The phase transition of rubidium hydrogen carbonate, RbHCO3

Rubidium hydrogen carbonate shows an order/disorder phase transition with the high-temperature phase (HT) having monclinic and the low-temperature phase triclinic symmetry. A comparison is made with the related HT/LT structures of potassium hydrogen carbonate.

In many cases, at higher temperatures, the hydrogen atoms are dynamically disordered between the connected oxoanions. On cooling, the disorder is 'frozen', resulting in a reduction of symmetry (order/disorder phase transition). Such phase transitions are of technological importance, for example in the KH 2 PO 4 (KDP) family of compounds and therefore have been studied extensively. At high temperatures, these compounds exist in a paraelectric tetragonal phase. On cooling below T C , they order into orthorhombic ferroelectrics. This kind of phase transition is likewise of theoretical interest, because it allows the study of proton quantum dynamics (Fillaux et al., 2008).
From a crystallographic point of view, these phase transitions offer the potential to study group/subgroup relationships (Mü ller, 2013). Moreover, in the case of a reduction of point symmetry, the lost symmetry is typically retained as a twin operation, leading to interesting as well as challenging problems.
A well known example of a hydrogen-bonding order/ disorder transition is potassium hydrogen carbonate, KHCO 3 (Kashida & Yamamoto, 1990). Above T C = 318 K, it crystallizes in a monoclinic C2/m phase featuring disorder of the hydrogen atom (Fillaux et al., 2008). On cooling, it transforms into an ordered P2 1 /a phase (Thomas et al., 1974). Rubidium hydrogen carbonate RbHCO 3 shows an analogous phase transition at T C = 245 K, which has been thoroughly studied by NMR spectroscopy (Odin, 2004). The published structural data, on the other hand, leave much to be desired. A structure model of the high-temperature (HT) modification in the C2 space group has been provided by Kim (1969). The structure was later redetermined by Cirpus (1997), establishing the correct space group C2/m and isotypism with KHCO 3 . The lattice metrics of the low-temperature (LT) modification were identified as triclinic by Mü ller & Roth (2005). Although a model was refined by these authors, structural data were not deposited. To fill this gap, in this communication we report detailed structural data of the LT modification of RbHCO 3 which were derived from a twinned crystal. We also redetermined the structure of the HT modification. The phase transition is discussed in detail and contrasted to the structural changes observed in KHCO 3 .

General
The structure model of HT-RbHCO 3 (C2/m) is in good agreement with that of Cirpus (1997). The crystal structures of HT-RbHCO 3 (C2/m) and LT-RbHCO3 (C1) are closely related. The central building blocks are pairs of HCO 3 À anion groups, which are connected by strong hydrogen bonds (Fig. 1, Tables 1 and 2). The prime cause for the order/disorder phase transition is the dynamic behaviour of the protons in these pairs. In HT-RbHCO 3 , they are dynamically disordered, resulting in a short [C-O1: 1.237 (4) Å ] and two symmetry-  Table 1 Hydrogen-bond geometry (Å , ) for HT-RbHCO3. Symmetry code: (i) Àx þ 1; y; Àz þ 1.

Symmetry reduction and relationship to KHCO 3
Whereas the HT-KHCO 3 and HT-RbHCO 3 phases are isotypic, the corresponding LT phases are not. To understand the different behaviour on cooling, it is useful to consider the structures as being made up of layers of [HCO 3 ] 2 2À pairs parallel to (100). In the HT phases, these layers possess the p12/m1 layer group symmetry. On cooling, owing to the ordering of the protons, the m [010] operation is lost. All [HCO 3 ] 2 2À pairs are rotated in the same direction about [001], resulting in layers with p1 symmetry.
Thus, the lower symmetry layers may appear in one out of two orientations with respect to the [010] direction. In the LT-RbHCO 3 phase, all layers feature the same orientation. Adjacent layers are related by translation symmetry (as in the C2/m HT phase) and therefore the translation lattice is retained. The symmetry loss concerns only the point symmetry. Since one out of two symmetry operations is retained (viz. the translations and inversions), the symmetry reduction is of the t2 kind, where t stands for translationengleiche and 2 for the index of 1 in 2/m (Mü ller, 2013).
In the LT-KHCO 3 phase, on the other hand, layers feature alternating orientation with respect to [010]. The layers are split in two sets of translationally equivalent layers. The translation lattice is therefore reduced by an index of two, which here corresponds to a change of the Bravais lattice (mC to mP) while retaining the volume of the cell in the (more convenient but non-standard) centred setting. In return, adjacent layers are related by an a glide reflection. Thus, the point symmetry 2/m is retained. The symmetry reduction is therefore of the k2 kind, where k stands for klassengleiche (Mü ller, 2013).
The structural relationships of the HT and LT phases of RbHCO 3 and KHCO 3 are represented in a Bä rnighausen family tree in Fig. 5. The atomic labelling and coordinates of the KHCO 3 modifications were adapted from the original literature (Fillaux et al., 2008;Thomas et al., 1974) to be comparable to the data presented here. Note that the fractional coordinates of all four phases depicted in Fig. 5 are remarkably similar.
The atoms on the reflection planes in the HT phases are located on general positions in the LT phases. The O2 atom, which is located on a general position in the HT phase, is split into two positions in the LT phase. In contrast, the position of the H atom, which is also located on a general position in the HT modification, is not split. Instead, its occupancy is raised from 0.5 to 1.

Twinning
Phase transitions are one of the classical causes of twinning (Hahn & Klapper, 2006;Stö ger et al., 2016). If the point symmetry of the structure is reduced, the lost operations may be retained as twin operations. Indeed, the crystals of RbHCO 3 were all systematically twinned below T C . The crystal under investigation was made up of two domains related by m [010] and equivalently 2 [010] , which corresponds precisely to the second coset in the coset decomposition of 1 in 2/m. The twin volume ratio was determined by the TWINABS software as 51.3:48.7, which compares well to the volume ratio obtained from the (abandoned, see Section 3.3) refinement against HKLF 5 style data [52.0:48.0 (4)].
Since the transformation into the triclinic C1 LT phase results in a substantial increase of the angle to = 92.748 (9) , the diffraction spots at higher k indices are clearly separated (Fig. 6). Such a twin cannot be treated as a twin by pseudo-merohedry. The angle, on the other hand, deviates only slightly from the monoclinic metrics [ = 89.343 (4) ]. The lattice of the layers therefore is pseudo-rectangular, which is consistent with the crystallo-chemical considerations above.
In KHCO 3 , the HT and LT phase feature the same point symmetry 2/m. Stacking faults therefore do not result in twinning but in antiphase domains (Wondratschek & Jeitschko, 1976). These kinds of domains are significantly more difficult to quantify using X-ray diffraction.

Synthesis and crystallization
Large crystals of RbHCO 3 were grown by dissolving commercial 'Rb 2 CO 3 ' (actually the sesquihydrate according to powder X-ray diffraction) in a small quantity of water followed by evaporation of the solution overnight at ca 295 K.

Data collection
Crystals were cut to sizes suitable for single crystal diffraction with a razor blade. Abrupt cooling of the crystals to below the phase-transition temperature by immersion into a cooled N 2 stream led to fourfold splitting of reflections as described by Mü ller & Roth (2005). Data reduction was successful using four orientation matrices and a reasonable structure model could be obtained. Nevertheless, the quality of the refinement was deemed not optimal (notably, the hydrogen atoms could not be located). From structural reasoning, only two domains are expected (see Section 2.2). The higher number of domains was therefore attributed to a cracking of the crystal under thermal stress. Therefore, a data collection was first performed above T C at 270 K. Then, the crystal was slowly (2 K h À1 ) cooled to 200 K and a full sphere of reciprocal space was collected with fine slicing. The first scan was discarded because it contained distinct reflections from the HT phase as well as two LT domains. The data set obtained from the remaining scans featured only the two expected LT twin domains.

Data processing
Data of the HT modification was subjected to routine processing using SAINT and SADABS (Bruker, 2016). For the LT phase, reflections of both domains were separated and reduced to intensity data using overlap information. An absorption correction was applied using the TWINABS (Bruker, 2016) software. This software outputs 'detwinned' conventional data (HKLF 4 style), usually used for structure solution and data with overlap information (HKLF 5 style). Surprisingly, the detwinned data set resulted in significantly better refinements. Not only were the residuals lower by two percentage points, additionally only in the detwinned data could the hydrogen atoms be located and refined. Therefore the discussion is based on the refinement using the detwinned data set.

Structure solution and refinement
An initial model of the HT modification was adapted from the data of Cirpus (1997). The structure of the LT modification was solved using the dual-space approach implemented in SHELXT (Sheldrick, 2015). Atomic coordinates and labelling were adapted to be analogous to those of the HT modification. The non-standard C1 setting of the P1 space group was chosen to facilitate comparison with the HT modification [lattice basis transformation from P1 to C1: (a C , b C , c C ) = (b P + 2c P , Àb P , a P )]. The structure models were refined against F 2 with JANA2006 (Petříček et al., 2014). The hydrogen atoms were located in difference Fourier maps and the O-H distances restrained to 0.850 (1) Å . Crystal data, data collection and structure refinement details are summarized in Table 3. Part of the hk2 plane in reciprocal space of LT-RbHCO 3 reconstructed from CCD data. The reciprocal basis vectors of the two twin domains are indicated. Computer programs: APEX3 and SAINT-Plus (Bruker, 2016), SHELXT (Sheldrick, 2015), JANA2006 (Petříček et al., 2014), ATOMS (Dowty, 2006) and publCIF (Westrip, 2010