Crystallization in the Three-Component Systems Rb 2 SO 4-MSO 4-H 2 O ( M = Mg , Co , Ni , Cu , Zn ) at 298 K

The crystallization in the three-component systems Rb2SO4-MSO4-H2O (M = Mg, Co, Ni, Cu, Zn) is studied by the method of isothermal decrease of supersaturation. It has been established that isostructural double compounds, Rb2M(SO4)2·6H2O (M = Mg, Co, Ni, Cu, Zn),     5 1 2 SG 2 h P c C , crystallize from the ternary solutions within wide concentration ranges. The infrared spectra are discussed with respect to the normal vibrations of the sulfate ions and water molecules. The unit-cell group theoretical treatment of the double salts is presented. The extent of energetic distortions of 4 SO  guest ions (about 2 mol%) matrix-isolated in the respective selenates,   2 4 2 2 M M SeO 6H O    (M' = K, Rb, 4 NH  ; M" = Mg, Co, Ni, Cu, Zn), is commented.


Introduction
The rubidium double sulfates belong to a large number of isomorphous compounds with a general formula   with two formula units in the unit-cell.The crystal structures are built up from isolated octahedra, [M''(H 2 O) 6 ], (three crystallographically different water molecules are coordinated to the M'' ions) and tetrahedra XO 4 .The polyhedra are linked by hydrogen bonds.All atoms, except the divalent metal ions, which lie at centre of inversion C i , are located at general positions C 1 .Recently, the crystal structures of some rubidium Tutton sulfates have been reported in Refs.[1,2].As an example the crystal structures of Rb 2 Co(SO 4 ) 2 •6H 2 O is presented in Figure 1.
In this paper we present the results on the study of the solubility in the three-component systems Rb 2 SO 4 -MSO 4  NH  ; M'' = Mg, Co, Ni, Cu, Zn), is analyzed.A practical point of studying is that the Tutton compounds could be considered as proton conductors due to the existence of comparatively strong hydrogen bonds determined by the strong proton acceptor capabilities of the sulfate ions.

Experimental
Rb 2 SO 4 was prepared by neutralization of Rb 2 CO 3 with dilute sulfuric acid solutions at 333 -343 K. Then the solutions were filtered, concentrated at 323 -333 K, and cooled to room temperature.The crystals were filtered, washed with alcohol and dried in air.The sulfates of divalent metals were commercial products.All reagents used were of reagent grade quality (Merck).The solubility in the three-component systems Rb 2 SO 4 -MSO 4 -H 2 O (M = Mg, Co, Ni, Cu, Zn) at 298 K was studied using the method of isothermal decrease of supersaturation.Solutions containing different amount of the salt compounds corresponding to each point of the solubility diagrams were heated at about 333 -343 K and cooled to room temperature.Then the saturated solutions were vigorously stirred [3,4].The equilibrium between the liquid and solid phases was reached in about 20 hours.The analysis of the liquid and the wet solid phases was performed as follows: the M'' ion contents were determined complexonometrically at pH 9.5 -10 using eriochrome black as indicator (magnesium ions) and at pH 5.5 -6 using xylenol orange as indicator (cobalt, nickel, copper and zinc ions); the sulfate ions were precipitated as Ba-SO 4 with Ba(NO 3 ) 2 solutions and the concentrations of the excess of Ba 2+ ions were determined complexonometrically using eriochrome black as indicator; the concentrations of the rubidium sulfate were calculated by difference [5].The compositions of the solid phases were identified by means of both the X-ray diffraction and the infrared spectroscopy methods.Tutton compounds Rb 2 M(SeO 4 )  SO  ions (the data for the potassium and ammonium selenates are taken from [9]).
The infrared spectra were recorded on a Bruker model IFS 25 Fourier transform interferometer (resolution < 2 cm −1 ) at ambient temperature using KBr discs as matrices.Ion exchange or other reactions with KBr have not been observed.In some cases Lorentz band profile for multi peak data was used to determine the correct band positions corresponding to asymmetric stretches of the included 2 4 SO  ions (ORIGIN PRO 6.1).The X-ray powder diffraction spectra were collected within the range from 5˚ to 50˚ 2θ with a step 0.02˚ 2θ and counting time 35 s/step on Bruker D8 Advance diffractometer with CuKα radiation and LynxEye detector.The lattice parameters of the double salts were calculated using the program ITO and refined with the program LSUCR.are summarized in Tables 1-5).It is seen that the simple salts Rb 2 SO 4 , MgSO   O crystallize within very narrow concentration ranges, whereas the rubidium double sulfates crystallize within wide concentration ranges, thus indicating that strong complex formation processes occur in the ternary solutions.

X-Ray Powder Diffraction Data of Rubidium Tutton Compounds
The X-ray powder diffraction patterns of the rubidium Tutton compounds are shown in  6.Our results coincide well with those determined from single crystal X-ray diffraction data [1,2].

Infrared Spectra of Neat Rubidium Tutton Sulfates
The free tetrahedral ions   4 XO n under perfect T d symmetry exhibit four internal vibrations:  1 (A 1 ), the symmetric X-O stretching modes,  2 (E), the symmetric XO 4 bending modes,  3 (F 2 ) and  4 (F 2 ), the asymmetric stretching and bending modes, respectively.The normal vibrations of the free sulfate ions in aqueous solutions are reported to appear as follows: [10].On going into solid state, the normal modes of the  

4
XO n ions are expected to shift to higher or lower frequencies.
The static field (related to the symmetry of the site on which the 4 XO n ions are situated) will cause a removal of the degeneracy of both the doubly degenerate  2 modes and the triply degenerate  3 and  4 modes.Since the tetrahedral ions in the structures of Tutton compounds occupy site symmetry C 1 , two bands for  2 (2A) SO  and H 2 O) yields: 69 modes of A g , A u , B g and B u symmetry and 48 modes of A g , A u , B g and B u symmetry for the translational and librational modes respectively [11].
Infrared spectra of Rb 2 M(SO 4 ) 2 •6H 2 O (M = Mg, Co, Ni, Cu, Zn) in the region of 4000 -400 cm −1 are shown in Figures 9 and 10.Some structural and spectroscopic data are summarized in  The  1 modes appear at 984 cm −1 .The bending modes  4 are detected in the spectral intervals of 632 -612 cm −1 . 2 appear at about 450 cm −1 (see Figure 9).
Our infrared spectroscopic findings differ slightly from those reported by Brown and Ross with respect to the number of the bands corresponding to  3 of the sulfate ions.The spectra of the rubidium compounds commented in [13] show more bands for  3 (some of them assigned as shoulders) as compared to our results.We believe that the difference between our spectra and those discussed by Brown and Ross is due probably to the temperatures at which the spectra are recorded.It is mentioned in [13] that some spectra are run at liquid nitrogen temperature.However, there is no indication which spectra are obtained at LNT.
The normal vibrations of the water molecules appear in the high frequency region of 3000 -4500 cm −1 .The three crystallographically different water molecules (C 1 site symmetry) in the structures of the Tutton sulfates are expected to display six infrared bands corresponding to the asymmetric and symmetric modes,  3 and  1 respectively.However, due to the strong interactions of identical oscillators O-H the different normal modes overlap and as a result one broad band centered at about 3230 cm −1 is observed in the spectra of the double Tutton salts (with exception of the copper compound) (Figure 10).
Three bands corresponding to  2 of the three crystallographically different water molecules are observed in the spectra of the compounds under study: 1709, 1630 and 1553 cm −1 (magnesium); 1734, 1641 and 1560 cm −1 (cobalt); 1734, 1631 and 1574 cm −1 (nickel); 1734, 1626 and 1590 cm −1 (copper), and 1734, 1621 and 1548 cm −1 (zinc).The band positions of the stretching modes indicate that comparatively strong hydrogen bonds are formed in the sulfates and the hydrogen bond strengths do not depend on the M'' chemical nature.The appearance of a band at a lower frequency (3100 cm −1 ) in the spectrum of the copper compound shows that stronger hydrogen bonds are formed in this salt as compared to other rubidium compounds.This spectroscopic finding is owing to the stronger synergetic effect of the Cu 2+ ions, i.e. to the strong Cu-OH 2 interactions (increasing of the acidity of the water molecules) [19,20].The formation of comparatively strong hydrogen bonds in the rubidium compounds is due to the strong proton acceptor capacity of the sulfate ions [19,20].
The water librations (rocking, twisting and wagging) appear in the region below 1000 cm −1 and a strong overlapping with vibrations of other entities in the structure is expected.Two types of water librations for the Tutton sulfates are discussed briefly in the literature-rocking and wagging, the former observed at higher frequencies [14].Each type is characterized with two broad bands.The water molecules bonded to the M'' ions via shorter M''-OH 2 bonds display water librations at higher frequencies as compared to those forming longer M''-OH 2 bonds (equatorial water molecules).The former M''-OH 2 bonds are much more polarized due to the stronger syn- ergetic effect of the M'' ions (stronger metal-water interactions).The mean wavenumbers for the rocking librations are reported to have values of 855 and 740 cm −1 , and 770 and 680 cm −1 for the potassium and ammonium sulfates, respectively.The respective wagging modes have mean values of 570 and 441 cm −1 for the potassium compounds, and 544 and 425 cm −1 for the ammonium ones [14].Thus, the bands in the interval of 895 -751 cm −1 are attributed to the rocking modes of the water molecules and the bands in the region of 589 -507 cm −1 to the wagging modes.The close wavenumbers of the water librations confirm the claim that the hydrogen bonds formed in the rubidium Tutton sulfates are of close strength (see Figure 9).

Infrared Spectra of 2 4 SO  Ions Matrix Isolated in Tutton Selenates
The method of crystal matrix-spectroscopy provides important information about the local potential at the lattice sites where the guest ions are located as deduced from their extent of distortion and the chemical nature of the ligand environments in the lattice.When the polyatomic ions are doped in host lattices at low concentration (up to 2 -7 mol%) the correlation field splitting, the dispersion of phonon curves (due to the interactions between identical oscillators) and LO/TO splitting effects (due to the long-range forces of electrostatic origin) are neglected.Thus, the vibrational spectra of the guest ions are determined by the site symmetry, which is assumed to be the same as that of the respective host ions (substitutional mixed crystals).The spectra of matrix-isolated polyatomic ions are an excellent probe of the local potential at called an energetic distortion in order to distinguish it from the geometrical distortion revealed by structural data [21][22][23].Both the site group splitting of the asymmetric modes ( as ) and the value of  max (the difference between the highest and the lowest wavenumbered components of the stretching and bending modes, respectively) are an adequate measure for the degree of energetic distortion of the polyatomic ions [22,24,25].Recently, the value of the ratio  as / c (where  c is the centro-frequency value of the asymmetric modes) has been proposed to calculate the relative splitting of the dopant ions [26].
The matrix-isolated SeO  host ions.Bands of small intensities around 980 cm −1 appear in the spectra which are assigned to  1 of the guest sulfate ions (the spectra are recorded at higher concentrations of the samples in KBr in order to distinguish the  1 mode; the spectra are not shown; see Table 8).When the larger 2 4 SeO  host ions are replaced by the smaller SO  guest ions are slightly shifted to lower frequencies as compared to those of the same ions in the neat sulfate compounds due to the smaller repulsion potential of the selenate matrices, i.e. to the larger unit-cell volumes of the respective selenates (compare Tables 7 and 8).
Several factors are expected to influence on the values of  3 and  3 / c : 1) the chemical nature of the metal ions; 2) the repulsion potential of the selenate matrices, and 3) the strength of the hydrogen bonds.The spectroscopic experiments show that the distortion of the 2 4 SO  guest ions as deduced from the values of  3 and  3 / c increase on going from the potassium to the ammonium compounds (see Table 8).The formation of hydrogen bonds between the  local potential at the lattice sites where the sulfate ions are located (i.e. to the larger unit-cell volumes of the rubidium selenates) [39].
As far as the influence of the M'' ion nature on the values of  3 and  3 / c of the sulfate ions is concerned the spectroscopic experiments show that the sulfate ions are stronger distorted in the case of (NH 4 ) 2 M(SeO 4 ) 1.98 (SO 4 ) 0.02 •6H 2 O (M = Ni, Cu, Zn) and Rb 2 Cu(SeO 4 ) 1.98 (SO 4 ) 0.02 •6H 2 O.These findings are due probably to the formation of stronger hydrogen bonds in these compounds, i.e. to the stronger interaction between the water molecules of the host compounds and the sulfate guest tetrahedra (stronger proton donor capacity of the water molecules coordinated to the copper, zinc and nickel cations, i.e. to the stronger synergetic effect of these ions) [19,20].
2) Isostructural compounds, Rb 2 M(SO 4 ) 2 •6H 2 O (M = Mg, Co, Ni, Cu, Zn), crystallize from the ternary solutions within wide concentration ranges due to the strong complex formation processes in the solutions.
3) Comparatively strong hydrogen bonds are formed in the rubidium Tutton sulfates as deduced from both the wavenumbers of the stretching modes of the water molecules and the water librations due to the strong proton acceptor strength of the sulfate ions.
4) The degree of energetic distortion of the

4 SO
-H 2 O (M = Mg, Co, Ni, Cu, Zn) at 298 K.The double Tutton compounds Rb 2 M(SO 4 ) 2 •6H 2 O are characterized by means of both the infrared spectroscopy and the X-ray powder diffraction methods.The vibrational behavior of 2  guest ions matrix-isolated in Tutton selenates,

3. 1 .
Solubility Diagrams of the Three-Component Systems Rb 2 SO 4 -MSO 4 -H 2 O (M = Mg, Co, Ni, Cu, Zn) at 298 K The solubility diagrams of the above systems are presented in Figures 2-6 (the respective experimental data

Figure 7 .
The double salts form monoclinic crystals .The calculated unit-cell parameters are presented in Table

Figure 10 .
Figure 10.Infrared spectra of Rb 2 M(SO 4 ) 2 •6H 2 O (M = Mg, Co, Ni, Cu, Zn) in the region of the stretching and bending modes of the water molecules.

4 NH
 ; M'' = Mg, Co, Ni, Cu, Zn; x is approximately 0.02) are presented in Figure 11.The infrared spectroscopic characteristics of the matrix-isolated 2 4

2 4 SO
 ions exhibit three bands corresponding to  3 in agreement with the low site symmetry C 1 of the 2 4

2 4 SO
 guest ions the mean values of the asymmetric stretching modes  3 of the2 4

Table 7
(for comparison the