agreement to the experimental solubility. Using the same correction scheme, nitrogen solubility in V-Mo was estimated to be four orders of magnitude higher at

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1000K for a 25 at.% V alloy composition compared to pure Mo. This theoretical study provides useful guidance for the discovery of promising materials for metallic membranes for ammonia synthesis.

1. INTRODUCTION The nitrogen cycle is one of the most significant biogeochemical cycles on Earth, as nitrogen is an essential nutrient for all forms of life. Although nitrogen is freely available in the atmosphere as dinitrogen (N2), nitrogen conversion processes from a gaseous to a fixed form are very limited in nature, e.g., occurring through plant growth. Today, industrial ammonia synthesis for fertilizer production, known as the Haber-Bosch process, requires intensive energy associated with high temperature (400-500 °C) and high pressure (up to 30 MPa) during the synthesis.1 These harsh operating conditions are necessary due to the high affinity of dissociated nitrogen atoms towards the catalyst surface in addition to the high activation barrier associated with N2 dissociation2. The overall process consists of continuous flow and frequent recovery of unreacted gases, resulting in a method capable of producing large amounts of ammonia. Approximately 141 million tonnes of ammonia were produced worldwide in 2015 through this industrial processes, and domestically, 88% of ammonia consumption was for fertilizer production. Given the high demand of ammonia and the high production capacity of plants that synthesize it, this process is considered the second most energy-intensive chemical manufacturing process in the US and worldwide3, accounting for 2% of total global energy use4 and about 1% of total global greenhouse gas emissions5. For these reasons, the need for advanced catalytic methods for the reduction of N2 to ammonia remains a requirement for sustainability in the food, energy and water systems cycle. The current study explores the potentiality of metallic membranes for N2 separation with the final intent to find an alternate route to producing ammonia. In a metallic membrane reactor for ammonia synthesis, a metallic membrane provides reaction sites for ammonia synthesis as well as separates nitrogen. In specific, a dense metallic layer permeable to nitrogen allows for high-purity atomic nitrogen stream to readily react with hydrogen available on a catalyst to produce ammonia. The feasibility of this approach depends on the nitrogen flux through the membrane, which follows the equation6: 2


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= ∙

, ,

(Eq. 1)

where is the nitrogen permeating flux through the membrane, P is the permeability, , and , are the partial pressures of nitrogen in the retentate and the permeate sides of the

membrane, respectively, and δ is the membrane thickness. n is an exponent of pressures, which is empirically determined. The permeating flux is inversely proportional to the membrane thickness and directly proportional to the nitrogen permeability, which is the product of solubility, S, and diffusivity, D, in the metal. The current study focuses specifically on evaluating atomic nitrogen solubility in open-structured body-centered-cubic (bcc) metals to screen good candidates for the metallic membrane reactors for ammonia synthesis. The solubility and diffusivity of nitrogen in metals have been reported in previous studies, but none of these previous studies have considered for the application to the nitrogen-selective membranes. Since permeability is the product of those two terms, nitrogen permeability can be estimated from the literature. Table 1 lists nitrogen solubility and diffusivity in various bcc metals reported in the literature. It is shown that Fe has much higher permeability than other metals, and V has also relatively high permeability. Note that the dominating factor is different in those two metals; V has a large solubility, whereas Fe has extremely high diffusivity. Group 5 metals (V, Nb, and Ta) have relatively high permeability than Group 6 metals (Cr, Mo, and W) at the same temperature. Since the nitrogen permeability values of Mo and W at 500 ˚C are significantly lower than those of Group 5 metals at 500 ˚C, the values at 800 ˚C are given for Mo and W to practically compare. Vanadium and Cr may be directly compared as a representative of Group 5 and 6, respectively. The nitrogen solubility is higher in V than in Cr, whereas the diffusivity is higher in Cr than in V. The permeability, in turn, is higher in V than in chromium. These trends imply that there might be a trade-off between the magnitudes of solubility and diffusivity; hence, a moderately high solubility and diffusivity may offer the highest permeability. If metals with different permeabilities form alloys, the permeability of those alloys may vary between the values of the pure metal components. In this way, the transport property of metallic membrane can be tuned in future studies. For the nitrogen-selective membranes to be feasible, a target permeability could be the value close to the hydrogen permeability in Pd,33-36 which has been commercialized for decades. Compared to Pd, pure V has higher solubility but much lower 3



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diffusivity, resulting in the low permeability. In bulk V, nitrogen was shown to bind strongly in the interstitial sites. The nitrogen binding 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 stable binding energy of nitrogen in the bulk V was approximately an order of magnitude stronger compared to H binding in Pd, i.e., –0.12 eV/H in the O-site.32 On the other hand, the nitrogen binding energy in Fe reported in the literature was 0.02 eV/atom,30-31 which is very close to the binding energy of H in Pd. Note that nitrogen diffusivity in Fe is considerably higher than that in any other bcc metals (Table 1), inferring that the binding energy close to zero may be an indicator of enhanced diffusion in metals with moderate solubility.

Nitrogen binding in the bcc metals and their alloys has been widely reported both theoretically and experimentally. In the literature, multiple experiments to measure nitrogen binding and diffusion have been performed for various metals, e.g., V,9,13-18 Nb,15,16 Ta,9,15,19-20 Cr,11,21-25 Mo,11,23-25 and Fe. 26-27 Also, theoretical studies focusing on nitrogen in the bulk metals have supported the O-site binding of nitrogen in V,28 W,29 and Fe.30-31 Lattice expansion often occurs due to the large atomic size of nitrogen compared to the size of interstitial sites.7-9 When other defect sites, such as vacancies, grain boundaries, and dislocations, exist in metal structures, those sites tend to exhibit stronger binding of nitrogen. 10-12 However, only limited number of nitrogen binds to those sites since the defect concentrations are limited, and the mobility of defects decreases with nitrogen binding. Introducing nitrogen to metals is often referred to as “nitriding.” In steel manufacture, nitriding is a metal strengthening process to enhance mechanical properties of steels. In this study, nitriding occurs at the initial step of nitrogen permeation, and metal surface may transform into non-bcc nitrides as suggested by many metal–nitrogen phase diagrams. The goal for the nitrogen-selective metallic membranes is to maintain a dilute solid solution phase, in which the mobility of interstitial nitrogen 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 geometry are demonstrated, and the electronic structure effect on the nitrogen binding in metals is analyzed. Pure V system with nitrogen interaction will be first discussed, followed by V-Ru and V-Mo 4


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alloy system discussion to expand possible selections of membrane materials beyond pure metals. Ruthenium (Ru) alloy was chosen because Ru is well known as a catalyst for ammonia synthesis, implying that the dissociation of molecular nitrogen may easily proceed on Ru surfaces. The effect of Ru as an alloy component in a V–Ru alloy on the nitrogen binding energy as well as the charge and electronic structure will be discussed. Another V-based alloy chosen in this study is the Mo–V alloy. Molybdenum has a bcc structure in its pure state, and is known to form bcc alloys with V in any composition, which may be helpful to diffuse atomic nitrogen in the bulk phase. At elevated temperatures, Mo may form nitrides, which are known to be good catalysts for ammonia synthesis. Since ammonia synthesis might occur simultaneously during the membrane operation with in situ nitride formation, testing Mo as an alloy component may provide insights into the development of nitrogen-selective membranes for ammonia synthesis. Various compositions of V–Mo alloys were studied with the aim of searching for membrane materials with sufficient nitrogen permeability. Table 1. Nitrogen solubility, diffusivity, and estimated permeability in various bcc metals Metal

T [˚C]

Solubility [at.%]

Diffusivity [10−15 m2/s]

Permeability [10−15 mol/m.s.Pa0.5]

Reference

V

500

2.66

0.32

1.6

13 16

Nb

500

0.15

0.09

0.020

16

Ta

500

1.7

0.01

0.025

20 37

Cr

500

0.02

4.0

0.19

38 39

Mo

800

–

–

0.63

24

W

800

–

–

0.0020

24

Fe

500

0.2

1400

600

26 27

5



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2. COMPUTATIONAL METHODOLOGY

2.1 DFT Calculation Parameters First-principles calculations based on DFT44,45 were performed using the Vienna ab initio Simulation Package (VASP, v5.2.12)46-49 with the projector augmented wave (PAW) method50,51 to describe nucleus-electron interactions. Electron exchange-correlation functionals were represented with the generalized gradient approximation (GGA) using the model of Perdew, Burke, and Ernzerhof (PBE).52-53 For V and V-Ru alloy studies, plane waves with a kinetic energy cutoff of 550 eV were used to describe electronic wave functions, while an energy cutoff of 400 eV was used for V-Mo alloy study. While the electronic energy in the self-consistent field was converged below 10−6 eV, the total energy convergence to within 1 meV/atom was achieved with respect to the energy cutoff and k-point parameters. The first-order Methfessel and Paxton smearing method54 with a width of 0.1 eV was used for the Fermi-level integration.

Geometry optimization was performed with a 3 × 3 × 3 conventional bcc supercell (54 atoms) in V and V-Ru alloy studies, and a 2 × 2 × 2 conventional bcc supercell (16 atoms) was used for VMo alloy study. The Monkhorst-Pack scheme55 was applied for the sampling of k-points in each of those supercells with k-spaces of 4 × 4 × 4 and 12 × 12 × 12, respectively. Both the lattice (shape and volume) and atomic positions were allowed for relaxation. The ionic positions were relaxed using the conjugate-gradient algorithm so that the absolute values of the forces on unconstrained atoms became less than 0.01 eV/Å or the total free energy change between ionic 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 box and choosing the Γ-point. The binding energy (BE) of atomic nitrogen in an interstitial binding site with respect to gaseous N2 was calculated by taking the total free energy difference between the initial (pure V and the nitrogen molecule in the gas phase) and the final state (one nitrogen bound in an interstitial site of the V structure):

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= − −

(Eq. 2)

such that , , and are the total energies of V with an interstitial nitrogen, the bulk V, and nitrogen in the gas phase, respectively. Note that, in this definition, a negative value of BE implies a thermodynamically-favored binding state of the interstitial nitrogen.

Vibrational frequencies of the binding nitrogen were calculated for a few stable O-sites in V and V alloys. The normal-mode vibrational frequencies of the nitrogen atom were calculated by a finite displacement method with a displacement size of 0.015 Å. The free energy and the vibrational frequency of a N2 molecule in the gas phase were calculated by placing one 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 Bader charge analysis56-58 and a projected density of states (PDOS) analysis. The Bader charge analysis provided a consistent way to partition the charge distribution calculated from the integrated electronic density in the DFT calculations and to assign charge values to individual atoms. This method is helpful in interpreting the redox reactions among adjacent chemical species. For example, the differences in the partitioned charge between pure metal and the metal with nitrogen absorption indicate the charge transfer between bulk metal and nitrogen, thereby identifying the charge interaction in the absorption process. In the Bader analysis on the bulk material, because the atoms are located at very short distances to each other, counting the electron transfer is possibly inaccurate due to the presence of core charges. Therefore, both core and valence electrons were considered in the Bader charge calculations, although the core electrons did not participate in any chemical interactions. The PDOS analysis demonstrates the electronic energy states of each chemical species with respect to the Fermi level. These energy states of different species may overlap each other, which indicates potential hybridization of the states leading to covalent bonding between those species. The changes in chemical environment may shift the DOS, and particularly, the shift in metal d-bands can be correlated to the reactivity

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of the metal.59 Thus, to quantitatively compare the d-band shift, the center of the metal d-bands was calculated.

3. RESULTS AND DISCUSSION

3.1 Nitrogen Absorption in Pure Vanadium

3.1.1 Geometry of Nitrogen Binding in Vanadium The geometry of an O-site in pure bcc metals is not a regular octahedron, but two vertices are closer to the center than the other four. After nitrogen binding in the O-site, the geometry of the binding site became elongated along the short vertices thereby forming a more regular octahedral shape. That is, only the two of the six metal atoms were displaced farther apart, but the rest of the atoms merely changed their positions or were slightly contracted to each other. In the literature, a similar deformation of the O-site has been reported for carbon and nitrogen binding in other bcc metals.19-22 Such deformation can be explained by energy minimization. The increased free energy due to lattice expansion upon nitrogen binding would be overcompensated by the lowered energy from the stabilized interaction between nitrogen and V in a deformed O-site. The expansion of the T-site would be more energetically costly compared to that of the O-site, because all of the four metal atoms consisting of the T-site need to be displaced. Therefore, the T-site binding was less stable than the O-site binding after the optimization of the metal lattices. The O-site preference of nitrogen binding in the bcc metals observed in this study agrees well with previous experimental and theoretical studies.23-25 The BEs of calculated in this study are −2.80 and −1.38 eV/N for the O-site and T-site binding, respectively. The difference in the BEs from previous the study is due to the size of supercell used in the calculations, as discussed in Section S2 of the Supplementary Information.

3.1.2 Multiple Nitrogen Binding in Vanadium For single nitrogen binding discussed in the previous section, an even distribution of nitrogen atoms was assumed for an equilibrium state. In practice, however, this assumption may become invalid as nitrogen concentration increases or when a dynamic process is considered for atomic nitrogen diffusion through bulk metals. For instance, two nitrogen atoms may stay nearby if

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attractive interaction exists, or there might be a threshold distance between two nitrogen atoms if repulsive interaction dominates. To test these hypotheses, various nitrogen configurations were tested by placing two nitrogen atoms at various distances in the O-sites and optimizing the geometry to determine the minimized free energy for each configuration.

The results of the first-principles calculations on each configuration are presented in Table 2, including an optimized N–N distance, an average BE per nitrogen atom, and the percentage of volume expansion. The N–N distances listed here are the shortest N–N distance measured in the optimized structure. The values in Tables 2 are summarized in Figure 1.

Table 2. Binding energy, atomic distance, and volume expansion of V containing two nitrogen atoms. Config. BE per N Final N–N lattice a lattice b lattice c No. [eV] dist. [Å] [Å] [Å] [Å] 1 −1.42 2.54 3.00 3.03 3.03 2 −2.33 2.47 3.03 2.99 3.03 3 −2.71 2.78 2.99 2.99 3.07 4 −1.74 3.58 3.14 2.96 2.96 5 −2.82 3.52 3.02 3.03 2.99 6 −2.77 3.65 2.99 3.03 3.03 7 −2.78 4.15 2.99 2.99 3.07 8 −2.66 4.61 3.03 2.99 3.03 9 −2.82 5.31 2.99 2.99 3.06 1 Vanadium lattice constant = 3.02: 2 N-N bond length = 1.25 [Å]

Vol Exp (%) 2.27 1.85 1.69 2.46 1.74 1.68 1.65 1.80 1.74

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Figure 1. Nitrogen BEs calculated from DFT and the associated optimized geometry in V54N2 system. Volume expansion (%) was calculated by comparing to the volume of pure vanadium. In a few cases where the initial N–N distance between two O-sites was extremely short, the Tsite binding was found to be the local minimum. In Figure 1, those cases were shown on a regime of high binding energy and high volume expansion. Although the T-site binding is generally unstable compared to the O-site binding, when two nitrogen atoms were forced to stay linearly along the neighboring O-sites, one or two nitrogen atoms moved to the T-site to avoid extremely high stresses associated with the shared V atom of the O-sites. Similar strain effect of nitrogen binding in the bcc metals has been reported in the literature.7,12

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 V seemed to have a strong correlation with the BE. These trends can be explained by the same mechanism suggested in the cases of single-nitrogen binding. The N–N interaction was not due to the direct interaction between nitrogen atoms, but due to the strain effect caused by nitrogen binding. The empirical correlation shown in Figure 1 between the BE and the volume expansion for each N–N configuration implies that the weak binding is mostly due to the high free energy caused by the strain associated with the volume expansion.

The BE for the strongest nitrogen binding site in the presence of another nitrogen nearby was shown to be approximately −2.7 to −2.8 eV/atom, which was close to the BE of a single nitrogen in V. A common feature in the geometry of the strong-binding cases was that the two O-sites did 10


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not share any metal atoms. This distinctive binding structure implies that nitrogen binding in a neighboring O-site is highly unlikely. In the case of hydrogen, a similar trend has been reported; the hydrogen binding in the presence of another hydrogen within 2.1Å is energetically prohibited. The threshold distance for nitrogen neighboring is slightly larger than that of hydrogen due to the large size of nitrogen atom. 3.1.3 Electronic Structure of Nitrogen in Vanadium The results of the Bader charge analysis are shown in Figure 2, which shows the charge distribution on individual atoms of V and nitrogen for both the O-site (Figure 2a) and T-site (Figure 2b) occupations. The electrons were donated mostly from V atoms surrounding nitrogen and transferred to the nitrogen atom. This donor-acceptor relationship can be also predicted by the electronegativity of individual elements. According to Pauling’s scale of electronegativity, the values of nitrogen and V are 3.04 and 1.63, respectively. Thus, nitrogen has a stronger tendency to pull more electrons (negative charge) than V. The nitrogen atom in the interstitial sites of V gained a charge of −1.61e (O-site) and −1.54e (T-site). Note that the charge gain on nitrogen atoms in the O- and T-sites were quite similar, despite their significantly different BEs. The absolute charge gain on nitrogen, therefore, does not seem to correlate with the strength of nitrogen binding in V.

It is noteworthy that the quantitative charge distribution on V atoms in those two binding sites appeared to be quite different. At the O-site, the two V atoms at the shortest vertices (dN–V = 1.89 Å) from the octahedral center donated 14.6% of the charge, whereas the four second-nearest V atoms (dN–V = 2.04 Å) donated 69.7% of the charge that nitrogen gained, thereby, in total, 84% of the charge coming from the metal atoms forming the octahedral shell. In the T-site, on the other hand, the four V atoms at the tetrahedral vertices (dN–V = 1.90 Å) donated 52.2% of the charge that nitrogen gained. Note that opposite charges would be electrostatically stabilized, and their distance would be inversely proportional to the electric potential energy. Thus, the “negatively-charged” nitrogen atom would be better stabilized by nearby “positively-charged” V atoms. In the O-site binding, a greater number of V atoms were present close to the nitrogen atom compared to the case of the T-site binding, implying that the high charge density on the Osite V atoms may have contributed to the stable binding of nitrogen in the O-site. 11



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

A similar Bader analysis was conducted for the system consisting of two nitrogen atoms in a V54 supercell, as shown in Figure 3. The binding configurations shown in Figures 3(a) and (b) correspond to the Configuration No. 2 and 5, respectively, as listed in Table 2. In the vicinity of the two nitrogen atoms, the V atoms donated more electrons than those far from nitrogen. The trend of the charge distribution in the O-site was similar to that observed in the single-nitrogen system: the four V atoms at farther vertices donated the most, and the other two atoms at closer vertices donated approximately half less. In Configuration 2, there were three V atoms shared in the two O-sites, which donated −0.5e, −0.5e, and −0.36e. Those at the far vertices donated −0.3e each, and those at the close vertices donated −0.16e each. In Configuration 5, only one V atom was shared within the two O-sites. This shared V atom donated the most (−0.57e), followed by those at the far vertices (−0.3e each) and those at the close vertices (−0.12e each). As a greater number of V atoms participated in the charge donation in Configuration 5 than in Configuration 2, slightly more charge was pulled to nitrogen in Configuration 5, enhancing the electrostatic attractive interaction between V and nitrogen. Also, the repulsive electrostatic interaction between two “negatively-charged” nitrogen atoms was much weaker in Configuration 5 than in Configuration 2 because of the longer N–N distance. These electrostatic interactions explain why

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the nitrogen binding in Configuration 5 is more stable than in Configuration 2. The calculated BEs of Configurations 2 and 5 are different by 0.5 eV/atom.

Figure 3. The Bader charge analysis on two nitrogen atoms in the O-sites in V. The corresponding configurations are shown in Table 2: (a) Configuration 2 (b) Configuration 5. The DOS analysis shows the chemical bonding nature of nitrogen in the O- and T-sites in V. In Figure 4, the peaks associated with V atoms near both the O- and T-sites overlapped with the energy states of the nitrogen atom, whereas no overlap was observed in the DOS of pure V. The overlapping peaks indicate that covalent character exists between nitrogen and V in the bulk binding site. These covalent interactions imply strong bonding between nitrogen and surrounding V atoms, agreeing with the highly negative BEs. In the literature, similar band hybridization between interstitial nitrogen and neighboring Fe atoms in the bcc Fe has been reported.12

In addition, the shift of the vanadium DOS peaks toward low energy levels before and after nitrogen absorption is clearly seen in the region of the nitrogen 1π state. In the O-site, the DOS of the V atom nearest to the nitrogen atom shows a shift slightly lower than that of 2nd-nearest V atom. Since it is difficult 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-site and T-site are shown in Figure 4 (a) and (b), respectively, in addition to listed in Table 3. The d-band center of the V atom nearest to the nitrogen atom in the O-site was determined to be −0.57 eV, whereas that of pure V appeared to be −0.25 eV, which agrees with 13



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the visual observation of the d-band shift. The shift in the d-band center of the 2nd-nearest 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 showed its d-band center at −0.46 eV, which shifted slightly less than that in the O-site. The O-site geometry seemed to allow for a more 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 of filling anti-bonding states, inferring the reduced reactivity of the metal toward nitrogen. That is, V atoms neighboring to nitrogen would be not as reactive as pure V to incorporate another nitrogen. This conclusion supports the binding energy results showing less stable binding of nitrogen in the vicinity of another nitrogen atom.

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

Table 3. The d-band centers for V atoms in the presence of nitrogen binding Pure bulk

O-site,

O-site, nd

T-site,

nearest

2 near

nearest

d-band center (eV)

−0.25

−0.57

−0.28

−0.46

Distance to nitrogen (Å)

N/A

1.89

2.06

1.90

14


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3.2 Nitrogen Absorption in Vanadium-Ruthenium Alloys 3.2.1 Geometry and Binding Energy of Nitrogen in V53Ru Alloy The optimized geometry of the V53Ru alloy was compared to the pure V supercell in Figure 5 (a). 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 a lattice constant of 3.00 Å, the lattice size including the Ru atom increased to 3.04 Å, whereas the size of the lattice without Ru slightly decreased to 2.99 Å, as shown in Figure 5 (a). The V lattice size far from the Ru atom remained similar to that of pure V.

Figure 5. Optimized geometries of (a)V53Ru and (b) V53Ru with nitrogen binding to an O-site Figure 5 (b) shows the case where a nitrogen atom was added to the optimized V53Ru supercell. The local geometry of the metal in this case was different from the case of nitrogen in pure V. The shortest distance between V and nitrogen in pure V supercell was 1.89 Å. On the other hand, in V53Ru, the V–N distance was shortened to 1.86 Å, while the Ru–N distance increased to 1.95 Å. Upon nitrogen absorption, the size of the V53Ru lattice increased by 25%, i.e., from 3.04 Å to 3.81 Å. It is noted that the strain caused by nitrogen in pure V54 was 26%. The lattice size perpendicular to the maximum strain was measured to be 2.89 Å, which corresponds to 3.6% of the lattice reduction due to the Poisson effect. For nitrogen binding in pure V54, the Poisson

15



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contraction was 4.0%. Thus, the mechanical stresses caused by nitrogen binding in pure V and that 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 of nitrogen in various sites in the alloy. Table 4 lists the binding energies of nitrogen and the distances of nitrogen to Ru before and after structure optimization. The same results were also plotted in Figure 6. The binding of nitrogen near Ru (< 3 Å) in the alloy appeared to be weaker than that in pure V. When the distance between Ru and N exceeded approximately 3 Å, the binding energy was not significantly affected by the presence of Ru. Note that the distance is nearly the size of a V lattice. If Ru is present in every other lattice, a nitrogen atom would not be affected by the presence of Ru. This simple approximation indicates that a Ru composition of at least 25 at.% in the V–Ru alloy 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 a result, the average binding energy of nitrogen in the alloys would become similar to that in pure V despite the Ru content. Since Ru is an expensive metal, the V–Ru alloy with a high Ru content of over 25 at.% may not be economically feasible. Also, alloys with a Ru content over 25 at.% are known to form a non-bcc structure,28 which may decrease nitrogen permeation through the alloys.

Table 4. Nitrogen binding energies in various O-sites in V53Ru Config. No. 10 11 12 13 14 15 16 17

Initial Ru–N (Å) 1.50 2.12 3.35 3.67 4.50 4.50 4.74 5.41

Optimized Ru–N (Å) 1.95 2.20 3.38 3.74 4.49 4.50 4.75 5.42

Binding energy (eV/atom) −1.64 −2.01 −2.60 −2.65 −2.70 −2.50 −2.71 −2.70

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Figure 6. Nitrogen binding energy in V53Ru alloy with respect to the distance of nitrogen to Ru. 3.2.2 Electronic Structure of Nitrogen in V53Ru Alloy The charge distribution trend between V and Ru can be explained by their electronegativity. According to Pauling’s scale on electronegativity, the values of V and Ru are 1.63 and 2.20, respectively, indicating that Ru pulls electrons from V. Figures 7 (a) and (b) show the Bader charge distribution in the V53Ru alloy with and without nitrogen, respectively. In V53Ru, Ru gained −1.55e in total from surrounding V atoms. The nearest neighbors donated −0.15e each, while the second-near neighbors donated −0.05e each. When nitrogen was bound in the O-site nearest to Ru, both Ru and nitrogen pull electrons from V. Since the electronegativity of nitrogen (3.04) is higher than that of Ru, slightly more negative charge was pulled toward nitrogen from Ru. Note that the values of the negative charge pulled to nitrogen were very similar in a different environment, as shown in Table 5: −1.61e in pure V, −1.51e in the vicinity of the Ru atom in V53Ru, and −1.61e in the case where the Ru atom was far away in the V53Ru alloy. On the other hand, the charge gain on Ru varied significantly by the presence of nitrogen. In the vicinity of nitrogen, Ru pulled much fewer electrons than in the absence of nitrogen. At a far distance from nitrogen, Ru pulled more electrons without competing with nitrogen.

While the attractive forces between nitrogen and V due to electrostatic interaction were similar to those in the pure V system, significant repulsion occurred between nitrogen and Ru, as they both were “negatively charged.” Although the magnitude of the charge gain on Ru was much smaller at a short Ru–N distance, the overall repulsion was affected more by the short distance between 17



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the point charges. As the distance between Ru and nitrogen became far, the repulsion barely affected the potential energy of the nitrogen-bound alloy, thereby maintaining the binding energy to the same level of that in pure V. Based on the binding energy and charge distribution in Configuration 12, the repulsive charge effect between Ru and N was determined to fade beyond 3 Å, as also shown in Figure 6.

The charge transfer between nitrogen and metals has also been reported in the literature. Due to the high electronegativity of nitrogen, charge transfer usually occurs from the metal to nitrogen. Compared to carbon, which has been studied more extensively, nitrogen involves more charge transfer, thereby a stronger electrostatic interaction with metals.

65

For interstitial carbon in Fe-

based metal alloys, the alloy component influenced the binding energy of carbon 1) via the large atomic size of the alloy, resulting in repulsive interactions and 2) via magnetic couplings among Fe, alloy and carbon, showing attractive interaction in limited alloys.66 In this study, however, nitrogen interaction with the alloy component through charge transfer well explains the trend in the binding energies rather than the geometric and magnetic coupling effect.

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

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Table 5. Bader charge on Ru and N in various nitrogen binding configurations in V53Ru alloy Config. Binding energy Bader charge Bader charge No. (eV/atom) on Ru (e) on N (e) 10 −1.64 −1.12 −1.51 11 −2.01 −1.15 −1.55 12 −2.60 −1.53 −1.61 17 −2.70 −1.53 −1.61 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 same region. This overlap occurred in a low-energy region of the d-band structure, indicating that the bonding interaction between Ru and V would likely exist. In addition to the overlap in the low-energy region, the PDOS of the V atom nearest to Ru showed a partial overlap at 1–2 eV. These high-energy states were potentially anti-bonding states, or conduction bands, and since these states were empty (as they were above the Fermi level), the bonding interaction was regarded as stable. Overall, the d-band center of V53Ru was slightly shifted by 0.03 eV to a lower energy level due to the presence of the low-energy states of Ru. Since Ru has its d-band at a much lower energy level than V, the local interaction for nitrogen binding would be more favored with V than Ru.

No. of states

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


8 7 6 5 4 3 2 1 0

Ru Pure V V, nearest V, 2nd near V, 3rd near

-7

-6

-5

-4

-3 -2 -1 E − EFermi (eV)

0

1

2

3

Figure 8. The PDOS analysis on Ru and V atoms in V53Ru alloy The PDOS trend indicating the V–Ru–N interaction varies with different binding sites in V53Ru. In Figure 9, the PDOS of nitrogen, Ru, and V in four different binding sites of V53Ru are shown. 19



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In the legend, “V, NN” and “V, NNN” represent the V atoms that are the nearest neighbor and the next nearest neighbor, respectively, to nitrogen. The peak(s) associated with nitrogen appeared between −7 and −5 eV. At a short Ru–N distance, e.g., 1.95 Å, (Figure 9 (a)), a sharp nitrogen peak showed a significant amount of overlap with the Ru and V peaks, indicating covalent character between nitrogen and the surrounding metal atoms. Also, the PDOS of Ru at a short distance to nitrogen was located at a lower energy level than those at a long distance to nitrogen. The d-band center of Ru in this case also showed a significant low-energy shift, as shown in Table 6. This lower-energy shift of the nitrogen-coupled Ru states implies that there would be a high chance of filling the Ru’s anti-bonding states compared to the unshifted bands; therefore, the binding of nitrogen in the presence of Ru may be weaker than that in the absence of Ru. The weakened binding energy of nitrogen near Ru may be partially attributed to this bandshift effect. At a slightly longer Ru–N distance, e.g., 2.20 Å (Figure 9 (b)), the overlapping regions of the PDOS between Ru and nitrogen were still present, and there might be a slight band-shift effect, which destabilized the nitrogen binding in this configuration. Beyond a Ru–N distance of 3 Å, the PDOS of Ru did not show a significant overlap with that of nitrogen (Figures 9 (c) and (d)); therefore, no substantial interaction between Ru and nitrogen was anticipated, as supported by the binding energy comparison.

Table 6. The d-band centers of Ru, VNN, VNNN in V53Ru in the presence of nitrogen Config. No. 10 11 12 17

Ru (eV)

VNN (eV)

VNNN (eV)

−2.18 −1.73 −1.70 −1.75

−0.64 −0.57 −0.60 −0.60

−0.27 −0.26 −0.28 −0.28

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

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3.2.3 Nitrogen Binding in V54-xRux (x = 2 – 6) Alloys To examine nitrogen binding within octahedral shells of varying Ru composition, octahedral V NN and NNN sites were systematically replaced with Ru to create 14 unique octahedral binding sites, with the total number of Ru atoms in NN and NNN positions ranging from 2 to 6 (see figure S1 for configurations). Due to the noted weakening of nitrogen binding proximal to Ru in the V53Ru structure, it was anticipated that increased Ru presence relative to nitrogen would serve to further destabilize interstitial binding. When compared to nitrogen binding in the V53Ru structure (–1.64 eV at an Ru–N separation of 1.95 Å), configurations with two Ru atoms in the octahedral shell surrounding nitrogen resulted in binding energies ranging from –1.24 to – 0.43 eV, where the greatest reduction in binding energy was observed for the configuration with two axially-oriented Ru atoms (Table 7). Interestingly, moving the two Ru atoms from axial to equatorial positions stabilized the nitrogen binding energy by ca. 0.80 eV. This is likely due to the greater proximity of Ru–N in the axial configuration (1.95 Å) when compared to the equatorial case (2.16 – 2.19 Å). Three unique configurations can be achieved with the substitution of three Ru atoms into NN and NNN positions, yielding nitrogen binding energies on the order of –0.58 to –0.03 eV. Here, as before, the weakest binding energy corresponds with the configuration where Ru occupies both axial positions. This case produces a result most similar to the benchmark 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 nitrogen binding in the full Ru octahedral shell (n = 6) was shown to be least stable of all configurations (+1.33 eV). The Ru–Ru distance (axial) of 3.88 Å is not sterically accommodating for interstitial nitrogen binding, and nitrogen is not likely to be observed in these higher at.% Ru configurations in the absence of extreme partial pressure N2. The Bader charge on nitrogen became less negative with increasing Ru substitution, owing to the stronger Pauling electronegativity value of Ru when compared to V. Generally, the nitrogen binding energy was strongly correlated to qN (r2 = 0.93). Thus, though Bader charge was shown to be ineffective at comparing relative O- and T-site binding, it may be viewed as a predictor of nitrogen binding strength in different O-sites.

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Table 7. Binding energy and Bader charge for nitrogen in octahedral shells of varying V/Ru composition. Nitrogen BE (eV) Bader Charge (e) System Ru:Va a 1:2 -1.10 -1.45 b 1:2 -1.18 -1.46 c 1:2 -1.24 -1.45 d 1:2 -0.43 -1.43 e 1:1 -0.49 -1.37 f 1:1 -0.58 -1.38 g 1:1 -0.03 -1.35 h 2:1 0.33 -1.22 i 2:1 0.11 -1.25 j 2:1 0.34 -1.21 k 2:1 0.41 -1.27 l 5:1 0.82 -1.19 m 5:1 0.82 -1.18 n 1.33 -1.08 ∞ a

Ratio of Ru atoms to V atoms in the 6-atom octahedral shell surrounding interstitially bound nitrogen.

3.3 Nitrogen Absorption in Vanadium-Molybdenum Alloys 3.3.1 Geometry Optimization of V-Mo Alloys The structures of six different binary alloy compositions of the Mo–V alloys, in addition to pure metals, were optimized, as shown in Figure 10. The lattice constants of the optimized structures are listed in Table 8. The calculated lattice constants agree well with the theoretically estimated values based on Vegard’s law. Note that these ideal alloy structures were created assuming that the Mo–V mixtures were close to equilibrium. In actual alloy structures, local disorder may exist due to dynamic equilibrium of the alloys.

In each of the optimized alloy structures, one nitrogen atom was introduced in the available Osite, and the entire structure was further optimized. All of the possible O-sites were tested in each alloy structure, considering the symmetry of the structure. After nitrogen introduction and optimization, one of the lattice axes was expanded by 3–7 %, along which the O-site expansion 23



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occurs. Exemplary results of the optimized nitrogen-binding structures in Mo15V are shown in Figure 11.

Figure 10. Mo–V alloys of various compositions (atomic ratio) tested in this study

Table 8. Optimized lattice constants of Mo, V, and various Mo–V alloys Composition Mo16 Mo15V1 Mo14V2 Mo13V3 Mo12V4 Mo8V8 Mo1V15 V16

Lattice constant (Å) calculated 3.169 3.158 3.148 3.136 3.124 3.072 3.002 2.998

Lattice constant (Å) Vegard’s law – 3.158 3.148 3.137 3.126 3.084 3.009 –

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

3.3.2 Binding Energy and Vibrational Frequency of Nitrogen in V-Mo Alloys The calculated binding energies of nitrogen in the various O-sites and the vibrational frequencies at the most stable binding sites are listed in Table 9. As the V content in the alloys increased, the nitrogen binding became stronger, which is clearly shown in Figure 12. The change in binding energy with varying alloy compositions implies that the binding energy can be tuned to give a proper level of solubility and diffusivity of nitrogen, thereby providing a high nitrogen permeability. It is noticeable that the BE of nitrogen in Mo12V4 (25 at.% V) is close to the value of hydrogen BE in Pd. Unlike the binding energy trend, the vibrational frequencies remain rather constant throughout the alloy compositions.

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Table 9. Binding energies and vibrational frequencies of nitrogen in the various O-sites of the Mo–V alloys Metal / Alloy Pure Mo Mo15V1

Mo14V2

Mo13V3

Mo12V4 Mo8V8 Mo1V15

Pure V

Label

O-site %

Binding Energy (eV)

O-site O1 O2 O3 O4 O5 O1 O2 O3 O1 O2 O3 O4 O1 O2 O1 O2 O1 O2 O3 O4 O5 O-site

100 12.5 25 25 25 12.5 25 50 25 37.5 25 25 12.5 50 50 50 50 12.5 25 25 25 12.5 100

0.835 0.004 0.744 0.787 0.842 0.845 −0.010 0.667 0.823 −0.041 0.61 0.551 0.822 −0.116 0.431 −1.423 −0.289 −2.485 −2.464 −2.448 −2.307 −1.638 −2.550

Vibrational Frequencies (cm-1) 831.4 791.1 – – – – 804.4 – – 806.9 – – – 817.2 – – 889.9 798 776.9

357.9 404.5 – – – – 399.2 – – 425.9 – – – 428.9 – – 382.7 491.8 428.9

357.7 404.5 – – – – 399.1 – – 425.9 – – – 428.8 – – 382.7 478.2 428.8

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Figure 12. Nitrogen binding energy as a function of V molar fraction in Mo–V alloys 3.4 Nitrogen Solubility in Metals Mo and Mo–V Alloys A related study was previously carried out by the authors on hydrogen solubility in a number of transition metals

62

and a different trend of hydrogen solubility with respect temperature was

found for the different investigated metals. 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 of the binding energy since the binding energy is equivalent to the enthalpy of dissolution or absorption. However, compared to hydrogen, the estimation of nitrogen solubility in metals using this same method may be limited mainly because of the two significant 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 differences ultimately lead to a high chance of a phase transition associated with 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 are formed after bond-breaking, they will be very unstable and highly reactive to metals. In addition, to break such a strong bond, high temperature is usually required. As a result, in the presence of atomic nitrogen at high temperature, metal nitride may become 27



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more stable than the strained metal with the large-sized interstitial nitrogen. Then, metal nitrides may start to grow, with nitrogen being stuck in the metal lattice structure, and with only little able to penetrate through the metal. This scenario likely happens in the case of metals with a strong affinity 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 phase transition will be less likely. In this case, the nitrogen solubility may be estimated by the same scheme used for hydrogen solubility in metals. However, the permeability of nitrogen through metals would be much lower compared to that of hydrogen because of the high energy barrier associated with nitrogen diffusion. The low permeability renders accurate experimental measurements to be much more difficult, as well as deteriorates the reliability of the experimental data. Therefore, theoretical methods to estimate nitrogen solubility, diffusivity, and permeability become greatly valuable in searching for potential membrane materials. This study focuses specifically on the nitrogen solubility estimation for less-reactive metals, in which dilute solid-solution assumption remains valid.

First, the solubility of nitrogen in pure Mo was estimated by combining the first-principles calculation results and the equations of thermodynamic equilibrium. Figure 13 shows the estimated solubility compared to the experimental solubility reported in the literature as a function of temperature (Figure 13a) and inverse temperature (Figure 13b).19,67 The solubility data were drawn on the log scale, as a function of temperature and inverse temperature. Since the binding energy was positive, the nitrogen absorption was endothermic, and, thus, the solubility increases with temperature increase.

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Figure 13. Calculated and experimental nitrogen solubility in log scale as a function of (a) temperature and (b) inverse temperature. Note that the absolute values of the slope of the linear plots in Figure 13 (b) represent the enthalpy of dissolution, ∆H. The solubility follows the Arrhenius equation as follows: =

!

ln = ln such that

is solubility,

!

∆&

∙ exp − ' ) (

!

∆& ,

− ' ) (

(Eq. 3) (Eq. 4)

is the maximum solubility given for infinite temperature, -. is

Boltzmann’s constant, and / is temperature in Kelvin. The calculated slopes are listed in Table 10. The enthalpy of dissolution derived from the calculated solubility showed a very similar value to those reported in the experimental literature,19,67 whereas the S0 values calculated showed a significant discrepancy from the literature.

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Table 10. Slope of the plots in Figure 14 (b) and calculated ∆H

EXP1 31 EXP2 32 Calculated

Slope −∆H/10000/kB −1.029 −0.9284 −1.031

Intercept ln S0 −2.978 −3.121 −8.157

R2

∆H [eV]

S0

1.0000 0.99992 0.99969

0.887 0.800 0.888

0.0509 0.0441 0.0003

To enhance the accuracy of the solubility estimation, the calculated solubility was corrected to match the experimental solubility by systematic adjustment of the two variables: binding energy and vibrational frequency. The sensitivity of the solubility estimation was analyzed upon changing the binding energy and vibrational frequency, as shown in Figure 14 (a) and (b), respectively. The decrease in binding energy led to the increase in solubility, and more importantly, both the slope and the magnitude of the plots changed in Figure 14 (b) when the binding energy was varied. On the other hand, when the vibrational frequency values were adjusted, the plots in Figure 14 (c) and (d) were shifted in parallel to each other, with the slope remaining constant. These observations provide a scheme for how to systematically correct the calculated solubility. Note that the calculated solubility showed nearly the same slope as that of experimentally reported solubility. Thus, the binding energy value was fixed, but the vibrational frequency was adjusted to match the experimental solubility. Another reason for correcting vibrational frequency but not the binding energy is because solid state phonon calculations were considered less accurate in general compared to the energy calculations. As demonstrated in Figure 14 (d), the vibrational frequency of 18% of the originally calculated frequencies provided the best match. Since no direct experimental results have been reported in the literature regarding nitrogen vibrational frequencies in Mo, it is unsure whether the corrected vibrational frequency is close to a real physical value.

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Figures 14. Solubility on the log scale as a function of temperature or inverse temperature with varying binding energies (in eV) and vibrational frequencies (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 of vibrational frequency. Using the correction factor of 18% on the vibrational frequencies, further solubility calculations were conducted for Mo–V alloys with high Mo content. As shown in Figure 15, the effect of a small concentration of V added to Mo was noticeable. The Mo–V alloy of 6.25 at.% vanadium showed the solubility 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 the same V content was more significant at lower temperature. In Mo–V alloys, the temperature dependence of the nitrogen solubility became much lower compared to that in pure Mo since the absolute value of the average binding energy in the alloys was close to zero. No experimental solubility values are currently available for comparison, but the estimating protocol was corroborated in pure metal systems with hydrogen and nitrogen. These theoretical predictions may guide the upper limit of nitrogen solubility in those alloys. 31



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Figure 15. Nitrogen solubility estimated in this study using first-principles calculation with vibrational frequency correction (scale factor of 18%) and thermodynamic equilibrium in dilute solid solutions. 4. CONCLUSIONS In 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 the O-site with the displacement of nearby metal atoms. Due to the displacement and the subsequent distortion of the lattice, the occupation of additional nitrogen was not favored in the nearby interstitial sites. Nitrogen binding in V was very strong with an approximate binding energy of −2.55 eV/atom, which was enhanced by the electrostatic and covalent interaction between nitrogen and surrounding metal atoms. Due to this strong binding, the formation of a dilute solid solution in V seemed unlikely, potentially leading to nitride formation. To improve nitrogen permeability in these metals, it was hypothesized that weaker binding may be favorable thereby leading to enhanced nitrogen diffusivity in the dilute solid solution. Thus, V-based alloys with weak binding energies including V–Ru and V–Mo were chosen for testing nitrogen binding characteristics. Reduced binding energies were observed in both alloys containing Ru or Mo, e.g., 32


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−1.64 eV/atom for both V53Ru and V15Mo alloys. In particular, Mo13V3 alloy showed a nitrogen BE of −0.041 eV, which is very similar to the BE of H in Pd. The nitrogen solubility in Mo was estimated by thermodynamic equilibrium assumption with systematic corrections to the calculated vibrational frequencies, showing agreement to the experimental solubility. Using the same correction scheme, the nitrogen solubility in V-Mo was estimated to be four orders of magnitude higher at 1000K for 25 at.% V alloy composition compared to pure Mo. This theoretical study has the potential to provide useful guidance to the discovery of promising materials for metallic membranes applied to ammonia synthesis.

SUPPORTING INFORMATION The effect of various relaxation modes and supercell size are provided in supporting information. In addition, the 14 unique configurations involving the O-site occupation of nitrogen in alloys of VRu are provided in Figure S1 of supporting information, as well as the details associated with the nitrogen solubility estimations. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Tel: (303) 273-3885. Fax: (303) 273-3730 ACKNOWLEDGMENTS We would like to acknowledge the Texas Advanced Computing Center (TACC), at the University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper: URL: http://www.tacc.utexas.edu. In addition, we acknowledge the Air Force Office of Scientific Research, Grant FA9550-16-1-0357 for supporting this work.

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Table of Contents Graphic

Charge accumulation in nitrogen upon occupation in the octahedral sites of vanadium.

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Theoretical Study of Nitrogen Absorption in Metals - ACS Publications

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