Joshua J.
Brown
^{a},
Youxiang
Shao
^{b},
Zhuofeng
Ke
^{b} and
Alister J.
Page
*^{a}
^{a}School of Environmental & Life Sciences, The University of Newcastle, Callaghan 2308, NSW, Australia. E-mail: alister.page@newcastle.edu.au
^{b}School of Materials Science & Engineering, PCFM Lab, Sun Yat-sen University, Guangzhou, 510275, P. R. China
First published on 22nd February 2021
Niobium perovskite oxynitrides are emerging as promising semiconductor materials for solar energy conversion processes, due to their physical properties and amenability to defect engineering. However, defect engineering in mixed-anion semiconductors such as perovskite oxynitrides is generally hindered by the absence of long-range order in the crystal lattice, a phenomenon known as anion-ordering. We demonstrate how anion ordering influences the stability and mobility of point defects in two exemplar perovskite oxynitrides, BaNbO_{2}N and LaNbON_{2}. Accurate first-principles calculations show that fully cis-anion orderings in BaNbO_{2}N are more stable than fully trans-anion orderings, whereas anion orderings with mixed dimensionality may be more prevalent in the lower-symmetry LaNbON_{2}. Anion ordering in LaNbON_{2} is also influenced by a pronounced A-site coordination sphere effect not observed in BaNbO_{2}N, whereby local La-(O,N)_{12} coordination environments give rise to alternating LaO and LaN layers in the bulk material. Anion order was predicted to effect the redistribution of electrons upon anion vacancy creation to the cation sublattice. Diffusion barriers for O^{2−} vacancies in trans-ordered BaNbO_{2}N were found to be lower than those for N^{3−} vacancies, suggesting that stabilising trans-ordered phases of BaNbO_{2}N will yield more effective retention of nitrogen content in this material. The reverse is the case for LaNbON_{2}, with N^{3−} vacancy defects exhibiting more facile diffusion than O^{2−} vacancy defects. We believe these insights will aid the emergent understanding of defect engineering in mixed-anion perovskite oxynitride semiconductors, and specifically help facilitate strategies for stabilising their nitrogen content.
However, niobium oxynitrides are known to be more prone to defect formation during their synthesis via nitridation, compared to other perovskite oxynitrides (e.g. tantalum oxynitrides). This is a feature, rather than a flaw. Structural defects, such as zero-dimensional defects (e.g. vacancy, interstitial and anti-site defects) and higher-dimensional defects (dislocations, grain boundaries, and volumetric defects) provide design parameters for modulating surface active sites, charge carrier mobilities, and band edge positions.^{7,8} Of these, zero-dimensional point defects have the strongest link to material non-stoichiometry.^{7} Niobium oxynitrides are therefore ideal candidates for defect engineering. For instance, the enhanced conductivity of BaNbO_{2}N compared to BaTaO_{2}N is suspected to arise from defect concentration in the former.^{9} Niobium oxynitrides also have larger absorption tails extending in the visible region of the spectrum, which is indicative of nitrogen vacancies and reduced B-site cations, compared to their tantalum counterparts.^{9}
However, engineering structural defects in perovskite oxynitride photocatalysts, such as AM(O,N)_{3} (M = Ti, Zr, Hf, Ta, Nb), in a controlled manner is complicated by the lack of long-range structural order in their crystal lattices. Such disorder is otherwise known as ‘anion ordering’; despite exhibiting local ordering of anions within individual MO_{6−x}N_{x} octahedra, long-range structural order is lost due to the similarity between the M^{n+}–O^{2−} and M^{n+}–N^{3−} orbital overlaps, and hence bond lengths. The slightly larger M^{n+}–N^{3−} bond length drives a predominantly cis-ordering in individual octahedra, giving rise to N^{3−}-M^{n+}–N^{3−} chains (or O^{2−}–M^{n+}–O^{2−} in the case of LaTaON_{2} and LaNbON_{2}).^{10} Anion ordering induces local distortions^{11} in the crystal structure, influencing the ferroelectricity,^{12,13} bandgap^{14,15} and effective charge carrier mobility of these materials.^{16–18}
Anion ordering in oxynitride perovskites can be categorised into by the regimes of cis- or trans-ordering as illustrated in Fig. 1, as well as by the dimensionality the ordering travels in i.e. 2D/3D for cis-ordering or 1D/2D for trans-ordering. Recent research has focused on characterising the relative stabilities of these different regimes. While cis-ordering is the more stable for d^{0} oxynitrides, both regimes are sensitive to stoichiometry, strain, and interfacial effects. For instance, synthetic conditions and A-site cation substitution can yield fully 2D or 3D trans-orderings.^{16–20} For instance, increased Sr^{2+} doping in CaTaO_{2}N induces partial trans-ordering, with cis-ordering becoming energetically prohibitive due to lattice strain.^{21} Similarly, Vonruti et al.^{22} have shown that >4% compressive strain stabilizes trans-ordering in bulk LaTiO_{2}N. Ninova et al.^{23} have predicted that, for LaTiO_{2}N, surface layers can favour trans-ordering due to the charge neutral stacking afforded by (LaN)-(TiO_{2}) layers.
However, the impact of anion ordering on anion vacancy defect formation and anion vacancy diffusion remains largely unexplored in perovskite oxynitride photocatalysts.
Understanding this relationship is the first step towards controlling their defect engineering for enhanced photocatalysis. Here we address this issue by demonstrating how the stability and mobility of O^{2−} and N^{3−} vacancy point defects are influenced by local anion ordering in two representative niobium perovskite oxynitrides, BaNbO_{2}N and LaNbON_{2}. Vacancy defect formation energies and migration barriers are investigated systematically as a function of both cis- and trans-ordering of N^{3−}-M^{n+}–N^{3−} (BaNbO_{2}N) and O^{2−}–M^{n+}–O^{2−} (LaNbON_{2}) chains using accurate first-principles calculations. Cis-anion orderings are in general more energetically favourable than trans-orderings in these materials. However, there are secondary ordering effects that arise from the stoichiometric distribution of anions in the A-site cation coordination sphere, most prevalent for LaNbON_{2}. We show below how both the stability and mobility of O^{2−} and N^{3−} vacancy defects are influenced by these two ordering effects.
The formation of a neutral oxygen vacancy in BaNbO_{2}N and LaNbON_{2} can be expressed in Kröger–Vink notation as,
(1) |
(2) |
The oxidation state of the M cations in the vicinity of the defect will be determined by the localization of the electron density, which may vary between and for a neutral oxygen vacancy, and and for a neutral nitrogen vacancy. As Nb is capable of exhibiting a range of oxidation states (+5 to −1), we reason that it will likely favour charged vacancies and reduced Nb cations in anion-deficient BaNbO_{2}N and LaNbON_{2}. To this end we investigate the effect of anion ordering effect on electron localization and Nb oxidation via a DDEC6 charge decomposition analysis.^{32–34}
For a neutral supercell, the anion vacancy formation energy, E_{f,vac}, can be obtained from the simplified expression:^{35}
(3) |
Fig. 3 N^{3−}Nb^{5+}–N^{3−} anion orderings in a 2 × 2 × 2 BaNbO_{2}N supercell (Ba^{2+} and O^{2−} atoms not shown for clarity). N^{3−} and Nb^{5+} are dark and light blue atoms, respectively. |
Fig. 4 also considers the relative stability of anion orderings in BaNbO_{2}N from the point of view of dimensionality, by highlighting which orderings are 2D and which are 3D. In general, cis-orderings are considered to be 2D, in that they consist predominantly of N^{3−}–Nb^{5+}–N^{3−} chains aligned parallel with each other. Introducing locally trans-ordered N^{3−}–Nb^{5+}–N^{3−} chains, either partially (Q configurations) or completely (T configurations) naturally increases the dimensionality of the ordering when ‘twists’ and ‘loops’ are present in the N^{3−}–Nb^{5+}–N^{3−} sublattice (see Fig. 3). Nevertheless, Fig. 4a shows that there is no clear relationship between dimensionality and stability here. For instance, the 2D fully cis-ordered structures are lowest in energy (e.g.C1, C2, C3) whereas the 2D half-trans-ordered structures (H1, H2, H3, H4) are less stable by up to ∼1.2 eV. Similarly, of the 3D orderings studied, the fully cis-C7, C10 and C11 and the quarter trans-Q1 and Q4 orderings have mostly very similar energies. Notably, the C10, Q1 and Q4 orderings are only ∼0.13 eV higher in energy than the most stable C1 configuration. On the other hand, the dimensionality of the ordering has a clear relationship with the degree of lattice anisotropy, measured here via the deviation of each lattice constant from its value for a pristine P_{mm} unit cell for each ordering (i.e. we define this value as the average of the a, b and c lattice constants in each case). Fig. 4b and c show that the 2D orderings considered here clearly induce greater anisotropy in the crystal lattice compared to 3D orderings, as anticipated. Indeed, lattice constant deviations correlate with the predominant alignment of N^{3−}–Nb^{5+}–N^{3−} chains in the 2 × 2 × 2 supercell. For instance, for the most stable C1 ordering, the N^{3−}–Nb^{5+}–N^{3−} chains are aligned along the a and c lattice vectors (Fig. 3). This alignment causes equivalent expansion in a and c of ∼0.03 Å, while the lattice is compressed in b approximately twofold, by ∼−0.07 Å (Fig. 4b). On the other hand, C7 yields an essentially isotropic P_{mm} structure, and Fig. 3 shows that alignment of the N^{3−}–Nb^{5+}–N^{3−} chains are balanced exactly in all three directions. These results suggest that inducing lattice strain in BaNbO_{2}N will yield selectivity over anion ordering which is in line with recent studies for other oxynitride perovskites.^{16,21,22} We return to a discussion of how these orderings influence thermokinetic parameters of vacancy defects below.
Beyond dimensionality, Fig. 4b and c show that these BaNbO_{2}N anion orderings fall into three distinct groups. The first of these comprise orderings that minimally distort the cubic symmetry of the ideal BaNbO_{2}N lattice, i.e. a ≈ b ≈ c. This isotropic group includes both high energy fully trans-orderings, as well as relatively stable C7 and Q2 orderings, and feature motifs in which N^{3−}–Nb^{5+}–N^{3−} chains form a closed loop within a 2 × 2 × 2 extension of the BaNbO_{2}N lattice. The second group consists of orderings that yield anisotropic compression/expansion in a single dimension (i.e. two lattice constants essentially equal but distinct from the third), such as C1, C2, C3, H1, H3, and H4. The third group are those orderings that yield complete anisotropy in the sense that all three BaNbO_{2}N lattice constants are unique (e.g.C3, C4Q3, Q4, Q5). In the second group, the C1, C2 & C3 orderings (the three most stable orderings overall) are compressed in one axis and expanded in the other two. Interestingly, the half trans-orderings in this group (H1, H3, H4) all show the opposite trend, i.e. compression along two axes, and expansion in the third. These results suggest that cis-orderings in perovskite oxynitrides may be stabilised generally via in-plane lattice expansion, while trans-ordering may be stabilised via in-plane lattice compression. Indeed, Oka et al.^{21} demonstrated the formation of a metastable trans-type anion orderings in CaTaO_{2}N via Sr^{2+} A-site doping, in which N^{3−} preferentially resided in axial sites in TaO_{4}N_{2} octahedra due to lattice strain induced by the A-site dopant. Similarly, Vonruti et al.^{22} predicted the stabilization of parallel trans-ordering of N^{3−} anions (akin to T2) in LaTiO_{2}N when in-plane compressive strains greater than 4% were applied to the lattice. While an exhaustive strain engineering study is beyond the scope of this work, results presented here indicate that intermediate partial trans-orderings potentially impede the stabilization of fully trans-orderings via compressive in-plane strain, and so are likely an important consideration in strain engineering of perovskite oxynitrides more generally.
Fig. 5b displays the relative energies of the different anion orderings for the 2 × 1 × 2 LaNbON_{2} cell. It is clear that cis-orderings are preferred over trans-orderings, consistent with results for BaNbO_{2}N presented in Fig. 4a. For LaNbON_{2} all trans-orderings considered here (LT1, LT2 & LT3) are >2 eV less stable than the most stable cis-ordering, LC9. The latter ordering features ‘zigzag’ O^{2−}–Nb^{5+}–O^{2−} chains running through the 2 × 1 × 2 supercell alternating between the (101) and (01) planes and perpendicular to the (011) and (01) directions. This zigzag motif is shared with the other stable anion orderings, LC1, LC2, and LC10, the only difference being the alignment of the motif within the crystal structure. For instance, in the LC10 ordering, the same zigzag O^{2−}–Nb^{5+}–O^{2−} chains are present in the 2 × 1 × 2 supercell as those observed in the LC9 ordering. However, they are perpendicular to the (110) and (10) lattice directions, and as a result are ∼0.2 eV higher in energy. Similarly, the LC1 and LC2 orderings also feature the zigzag O^{2−}–Nb^{5+}–O^{2−} chain motif, but perpendicular to the (101) and (01) lattice directions, respectively. Both orderings are only ∼0.15 eV less stable than the most favourable ordering, LC9. The other cis-orderings considered here consist of different structural motifs and are less stable than the zigzag motif. These include the LC3, LC4, LC5 and LC6 orderings, all of which consist of O^{2−}Nb^{5+}–O^{2−} chains that create a repeating square-tooth pattern in the 2 × 1 × 2 LaNbON_{2} supercell and are ∼0.3–0.6 eV less stable than LC9, and the ring-like LC7 and LC8 motifs, which are both ∼0.5 eV less stable than LC9.
Fig. 5b shows that the dimensionality of the ordering is also apparently unrelated to its stability. For instance, LC9 and LC10 are both 3D orderings, whereas all their cis-orderings of O^{2−}–Nb^{5+}–O^{2−} chains in LaNbON_{2} are 2D. This is different from what was found in Fig. 4 for BaNbO_{2}N, and suggests that controlling for 2D or 3D more ordering may not be possible in LaNbON_{2}. Though we note that 2D–3D ordering transition temperatures have been observed in the comparable structure LaTaON_{2}.^{20}
Further, comparison of Fig. 5b with equivalent results for BaNbO_{2}N (Fig. 3 and 4a), shows striking similarities between the relative stabilities of comparable O^{2−}–Nb^{5+}–O^{2−} orderings in LaNbON_{2} and N^{3−}–Nb^{5+}–N^{3−} orderings in BaNbO_{2}N. For instance, cis-orderings featuring zigzag chain motifs are the most stable in both materials, and fully trans-anion orderings are significantly higher in energy (by ∼1 eV). Further, the ring-like and loop-like motifs are also energetically similar in both cases. For instance, LC3, LC4, LC5 and LC6 in LaNbON_{2} and C4, C5 and C6 in BaNbO_{2}N both feature repeating square tooth O^{2−}–Nb^{5+}–O^{2−} and N^{3−}–Nb^{5+}–N^{3−} motifs and have comparable relative energies (∼0.3–0.4 eV). Similarly, the loop motifs in LC7 and LC8 for LaNbON_{2} and C8 and C9 in BaNbO_{2}N are structurally similar and ∼0.5–0.6 eV higher in energy than the most favourable ordering.
Nevertheless, the La^{3+} and Ba^{2+} A-site cations also drive secondary ordering effects that differ between BaNbO_{2}N and LaNbON_{2}. Comparing the La-(O,N)_{12} coordination spheres between different orderings for LaNbON_{2}, the lowest energy orderings (LC1–LC4 and LC9–10) all possess stoichiometric La-O_{4}N_{8} coordination spheres, whereas the LC5–LC8 orderings feature a mix of La-O_{6}N_{6} and La-O_{2}N_{10} coordination spheres. This mix creates alternating LaO and LaN layers between NbON^{3−} sheets aligned perpendicular to the b-axis in the 2 × 1 × 2 LaNbON_{2} supercell. There is a clear energetic difference between these two groups, with LC5–LC8 being ∼0.3 eV higher on average than LC1–LC4 and LC9–10. This A-site effect is notably absent in the BaNbO_{2}N orderings, shown in Fig. 4. While the most stable zigzag orderings in BaNbO_{2}N do indeed create an even distribution of Ba-O_{8}N_{4} coordination spheres, other orderings like C6 & C8 have energies 0.15–0.30 eV higher than orderings with comparable Ba-(O,N)_{12} coordination sphere distributions. Thus, the N^{3−}–Nb^{5+}–N^{3−} chain ordering in the more densely packed BaNbO_{2}N supercell effectively masks the effect of the Ba-(O,N)_{12} coordination sphere on the stability of the material.
Fig. 6 (a and b) Depiction of the 12 unique anion positions in the centroid of the (a) 2 × 2 × 2 BaNbO_{2}N and (b) 2 × 1 × 2 LaNbON_{2} supercells. Light and dark blue spheres as in Fig. 3, red, green and yellow spheres represent oxygen, barium and lanthanum atoms respectively. (c and d) PBEsol vacancy formation energies V_{N} and V_{O} in positions 1–12 as a function of anion ordering for the (c) 2 × 2 × 2 BaNbO_{2}N and (d) 2 × 1 × 2 LaNbON_{2} supercells; red indicates an O^{2−} vacancy defect and blue indicates an N^{3−} vacancy defect at that position. The colour depth indicates the magnitude of the formation energies V_{N} and V_{O} (blue and red, respectively) in eV, as indicated by the scale bar. |
The E_{f,Vo} formation energies vary quite significantly across the fully cis- (4.87–6.08 eV) and partial trans- (4.87–5.98 eV) orderings, compared to fully trans- (5.37–5.60 eV). This indicating that neutral oxygen vacancy formation energies are more sensitive to N^{3−}–Nb^{5+}–N^{3−} chain disorder, whereas nitrogen vacancy formation energies depend simply on whether the site is in a cis- or trans-chain. N^{3−} anions in trans-N^{3−}–Nb^{5+}–N^{3−} chains, whether they be partially or fully trans-, have a reduced E_{f,VN} formation energy.
The question as to whether anion vacancies have the potential to affect local anion order in BaNbO_{2}N is considered in Fig. S1 (ESI†), which shows the relative energies of these anion orderings in the presence of V_{O} and V_{N} defects. Compared to the defect-free relative energies in Fig. 4a, it can be seen in Fig. S1a (ESI†) that in several cases anion vacancies likely influence the anion ordering. For instance, the quarter-trans orderings (Q1–5) become energetically indistinguishable from the cis (C1-11) orderings in the presence of a neutral oxygen vacancy defect. Additionally, the relative orderings in the presence of a neutral nitrogen vacancy defect (Fig. S1b, ESI†) are significantly different from the defect-free orderings. While the cisC1-11 orderings are effectively equivalent in energy with and without a V_{N} defect, the Q1–5 orderings are lowered by ∼0.5 eV, as the defect disrupts an N^{3−}–Nb^{5+}–N^{3−} chain, thus making them the most favourable ordering.
Finally, we consider whether or not V_{O} and V_{N} defects in LaNbON_{2} have the potential to influence the relative stabilities of these anion orderings. Fig. S2 (ESI†) shows the relative energies of the anion orderings in the defective LaNbON_{2} structures. Compared to the defect-free relative energies in Fig. 5a and Fig. S2a (ESI†) the presence of V_{O} does not appreciably influence the relative stability of many of the orderings. However, the LC5–9 orderings become the most stable orderings, as they can be lowered by up to ∼0.2 eV. Fig. S2b (ESI†) shows that, by comparison, V_{N} defects are much more influential on the stabilities of these anion orderings, with all LC orderings being lowered by up to ∼0.5 eV. Nevertheless, the relative stabilities for all LC orderings become virtually indistinguishable in the presence of a V_{N} defect.
BaNbO_{2}N | LaNbON_{2} | ||||||||
---|---|---|---|---|---|---|---|---|---|
C1 | T2 | LC9 | LT2 | ||||||
V_{O} | V_{N} | V_{O} | V_{N} | V_{O} | V_{N} | V_{O} | V_{N} | ||
Partial Charge | Adjacent Nb | 1.89 | 1.73 | 1.93 | 1.84 | 1.78 | 1.64 | 1.64 | 1.89 |
Other Nb | 2.21 | 2.20 | 2.20 | 2.17 | 2.08 | 2.08 | 2.09 | 2.08 | |
Charge Redistribution | Ba/La | −0.25 | −0.30 | −0.28 | −0.32 | −0.27 | −0.35 | −0.46 | −0.34 |
Nb | −1.26 | −1.65 | −1.15 | −1.47 | −0.79 | −1.11 | −1.71 | −1.36 | |
Total | −1.51 | −1.95 | −1.43 | −1.79 | −1.06 | −1.46 | −2.17 | −1.70 |
For BaNbO_{2}N, Table 1 shows that charge redistribution, due to delocalisation of the electron density around the defect site, leads to the ‘true’ charge of and defects being only 65–75% of the expected formal values. For instance, for the C1 ordering the total charge redistribution in the BaNbO_{2}N lattice around a V_{O} defect is −1.51 e (rather than exactly −2), while for a V_{N} defect this figure is −1.95 e (rather than exactly −3 e). Charge redistribution is slightly smaller for the T2 ordering (1.43 and 1.79 e, respectively), indicating that anion vacancies near trans-N^{3−}–Nb^{5+}–N^{3−} anion configurations in BaNbO_{2}N lead to less charge redistribution away from the vacancy site in the cation sublattice. Table 1 also shows that, following the formation of a neutral oxygen or nitrogen vacancy defect in BaNbO_{2}N, the oxidation state of a Nb cation depends on its vicinity to the defect. For instance, the average partial charge of adjacent Nb cations is ∼0.5 e lower than those not coordinated to the vacancy. This is true for both the C1 and T2 anion orderings, although the effect is again marginally smaller for the latter (∼0.3 e), likely for the same reason noted above.
Very similar trends are observed in Table 1 regarding partial charges of adjacent and uncoordinated Nb cations in LaNbON_{2}. For instance, for the lowest energy LC9 ordering, Nb cations adjacent to a V_{O} defect are more reduced by ∼0.3 e, compared to Nb cations further away. Similarly, for a V_{N} defect, the difference is ∼0.4 e (adjacent Nb cations being more reduced). Nb partial charges in the LT2 ordering are analogous by comparison. As for BaNbO_{2}N, Table 1 shows that the DDEC6 charges obtained using PBEsol are notably lower than the expected formal values. For instance, in the LC9 ordering, the LaNbON_{2} lattice is reduced by only 1.06 e (V_{O}) and 1.46 e (V_{N}), respectively. However, a marked increase in charge distribution is observed for an oxygen vacancy defect in the LT2 ordering. Here, the LaNbON_{2} lattice is reduced by 2.17 e, which is comparable to the expected formal charge (i.e. −2). This is attributed to the effect of the ordering itself. While the pristine LT2 and LC9 structures exhibit essentially equivalent average Nb partial charges (2.14 compared to 2.10, not shown in Table 1), the introduction of the V_{O} defect disrupts a trans-O^{2−}–Nb^{5+}–O^{2−} chain in the LT2 structure, but leaves the chain in the cisLC9 ordering unperturbed. This reduces the Nb sublattice by ∼1 e (−1.71 e) more in LT2, compared to LC9 ordering (−1.06 e).
Fig. 7 V_{N} & V_{O} diffusion pathways and associated PBEsol diffusion barriers (eV) for the most stable cis- and trans-anion orderings in (a and b) BaNbO_{2}N and (c and d) LaNbON_{2}. (a) BaNbO_{2}N, C1 ordering, (b) BaNbO_{2}N, T2 ordering, (c) LaNbON_{2}, LC9 ordering, (d) LaNbON_{2}, LT1 ordering. All diffusion pathways were calculated in the complete 3 × 3 × 3 and 2 × 1 × 2 supercells, respectively, however only the core region is depicted here for clarity. Anion positions are defined in Fig. 5a and b for BaNbO_{2}N and LaNbON_{2}, respectively. |
Consistent with BaNbO_{2}N, the diffusion barriers are seen to be sensitive to whether the diffusion path is between adjacent anion positions or non-adjacent positions with O10 → O12 in LC9 predicted to have a barrier height of 0.71 eV, while O6 → O7 in LT2 is 3.12 eV. However, the difference in the diffusion barriers for adjacent and non-adjacent paths is greatly reduced compared to BaNbO_{2}N. In LC9 the adjacent pathway height is 1.56 eV with the non-adjacent path barrier only 0.29 eV higher, while in LT2 the adjacent diffusion is now 0.72, with the non-adjacent barrier merely 0.82 eV. Interestingly, the kinetic stability of N^{3−} vacancy defects in LaNbON_{2} is significantly reduced from that observed in BaNbO_{2}N. In particular, in the less stable LT1trans-ordering, N^{3−} vacancies diffuse more easily than O^{2−} vacancies. The origin of this reduction is a cooperative effect in which the migrating vacancy partially displaces an adjacent O^{2−} anion. The additional space created by this displacement gives rise to an asymmetric path, in which the vacancy does not pass directly between adjacent La^{3+} cations along the diffusion pathway. In doing so, the migrating vacancy partially displaces an adjacent O^{2−} anion and so reduces the diffusion barrier.
For BaNbO_{2}N, our results show clearly that fully cis-anion orderings are more stable than fully trans-anion orderings. The influence of these orderings on the cubic lattice vectors however demonstrates differing degrees of anisotropy. This ultimately has implications for strain engineering in this oxynitride; specifically, it may be difficult to stabilize the fully trans-orderings in BaNbO_{2}N, over half-trans or fully-cis orderings, via in-plane compression of the crystal lattice. In LaNbON_{2}, 2D & 3D orderings have comparable energies, meaning that mixed dimensionality in anion ordering may be more prevalent in this material. However, our results show the presence of a secondary ‘A-site coordination sphere effect’ influencing the stability of different orderings in LaNbON_{2}, where the stoichiometric distribution of O^{2−} and N^{3−} in La-(O,N)_{12} gives rise to obvious differences in the relative energies of different fully cis-anion orderings. This effect is less obvious in BaNbO_{2}N, which we contend is due to the more densely packed lattice having a higher degree of symmetry, which masks any Ba-(O,N)_{12} coordination sphere on the overall stability of the material. Vacancy defect formation energies for BaNbO_{2}N indicate that domains rich in cis-anion orderings (the most favourable) may preferentially stabilise O^{2−} anion vacancies less uniformly in their structure, whereas N^{3−} anion vacancies are less likely. On the other hand, O^{2−} defect formation energies in LaNbON_{2} are more sensitive to the local anion ordering, than its overall cis- or trans-character. This is attributed to the effect of the La^{3+} A-site cation, which for particular orderings considered here gives rise to alternating layers of LaO and LaN that reduce significantly O^{2−} vacancy defect formation energy.
For BaNbO_{2}N, diffusion barriers were found to be lower than , most notably in trans-ordered phases. It is predicted that this will impede control over long range ordering in BaNbO_{2}N. Stabilising trans-ordered phases of this material is thus predicted to yield more effective retention of nitrogen content in its structure, irrespective of long-range anion order. In this sense, BaNbO_{2}N bears some resemblance to TaON, for which migration barriers are potentially low enough to displace nitrogen content from the oxynitride.^{40} The reverse is observed true for in LaNbON_{2}, i.e. N^{3−} vacancy defects exhibit lower diffusion barriers than O^{2−} vacancy defects. V_{N} diffusion via both adjacent and non-adjacent pathways in LaNbON_{2} benefits from the lower orthorhombic symmetry. In part this is due to the disruption the migrating N^{3−} defect has on the local coordination environment; when rotating around a local La^{3+} cation the N^{3−} anion vacancy partially displaces an adjacent O^{2−} ion to lower the diffusion barrier.
Footnote |
† Electronic supplementary information (ESI) available: Relative energies of LaNbO_{2}N, BaNbON_{2} anion orderings in the presence of vacancy defects, comparison of vacancy diffusion barrier heights as a function of supercell size. See DOI: 10.1039/d1ma00122a |
This journal is © The Royal Society of Chemistry 2021 |