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The order/disorder phase transition of hypophosphorous acid H3PO2

  • Martin Nastran and Berthold Stöger EMAIL logo
Published/Copyright: June 24, 2021
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Zeitschrift für Kristallographie - Crystalline Materials
From the journal Zeitschrift für Kristallographie - Crystalline Materials Volume 236 Issue 5-7

Abstract

Hypophosphorous acid, H3PO2 is dimorphic with a phase transition in the 200–225 K range. The H3PO2 molecules are connected by hydrogen bonding to infinite chains extending in the [100] direction. In the high-temperature phase (P21212, Z′=12), the hydrogen bonds are disordered about a two-fold rotation axis. On cooling below the phase transition temperature, the hydrogen bonds become ordered, resulting in a symmetry reduction of the klassengleiche type of index 2. In the low-temperature phase (P212121, Z′=1), the c parameter is doubled with respect to the high-temperature phase. The hydrogen-bonding topology of the high- and low-temperature phases are double-infinite directed and undirected linear graphs, respectively.

Keywords: hydrogen bond; order/disorder phase transition; single crystal diffraction; topology

1 Introduction

Solids with O–H⋯O hydrogen bonds involving acidic OH groups often undergo order/disorder solid-state phase transitions, where the hydrogen bond is disordered at high temperatures while ordered at low temperatures. Arguably, the most well studied example of these transitions is the potassium dihydrogen phosphate (KDP) family of compounds, which are paraelectric above and ferroelectric below the phase transition temperature [1].

These order/disorder phase transitions can lead to complex crystallographic behavior. For example, we have recently described such a phase transition leading to threefold twinning [2]. In other cases, the ordered phases are incommensurately modulated [3].

In contrast, in this communication we report on the phase transition of hypophosphorous acid H3PO2, which we required as a precursor to fluorinated P(I) compounds. The structure comprises of only Z′=1/2 acid molecules in the high-temperature (HT) and Z′=1 molecules in the low-temperature (LT) phase. Thus, this is a particularly simple example of an order-disorder phase transition. The phase transition will be discussed with special attention paid to symmetry relationships and the topology of the hydrogen bonding.

The HT structure of H3PO2 has previously been derived using X-ray and neutron diffraction methods [4], though doubts about the nature of the disordered hydrogen bonds remained. The LT phase has not yet been described.

Besides its crystal-chemical interest, H3PO2 in combination with catalytic amounts of I2 is a reagent for the reduction of benzylic ketones and alcohols to alkanes under mild conditions [5, 6].

2 Experimental

2.1 Crystal growth

Commercial ca. 50 wt. % aqueous H3PO2 solution was held under vacuum (10−4 mbar) in a round bottom flask using a rotary vane vacuum pump for three days at 278 K and protected from light. The colorless crystals were stored at 260 K. At room temperature, the anhydrous acid darkens readily.

2.2 Data collection and refinement

The cooled, deliquescent crystals were immersed in perfluorinated oil and selected under a polarizing microscope. To prevent melting, the work space was cooled by vapors of boiling N2. Crystals were attached to Kapton micro mounts and quickly transferred to the single crystal diffractometer.

Intensity data was collected on a Bruker KAPPA APEX II diffractometer system in a dry stream of nitrogen using graphite monochromatized MoKα radiation using fine sliced ω- and ϕ-scans. Eight data sets of the same crystal were collected in succession in the 100–290 K range with the same measurement strategy.

The structures were solved with the dual space methods implemented in Shelxt [7] and refined against F2 using Shelxl [8]. Non-H atoms were refined with anisotropic displacement parameters. Hydrogen atoms were located from difference Fourier maps. The O–H distances were restrained to 0.90 (2) Å, whereas the H atoms attached to P were refined freely.

More data collection and structure refinement details are collected in Tables 1 and 2. Model data are deposited in the CIF format at the CCDC and can be retrieved using the deposition numbers listed at the bottom of the tables. Note that the crystal moved during the data collection at 250 K, which resulted in an increase of the standard uncertainty on the cell parameters by an order of magnitude. The data set is nevertheless included for the sake of completeness.

Table 1:

Data collection and structure refinement details of the 100–200 K measurements of H3PO2.

100 K150 K175 K200 K
Crystal data
a, b, c (Å)4.5149 (7), 6.7238 (10), 7.8515 (12)4.5111 (6), 6.7460 (9), 7.8778 (10)4.5109 (9), 6.7635 (14), 7.8956 (16)4.5119 (4), 6.7798 (6), 7.9158 (7)
V (Å3)238.35 (6)239.74 (5)240.89 (8)242.14 (4)
μ (mm−1)0.800.800.790.79
Data collection
Tmin, Tmax0.424, 0.5010.407, 0.5010.393, 0.5010.368, 0.501
No. of measured, independent and observed [I>2σ (I)] reflections3093, 1507, 12613086, 1498, 11693098, 1506, 10923097, 1504, 968
Rint0.0180.0180.0190.020
Refinement
(sin θ/λ)max (Å−1)0.9130.9080.9080.908
R[F2>2σ (F2)], wR(F2)
 All reflections0.025, 0.0610.026, 0.0670.030, 0.0740.033, 0.078
 l even0.018, 0.0480.019, 0.0520.022, 0.0590.024, 0.059
 l odd0.074, 0.1400.087, 0.1510.113, 0.1830.187, 0.302
S1.051.041.061.03
No. of reflections1507149815061504
Δρmax, Δρmin (e Å−3)0.39, −0.480.37, −0.550.40, −0.370.36, −0.52
Flack parameter0.14 (19)−0.1 (2)−0.1 (2)0.1 (3)
CCDC number2060992206099320609942060995

  1. Mr: 65.99; orthorhombic P212121; Z = 4; Mo Kα‾ radiation; crystal size 0.30 × 0.24 × 0.22 mm3; 41 parameters; 3 restraints.

Table 2:

Data collection and structure refinement details of the 225–290 K measurements of H3PO2.

Temperature (K)225 K250 K275 K290 K
Crystal data
a, b, c (Å)4.5123 (5), 6.8004 (7), 3.9685 (4)4.507 (4), 6.832 (6), 3.985 (4)4.5156 (5), 6.8432 (8), 3.9969 (4)4.5133 (8), 6.8475 (11), 4.0008 (7)
V (Å3)121.78 (2)122.71 (19)123.51 (2)123.64 (4)
μ (mm−1)0.780.780.770.77
Data collection
Tmin, Tmax0.328, 0.5010.353, 0.5010.354, 0.5010.393, 0.501
No. of measured, independent and observed [I>2σ(I)] reflections1536, 761, 6981297, 742, 6511548, 770, 6891556, 772, 674
Rint0.0150.0170.0140.016
Refinement
(sinθ/λ)max (Å−1)0.9090.9080.9080.908
R[F2>2σ(F2)], wR(F2), S0.024, 0.055, 1.110.027, 0.056, 1.090.025, 0.057, 1.080.028, 0.062, 1.12
No. of reflections761742770772
Δρmax, Δρmin (e Å−3)0.39, −0.480.37, −0.550.40, −0.370.36, −0.52
Flack parameter0.2 (3)0.2 (3)−0.1 (3)0.0 (3)
CCDC number2060996206099720609982060999

  1. Mr: 65.99; orthorhombic P21212; Z = 2; Mo Kα‾ radiation; crystal size 0.30 × 0.24 × 0.22 mm3; 24 parameters; 3 restraints.

Difference Fourier maps were plotted using the PLATON software suite [9].

3 Results and discussion

3.1 General remarks on the crystal-chemistry of H3PO2

In the solid state, H3PO2 exists as the tetrahedral HOP(O)H2 tautomer, where two H atoms are connected to P and the third H atom to O. Only the latter is acidic, whereas the atoms attached to P are hydridic and do not partake in hydrogen-bonding. The minor trigonal pyramidal HP(OH)2 tautomer exists for example in water or methanol solution according to the scheme.

It can be evidenced by the ready exchange of the hydridic Hs by D [10].

The P–H distances refined to ca. 1.28 Å (Table 3), which is by 0.07 Å (5%) shorter than the P–H distance in the H2PO2− (1.35 Å) ion as determined using neutron diffraction [11].

Table 3:

Refined P–H distances in H3PO2.

T (K)d (P–H) (Å)
1001.250 (15), 1.277 (16)
1501.275 (15), 1.276 (15)
1751.276 (16), 1.283 (17)
2001.274 (19), 1.279 (19)
2252 × 1.273 (16)
2502 × 1.27 (2)
2752 × 1.281 (18)
2902 × 1.285 (17)

3.2 Diffraction pattern

Before discussing the structure of H3PO2, let us analyze the diffraction patterns. Crystals of the HT phase can be indexed with an orthorhombic lattice and the systematic absences suggest the P21212 symmetry. On cooling, additional reflections appear at half-integer l values, which corresponds to a loss of translation symmetry, in particular to a doubling of the length of the c axis (Figure 1). These additional reflections are called superstructure reflections, in contrast to the main reflections, which are also produced by the HT phase.

Figure 1: (h0l)*${\left(h0l\right)}^{\text{{\ast}}}$ plane of reciprocal space of H3PO2 reconstructed from CCD data collected at 100, 200, 225 and 290 K.
Figure 1:

(h0l)* plane of reciprocal space of H3PO2 reconstructed from CCD data collected at 100, 200, 225 and 290 K.

The superstructure reflections are clearly observed at 200 K and absent at 225 K. Thus, the phase transition happens between these two temperatures.

The intensities of the superstrare generally weak and easily overlooked. This indicates rather subtle structural changes during the phase transition. With decreasing temperature, the relative intensity of the superstructure reflections increases, as seen in the Wilson plot in Figure 2(a). Accordingly, reliable intensity data of the superstructure reflections are available only for low-angle reflections (Figure 2(b)). As expected log (I) shows a nearly linear decrease with |s|2, owing to the atomic form factors and the thermal vibration. With increasing temperature and thus more thermal vibration, the slope becomes steeper. Interestingly, the effect is less pronounced for the superstructure reflections. This in turn means that the ratio Isuper:Ibasic increases with diffraction angle as shown in Figure 3(b). At low scattering angles, the superstructure reflections are weaker by more than two orders of magnitude; At higher scattering angles only by a factor of ca. 30.

Figure 2: Plots of (a) log (I/Imax)$\text{log\,}\left(I/{I}_{\text{max}}\right)$ and (b) I/σ(I)$I/\sigma \left(I\right)$ against |s|2=(2 sin θ/λ)2${\vert \mathbf{s}\vert }^{2}={\left(2\mathrm{\,sin\,}\theta /\lambda \right)}^{2}$ for the reflection classes l = 2n (main) and l = 2n + 1 (super), n∈ℤ$n\in \mathrm{ℤ}$ in the LT measurements of H3PO2. Intensity data were averaged in 0.4 Å−2 bins.
Figure 2:

Plots of (a) log (I/Imax) and (b) I/σ(I) against |s|2=(2 sin θ/λ)2 for the reflection classes l = 2n (main) and l = 2n + 1 (super), n∈ℤ in the LT measurements of H3PO2. Intensity data were averaged in 0.4 Å−2 bins.

Figure 3: Plot of the logarithm of the ratio of the superstructure and main reflection intensities against |s|2=(2 sin θ/λ)2${\vert \mathbf{s}\vert }^{2}={\left(2\mathrm{\,sin\,}\theta /\lambda \right)}^{2}$. Intensity data were averaged in 0.4 Å−2 bins.
Figure 3:

Plot of the logarithm of the ratio of the superstructure and main reflection intensities against |s|2=(2 sin θ/λ)2. Intensity data were averaged in 0.4 Å−2 bins.

3.3 Refinement of the hydrogen bond

3.3.1 The HT phase

The hydrogen bond in the HT phase is located on a twofold axis. In such a case, the hydrogen bond might either be symmetric with the H atom located on the rotation axis (O–H–O) or it might be statistically disordered ([O–H⋯O] ↔ [O⋯H–O]).

As mentioned in the introduction, conflicting information is found in the literature on this matter. 4 report of neutron diffraction measurements at −40 °C (233 K), slightly above the phase transition temperature, with indication of a splitting of the hydrogen position in Fourier maps. However, refinements carried out by 4 failed when using a split and therefore these authors attribute the apparent disorder to ‘series termination errors’. A symmetric hydrogen bond is likewise suggested by vibrational spectroscopy [12].

In this work, in all HT measurements, the maxima in difference Fourier maps were clearly split, suggesting an asymmetric bond (Figure 4). Moreover, refinements with a disorder model (H occupancy of 1/2) converged with and without distance restraints in place. The final refinements were performed with restraint of the O–H bond lengths, because free refinement led to unreasonably short O–H distances of ca. 0.7 Å.

Figure 4: Difference Fourier map of H3PO2 at 275 K after omission of the contribution of H2 to Fcalc. The coordinates of the remaining atoms were taken from the fully refined model. The shown section is defined by the O1 atoms of a chain of H3PO2 molecules. Positive (green) and negative (blue) contours are drawn at the 0.02 e Å−3 levels. Symmetry codes: i: −1 − x, 1 − y, z; ii: −x, 1 − y, z.
Figure 4:

Difference Fourier map of H3PO2 at 275 K after omission of the contribution of H2 to Fcalc. The coordinates of the remaining atoms were taken from the fully refined model. The shown section is defined by the O1 atoms of a chain of H3PO2 molecules. Positive (green) and negative (blue) contours are drawn at the 0.02 e Å−3 levels. Symmetry codes: i: −1 − x, 1 − y, z; ii: −x, 1 − y, z.

Thus, with the caveat of an inherent difficulty of locating half-occupied H positions using X-ray data, we prefer a model with an asymmetric disordered hydrogen bond.

3.3.2 LT phase

In the LT phase, the hydrogen bond is ordered, i.e. there are distinct donor and acceptor O atoms. Figure 5 shows the difference Fourier maps obtained without the acidic H atom at the various measurement temperatures. The electron density becomes more diffuse close to the phase transition temperature, which anticipates the disordering of the hydrogen bond.

Figure 5: Difference Fourier maps of H3PO2 in the LT phase after omission of the contribution of H3 to Fcalc (see Figure 4).The shown section is defined by the O1 and O2 atoms of a chain of H3PO2 molecules. Color codes and contours as in Figure 5. Symmetry codes: i: x − 1, y, z.
Figure 5:

Difference Fourier maps of H3PO2 in the LT phase after omission of the contribution of H3 to Fcalc (see Figure 4).

The shown section is defined by the O1 and O2 atoms of a chain of H3PO2 molecules. Color codes and contours as in Figure 5. Symmetry codes: i: x − 1, y, z.

In an attempt to quantify the diffuseness of the electron density, refinements without restraining the O–H distance were performed. However, these led to unreasonably long O–H distances. While such long bonds might be due to strong hydrogen bonding [13], they are in contradiction with the observed maximum of the electron density. Refinements of the hydrogen atom as positionally disordered were inconclusive. Notably, the occupation ratio was independent of the temperature. A more detailed analysis of the dynamics and the geometry will require novel neutron diffraction experiments and/or charge-density refinements.

3.4 Hydrogen bonding topology

In crystalline H3PO2, the acid molecules are connected by hydrogen bonds to infinite chains extending along the [100] direction (Figure 6). Below the phase transition temperature, the hydrogen bonding is ordered and two adjacent H3PO2 molecules are related by translation along a [Figure 6(a)]. As expected, the P–OH bond is distinctly longer than the P=O bond [1.5086 (8) and 1.5455 (7) Å at 100 K] and the molecule is of symmetry 1. The rod therefore has symmetry 1 [14], where the subscript indicates the direction of translation symmetry.

Figure 6: Rods of hydrogen-bonded H3PO2 molecules (a) below and (b) above the order-disorder phase-transition temperature.Atoms are represented by red (O) and white (H) spheres of arbitrary radius. Symmetry elements are indicated by the usual symbols.
Figure 6:

Rods of hydrogen-bonded H3PO2 molecules (a) below and (b) above the order-disorder phase-transition temperature.

Atoms are represented by red (O) and white (H) spheres of arbitrary radius. Symmetry elements are indicated by the usual symbols.

The hydrogen bond geometries are compiled in Table 4. With an O⋯O distance of approximately 2.45 Å, the bonds are strong according to the classification of [15], as is expected for resonance assisted hydrogen bonds [16].

Table 4:

Hydrogen bond geometries in H3PO2.

T (K)O–H⋯Od (O–H) (Å)d (H⋯O) (Å)∠(O–H⋯O) (°)d (O⋯O) (Å)
100O2–H3⋯O1i0.980 (17)1.475 (17)177 (2)2.4546 (11)
150O2–H3⋯O1i0.992 (16)1.461 (16)175 (2)2.4505 (11)
175O2–H3⋯O1i0.964 (19)1.488 (19)174 (3)2.4484 (13)
200O2–H3⋯O1i0.94 (2)1.51 (2)173 (3)2.4474 (15)
225O1–H2⋯O1ii0.85 (2)1.61 (2)169 (4)2.4473 (16)
250O1–H2⋯O1ii0.86 (2)1.60 (2)168 (5)2.444 (3)
275O1–H2⋯O1ii0.84 (2)1.62 (2)170 (4)2.4491 (19)
290O1–H2⋯O1ii0.84 (2)1.61 (2)172 (4)2.448 (2)

  1. Symmetry codes: i: (x−1,y,z); ii: (−x−1,−y+1,z).

On heating above the phase transition temperature, the acidic hydrogen becomes dynamically disordered in a 1:1 manner between two H3PO2 molecules [Figure 6(b)]. The hydrogen bond strength does not change significantly at the phase transition temperature, with O⋯O distances still in the 2.45 Å range (Table 4).

Thus, the symmetry of the H3PO2 molecules is increased from 1 to 2 and the distinct hydride-H and O positions of the LT phase become equivalent in the HT phase. The crystallographically unique P–O bond in the HT phase adopts a length between the two bonds of the LT phase [1.5153 (10) at 290 K]. The acidic H atom is likewise disordered around a position with site symmetry 2, which results in an overall 112 rod symmetry (non-standard setting of 211) of the hydrogen-bonded chains. Two adjacent molecules are, like in the LT phase, related by a translation along a.

Thus the symmetry relationship of the infinite chains in the HT and LT phases is of the translationengleiche type: The translation symmetry remains whereas the point groups of the rods are in a group/subgroup relationship of index 2 (i.e. every second point operation is lost on cooling).

The topology of a hydrogen-bonding network is conveniently represented by a graph (in the mathematical sense), where vertices represent ions or molecules and edges hydrogen bonds. In H3PO2, only inter-molecular hydrogen bonds exist and there is only one bond between two molecules. Therefore, the hydrogen-bonding graph is simple, which means that there are no loops (a vertex connected to itself) and at most one edge connecting two vertices.

Hydrogen bonds are directed (from donor to acceptor), and can be represented by directed edges, which results in a directed graph or, for short, digraph. The hydrogen-bonding topology of the LT phase of H3PO2 is thus represented by the double-infinite digraph

(1)⋯→P→P→P→⋯

where P stands for a H3PO2 molecule.

If the hydrogen bond is disordered in a 1:1 manner, as in the HT phase of H3PO2, it may be represented as a non-directed edge, resulting in the undirected graph

(2)⋯—P—P—P—⋯

This particular graph is the double-infinite linear graph.

Thus, from a topological point of view, the symmetry increase from the LT to the HT phase corresponds to the mapping of a digraph onto the corresponding undirected graph. In mathematics, such a mapping is said to ‘lose’ algebraic structure, namely the direction of the edges.

To simplify infinite connectivity graphs, one can ‘factor out’ translationally equivalent molecules to obtain quotient graphs [17]. In such a graph, each vertex represents a molecule in the unit cell and all of its translational equivalents. The quotient graphs of the H3PO2 phases consist of a single node, because all molecules in the chains are related by a lattice translation.

Each edge is marked with a label, which is called the voltage, which indicates the translational component needed to move the molecule into the unit cell when crossing unit-cell boundaries. In the graph above, the 1‾00 label thus means that the molecule in the unit cell is connected via a hydrogen bond to a molecule outside the unit cell. This molecule is translated back into the unit cell by a translation of −a. In analogy to the infinite graphs, the symmetry increase is again characterized by a loss of algebraic structure, viz. the directionality of the edges.

3.5 Space group symmetry

Our experiments confirm the P21212 space group symmetry of the HT phase described by 4. The chains of hydrogen-bonded H3PO2 molecules are arranged in a checkerboard pattern as shown in Figure 7(a). The chains alternately appear in two orientations with respect to [001], which is the direction of the twofold axes.

Figure 7: Crystal structures of (a) the HT and (b) the LT phase of H3PO2. Atom colors and symbols as in Figure 6.
Figure 7:

Crystal structures of (a) the HT and (b) the LT phase of H3PO2. Atom colors and symbols as in Figure 6.

As has been mentioned above, on transition from LT to HT, directionality in the [100] direction is lost. In return, given a HT chain, the corresponding LT chain can adopt one out of two orientations with respect to the a-axis.

There is in principle an infinity of ways of distributing the two orientations, which can lead to either loss of translational symmetry, point group symmetry, or both with respect to the HT phase.

In the actual crystals, the orthorhombic 222 point group is retained and the translation symmetry is reduced. This corresponds to a klassengleiche symmetry reduction, i.e. the crystal class stays unchanged. In particular, the c cell parameter is doubled, because the chains related by a c translation in the HT phase possess opposite orientation of the hydrogen bonding in the LT phase [Figure 7(b)].

Note that whereas the point symmetry of the overall structure is retained on cooling (klassengleiche transition), the point symmetry of the individual H3PO2 chains is reduced while the translation lattice is retained (translationengleiche transition). However, the lost twofold rotation of the chains is retained as a 21 screw rotation of the overall crystal structure, resulting in an overall P212121 symmetry.

The ordering of the hydrogen bonding network in the LT phase is accompanied by a very subtle tilting of the H3PO2 molecules with respect to the HT phase owing to the loss of the twofold rotation (Figure 7). It can be quantified by the angle of the O–O segment of the H3PO2 molecule to the (001) plane. As expected, the deviation from the HT symmetry is more pronounced the lower the temperature [100 K: 3.11°; 150 K: 2.83°; 175 K: 2.54°; 200 K: 1.92°; ≥225 K: 0°]. The larger deviation from the HT symmetry causes higher-intensity superstructure reflections.

3.6 Twinning

Both H3PO2 phases are enantiomorphous. Their 222 point group is a merohedry, i.e. the symmetry is a subgroup of the mmm point symmetry of the lattice. This means that in principle the crystals could be twinned by merohedry, here by inversion. Unfortunately, the present data is not of sufficient quality to confirm or preclude such twinning. Even though the Flack parameter [18] refines to zero within the standard uncertainty, the latter is too large for any definite statement (ca. 0.2–0.3). This also means that the absolute structure could not be determined.

From a crystal-chemical point of view, such a twinning is unlikely. The hydrogen-bonded H3PO2 chains are enantiomorphous (Figure 6) and all chains in the crystal are of the same orientation (both phases crystallize in Sohnke space groups). Twinning by inversion would require a structural transition from one chain enantiomorph to the other.

Since the phase transition from HT to LT is of the klassengleiche type, i.e. the point symmetry is retained, there are no additional orientation states in the LT phase. Thus, the phase transition does not lead to twinning on cooling. On the other hand, due to loss of translation symmetry, there are two domain states of the LT phase, which are related by a c translation of the HT phase. An association of such domains is known as antiphase domains [19] and difficult to detect with routine diffraction methods. Notably, in the diffraction patterns of LT H3PO2 we did not observe broadening of reflections, which would be indicative of small domain sizes.

3.7 Evolution of lattice parameters

Figure 8 gives the evolution of the a, b and c cell parameters with temperature. There is no distinct point of discontinuity at the phase transition temperature. Whereas the b and c cell parameters increase with temperature, the a cell parameter is virtually constant.

Figure 8: Evolution of the a, b and c lattice parameters with temperature. The length axes are at the same scale. With the exception of the 250 K measurement, error bars are smaller than the symbol size.
Figure 8:

Evolution of the a, b and c lattice parameters with temperature. The length axes are at the same scale. With the exception of the 250 K measurement, error bars are smaller than the symbol size.

4 Conclusion and outlook

Since the first crystal structure determinations in 1913, the limits of single crystal diffraction has been pushed to ever more complex structures. Here, we went the opposite direction and present a remarkably simple structure. In fact, it represents the simplest possible infinite hydrogen-bonding topology, as evidenced by a single-node, single-edge quotient graph.

Such a seemingly trivial structure is didactically valuable, since it demonstrates in a simple way one possible effect of symmetry descent on the hydrogen bonding topology: the directed graph is mapped onto an undirected graph. A more complex example of a similar relationship was recently described by our group [2]. Establishing relationships between algebraic structures is the main application of the category theory [20]. For example, the classes of digraphs and undirected graphs represent different categories and the mapping of the former onto the latter is a functor between categories. The category theory has innumerable uses, but has not yet found the adoption in crystallography, which it deserves.

Corresponding author: Berthold Stöger, X-Ray Centre, TU Wien, Getreidemarkt 9, 1060, Vienna, Austria, E-mail:

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-02-20
Accepted: 2021-06-07
Published Online: 2021-06-24
Published in Print: 2021-06-25

© 2021 Martin Nastran and Berthold Stöger, published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

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  1. Frontmatter
  2. In this issue
  3. Inorganic Crystal Structures (Original Papers)
  4. ErNi2.23Al2.77 and YbNi2.31Al2.69 – i3 superstructures of the CaCu5 type
  5. New compound Sm2Ru3Sn5 with a structure derived from Ru3Sn7
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  7. SmPt2In2 – a new ternary indide with a Pt–In polyanionic framework
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  9. KCu(SeO4)Cl(H2O)2, a first copper chloride selenate
  10. The germanides APtGe2 (A = Ca, Sr, Eu)
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https://doi.org/10.1515/zkri-2021-2014
Keywords for this article
hydrogen bond; order/disorder phase transition; single crystal diffraction; topology
Creative Commons
BY 4.0

Articles in the same Issue

  1. Frontmatter
  2. In this issue
  3. Inorganic Crystal Structures (Original Papers)
  4. ErNi2.23Al2.77 and YbNi2.31Al2.69 – i3 superstructures of the CaCu5 type
  5. New compound Sm2Ru3Sn5 with a structure derived from Ru3Sn7
  6. Site preference and atomic ordering in the ternary Rh5Ga2As: first-principles calculations
  7. SmPt2In2 – a new ternary indide with a Pt–In polyanionic framework
  8. The order/disorder phase transition of hypophosphorous acid H3PO2
  9. KCu(SeO4)Cl(H2O)2, a first copper chloride selenate
  10. The germanides APtGe2 (A = Ca, Sr, Eu)
  11. Organic and Metalorganic Crystal Structures (Original Paper)
  12. Crystal structure analysis and supramolecular association in ethyl N-[amino(iminio)methyl]carbamate dichloride hemi-hydrate
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