Redetermination of diammonium trivanadate, (NH4)2V3O8

The crystal structure of (NH4)2V3O8 has been redetermined using data collected at 0.61 Å resolution, showing that the ammonium cation is disordered by rotation around a non-crystallographic axis.

This mixed-valence oxide belongs to an isotypic series of A 2 V 3 O 8 compounds (A = K, Rb, Cs, NH 4 ; Yeon et al., 2013) adopting the crystal structure of fresnoite, a pyrosilicate mineral with formula Ba 2 TiSi 2 O 8 . Anions (V 3 O 8 ) 2form a layered structure extending parallel to (001), based on [V V O 4 ] and [V IV O 5 ] polyhedra sharing oxygen atoms, while NH 4 + 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 0.45Â0.30Â0.03 mm 3 . The refinement seems to be of very good quality. However, the authors mention that H-atom positions for the cation NH 4 + 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 (NH 4 ) 2 V 3 O 8 , using a very small plate-shaped crystal with dimensions 0.04Â0.03Â0.004 mm 3 , 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 (NH 4 ) 2 V 3 O 8 (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.
We identified that the NH 4 + 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 NH 4 + 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 Å 2 , while U iso (H1) ' 0.05 Å 2 . 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) Figure 1 Crystal structure of (NH 4 ) 2 V 3 O 8 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 (V 3 O 8 ) 2layer normal to [001] is represented, and a single position for the disordered NH 4 + cation has been accentuated. Blue planes are the mirror m elements of space-group type P4bm. Table 1 Bond lengths (Å ) and angles ( ) in (NH 4 ) 2 V 3 O 8 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.  (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.
parameters in the range 0.051 (12) to 0.10 (4) Å 2 and N-H bond lengths between 0.78 (3) and 0.83 (3) Å . As a consequence, only one significant N-HÁ Á ÁO 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 (  Fig. 3). This makes a difference, for instance, with the structure of ammonium metavanadate, NH 4 VO 3 , for which the ammonium cation is ordered and which forms at least two strong hydrogen bonds with the vanadium oxide matrix (Pé rez-Benítez & Bernè s, 2018). The rather poor interaction of the ammonium cation with the (V 3 O 8 ) 2À layers in the crystal structure of (NH 4 ) 2 V 3 O 8 could be of interest for its application as a cathode material for supercapacitors, since the replacement of NH 4 + 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 Li 2 V 3 O 8 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+x V 3 O 8 show that these vanadates crystallize in the hewettite structural type, in space-group type P2 1 /m, as does Na 2 V 3 O 8 (Bachmann & Barnes, 1962). On the other hand, to the best of our knowledge, no studies have been made hitherto on the pseudo-binary system Li 2 V 3 O 8 -(NH 4 ) 2 V 3 O 8 .

Figure 3
Part of the crystal structure of (NH 4 ) 2 V 3 O 8 showing the N-HÁ Á ÁO hydrogen bonds. The NH 4 + 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-H1Á Á ÁO1 hydrogen bond is represented.

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 (R 1 = 0.0183, wR 2 = 0.0420). The difference map is plotted at the 0.18 e À Å À3 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 bond and missing H atoms. Positions for all H atoms in the final refinement (R 1 = 0.0163, wR 2 = 0.0296) are superimposed on the calculated difference map, showing the fit between the experimental data and the proposed model.

data reports Refinement
Crystal data, data collection and structure refinement details are summarized in Table 3. The five H atoms modelling the disordered NH 4 + 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 HÁ Á ÁH separations to (8/3) 1/2 Âd, 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).