Redetermination of di­ammonium trivanadate, (NH₄)₂V₃O₈

The crystal structure of (NH₄)₂V₃O₈ has been reported twice using single-crystal X-ray data [Theobald et al. (1984). J. Phys. Chem. Solids, 45, 581–587; Range et al. (1988). Z. Naturforsch. Teil B, 43, 309–317]. In both cases, the orientation of the ammonium cation in the asymmetric unit was poorly defined: in Theobald's study, the shape and dimensions were constrained for NH₄⁺, while in Range's study, H atoms were not included. In the present study, we collected a highly redundant data set for this ternary oxide, at 0.61 Å resolution, using Ag Kα radiation. These accurate data reveal that the NH₄⁺ cation is disordered by rotation around a non-crystallographic axis. The rotation axis coincides with one N—H bond lying in the mirror m symmetry element of space-group type P4bm, and the remaining H sites were modelled over two disordered positions, with equal occupancy. It therefore follows that the NH₄⁺ cations filling the space available in the (001) layered structure formed by (V₃O₈)^2– ions do not form strong N—H⋯O hydrogen bonds with the mixed-valent oxidovanadate(IV,V) anions. This feature could have consequences for the Li-ion inter­calation properties of this material, which is used as a cathode for supercapacitors.

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Structure description

Di­ammonium trivanadate, (NH₄)₂V₃O₈, is a well-studied mixed-valent ternary vanadium(IV,V) oxide, in particular for the building of cathodes for supercapacitors, including lithium-ion batteries. Of particular inter­est is its very high specific capacity, which could theoretically reach 442 mA h/g, with a Coulombic efficiency close to 100% (Xu et al., 2016). Moreover, it can be obtained cheaply and simply, for example by hydro­thermal reduction of NH₄VO₃ (Ren et al., 2007), by electroreduction of NH₄VO₃ (Andrukaitis et al., 1990), or by solid-state reaction between NH₄VO₃ and V₂O₃ at low pressure (Liu & Greedan, 1995).

This mixed-valence oxide belongs to an isotypic series of A₂V₃O₈ compounds (A = K, Rb, Cs, NH₄; Yeon et al., 2013) adopting the crystal structure of fresnoite, a pyrosilicate mineral with formula Ba₂TiSi₂O₈. Anions (V₃O₈)^2– form a layered structure extending parallel to (001), based on [V^VO₄] and [V^IVO₅] polyhedra sharing oxygen atoms, while NH₄⁺ cations are sandwiched by the anionic layers (The Materials Project, 2019). The crystal structure in space group P4bm has been determined at least twice by single-crystal X-ray diffraction. The first report (Theobald et al., 1984) is based on X-ray data collected on a PW-1100 diffractometer, up to 0.62 Å resolution, with a rather large crystal, with dimensions 0.45×0.30×0.03 mm³. The refinement seems to be of very good quality. However, the authors mention that H-atom positions for the cation NH₄⁺ retrieved from a difference map did not result in a satisfactory refinement, so the shape and dimensions were constrained for the cation. The second independent report (Range et al., 1988) is based on X-ray data at even higher resolution, measured on a CAD-4 diffractometer. However, H-atom positions were not included for this refinement. For both refinements, only one octant of the reciprocal space was collected [0 ≤ h ≤ h_max, 0 ≤ k ≤ k_max and 0 ≤ l ≤ l_max], a common practice in the 1980s. This, however, precludes an accurate correction of data for absorption and other crystal-shape-related effects. A third article published in 2007 mentioned a single-crystal X-ray study for (NH₄)₂V₃O₈, using a very small plate-shaped crystal with dimensions 0.04×0.03×0.004 mm³, collected on an IPDS diffractometer equipped with a rotating anode (Ren et al., 2007). Apparently, H atoms were included, but details about the structure were not provided in this article.

We have now redetermined the crystal structure of (NH₄)₂V₃O₈ (Fig. 1), after collecting a highly redundant data set at 295 K: redundancy was 33 for a resolution of 0.61 Å. The dimensions of the vanadium oxide layers are remarkably close to those determined by Theobald et al. (1984), apart for the axial bond lengths V1=O1 and V2=O4, which were overestimated by ca 0.02–0.06 Å (see comparison in Table 1). This difference could be a consequence of the wrong positions of some H atoms in Theobald's model.

Table 1
Bond lengths (Å) and angles (°) in (NH₄)₂V₃O₈ for vanadium sites determined in this work, compared to those reported in previous studies

Labelling scheme for atomic sites is that used in the present work.

Parameter	1984 study ^a	1988 study ^b	This work
Bond lengths (Å)
V1—O1	1.660 (5)	1.618	1.6353 (18)
V1—O2	1.793 (2)	1.803	1.7958 (9)
V1—O3 (×2)	1.709 (3)	1.720	1.7123 (12)
V2—O3 (×4)	1.962 (3)	1.972	1.9647 (12)
V2—O4	1.650 (8)	1.576	1.592 (3)
Bond angles (°)
O1—V1—O2	109.2 (3)	110.1	109.20 (10)
O1—V1—O3 (×2)	111.3 (3)	112.2	111.16 (6)
O3—V1—O2 (×2)	107.9 (3)	106.9	107.89 (7)
O3—V1—O3	109.2 (3)	108.1	109.42 (8)
O3—V2—O3 (×2)	146.1 (2)	143.9	145.99 (10)
O3—V2—O3 (×4)	85.1 (1)	84.5	85.09 (3)
O4—V2—O3 (×4)	107.0 (1)	108.0	107.01 (5)
Notes: (a) Theobald et al. (1984); (b) Range et al. (1988); parameters for this refinement were calculated from the published unit-cell parameters and atom coordinates.

Figure 1 Crystal structure of (NH4)2V3O8 viewed approximately down the c axis. The asymmetric unit is represented with displacement ellipsoids drawn at the 90% probability level, and other vanadate groups are drawn with a polyhedral representation. Only one (V3O8)^2– layer normal to [001] is represented, and a single position for the disordered NH4^+ cation has been accentuated. Blue planes are the mirror m elements of space-group type P4bm.

We identified that the NH₄⁺ cation is disordered by rotation around a non-crystallographic axis. The N atom lies in the mirror plane m of space group P4bm (Wyckoff position 4c), and after refining positions and displacement parameters for all non-H atoms, the highest positive residual electron density is found in the same plane and can be refined as an H atom (H1). The subsequent difference map suggests that the three missing H atoms are continuously disordered along a ring normal to the m plane (Fig. 2). The best model was eventually reached with the second ammonium H atom equally disordered over two 4c positions (H2A and H2B), and the last H atom placed in a general position (8d), also disordered over two sites, H3A and H3B, with occupancies of 0.5 (Fig. 2). Both NH₄⁺ parts were refined with soft restraints (see Refinement details). The correctness of the model is validated through the refinement of isotropic displacement parameters for all H atoms. Any ordered model for H2 and H3 converged towards too high U_iso parameters, in the range 0.12 to 0.18 Ų, while U_iso(H1) ≃ 0.05 Ų. Moreover, N—H bond lengths refined around 0.74 Å, whereas a bond length close to 0.80 Å is expected. In contrast, the proposed model has refined U_iso(H) parameters in the range 0.051 (12) to 0.10 (4) Ų and N—H bond lengths between 0.78 (3) and 0.83 (3) Å.

Figure 2 Difference electron-density map in the vicinity of the N-atom site calculated on the basis of a model including N1 and H1 atoms (R1 = 0.0183, wR2 = 0.0420). The difference map is plotted at the 0.18 e^− Å^−3 level with a resolution of 0.05 Å (Dolomanov et al., 2009). At this level, only positive residuals are observed (green wire), corresponding essentially to the N—H σ bond and missing H atoms. Positions for all H atoms in the final refinement (R1 = 0.0163, wR2 = 0.0296) are superimposed on the calculated difference map, showing the fit between the experimental data and the proposed model.

As a consequence, only one significant N—H⋯O hydrogen bond of medium strength is formed in the crystal structure, involving the N1—H1 bond, which is also the non-crystallographic rotation axis for the disordered cation (Table 2, first entry). All other N—H⋯O contacts are weaker, with H⋯O separations in the range 2.24 (3)–2.49 (3) Å (Table 2, entries 2–6; Fig. 3). This makes a difference, for instance, with the structure of ammonium metavanadate, NH₄VO₃, for which the ammonium cation is ordered and which forms at least two strong hydrogen bonds with the vanadium oxide matrix (Pérez-Benítez & Bernès, 2018). The rather poor inter­action of the ammonium cation with the (V₃O₈)²⁻ layers in the crystal structure of (NH₄)₂V₃O₈ could be of inter­est for its application as a cathode material for supercapacitors, since the replacement of NH₄⁺ cations by Li⁺ should be a process with a low free enthalpy, compared to that of other fresnoite-type vanadates. From the structural point of view, however, the matter is more complex: although no definitive data are available so far, it seems that Li₂V₃O₈ does not belong to the fresnoite structural type. Theoretical (Koval'chuk et al., 2002) and experimental (de Picciotto et al., 1993; Jouanneau et al., 2005) data for Li_1+xV₃O₈ show that these vanadates crystallize in the hewettite structural type, in space-group type P2₁/m, as does Na₂V₃O₈ (Bachmann & Barnes, 1962). On the other hand, to the best of our knowledge, no studies have been made hitherto on the pseudo-binary system Li₂V₃O₈–(NH₄)₂V₃O₈.

Table 2
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N1—H1⋯O1	0.78 (3)	2.07 (3)	2.842 (3)	168 (3)
N1—H2A⋯O3^i	0.81 (3)	2.41 (4)	2.980 (3)	129 (4)
N1—H3A⋯O1^ii	0.83 (3)	2.24 (3)	3.006 (2)	153 (4)
N1—H2B⋯O1^iii	0.81 (3)	2.37 (2)	3.006 (3)	136 (1)
N1—H3B⋯O3^iv	0.81 (3)	2.49 (3)	3.274 (3)	162 (4)
N1—H3B⋯O3^v	0.81 (3)	2.39 (4)	2.980 (3)	130 (4)
Symmetry codes: (i) x, y, z+1; (ii) -y+1, x+1, z; (iii) y, -x+1, z; (iv) ; (v) .

Figure 3 Part of the crystal structure of (NH4)2V3O8 showing the N—H⋯O hydrogen bonds. The NH4^+ cation is disordered over two positions, N1/H1/H2A/H3A (green) and N1/H1/H2B/H3B (orange). Hydrogen bonds are represented as dashed lines, with a label referring to entries in Table 2. The inset shows how the cations inter­act with the vanadium oxide matrix. Only the strongest N1—H1⋯O1 hydrogen bond is represented.

Synthesis and crystallization

Good-quality single crystals of (NH₄)₂V₃O₈ were obtained as a by product during the reaction between ammonium metavanadate (NH₄VO₃, 0.5 g, 4.27 mmol), and metformin hydro­chloride (HMetf⁺Cl⁻, 0.425 g, 2.56 mmol) in 75 ml of distilled water and 1 ml of acetic acid 5% v/v. Ammonium metavanadate and metformin hydro­chloride were dissolved in water by gently heating the mixture. Given that our main purpose was to synthesize deca­vanadate salts (HMetf)₆(V₁₀O₂₈)·n(H₂O), a small amount of acetic acid was added to the mixture, to achieve a pH of ca 6.5. In fact, under these conditions, a mixture of two different hydrates of the desired compound were obtained, (HMetf)₆(V₁₀O₂₈)·6(H₂O) (orange needles) and (HMetf)₆(V₁₀O₂₈)·4(H₂O) (orange plates). Other crystallized products were the double salt (NH₄)₂(H₂Metf)₂(V₁₀O₂₈)·10(H₂O) (orange needles), the unreacted colourless HMetf⁺Cl⁻, and a tiny amount of dark-blue single-crystals of (NH₄)₂V₃O₈, the structure of which is discussed here.

Refinement

Crystal data, data collection and structure refinement details are summarized in Table 3. The five H atoms modelling the disordered NH₄⁺ cation were refined with free coordinates and free isotropic displacement parameters. While H1 fully occupies its site, H2 and H3 are equally disordered over two sites, H2A/H2B and H3A/H3B, respectively. All N—H bond lengths were restrained to a common free variable d, with a standard deviation of 0.02 Å (5 restraints), and the tetra­hedral shape of each disordered part was upheld by restricting H⋯H separations to (8/3)^1/2×d, within a standard deviation of 0.03 Å (12 restraints). The free variable d converged to 0.81 (2) Å (Sheldrick, 2015b). The crystal was considered as a racemic twin, and the batch scale factor refined to x = 0.36 (4).

Table 3
Experimental details

Crystal data
Chemical formula	(NH4)2V3O8
Mr	316.90
Crystal system, space group	Tetragonal, P4bm
Temperature (K)	295
a, c (Å)	8.9062 (4), 5.5784 (3)
V (Å^3)	442.48 (5)
Z	2
Radiation type	Ag Kα, λ = 0.56083 Å
μ (mm^−1)	1.60
Crystal size (mm)	0.06 × 0.06 × 0.03
Data collection
Diffractometer	Stoe Stadivari
Absorption correction	Multi-scan (X-RED32; Stoe & Cie, 2019)
Tmin, Tmax	0.410, 1.000
No. of measured, independent and observed [I > 2σ(I)] reflections	26907, 1106, 930
Rint	0.061
(sin θ/λ)max (Å^−1)	0.823
Refinement
R[F^2 > 2σ(F^2)], wR(F^2), S	0.016, 0.030, 0.87
No. of reflections	1106
No. of parameters	57
No. of restraints	18
H-atom treatment	All H-atom parameters refined
Δρmax, Δρmin (e Å^−3)	0.44, −0.23
Absolute structure	Refined as an inversion twin.
Absolute structure parameter	0.36 (4)
Computer programs: X-AREA (Stoe & Cie, 2019), SHELXT2018 (Sheldrick, 2015a), SHELXL2018 (Sheldrick, 2015b), Mercury (Macrae et al., 2020) and publCIF (Westrip, 2010).

Structural data

Computing details

Data collection: X-AREA (Stoe & Cie, 2019); cell refinement: X-AREA (Stoe & Cie, 2019); data reduction: X-AREA (Stoe & Cie, 2019); program(s) used to solve structure: SHELXT2018 (Sheldrick, 2015a); program(s) used to refine structure: SHELXL2018 (Sheldrick, 2015b); molecular graphics: Mercury (Macrae et al., 2020); software used to prepare material for publication: publCIF (Westrip, 2010).

Diammonium trivanadate

Crystal data

(NH4)2V3O8	Dx = 2.379 Mg m^−3
Mr = 316.90	Ag Kα radiation, λ = 0.56083 Å
Tetragonal, P4bm	Cell parameters from 21170 reflections
a = 8.9062 (4) Å	θ = 2.9–32.5°
c = 5.5784 (3) Å	µ = 1.60 mm^−1
V = 442.48 (5) Å^3	T = 295 K
Z = 2	Prism, blue
F(000) = 310	0.06 × 0.06 × 0.03 mm

Data collection

Stoe Stadivari diffractometer	1106 independent reflections
Radiation source: Sealed X-ray tube, Axo Astix-f Microfocus source	930 reflections with I > 2σ(I)
Graded multilayer mirror monochromator	Rint = 0.061
Detector resolution: 5.81 pixels mm^-1	θmax = 27.5°, θmin = 2.6°
ω scans	h = −14→14
Absorption correction: multi-scan (X-RED32; Stoe & Cie, 2019)	k = −14→14
Tmin = 0.410, Tmax = 1.000	l = −9→9
26907 measured reflections

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.016	All H-atom parameters refined
wR(F^2) = 0.030	w = 1/[σ^2(Fo^2) + (0.0141P)^2] where P = (Fo^2 + 2Fc^2)/3
S = 0.87	(Δ/σ)max < 0.001
1106 reflections	Δρmax = 0.44 e Å^−3
57 parameters	Δρmin = −0.23 e Å^−3
18 restraints	Absolute structure: Refined as an inversion twin.
0 constraints	Absolute structure parameter: 0.36 (4)
Primary atom site location: dual

Special details

Refinement. Refined as a 2-component inversion twin.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
V1	0.13352 (2)	0.63352 (2)	0.29279 (12)	0.01254 (6)
V2	0.500000	0.500000	0.28825 (18)	0.01385 (9)
O1	0.13050 (15)	0.63050 (15)	0.5859 (3)	0.0251 (4)
O2	0.000000	0.500000	0.1799 (4)	0.0208 (5)
O3	0.30693 (14)	0.58500 (14)	0.1852 (3)	0.0237 (2)
O4	0.500000	0.500000	0.5737 (5)	0.0326 (6)
N1	0.33009 (19)	0.83009 (19)	0.8234 (6)	0.0309 (6)
H1	0.280 (2)	0.780 (2)	0.740 (5)	0.051 (12)*
H2A	0.317 (5)	0.817 (5)	0.965 (6)	0.10 (4)*	0.5
H3A	0.320 (3)	0.921 (3)	0.794 (9)	0.08 (2)*	0.5
H2B	0.385 (3)	0.885 (3)	0.749 (11)	0.06 (3)*	0.5
H3B	0.279 (4)	0.880 (4)	0.914 (6)	0.09 (2)*	0.5

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
V1	0.00932 (8)	0.00932 (8)	0.01900 (14)	−0.00001 (10)	0.00065 (19)	0.00065 (19)
V2	0.00970 (11)	0.00970 (11)	0.0222 (2)	0.000	0.000	0.000
O1	0.0275 (6)	0.0275 (6)	0.0202 (8)	−0.0048 (7)	−0.0022 (5)	−0.0022 (5)
O2	0.0208 (7)	0.0208 (7)	0.0208 (12)	−0.0085 (9)	0.000	0.000
O3	0.0126 (5)	0.0218 (6)	0.0365 (6)	0.0056 (5)	0.0016 (5)	0.0049 (5)
O4	0.0356 (10)	0.0356 (10)	0.0266 (15)	0.000	0.000	0.000
N1	0.0352 (8)	0.0352 (8)	0.0225 (17)	−0.0173 (9)	0.0000 (7)	0.0000 (7)

Geometric parameters (Å, º)

V1—O1	1.6353 (18)	V2—O4	1.592 (3)
V1—O2	1.7958 (9)	N1—H1	0.78 (3)
V1—O3	1.7123 (12)	N1—H2A	0.81 (3)
V1—O3^i	1.7123 (12)	N1—H3A	0.83 (3)
V2—O3	1.9647 (12)	N1—H3A^i	0.83 (3)
V2—O3^ii	1.9647 (12)	N1—H2B	0.81 (3)
V2—O3^iii	1.9647 (12)	N1—H3B	0.81 (3)
V2—O3^iv	1.9647 (12)	N1—H3B^i	0.81 (3)
O1—V1—O2	109.20 (10)	O4—V2—O3	107.01 (5)
O1—V1—O3	111.16 (6)	V1—O2—V1^v	138.94 (15)
O1—V1—O3^i	111.16 (6)	V1—O3—V2	141.64 (9)
O3—V1—O2	107.89 (7)	H1—N1—H2A	115 (5)
O3^i—V1—O2	107.89 (7)	H1—N1—H3A	112 (3)
O3—V1—O3^i	109.42 (8)	H2A—N1—H3A	109 (3)
O3^ii—V2—O3^iii	145.99 (10)	H1—N1—H3A^i	112 (3)
O3^ii—V2—O3^iv	85.09 (3)	H2A—N1—H3A^i	109 (3)
O3^iii—V2—O3^iv	85.09 (3)	H3A—N1—H3A^i	99 (4)
O3^ii—V2—O3	85.09 (3)	H1—N1—H2B	113 (5)
O3^iii—V2—O3	85.09 (3)	H1—N1—H3B	111 (3)
O3^iv—V2—O3	145.99 (10)	H2B—N1—H3B	109 (3)
O4—V2—O3^ii	107.01 (5)	H1—N1—H3B^i	111 (3)
O4—V2—O3^iii	107.01 (5)	H2B—N1—H3B^i	109 (3)
O4—V2—O3^iv	107.01 (5)	H3B—N1—H3B^i	103 (5)
O1—V1—O2—V1^v	0.000 (1)	O1—V1—O3—V2	11.34 (15)
O3—V1—O2—V1^v	120.94 (6)	O3^i—V1—O3—V2	134.50 (8)
O3^i—V1—O2—V1^v	−120.94 (6)	O2—V1—O3—V2	−108.36 (14)

Symmetry codes: (i) y−1/2, x+1/2, z; (ii) −y+1, x, z; (iii) y, −x+1, z; (iv) −x+1, −y+1, z; (v) −x, −y+1, z.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1···O1	0.78 (3)	2.07 (3)	2.842 (3)	168 (3)
N1—H2A···O3^vi	0.81 (3)	2.41 (4)	2.980 (3)	129 (4)
N1—H3A···O1^vii	0.83 (3)	2.24 (3)	3.006 (2)	153 (4)
N1—H2B···O1^iii	0.81 (3)	2.37 (2)	3.006 (3)	136 (1)
N1—H3B···O3^viii	0.81 (3)	2.49 (3)	3.274 (3)	162 (4)
N1—H3B···O3^ix	0.81 (3)	2.39 (4)	2.980 (3)	130 (4)

Symmetry codes: (iii) y, −x+1, z; (vi) x, y, z+1; (vii) −y+1, x+1, z; (viii) −x+1/2, y+1/2, z+1; (ix) y−1/2, x+1/2, z+1.