#
Implementation of Phase Transitions in Rb_{3}H(SO_{4})_{2} under K Substitution

^{*}

## Abstract

**:**

_{m}H

_{n}(AO

_{4})

_{(m + n)/2}·yH

_{2}O (where M = K, Rb, Cs, NH

_{4}; AO

_{4}= SO

_{4}, SeO

_{4}, HPO

_{4}, HAsO

_{4}), is characterized by high values of own proton conductivity, which arises as a result of a phase transition through the formation of a dynamically disordered hydrogen bond network. Such superprotonic phase transitions are observed, however, not for all compounds of the family and Rb

_{3}H(SO

_{4})

_{2}is one of them. The occurrence of superprotonic phase transitions has been experimentally demonstrated in the (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}solid solutions through cation substitution. The high-temperature phases are unstable towards decomposition reaction, and their temperature range of existence is about 1–7 °C. The implementation of superprotonic transitions is discussed in terms of hydrogen bond lengths.

## 1. Introduction

_{3}H(AO

_{4})

_{2}(M = Na, K, NH

_{4}, Rb; A = S, Se) are part of the superprotonic family and belong to monoclinic symmetry. Some of them undergo superprotonic phase transition (C2/c-R$\overline{3}$m) upon heating at ambient pressure [3]. The crystal structure of the low-temperature monoclinic phase of M

_{3}H(SO

_{4})

_{2}crystals (M = K, Rb) is shown in Figure 1. The independent region of the elementary cell contains one AO

_{4}tetrahedron and two non-equivalent M atoms, one of which is located in the special position M1 (4e) and another in the general position M2 (8f). The structure is characterized by an ordered system of hydrogen bonds that connect the SO

_{4}tetrahedra. The structure of the superprotonic phase is similar to the low-temperature phase, but the hydrogen bond network is disordered [4,5].

_{3}H(AO

_{4})

_{2}group is in good agreement with the change in configurational entropy ΔS = R ln 3 (9.13) J/(mol·K) [3]. The range of existence of the trigonal phase for solid acid compounds, M

_{3}H(AO

_{4})

_{2}, is different and is determined by the stability of the phases with respect to the dehydration reaction, which can be represented by the general scheme:

_{3}H(SO

_{4})

_{2}↔ M

_{2}S

_{2}O

_{7}+ 2M

_{2}SO

_{4}+ H

_{2}O,

_{3}H(SO

_{4})

_{2}is a member of the M

_{3}H(AO

_{4})

_{2}group, but the phase transition does not occur under normal pressure [6] but is realized under pressure [7]. Another superprotonic compound, K

_{3}H(SO

_{4})

_{2}, despite the fact that its structure is similar to other representatives of the M

_{3}H(SO

_{4})

_{2}group, exhibits anomalously slow kinetics of the superprotonic phase transition. To reveal a transition and correctly determine its temperature, the measurements must be carried out upon stepwise heating with long exposures at a constant temperature [8,9]. On the other hand, the influence of cationic substitution on the phase transition in K

_{3}H(SO

_{4})

_{2}was demonstrated. The phase transition kinetics radically changes due to the change in the system of hydrogen bonds [4], whose formation involves additional ammonium protons. So, the purpose of the work was to investigate the influence of composition on the phase transitions in Rb

_{3}H(SO

_{4})

_{2}and K

_{3}H(SO

_{4})

_{2}crystals.

## 2. Materials and Methods

_{2}SO

_{4}(high-purity grade, TU (Technical Requirements) no. 6-09-04-198-83), H

_{2}SO

_{4}(special purity grade, 99.8%), and K

_{2}SO

_{4}(reagent grade, TU no. 6-09-04-201-82) were used as initial agents. These agents were used without any additional purification.

_{2}SO

_{4}–Rb

_{2}SO

_{4}–H

_{2}SO

_{4}–H

_{2}O system were studied by using the simultaneous parallel crystallization method.

_{9}H

_{7}(SO

_{4})

_{8}·H

_{2}O and M

_{2}SO

_{4}[10]. Therefore, obtaining high-quality single crystals for composition 1:1 proved to be unsuccessful, and for the 6:4 composition, only unit cell parameters were measured.

_{α}radiation, continuous mode at a rate of 1.0–3.0 degrees/min, step size 0.01°, 2θ range 5–75°, static sample, ambient atmosphere). Unit cell parameters were calculated by means of Le Bail refinement (Jana 2006 [11]).

_{α}).

^{7}Hz (Alpha-A impedance measurement system, Novocontrol, montabaur, Germany). Frequency-dependent impedance measurements were carried out during stepwise heating with temperature stabilization; the average temperature change rate was 0.07 K/min. Static bulk conductivity was calculated using equivalent circuit models obtained from the impedance spectra. Naturally faceting crystals (K

_{x}Rb

_{1-x})

_{3}H(SO

_{4})

_{2}possess a well-developed crystal plane (011). Therefore, single crystal samples with an orientation along the [100] axis were prepared by slightly polishing the crystal surface to form thin plates with characteristic linear dimensions of 5 mm and a thickness of 1 mm. Polycrystalline samples were obtained by grinding single crystals to a powder with the characteristic grain size of 5 μm and subsequently pressing (2 t/cm

^{2}) into tablets. The silver paste was used as electrodes.

## 3. Results

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}, (where x = 0–1) were determined, and the data are summarized in Table A1.

_{3}H(SO

_{4})

_{2}and Rb

_{3}H(SO

_{4})

_{2}have the same symmetry (C2/c) but slightly different atomic coordinates; therefore, they are not isostructural. To determine the cell parameters of (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}, we used the initial lattice parameters of Rb

_{3}H(SO

_{4})

_{2}(ICSD #249556) for x = 0–0.64, and K

_{3}H(SO

_{4})

_{2}(ICSD #174401) for x = 0.66–1. Dependence of the unit cell parameters, Figure S3, and the volume of the elementary cell on the composition of the solid solution, (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}, Figure 2, demonstrates a break at structure changes around x ≈ 0.66. Within the structural type, the dependence on the composition is nearly linear and satisfies Vegard’s rule. Reliable data on the hydrogen bond lengths and the site occupancy of the M1 and M2 positions by potassium and rubidium cations are better obtained from structural studies of single crystals, which will be completely conducted in a separate study. In the present work, the structure was determined for one of the samples, occupancy positions were identified, and the hydrogen bond length was resolved based on single crystal X-ray diffraction (XRD) data. Complete experimental data and atomic coordinates are provided in Table A2 and Table A3, respectively. Cell parameters are in good agreement with the powder XRD data and have also been included in Figure S3 and Figure 2.

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}, thermal properties study are presented in Figure 3. The large endothermic effect in the temperature range of 180-210 °C and additional effect around 220 °C (x = 0.69–0.9) corresponds to the decomposition multistep process and are accompanied by a mass loss (Figure S4) of the sample at the temperature of the effect of about 0.5% by mass [6,12]. It is clearly seen that for compositions, x = 0.23–0.64, an additional endothermic peak appears.

_{3}H(SO

_{4})

_{2}and solid solutions based on it, the phase transition does not manifest in DSC due to its slow kinetics [4]; therefore, only the decomposition reactions show thermal effects.

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}x = 0–0.64 and single crystals, Figures S7 and S10. As mentioned in the experimental description, the average rate of stepwise heating was 0.07 K/min, which is an order of magnitude lower than the heating rate used in synchronous thermal analysis experiments. It turned out that the shape of the conductivity curve for solid solutions does not differ from the curve for decomposition in Rb

_{3}H(SO

_{4})

_{2}, accompanied by a conductivity jump, and this behavior is reproducible in subsequent thermal cycles, Figure S7. A two-step conductivity jump was expected upon heating (Figure 5), so it could be attributed to the very narrow range of existence of the superprotonic phase. The two processes lead to conductivity growth: phase transition and solid phase decomposition. If they are not separated by temperature or are weakly separated, we can expect a behavior similar to Figure 4. However, it can be seen that the temperature range of conductivity jump widens with increasing potassium content and reaches about 13 °C for the composition x = 0.64. Such behavior can also be attributed to compositional inhomogeneity. Moreover, the conductivity of compositions x = 0.1 and 0.23 exhibits peculiarities in the temperature range of 170–190 °C, which could be associated with surface decomposition processes of the sample, as well as phase transitions. A similar behavior is observed for solid solutions with x = 0.81–1, Figure 5. For the pure K

_{3}H(SO

_{4})

_{2}sample, a phase transition occurs at 180 °C, and the conductivity jump at 188 °C corresponds to the decomposition process. The existence range of the superprotonic phase is narrow and is only 8 °C. In solid solutions, the conductivity plateau corresponding to the superprotonic phase disappears, and the magnitude of the conductivity jump becomes comparable to the jump in conductivity due to decomposition. Additionally, anomalies in conductivity appear at x = 0.87 and 0.81 in the temperature range of 170 °C to 190 °C, resembling conductivity plateaus similar to K

_{3}H(SO

_{4})

_{2}. However, the conductivity jump is small, so attributing these anomalies to phase transitions is questionable and could be associated with surface decomposition reactions of the samples. Such temperature behavior indicates the loss of stability of the superprotonic phase (confirmed by weight loss Figure S4) in relation to the decomposition reaction under substitution. Thus, conductivity studies are unable to reliably establish the presence of phase transitions and determine their temperatures, except for the clearly manifesting phase transition in K

_{3}H(SO

_{4})

_{2}.

_{3}H(SO

_{4})

_{2}group, allowing for direct observation of both decomposition processes and the movement of phase front boundaries during phase transitions.

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}, where x = 0–0.64, are shown in Figure 6 and Figure S11.

_{3}H(SO

_{4})

_{2}group (C2/c ↔ R$\overline{3}$m).

## 4. Discussion

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}x = 0.23–0.64 compositions. Such conditions are still not sufficient to detect phase transitions in solid solutions with a high potassium content, the kinetics of which are even slower. Reducing the rate to 0.07 K/min and using polycrystalline samples (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}, where x = 0.81–1, allows the observation of a transition in K

_{3}H(SO

_{4})

_{2}at conductivity studying, but even this slow rate is insufficient to observe transitions in single crystals and isothermal exposure for several hours is required. The effect of the heating rate on the temperature of phase transitions and the decomposition from DSC data, conductivity, and optical observations is shown in Figure 10. It is clearly visible that it can be roughly approximated by two linear dependencies with a break corresponding to the change in the structure type at x ≈ 0.66. It should be noted that the temperatures of the presumed phase transitions for compositions of x = 0 and 0.1 are higher than the decomposition temperatures. However, such transitions will be observed when the decomposition reaction is suppressed by applying an external pressure.

_{3}H(AO

_{4})

_{2}(M = Na, K, NH

_{4}, Rb; A = S, Se) was demonstrated in [14]. Based on this idea, we propose to use hydrogen bond length as a criterion for occurring phase transitions. Phase transitions and proton conductivity of the group, M

_{3}H(AO

_{4})

_{2}, have been well studied up to the present, and the group itself is a model for such research. Known data on hydrogen bond lengths for structures near room temperature, superprotonic structures and phase transitions are given in Table 2. Similar lithium compounds are absent. We also have not found any structural data for Cs

_{3}H(SO

_{4})

_{2}and Na

_{3}H(SeO

_{4})

_{2}. Attempts to crystallize these compositions failed, so we consider their existence to be doubtful.

_{3}H(AO

_{4})

_{2}group for low-temperature and superprotonic phases. The diagram clearly shows the separation of all low-temperature phases into two regions relative to the phase transition, where the phase transition occurs and where the decomposition of the compound (Na, Rb) takes place (dotted line, Figure 11) [14]. Thus, the value of the bond length d

_{O-O}≈ 2.49 Å at room temperature serves as a threshold for the implementation of the phase transition into the superprotonic phase. We suggest that the bond length in the superprotonic state could be considered as the criterion for achieving the phase transition when the rotational disorder of oxoanions begins. Accordingly, the bond lengths for these superprotonic R$\overline{3}$m phases are shown in Figure 11. From Figure 11 and Table 1, it can be seen that for trigonal phases, the range of bond lengths is very narrow, with a maximum difference in transition temperatures of about 120 °C. This means that the phase transition occurs when the threshold bond length is reached, and the transition temperature, in this case, is a dependent parameter. We have evaluated the range of hydrogen bond lengths as d

_{O-O}≈ 2.645–2.673 Å (dash lines in Figure 11) for the M

_{3}H(SO

_{4})

_{2}group (M = Na, K, NH

_{4}, Rb, Cs; A = S, Se), which includes the minimum energy of the hydrogen bond system at 2.669 Å (0.24 eV) (the intersection of the energy of hydrogen bond formation and the energy of proton on bond hopping) (Figure 11). Hydrogen bond length for the trigonal phase K

_{3}H(SeO

_{4})

_{2}, only presented in one study [20], although included in Table 1, is missing in Figure 11 and is considered to have a systematic error.

_{3}H(SO

_{4})

_{2}: the transition is not realized under normal pressure [10] but is realized under pressure [24]. Thus, upon heating Rb

_{3}H(SO

_{4})

_{2}, the elongation process of hydrogen bonding begins, but the threshold bond length is not reached, and a decomposition process occurs. Application of external pressure allows for suppression of the dehydration reaction (1) (according to Le Chatelier’s principle), the threshold bond length will be achieved, and a phase transition will occur. It should be noted that the application of pressure changes the threshold length of the hydrogen bond. The thermodynamic potential takes the form:

_{O-O}= 2.485(9) Å (Rb

_{3}H(SO

_{4})

_{2}) and d

_{O-O}= 2.496(1) Å (K

_{3}H(SO

_{4})

_{2}) at room temperature. This is confirmed by the structural studies of the crystal (K

_{0.64}Rb

_{0.36})

_{3}H(SO

_{4})

_{2}, where the hydrogen bond length was determined d

_{O-O}= 2.4957(11). The substitution of potassium leads to an increase in the hydrogen bond length, resulting in a phase transition upon heating. From this point of view, phase transitions in other solid solutions can also be interpreted. The introduction of about 5% at. ammonium into K

_{3}H(SO

_{4})

_{2}leads to an elongation of hydrogen bonds (d

_{O-O}= 2.496(1) Å → 2.549(8) Å) and anomalously slow kinetics of the phase transition becomes typical for superprotonic transitions [27]. The introduction of 57% at. leads to the occurrence of a disordered hydrogen bond network already at room temperature (d

_{O-O}= 3.2 Å RT) [28].

_{x}Rb

_{1−x})

_{3}H(SeO

_{4})

_{2}solid solutions, it has been shown that with the substitution of rubidium, it predominantly occupies the M2 sites between the layers of selenate tetrahedra [29]. Therefore, such a substitution has practically no effect on the hydrogen bond length and, as a consequence, weakly affects the phase transition temperature. We assume a similar uneven occupancy of crystallographic sites in (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}solid solutions. Furthermore, the substitution also affects the conductivity of solid solutions in the monoclinic phase, depending on their composition. When potassium is replaced by rubidium, the conductivity increases, leading to a decrease in hydrogen bonding. Whereas, in the case of the Rb substitution, the conductivity remains almost unchanged, indicating the occupation of rubidium in the M2 position of the structure.

_{4}group. The hydrogen bond network of this group is complex and three-dimensional. For the best-known representative of the group CsHSO

_{4}, the determination of hydrogen bond lengths is a difficult task. The location of the heavy atoms could be determined precisely, but several models were proposed for oxygen and hydrogen atoms. As a result, the last published data on hydrogen bond lengths in the superprotonic phase were d

_{O-O}= 2.56 Å and 2.98 Å, but these data are given for a specific model [30]. For the CsHSeO

_{4}crystal, d

_{O-O}= 3.35(1) Å and 3.50(1) Å were supposed to be the potential hydrogen bonds. These distances were calculated between the centers of thermal ellipsoids. However, the authors supposed that due to the strong librating movement of oxygen atoms, the momentary distances are much shorter, approximately 2.5 Å [31]. Thus, in the case of a complex three-dimensional hydrogen bond network in the MHAO

_{4}group, the data on hydrogen bonds are not as unambiguous as for the M

_{3}H(AO

_{4})

_{2}group. Therefore, the conclusions drawn in this paper apply to the M

_{3}H(AO

_{4})

_{2}group, and the concept of using the hydrogen bond length as a criterion for phase transition requires further verification.

_{3}H(AO

_{4})

_{2}), these data can be extrapolated to the critical bond length value and the temperature of the superprotonic phase transition can be estimated.

## Supplementary Materials

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}on the composition of the initial solution; Figure S2. XRD patterns of the (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}solid solutions at room temperature. Multiphase sample corresponds to K:Rb = 0.5 solution; Figure S3. Lattice parameters of the (K

_{x}Rb

_{1− x})

_{3}H(SO

_{4})

_{2}at room temperature. Red dot responds to the single crystal XRD data; Figure S4. DSC signal and weight loss of (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}powders at heating rate 1K/min; Figure S5. DSC signal and weight loss of (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}single crystals at heating rate 1K/min; Figure S6. DSC signal and weight loss of (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}polycrystalline samples at heating rate 5K/min; Figure S7. Temperature dependencies of conductivity of the (K

_{0.23}Rb

_{0.77})

_{3}H(SO

_{4})

_{2}single crystal in two subsequent heating-cooling cycles; Figure S8. (K

_{0.23}Rb

_{0.77})

_{3}H(SO

_{4})

_{2}single crystal. (

**a**) Nyquist plots and fits for different temperatures. The complete impedance spectrum is shown in the inset as well as equivalent circuit for fitting; (

**b**) and (

**c**) Bode plots and fits for different temperatures; Figure S9. (K

_{0.23}Rb

_{0.77})

_{3}H(SO

_{4})

_{2}single crystal. (

**a**) Nyquist plots and fits for different temperatures. The complete impedance spectrum is shown in the inset as well as equivalent circuit for fitting; (

**b**) and (

**c**) Bode plots and fits for different temperatures.; Figure S10. Conductivity of (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}(x = 0–0.38) single crystals at stepwise heating, mean heating rate was 0.07K/min; Figure S11. Microphotographs of single crystals (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}, x = 0–0.64, under polarized light, crossed Nicols, at different temperatures. Temperature stabilization time was 15-30 min. The values of x are given next to the corresponding crystals; Figure S12. Microphotographs of single crystals (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}x = 0.68–1 under polarized light. (Crossed Nicols—black background, parallel Nicols—light background). The pictures were taken for the same samples state. Trigonal phase and decomposition regions are marked by narrows.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Lattice parameters and cation compositions of (K

_{x}Rb

_{1 − x})

_{3}H(SO

_{4})

_{2}at room temperature.

Composition (EDXS) | Rb_{3}H(SO_{4})_{2}ICSD #249556 | (K_{0.1}Rb_{0.9})_{3} | (K_{0.23}Rb_{0.77})_{3} | (K_{0.38}Rb_{0.62})_{3} | (K_{0.64}Rb_{0.36})_{3} | (K_{0.68}Rb_{0.32})_{3} | (K_{0.81}Rb_{0.19})_{3} | (K_{0.87}Rb_{0.13})_{3} | (K_{0.95}Rb_{0.05})_{3} | K_{3}H(SO_{4})_{2}ICSD #174401 |
---|---|---|---|---|---|---|---|---|---|---|

Sp.gr.; Z | C 1 2/c 1, 4 | C 1 2/c 1, 4 | C 1 2/c 1, 4 | C 1 2/c 1, 4 | C 1 2/c 1, 4 | C 1 2/c 1, 4 | C 1 2/c 1, 4 | C 1 2/c 1, 4 | C 1 2/c 1, 4 | C 1 2/c 1, 4 |

a, Å | 15.1460(5) | 15.106(9) | 15.062(19) | 15.033(6) | 14.967(7) | 14.809(1) | 14.75(20) | 14.718(4) | 14.695(9) | 14.685(3) |

b, Å | 5.8914(19) | 5.875(3) | 5.858(8) | 5.850(2) | 5.820(3) | 5.741(5) | 5.714(5) | 5.696(4) | 5.684(8) | 5.676(1) |

c, Å | 10.1590(3) | 10.116(6) | 10.079(13) | 10.056(3) | 10.001(5) | 9.872(8) | 9.827(3) | 9.799(8) | 9.783(3) | 9.772(1) |

β, ° | 102.540(6) | 102.62(17) | 102.69(4) | 102.75(2) | 102.82(5) | 102.96(7) | 102.98(7) | 103.00(6) | 103.00(9) | 103.2(1) |

V, Å^{3} | 884.87 | 876.06(9) | 867.55(20) | 862.53(6) | 849.52(8) | 818.0(3) | 807.2(5) | 800.6(2) | 796.3(8) | 793.00 |

**Table A2.**Main crystal data, characteristics of X-ray diffraction experiments, and the refinement parameters of the (K

_{0.64}Rb

_{0.36})

_{3}H(SO

_{4})

_{2}structure.

Chemical Formula | (K_{0.64}Rb_{0.36})_{3}H(SO_{4})_{2} |
---|---|

T, K | 293 |

M_{r} | 387.5 |

Space group, Z | C2/c, 4 |

a, Å | 14.957(1) |

b, Å | 5.816(1) |

c, Å | 9.993(2) |

β, deg | 102.83(1) |

V, Å | 847.59(3) |

D_{x}, g/cm^{3} | 3.0369 |

Crystal size, mm | 0.184 × 0.1 × 0.056 |

Radiation; λ, Å | MoK_{α}; λ = 0.71073 |

μ, cm^{−1} | 10.784 |

Diffractometer | XtaLAB Synergy-DW |

Scan mode | ω |

Absorption correction; T_{min}, T_{max} | Numerical over a multifaceted crystal model, Empirical using spherical harmonics; 0.891/1 |

θ_{max}, deg | 44.62 |

Limiting h, k, l indices | −27/29 −11/11 −18/19 |

No. of measured/independent/observed [I > 3σ(I)] reflections | 38006/3016/1875 |

R_{int} | 0.0291 |

Refinement method | Least-squares on F^{2} |

Weighting scheme | 1/(σ^{2}(I) + 0.0004 I^{2}) |

Number of parameters | 67 |

Extinction correction, coefficient (isotropic type 2) | 0.1890 (130) |

R1/wR2 | 0.0179/0.0383 |

S | 1.10 |

Δρ_{min}/Δρ_{max}, e/Å^{3} | −0.49/0.46 |

Software | CrysAlisPro, Jana 2006 |

**Table A3.**Coordinates (x/a, y/b, z/c), position, site occupancy (q), and equivalent isotropic parameters of thermal vibrations (U

_{eq}, Å

^{2}) of the basic atoms in the structure at 293 K.

Atoms | Position | q | x/a | y/b | z/c | U_{eq} |
---|---|---|---|---|---|---|

Rb1 | 4b | 0.2094(12) | 0.5 | 0.24504(3) | 0.75 | 0.02307(7) |

K1 | 4b | 0.7906(12) | 0.5 | 0.24504(3) | 0.75 | 0.02307(7) |

Rb2 | 8f | 0.7268(13) | 0.306546(7) | 0.23137(2) | 0.34832(1) | 0.02331(4) |

K2 | 8f | 0.2732(13) | 0.306546(7) | 0.23137(2) | 0.34832(1) | 0.02331(4) |

S1 | 8f | 1 | 0.61371(2) | 0.72578(3) | 0.96157(2) | 0.01767(6) |

O1 | 8f | 1 | 0.51029(4) | 0.6832(1) | 0.94017(7) | 0.0302(2) |

O2 | 8f | 1 | 0.65152(4) | 0.5293(1) | 0.90123(6) | 0.0253(2) |

O3 | 8f | 1 | 0.65013(5) | 0.73765(9) | 1.10991(7) | 0.0250(2) |

O4 | 8f | 1 | 0.62557(4) | 0.9406(1) | 0.89317(6) | 0.0279(2) |

H1 | 8f | 0.5 | 0.4931(17) | 0.441(4) | 1.021(2) | 0.028(6) |

## References

- Jansen, M. Volume Effect or Paddle-Wheel Mechanism—Fast Alkali-Metal Ionic Conduction in Solids with Rotationally Disordered Complex Anions. Angew. Chem. Int. Ed. Engl.
**1991**, 30, 1547–1558. [Google Scholar] [CrossRef] - Merinov, B.V. Mechanism of Proton Transport in Compounds Having a Dynamically Disordered Hydrogen Bond Network. Solid State Ion.
**1996**, 84, 89–96. [Google Scholar] [CrossRef] - Baranov, A.I. Crystals with Disordered Hydrogen-Bond Networks and Superprotonic Conductivity. Review. Crystallogr. Rep.
**2003**, 48, 1012–1037. [Google Scholar] [CrossRef] - Makarova, I.P.; Chernaya, T.S.; Filaretov, A.A.; Vasil’Ev, A.L.; Verin, I.A.; Grebenev, V.V.; Dolbinina, V.V. Investigation of the Structural Conditionality for Changes in Physical Properties of K
_{3}H(SO_{4})_{2}Crystals. Crystallogr. Rep.**2010**, 55, 393–403. [Google Scholar] [CrossRef] - Magome, E.; Sawada, K.; Komukae, M. X-Ray Structure Analysis of Rb
_{3}H(SeO_{4})_{2}in the High-Temperature Phase. Ferroelectrics**2009**, 378, 157–162. [Google Scholar] [CrossRef] - Cowan, L.A.; Morcos, R.M.; Hatada, N.; Navrotsky, A.; Haile, S.M. High Temperature Properties of Rb
_{3}H(SO_{4})_{2}at Ambient Pressure: Absence of a Polymorphic, Superprotonic Transition. Solid State Ion.**2008**, 179, 305–313. [Google Scholar] [CrossRef] - Sinitsyn, V.V. Dinamical and Statistical Disorder in Condessed Matters at High Pressure. Doctoral Dissertation
**2014**, 1–327. [Google Scholar] - Chen, R.H.; Chen, S.C.; Chen, T.M. High-Temperature Structural Phase Transition in Na
_{3}H(SO_{4})_{2}Crystal. Phase Transit.**1995**, 53, 15–22. [Google Scholar] [CrossRef] - Friese, K.; Aroyo, M.I.; Schwalowsky, L.; Adiwidjaja, G.; Bismayer, U. The Disordered High-Temperature Structure of (NH
_{4})_{3}H(SO_{4})_{2}and Its Relationship to the Room-Temperature Phase. J. Solid State Chem.**2002**, 165, 136–147. [Google Scholar] [CrossRef] - Komornikov, V.A.; Grebenev, V.V.; Timakov, I.S.; Ksenofontov, D.A.; Andreev, P.V.; Makarova, I.P.; Selezneva, E.V. Production of Complex Hydrosulphates in the K
_{3}H(SO_{4})_{2}–Rb_{3}H(SO_{4})_{2}Series: Part I. Crystallogr. Rep.**2019**, 64, 479–483. [Google Scholar] [CrossRef] - Petricek, V.; Dusek, M.; Palatinus, L. Crystallographic computing system JANA2006: General FEATures. Z. Krist.
**2014**, 229, 345–352. [Google Scholar] - Calum, R.C.; Haile, S.M. High-Temperature Phase Transitions in K
_{3}H(SO_{4})_{2}. Solid State Ion.**2001**, 145, 179–184. [Google Scholar] - Matsuo, Y.; Hatori, J.; Nakashima, Y.; Ikehata, S. Superprotonic and Ferroelastic Phase Transition in K
_{3}H(SO_{4})_{2}. Solid State Commun.**2004**, 130, 269–274. [Google Scholar] [CrossRef] - Sanghvi, S.; Haile, S.M. Crystal Structure, Conductivity, and Phase Stability of Cs
_{3}(H_{1.5}PO_{4})_{2}under Controlled Humidity. Solid State Ion.**2020**, 349, 115291. [Google Scholar] [CrossRef] - Catti, M.; Ferraris, G.; Ivaldi, G. A Very Short, and Asymmetrical, Hydrogen Bond in the Structure of Na
_{3}H(SO_{4})_{2}and S–OH vs O–H...O Correlation. Acta Crystallogr. Sect. B Struct. Crystallogr. Cryst. Chem.**1979**, 35, 525–529. [Google Scholar] [CrossRef] - Fortier, S.; Fraser, M.E.; Heyding, R.D. Structure of Trirubidium Hydrogenbis(Sulfate), Rb
_{3}H(SO_{4})_{2}. Acta Crystallogr. Sect. C Cryst. Struct. Commun.**1985**, 41, 1139–1141. [Google Scholar] [CrossRef] - Pietraszko, A.; Łukaszewicz, K.; Augustyniak, M.A. Structure of Phase III of (NH
_{4})_{3}H(SeO_{4})_{2}. Acta Crystallogr. Sect. C Cryst. Struct. Commun.**1992**, 48, 2069–2071. [Google Scholar] [CrossRef] - Lukaszewicz, K.; Pietraszko, A.; Augustyniak, M.A. Structure of (NH
_{4})_{3}H(SeO_{4})_{2}in High Temperature Phases I and II. Acta Crystallogr. Sect. C Cryst. Struct. Commun.**1993**, 49, 430–433. [Google Scholar] [CrossRef] - Ichikawa, M.; Sato, S.; Komukae, M.; Osaka, T. Structure of Ferroelastic K
_{3}H(SeO_{4})_{2}. Acta Crystallogr. Sect. C Cryst. Struct. Commun.**1992**, 48, 1569–1571. [Google Scholar] [CrossRef] - Shikanai, F.; Tomiyasu, K.; Kiyanagi, R.; Yonemura, M.; Iwase, K.; Sulistyanintyas, D.; Wurnisha, T.; Mori, K.; Ishigaki, T.; Tsukushi, I.; et al. Neutron Powder Diffraction Study of Protonic Conductor K
_{3}H(SeO_{4})_{2}. Ferroelectrics**2007**, 347, 74–78. [Google Scholar] [CrossRef] - Makarova, I.P.; Verin, I.A.; Shchagina, N.M. Crystal structure of rubidium hydroselenate Rb
_{3}H(SeO_{4})_{2}. Kristallografiya**1986**, 31, 178–180. [Google Scholar] - Sonntag, R.; Melzer, R.; Knight, K.S.; Radaelli, P.G. Structural Study of the Proton Conductor Cs
_{3}H(SeO_{4})_{2}by High Resolution Neutron Powder Diffraction. Mater. Sci. Forum**1998**, 278–281, 726–731. [Google Scholar] [CrossRef] - Sonntag, R.; Melzer, R.; Knight, K.S. Determination of the Hydrogen Position in Cs
_{3}H(SeO_{4})_{2}at 483 K. Phys. B Condens. Matter**1997**, 234–236, 89–91. [Google Scholar] [CrossRef] - Sinitsyn, V.V.; Baranov, A.I.; Ponyatovsky, E.G.; Shuvalov, L.A. P-T-Phase Diagram of Superprotonic Conductor Rb
_{3}H(SeO_{4})_{2}. Ferroelectrics**1995**, 167, 67–72. [Google Scholar] [CrossRef] - Lippincott, E.R.; Scheoeder, R. One-Dimensional Model of the Hydrogen Bond. J. Chem. Phys.
**1955**, 23, 1099–1106. [Google Scholar] [CrossRef] - Yomosa, S.; Hasegawa, M. Valence Bond Study of the Hydrogen Bond. III. Formation and Migration of Ionic Defects in Water and Ice. J. Phys. Soc. Jpn.
**1970**, 29, 1329–1334. [Google Scholar] [CrossRef] - Choudhury, R.R.; Chitra, R.; Selezneva, E.V.; Makarova, I.P. Effect of Cationic Substitution on the Double-Well Hydrogen-Bond Potential in [K
_{1-x}(NH_{4})_{x}]_{3}H(SO_{4})_{2}Proton Conductors: A Single-Crystal Neutron Diffraction Study. Acta Crystallogr. Sect. B Struct. Sci. Cryst. Eng. Mater.**2017**, 73, 863–867. [Google Scholar] [CrossRef] - Selezneva, E.V.; Makarova, I.P.; Malyshkina, I.A.; Gavrilova, N.D.; Grebenev, V.V.; Novik, V.K.; Komornikov, V.A. New Superprotonic Crystals with Dynamically Disordered Hydrogen Bonds: Cation Replacements as the Alternative to Temperature Increase. Acta Crystallogr. Sect. B Struct. Sci. Cryst. Eng. Mater.
**2017**, 73, 1105–1113. [Google Scholar] [CrossRef] - Yi, D.; Sanghvi, S.; Kowalski, C.P.; Haile, S.M. Phase Behavior and Superionic Transport Characteristics of (M
_{x}Rb_{1-x})_{3}H(SeO_{4})_{2}(M = K or Cs) Solid Solutions. Chem. Mater.**2019**, 31, 9807–9818. [Google Scholar] [CrossRef] - Merinov, B.V. Localization of hydrogen atoms in protonic conductors with a dynamical disordered network of hydrogen bonds: Effect of anonalous manifestation of hydrogen atoms on electron-density maps. Crystallogr. Rep.
**1997**, 42, 906–917. [Google Scholar] - Zakharov, M.A.; Troyanov, S.I.; Kemnitz, E. Superprotonic High Temperature Phase and Refinement of the Low Temperature Structure of CsHSeO
_{4}. Z. Krist.**2001**, 216, 172–175. [Google Scholar] [CrossRef]

**Figure 2.**Dependency of the volume of the elementary cell of solid solutions (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}on composition. Red dot responds to the single crystal XRD data.

**Figure 3.**DSC signal of the solid solutions (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}powders, including pure compounds, at a heating rate of 1K/min.

**Figure 4.**Temperature dependencies of conductivity in solid solutions (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}, x = 0–0.64.

**Figure 5.**Temperature dependence of conductivity in solid solutions (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}, x = 0.81–1.

**Figure 6.**Microphotographs of single crystals (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}, x = 0–0.64 under polarized light in crossed Nicols at different temperatures. Temperature stabilization time was 15–30 min. The values of x are given next to the corresponding crystals.

**Figure 7.**Single crystal (K

_{0.23}Rb

_{0.77})

_{3}H(SO

_{4})

_{2}at different temperatures. The light background corresponds to parallel Nicols, black-crossed Nicols. The sample boundary is shown for clarity and the arrows indicate the path and current position of the phase front.

**Figure 8.**Single crystal (K

_{0.64}Rb

_{0.36})

_{3}H(SO

_{4})

_{2}at heating–cooling–heating thermal cycle. The light background corresponds to parallel Nicols and black-crossed Nicols; times of isothermal exposures are given next to the corresponding pictures.

**Figure 9.**Microphotographs of single crystals (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}x = 0.68–1 under polarized light in crossed Nicols at different temperatures. Temperature stabilization time was 20–45 min. The values of x are indicated next to the corresponding crystals.

**Figure 10.**The dependence of the phase transition temperature on the composition x of solid solutions (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}. Open symbols represent the decomposition process of compounds for which the phase transition was not detected.

**Figure 11.**The lengths and corresponding energies of hydrogen bond formation for the group M

_{3}H(AO

_{4})

_{2}(M = Na, K, NH

_{4}, Rb; A = S, Se). The dotted line represents boundary for hydrogen bond lengths near room temperature (black marks for sulfates and red marks for selenates), which divide the compositions relative to phase transition or decomposition. The two dashed lines represent the bond lengths for the superprotonic phases (blue marks for sulfates and green marks for selenates).

**Table 1.**Temperatures of thermal effects for polycrystalline samples of solid solutions (K

_{x}Rb

_{1−x})

_{3}H(SO

_{4})

_{2}at a heating rate of 1 K/min, where T

_{d}is the decomposition temperature, T

_{onset tr}is the extrapolated onset temperature of the phase transition, ΔS

_{tr}is the change in configurational entropy during the phase transition.

(K_{x}Rb_{1−x})_{3}H(SO_{4})_{2}, x | T_{onset tr}, °C | ΔS_{tr}, J/(mol·K) | T_{d}, °C |
---|---|---|---|

0 | 201.9 | ||

0.1 | 195.4 | ||

0.23 | 187.5 | 7.8 | 189.5 |

0.38 | 185.0 | 8.9 | 184.8 |

0.64 | 175.9 | 9.8 | 182.7 |

0.81 | 180.7 | ||

0.87 | 182.8 | ||

0.95 | 180.6 | ||

1 | 196.3 |

**Table 2.**Data on the lengths of hydrogen bonds in M

_{3}H(AO

_{4})

_{2}solid acids for low-temperature and high-temperature phases are presented, including X-ray experiment temperatures and phase transition temperatures.

Composition | Sp.gr. | T, °C | d_{O-O}, Å | T_{sp}, K | Sp.gr. | T, °C | d_{O-O}, Å |
---|---|---|---|---|---|---|---|

(Na)_{3}H(SO_{4})_{2} | P2_{1}/c | RT | 2.434(4) [15] | 240 | hexagonal [8] | - | - |

(NH_{4})_{3}H(SO_{4})_{2} | C2/c | 20 | 2.572(2) [9] | 140 | R$\overline{3}$m | 147 | 2.674(3) [9] |

K_{3}H(SO_{4})_{2} | C2/c | 20 | 2.496(1) [4] | 182 | R$\overline{3}$m | 185 | 2.648(5) [4] |

Rb_{3}H(SO_{4})_{2} | C2/c | 19 | 2.485(9) [16] | Decomposition ^{1} [6] | |||

Cs_{3}H(SO_{4})_{2} | Doubtful | ||||||

(Na)_{3}H(SeO_{4})_{2} | Doubtful | ||||||

(NH_{4})_{3}H(SeO_{4})_{2} | C$\overline{1}$ | 23 | 2.535(6) [17] | 59 | R$\overline{3}$m R$\overline{3}$ | 82 37 | 2.674(17) [18] 2.696(16) [18] |

K_{3}H(SeO_{4})_{2} ^{2} | C2/c | 26 | 2.524(5) [19] | 115 | R$\overline{3}$m | 120 | 2.601(10) [20] |

Rb_{3}H(SeO_{4})_{2} | C2/c | RT | 2.514(7) [21] | 178 | R$\overline{3}$m | 182 | 2.63(2) [5] |

Cs_{3}H(SeO_{4})_{2} | C2/c C2/m | 127 27 | 2.57(2) [22] 2.506(7) [22] | 183 | R$\overline{3}$m | 210 | 2.66(2) [23] |

^{1}. The transition of Rb

_{3}H(SO

_{4})

_{2}to the R$\overline{3}$m phase occurs under pressure [7,24].

^{2}. K

_{3}H(SeO

_{4})

_{2}—the data requires verification because [20] is the only study with data on hydrogen bond length in the superprotonic phase, but the reported data for room temperature significantly differ from data obtained in other studies [19].

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## Share and Cite

**MDPI and ACS Style**

Timakov, I.S.; Komornikov, V.A.; Selezneva, E.V.; Grebenev, V.V.
Implementation of Phase Transitions in Rb_{3}H(SO_{4})_{2} under K Substitution. *Crystals* **2023**, *13*, 1401.
https://doi.org/10.3390/cryst13091401

**AMA Style**

Timakov IS, Komornikov VA, Selezneva EV, Grebenev VV.
Implementation of Phase Transitions in Rb_{3}H(SO_{4})_{2} under K Substitution. *Crystals*. 2023; 13(9):1401.
https://doi.org/10.3390/cryst13091401

**Chicago/Turabian Style**

Timakov, Ivan S., Vladimir A. Komornikov, Elena V. Selezneva, and Vadim V. Grebenev.
2023. "Implementation of Phase Transitions in Rb_{3}H(SO_{4})_{2} under K Substitution" *Crystals* 13, no. 9: 1401.
https://doi.org/10.3390/cryst13091401