Neutron and high-pressure X-ray diffraction study of hydrogen-bonded ferroelectric rubidium hydrogen sulfate

Synopsis The hydrogen-bonded ferroelectric material rubidium hydrogen sulfate has been investigated through a combination of high-pressure X-ray diffraction and neutron Laue diffraction. This study confirms the order-disorder origin of the ferroelectric transition as well as fully characterising the high-pressure phase transition. Abstract The pressure-and temperature-dependent phase transitions in the ferroelectric material rubidium hydrogen sulfate (RbHSO 4 ) are investigated by a combination of neutron Laue diffraction and high-pressure X-ray diffraction. The observation of disordered oxygen atom positions in the hydrogen sulfate anions is in agreement with previous spectroscopic measurements in the literature. Contrary to the mechanism observed in other hydrogen-bonded ferroelectric materials, hydrogen atom positions are well defined and ordered in the paraelectric phase. Under applied pressure RbHSO 4 undergoes a ferroelectric transition before transforming to a third, high-pressure phase. The symmetry of this phase is revised to the centrosymmetric space group P 2 1 / c , resulting in the suppression of ferroelectricity at high pressure.


Introduction
Rubidium hydrogen sulfate, (RbHSO4) is one member of the general family of solid-acid proton conductors, MHAO4, where M = Na + , K + , Rb + , Cs + , or NH4 + and A = S or Se.These materials have attracted attention as model hydrogen-bonded ferroelectric materials and for the superprotonic conduction phases achievable under relatively mild thermodynamic conditions.
Ferroelectric behaviour in RbHSO4 was first reported by Pepinsky & Vedam (1960).Their efforts to understand ferroelectricity in ammonium hydrogen sulfate (NH4HSO4) focused on ordering within the N-H…O hydrogen bonds.To their surprise, isomorphous RbHSO4 also showed a low-temperature ferroelectric phase without the requirement of cation-anion hydrogen bonds.Further measurements have shown ferroelectric transitions to be prevalent throughout the MHAO4 family (Sinitsyn, 2010).
Subsequent dielectric studies have revised the transition temperature, and recent piezoresponse force microscopy settled on the generally accepted Curie temperature of 264 K (Lilienblum et al., 2013).
Initial structural investigations of MHAO4 in general focused on low temperatures, and to some degree high pressures, in order to understand the ferroelectric transitions in these materials.Following the discovery of superprotonic conductivity, the high-temperature high-pressure regions of the PT phase diagrams were explored using electrical conductivity measurements (Ponyatovskii et al., 1985).
Collating over a range of M and A has allowed a general phase diagram to be produced (Sinitsyn, 2010).The phase diagram for RbHSO4 is shown in Figure 1.
Despite the topological similarity amongst the PT phase diagrams of members of the MHAO4 family, corresponding phases are not necessarily isostructural.RbHSO4 and RbHSeO4 share a phase sequence superprotonic → paraelectric → ferroelectric, which occurs at ambient pressure for RbHSeO4 and at pressures ≥ 0.28 GPa in RbHSO4 , reflecting the 'chemical pressure' induced by substituting Se for S (Suzuki et al., 1979).However, neither the paraelectric nor the ferroelectric phases are isostructural; RbHSeO4 has space group P1 in the ferroelectric phase and I2 in the paraelectric phase (Waskowska et al., 1980, Brach et al., 1983), while the space groups of the corresponding phases in RbHSO4 are Pc (phase II, ferroelectric) and P21/c (phase I, paraelectric), respectively.In RbHSeO4 the ferroelectric transition is due to proton ordering over a disordered hydrogen bond in contrast to the proposed mechanism, described below, in RbHSO4 (Itoh & Moriyoshi, 2003).
The ambient-pressure phases of the well-studied analogue CsHSO4, CsHSO4-II, and CsHSO4-III, are not isostructural with RbHSO4 and do not exhibit a low-temperature ferroelectric transition, both have space-group symmetry P21/c.CsHSO4 also shows a very strong isotopic dependence, with metastable phase CsHSO4-III only observed in the undeuterated material (Chisholm & Haile, 2000).The structures of phases I and II of RbHSO4 were investigated by X-ray and neutron diffraction by Ashmore and Petch (1975).The neutron study revealed that the hydrogen atom positions are fully ordered in the paraelectric phase, in contrast to paraelectric phases in analogous hydrogen-bonded ferroelectric materials.By analogy with the disorder-order transition observed in NH4HSO4, attempts were made to refine a disordered sulfate model, but the results were inconclusive.Ozaki (1980) suggested that disorder should play an intrinsic role in the phase transition.In an attempt to confirm this, Itoh et al. (1995) report a disordered paraelectric structure for phase I, citing the large anisotropic displacement parameters of the oxygen and hydrogen atoms of one HSO4 − group, and the successful refinement of a disordered paraelectric phase of NH4HSO4, in support of the disordered model.

Dielectric measurements by
In a subsequent study, Itoh & Moriyoshi (2003) analysed the temperature dependence of thermal parameters above and below the Curie temperature, determining the ferroelectric structure for the first time.Again they conclude that one HSO4 − anion shows disorder in two oxygen atom positions rather than all four.A Raman spectroscopy study by Toupry et al. (1981) found the temperature dependence of the O-H frequency to be consistent with a change in ionic orientation.
To complicate matters, an X-ray diffraction study by Nalini & Guru Row (2003) has cast doubt on the disordered paraelectric model.They find no evidence of distortion in the sulfate geometries or significant residual electron density; they record notable distortions to the sulfate moieties only after cooling into the ferroelectric phase II.
While investigating the pressure dependence of the I → II transition, Gesi & Ozawa (1975) identified a high-pressure phase which was subsequently investigated by Asahi & Hasebe (1996) at pressures of 0.96 and 1 GPa, this phase III is described as monoclinic P21.
Clearly there remains some uncertainty as to the structure of the paraelectric phase I which modern neutron diffraction data can help to answer.State-of-the-art thermal-neutron Laue diffractometers allow collection of extensive diffraction data to a similar precision as traditional monochromatic instruments with a gain in data collection rate of one-to-two orders of magnitude (McIntyre et al., 2006).We show that this technique enables confirmation of the ordered proton positions as well as yielding accurate O-H bond lengths which help to clarify the mechanism of ferroelectricity in rubidium hydrogen sulfate.

Methods
Clear, block-like crystals of rubidium hydrogen sulfate (RbHSO4) were grown from aqueous solutions of equimolar quantities of RbSO4 and H2SO4.
X-ray diffraction data were collected on a Bruker SMART APEX II diffractometer with graphitemonochromated Mo Kα radiation (λ = 0.71073 Å) equipped with an Oxford Cryosystems variabletemperature device.High-pressure X-ray diffraction experiments were carried out using a Merrill-Bassett diamond-anvil cell with a tungsten gasket and tungsten carbide backing plates with an accessible semi angle of 40° (Merrill & Bassett, 1974, Moggach et al., 2008).The sample crystal and a chip of ruby were loaded with Fluorinert FC70 as the hydrostatic medium.The phase transition from I to II was initially found to occur on raising the pressure from 0 to 0.5 GPa.A second loading was used for fill in extra pressure points at 0.2 and 0.4 GPa, defining the transition pressure more precisely.Both loadings were carried out with crystals of similar sizes (0.10 x 0.12 x 0.20 and 0.10 x 0.15 x 0.20 mm).Pressure-dependent ruby fluorescence was used as a pressure measure (Piermarini et al., 1975).
Diffraction data were integrated using SAINT (Bruker, 2007).Dynamic masks were applied to account for cell-body shading in the high-pressure data sets (Dawson et al., 2004).Absorption corrections were carried out in SADABS (Sheldrick, 2008).The program SHADE was used to identify and discard partially shaded and diamond reflections (Parsons, 2004).Structures were solved by direct methods or charge flipping using SIR92 or SUPERFLIP (Altomare et al., 1993, Palatinus & Chapuis, 2007).
Neutron Laue diffraction data were collected at 300 K and 150 K at ambient pressure on the KOALA Laue diffractometer, at ANSTO, using a crystal of dimensions 1.2 x 1.1 x 0.8 mm 3 .Laue patterns were collected for 4 hours each; a total of twelve patterns were collected at 300 K, fourteen at 150 K.
In both cases the vertical rotation angle was 15° to account for the low symmetry of these crystals.
The diffraction patterns were indexed and processed using the program LaueG (Piltz, 2016).
Reflection intensities were integrated with a modified two-dimensional version of the algorithm formulated by Wilkinson et al. (1988) and Prince et al. (1997).The data were normalised to a single common incident wavelength using the program LAUE4 for a wavelength spectrum of 0.85−1.7 Å (Piltz, 2011).For phase I, data were integrated to a resolution of d = 0.78 Å.A total of 8517 reflections were merged to a common incident wavelength giving an Rmerge = 9.1% with a completeness of 77.1%.Data for phase II were integrated to a resolution of d = 0.67 Å. Unit-cell dimensions were taken from X-ray diffraction results at 150 and 300 K.A total of 13194 reflections were normalised and merged to a common incident wavelength with Rmerge = 9.7% and a completeness of 74.3%.Laue diffraction suffers from intrinsic harmonic overlap that limits completeness values to a theoretical maximum of 83.3% (Cruickshank et al., 1987, Cruickshank et al., 1991).No absorption correction was applied due to the small crystal size and nearly spherical crystal form.
All structure refinements were carried out against |F| 2 in CRYSTALS (Betteridge et al., 2003); initial atomic coordinates were derived from X-ray diffraction data.Hydrogen atoms were refined with standard riding-model constraints in the refinements against X-ray data.In the refinements against neutron data, H-atom positional and anisotropic displacement parameters were refined freely.Crystal and refinement data are given in Table 1.Selected bond lengths and angles for the different phases discussed in the following sections are compared in Table 2. Table 3 gives crystal and refinement details for refinements of high-pressure single-crystal X-ray diffraction data.
Tables of the final refined atomic coordinates and displacement parameters are given in Supplementary Information.

Ferroelectric phase II
The structure of rubidium hydrogen sulfate phase II was determined at 150 K in the non-standard polar space group Pn, with a = 14.2651( 5 The final agreement factor for the neutron diffraction data for phase II was low, R[F 2 > 2σ(F 2 )] = 0.048.Possibilities for twinning were investigated by coset decomposition, however none of the applied twin laws improved data-fitting.
Neutron diffraction data were refined against structures derived from ambient-pressure X-ray diffraction and the refined structures from each radiation are the same within error, with the exception of hydrogen-atom positions and displacement parameters.Geometric parameters quoted in the following discussion of the ambient-pressure structures are derived from neutron diffraction data.
1 Values derived from X-ray diffraction.

Paraelectric phase I
At room temperature rubidium hydrogen sulfate has unit-cell dimensions a = 14.Below Tc, interaction between HSO4 − ions outweighs thermal motion (Toupry et al., 1981).The paraelectric-to-ferroelectric transition therefore involves the ordering of two alternative anionic orientations representing minima between which HS(1)O4 − ions are able to oscillate in the paraelectric phase.Symmetry analysis using ISODISTORT (Campbell et al., 2006) indicates that the phase I to II transition occurs via a ferroelectric mode of Γ2 − symmetry, which is IR active, but Raman inactive.
The absence of any mode softening as reported by Toupry et al. is  As is implied by the ferroic nature of this transition, this transition occurs via a translationengeleiche maximal group-subgroup relationship between phases I and II.In such a transition unit-cell dimensions remain essentially fixed and the point group symmetry of the crystal is decreased (Müller, 2013).

High-pressure X-ray diffraction
RbHSO4 is reported to undergo two phase transitions with pressure at room temperature.Above 0.4 GPa phase I (P21/n) undergoes a transition, which has been described as second-order (Kalevitch et al., 1995, Itoh & Moriyoshi, 2003), to phase II (Pn), which then undergoes a first-order transformation at 0.75 GPa to phase III reported to be P1121 (Asahi & Hasebe, 1996).
Up to 0.4 GPa the unit-cell volume decreases by 10.8(8) Å 3 (1.3 %), axial compression is small, the most significant change is in c with a reduction of 0.052(9) Å, a decreases by 0.026( 5 indicating the presence of the 21 screw symmetry element in phases I and III.For phase II, refinement in P21/n resulted in a significantly higher agreement factor, R = 9.91 % versus R = 4.37 % in Pn, confirming the systematic absence analysis.The resulting structure for phase III is similar to that described by Asahi & Hasebe (1996), although with space group symmetry reassigned (Figure 5).Of the 279 reflections affected by the presence of c-glide symmetry, three have I/σ(I) > 3, <I/σ(I)> = 0.5, <I> = 0.3.This structure is isostructural with the corrected structure of CsHSO4-II reported by Chisholm & Haile (2000).There are no statistically significant changes to bond lengths within the HSO4 − anions up to 1.1 GPa.
In phase III, rubidium cations are coordinated by 11 oxygen atoms, an increase in coordination number of one as shown in Figure 5. Two HSO4 − anions bind in a bidentate fashion through two oxygen atoms, the remaining anions bind in a monodentate manner.Rubidium-oxygen bonds adopt a wider range of lengths in this phase, from 2.861(9) to 3.589(12) Å, and as a result the average Rb-O bond length (3.121(9) Å) is the same within error as at ambient pressure (3.077(3) Å).This is an example of the widely-observed 'pressure-distance paradox' whereby pressure-driven coordination number increases are accompanied by an increase in bond length (Kleber & Wilke, 1969).
The pressure response of donor-acceptor distances are shown in

Conclusions
The paraelectric → ferroelectric transition in RbHSO4 has been investigated with neutron Laue diffraction.Hydrogen atoms were refined to singly-occupied positions with no sign of possible double-well occupancy.One HSO4 − moiety could be refined with two disordered oxygen atoms; this disordered model resulted in better agreement with the neutron data over an ordered model with distended oxygen ADPs.An isothermal pressure series up to 1.1(1) GPa was carried out by singlecrystal X-ray diffraction covering the two pressure-driven phase transitions observed to date.The  (Bruker, 2007), SADABS (Sheldrick, 2008), SIR92 (Altomare et al., 1993), CRYSTALS (Betteridge et al., 2003).

Figure 1
Figure 1 Pressure-temperature phase diagram of RbHSO4 following Sinitsyn (2010) and references within.Phases I and II can also be described in P21/c and Pc, respectively, by a different choice of unit-cell axes.
HSO4 − anions form infinite hydrogen-bonded chains in the b-direction, running parallel to ribbons of Rb atoms (Figure 2(a)).These chains have similar O…H distances of 1.551(6) and 1.580(7) Å, but different O-H…O angles of 174.2(7)° and 172.7(6)° reflecting the two orientations adopted by the disordered anion on cooling.The S-O(-H) bond is elongated by 0.12(1) Å on average relative to the other three S-O bonds and O-S-O bond angles range from 103.13(12)° to 113.35(15)°.The remaining twelve S-O bond lengths and range in length from 1.438(7) to 1.466(6) Å.Each Rb atom is coordinated by six HSO4 − anions, four anions coordinate in a bidentate fashion, and the remaining two coordinate via a single oxygen atom giving a total coordination number of ten (Figure 2(b)).Rb-O coordination distances vary between 2.881(4) and 3.443(6) Å with the two shortest Rb-O bonds formed with the monodentate HSO4 − anions.The origin of this structure was selected to match that of phase I to facilitate comparison.

Figure 2
Figure 2 (a) Four unique hydrogen-bonded chains of hydrogen sulfate anions along the b-axis in the asymmetric unit of phase II at 150 K; (b) The ten-atom coordination environment of Rb1, essentially identical to Rb2-4.The shortest Rb-O distances are given in the figure and are formed to the 3602(19), b =   4.6156(6), c = 14.413(2)Å, and β = 118.069(8)°,space group P21/n, the non-standard setting chosen to give a smaller β angle closer to 90°.The asymmetric unit of phase I contains two Rb + cations and two HSO4 − anions.The H-bonded chains of anions observed in phase II persist in phase I, and indeed the structures of both phases are generally rather similar.Each HSO4 − is distorted by the elongation of the S-O(-H) bond by 0.121(4) Å.Beyond the elongation of the S-O(H) bond, the remaining S-O bonds are statistically equal, bond angles within HSO4 − units range from 103.60(15)° to 116.7(16)°.At 300 K, one rubidium cation (Rb1) is coordinated to six hydrogen sulfate anions in the same manner as at 150 K, four HSO4 − bonding in a bidentate fashion, the remaining two being monodentate.The other Rb atom (Rb2) is 9-coordinate at 300 K, with three bidentate HSO4 − and three monodentate HSO4 − anions.Rubidium-oxygen bond distances vary over a similar range to those in phase II, from 2.924(3) to 3.256(4) Å.The reduction in coordination number is caused by the shift in HSO4 − orientation through the II-I transition which results in a long Rb-O distance of 4.107(4) Å compared to the bonding distance of 3.443(6) Å in phase II.In phase I, both hydrogen-bonded chains are statistically similar, including the two hydrogen bonds formed by the disordered HS(1)O4 − anions.For HS(1)O4 − chains the O…H distance is 1.604(14) Å to O30, and 1.521(15) Å to O31, O -H…O angles are 170.3(5)°and 172.7(5)° respectively.Hydrogen-bonded chains formed by HS(2)O4 − anions have O…H distances of 1.610(4) Å with an O-H…O angle of 171.2(3) °.In light of the disagreement in the literature regarding the disordered nature of HS(1)O4 − anion, both ordered and disordered models were refined against the neutron diffraction data for phase I, and the corresponding asymmetric units are shown in Figure3(a) and (b).AsItoh & Moriyoshi (2003) note, anomalously large atomic displacement parameters (ADPs) are observed for the oxygen atoms of the HS(1)O4 − tetrahedron, in particular O(3) which acts as the donor in the O(1)-H(1)…O(3) hydrogen-bonded infinite chain (Figure3(a)).This is clearly illustrated by comparison of the average equivalent isotropic displacement parameter (Ueq) for oxygen atoms bound only to S, (0.0456(8) Å 2 ) and that of O3 (0.0707(12) Å 2 ).These results, along with earlier spectroscopic work byOzaki (1980) andToupry et al. (1981), are consistent with dynamic disorder in the two oxygen positions.Two oxygen atoms of HS(1)O4 − can be refined against the neutron data obtained in the present study over two split positions each with refined occupancies of 0.51(2) and 0.49(2) for O(20/21) and 0.50(2) for O(30/31).Hydrogen atoms, located in difference maps, occupy well-defined positions with no indication of split occupancy.The final agreement factor for the ordered model was R = 5.52 %, that for the disordered model is R = 5.08 %.This disordered model results in Ueq values for O30 and O31 that do not differ significantly from the average oxygen Ueq values, in contrast to the ordered model.
in agreement with Raman and IR selection rules for this symmetry.Comparison of the phase I and II structures in Figure 3(c) and (d) shows the two disordered sites in the HS(1)O4-I unit are overlapped orientations of the HS(1)O4-II and HS(3)O4-II units in the ferroelectric phase II. Figure 3(c) shows two asymmetric units in phase I related by inversion symmetry.As the sample is cooled, half the HS(1)O4-I units occupy the orientation of HS(1)O4-II with the other half occupying the HS(3)O4-II orientation as shown in Figure 3(d).This breaks the inversion symmetry creating a non-centrosymmetric polar structure and giving rise to spontaneous electric polarisation.

Figure 3
Figure 3 (a) Asymmetric unit of RbHSO4 phase I, ordered model.The enlarged ADPs of O(2) and O(3) are clearly visible; (b) Asymmetric unit of RbHSO4 phase I, disordered model, splitting of O(2) and O(3) sites results in a lower R-factor and is supported by dielectric and solid-state NMR measurements.The two orientations of the disordered HS(1)O4-I anions shown in (c) are approximately equivalent to the phase II anions HS(1)O4-II and HS(3)O4-II shown in (d).

Figure 4
Figure 4 (a) Change in unit-cell volume for phases I and II with pressure; (b) Change in <I/σ(I)> for reflections of the type k = 2n + 1, with pressure showing the clear presence of a 21 screw symmetry element in phases I and III.

Figure 5 (�
Figure 5 (Left) Unit cell of RbHSO4 phase III, two alternating HSO4 − hydrogen-bonded chains form along the c axis; (Right) Coordination environment of Rb in phase III.

Figure 6
Figure 6 Reorientation of Rb + cations and HSO4 − anions through the pressure-induced phase transition; (a) Illustrates the asymmetric diamond channels in phase I, shifts in Rb + positions leading to the formation of staggered hexagonal channels containing reoriented HSO4 − anions; (b) Formation of a new hydrogen-bonding system in phase III.The linear chains along bI are broken by the movement of HSO4 − anions to form new zig-zagging chains along the cIII direction.

Figure 7 .
Up to 0.4 GPa the hydrogen-bonding distances in the HS(1)O4,I and HS(2)O4,II chains remain distinct with the difference in O(H)…O distances increasing from 0.074(6) Å at ambient pressure to 0.13(2) Å at 0.4 GPa.Upon the transition to phase II, O(H)…O distances are not statistically distinguishable for each symmetryindependent chain.The increase in symmetry over the phase II → III transition means that phase III contains only one unique hydrogen bond, in which the O(H)…O distance is 2.576(15) Å, which is not significantly different to the ambient-pressure values.

Figure 7
Figure 7 Changes in hydrogen bonding donor-acceptor distances (D…A) with pressure in RbHSO4.The two symmetry-independent hydrogen-bonded chains in phase I are shown by open and closed black squares.Phase II data are shown by open red circles.Phase III datum is shown by a closed blue circle.

Table 1
Crystal data and details of the structure determination of RbHSO4 phases I and II by neutron Laue diffraction.

Table 2
Bond distances and angles for RbHSO4 phases I and II at 300 K and 150 K, respectively.

Table 3
Crystal data and details of the structure determination of RbHSO4 phases I, II, and III by high-pressure X-ray diffraction