CoSO 4 ·H 2 O and its continuous transition compared to the compression properties of isostructural kieserite-type polymorphs

: The kieserite-type compound cobalt(II) sulfate monohydrate, CoSO 4 ·H 2 O, has been investigated under isothermal ( T = 295 K) hydrostatic compression up to 10.1 GPa in a diamond anvil cell by means of single-crystal X-ray diffraction and Raman spectroscopy. The monoclinic α -phase (space group C 2/ c ) undergoes a second-order ferroelastic phase transition at P c = 2.40(3) GPa to a triclinic β -phase (space group P 1). Lattice elasticities derived from ﬁ tting third-order Birch-Murnaghan equations of state to the pressure dependent unit-cell volume data yield V 0 = 354.20(6) Å 3 , K 0 = 53.0(1.7) GPa, K ′ = 5.7(1.8) for the α -phase and V 0 = 355.9(8) Å 3 , K 0 = 45.2(2.6) GPa, K ′ = 6.6(6) for the β -phase. Crystal structure data of the high-pressure polymorph were determined at 2.98(6) and 4.88(6) GPa. The most obvious structural feature and thus a possible driving mechanism of the phase transition, is a partial rearrangement in the hydrogen bonding system. However, a comparative analysis of pressure-induced changes in the four kieserite-type compounds investigated to date suggests that the loss of the point symmetry 2 at the otherwise rather rigid SO 4 tetrahedron, allowing symmetrically unrestricted tetrahedral rotations and edge tiltings in the β -phase, could be the actual driving mechanism of the

Apart from a magnetic order-disorder transition reported for FeSO 4 ·H 2 O at 29.6 K [20], none of the M(II) SO 4 ·H 2 O compounds hitherto studied under variation of temperature reveal any temperature-induced structural phase transitions [14,15]. At high pressures, however, endmember representatives with M(II) = Fe, Ni, and Mg display a ferroelastic phase transition under hydrostatic conditions [16][17][18]. The structural transformation is accompanied by a symmetry change from C2/c to P1 with a critical transition pressure occurring between 2.47 and 6.15 GPa. The mechanism of the phase transition shows all the properties of a typically continuous transformation, without any detectable volume discontinuity and without hysteresis with respect to the direction of transformation. From point of view of structural chemistry, a comparable, purely displacive mechanism for the transformation has been derived for the three representatives (i.e. FeSO 4 ·H 2 O, NiSO 4 ·H 2 O and MgSO 4 ·H 2 O) investigated so far. Without changing the actual polyhedral topology, the lattice distortion leads only to changes in the hydrogen bonding system, in which a shortened interpolyhedral O···O contact is included as acceptor, following the symmetry changes involved. For NiSO 4 ·H 2 O a second very subtle transition was discussed at higher but still hydrostatic pressure conditions and was explained from a crystallographic point of view by a disordered oxygen position, which in turn leads to a further diversification of the existing hydrogen bonds.
For any systematic interpretation of the critical quantities, which are driving the actual transformation and which determine the relative stability criteria between the two polymorphs involved, too few crystallographic data have been available so far. In order to be able to assess the systematic relationships and influencing variables, the role of the different cations and their size, the cobalt representative CoSO 4 ·H 2 O and its high-pressure behavior have been determined in the course of this work.

Synthesis of CoSO 4 ·H 2 O
Sample crystals were grown under low hydrothermal conditions by a similar technique to that described earlier [12][13][14][15]

High-pressure sample environment
Selected crystals of CoSO 4 ·H 2 O were loaded into ETH-type [21] diamond-anvil cells (DAC) equipped with either standard brilliant-cut or Böhler Almax-type [22] type-I diamond anvils (culet diameter = 0.6 mm). Pressure chambers were prepared from stainless steel gaskets pre-indented to ∼90-100 μm thickness with boreholes with 250 μm in diameter. 4:1 methanol-ethanol mixtures were used as pressure-transmitting medium for the X-ray diffraction investigations, while in-situ vibrational spectroscopy was carried out on crystals pressurized in cryogenically loaded argon. Pressures were determined using conventional quartz and ruby standards, applying calibration according to [23] and [24], respectively. The uncertainties in pressure obtained by the internal quartz standard were derived from the unit-cell volume data and their estimated standard deviations. Those obtained from the R 1 -line shift of the ruby luminescence spectra have been estimated to be ±0.06 GPa after averaging repeated measurements.

In-situ Raman investigations
In-situ Raman spectra were collected from a 140 × 70 × 50 µm 3 sized CoSO 4 ·H 2 O crystal compressed in dense argon. Spectra were acquired by means of a confocal Horiba Jobin Yvon LabRAM-HR 800 spectrometer using a red He-Ne laser source (operated at 20 mW power at a wavelength of 632.8 nm), an Olympus BX41 microscope, a mercury-cadmium-telluride detector, and an Olympus LMPlanFL N 50× objective with a long working distance of 10.6 mm. A diffraction grating with 600 lines per mm was used for the measurements, and spectra were acquired using the software LabSpec 6 (HORIBA Scientific) in the spectral range from 35 to 1190 cm −1 shift with an exposure time of 2 × 60 s. The recorded spectra were fitted with the Gauss-Lorentz-area method after background subtraction achieved using the program Peakfit 4.1.2 (Systat Software Inc.).

2.4
Single-crystal X-ray diffraction XRD Bragg peak positions were measured on a Stoe AED II diffractometer using a conventional scintillation counter, non-monochromatized Mo radiation, with the peak centering procedure being controlled through the SINGLE [25] software. For each pressure point, [16][17][18][19][20][21][22][23] individual Bragg reflections were measured in the 8-position centering mode [26]. Lattice parameters were refined in a first step without any symmetry constraints in order to identify changes in metrics and were finally constrained to monoclinic symmetry for the data points ≤2.40(3) GPa. The equations of state (EoS) were fitted by applying weighted least-square techniques using the software EoSFit7 [27]. Normalized pressure-strain analyses were carried out in order to determine the relevant order of truncation of the Birch-Murnaghan (BM) EoS. Intensity data collections were performed on a bicrystal mount (crystal sizes: 230 × 30 × 30 µm 3 and 240 × 50 × 40 µm 3 ). The intensity data sets were measured on a Stoe StadiVari diffractometer using a DECTRIS Pilatus 300K detector with a 450 μm silicon layer and an air-cooled Incoatec IμS molybdenum high-brilliance micro-focus tube source (50 kV, 1 mA, beam size ≈ 110 µm). Frames were collected with angular steps of 0.5°in ω rotational mode with the χ circle fixed to a value ranging from 0°to 90°. Data were collected on both sides of the DAC as achieved by a 180°rotation of the φ circle after each run. The exposure time was set to 100 s per frame. Intensities were integrated using the X-area 1.72 (STOE & Cie GmbH) software and corrected for absorption through the sample and DAC components by using the ABSORB [28] code. Initial positional parameters for the refinements were assigned according to those reported by [16]. Hydrogen positions were derived from difference-Fourier summation and refined with an isotropic displacement parameter U iso , for the high-P data sets constrained to a value of 0.05 Å 2 . All refinements were carried out using neutral scattering curves from the International Tables for Crystallography [29] using SHELXL [30] and the graphical user interface SHELXLE [31]. For data sets measured in the DAC, refinements were carried out with isotropic displacement parameters even for the oxygen atoms, while the 1-bar data were refined with anisotropic displacement parameters for all non-hydrogen atoms. For consistency it should be mentioned that the hydrogen bond donor atom here referred to as Ow corresponds to the O3 atom reported elsewhere [e.g. 11-15, 18, 20].
CSD 2099572-2099574 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam. ac.uk/data_request/cif.

Evidence of transformation in CoSO 4 ·H 2 O Raman spectra
In-situ high-pressure Raman spectra have been collected in a sequence of 24 individual spectra in total, recorded between 0.4 and 10.1 GPa (Figure 1). All spectra were acquired in the Raman shift range 35-1190 cm −1 , while any attempt to measure the vibration response related to the molecular H 2 O in the range 2600-3500 cm −1 failed due to high background luminescence. , and can be assigned following [15]. The typical blueshifts on increasing pressure correspond to rates between 1.52(4) and 7.62(7) cm −1 /GPa for the bands at 1027.2(2) and 279.0(5) cm −1 , respectively. As with the other isostructural representatives, the appearance of the bands and their pressure dependencies in CoSO 4 ·H 2 O do not necessarily reveal a transformation immediately. This finding once again indicates that the changes in the crystal structure are only very subtle and do not involve a change in coordination or any comparable change related to the bonding topology. Only on closer inspection, one recognizes for several bands that the quasilinear shift slightly changes its slope at around 2.4 GPa, with different dṽ/dP values before and after the presumable critical pressure (Figure 1). This observation was also made earlier with the isotypic compounds, where evidence for potential transformations has also been attributed exclusively to the change in the dṽ/dP slopes. The lack of band splitting also applies to CoSO 4 ·H 2 O, which can be attributed to the fact that the point symmetries of the most prominent functional groups remain largely unchanged across the transformation itself. A splitting of the prominent ṽ 1 (SO 4 ) stretching mode as described for the Ni representative, forming a shoulder on the low-frequency side of this band, could not be observed. Hence, a further transformation, inferable from such diagnostic features, was not detected in CoSO 4 ·H 2 O within the investigated pressure range.

Lattice properties and static elasticity of CoSO 4 ·H 2 O
The lattice properties, on the other hand, show a completely different picture with evident changes that clearly reveal a triclinic distortion of the originally monoclinic structure   Figure 2). Precise lattice parameters and the unitcell volume were measured at 32 pressure points under hydrostatic conditions between 0.51 and 8.94 GPa. Both the base vector lengths a, b and c but also the deviations from angles set for the monoclinic system suggest the onset of transformation between 2.40 and 2.63 GPa. The adherence to identical parameters within the reduced cell (i.e. a red = b red , α red = β red ) in the monoclinic low-pressure phase, compared to the apparent diversification of these values at higher pressures, clearly proves the triclinic distortion (Table 1, Figure 2). The fashion of distortion is absolutely equivalent to what has been reported for the other kieserite-type monohydrates [16][17][18]. Moreover, the calculated spontaneous strain matches the previously reported evolution of strain tensor components and their eigenvalues. A fit of the lattice angle γ follows the power- law function with a critical exponent β being close to the ideal value of 0.5 as typical for a second-order phase transition.
Fitting the values for the unit-cell volumes and the base vectors in superordinate C2/c setting ( Figure 2) to parametrized equations of state (EoS), the resulting moduli, i.e. the bulk modulus K and the axial moduli M i and their pressure derivatives, match very well with those for the other isostructural kieserite-type representatives ( Table 2). The EoS fits for the low-P polymorph α-CoSO 4 ·H 2 O are limited to a relatively narrow pressure range between 10 −4 and 2.4 GPa and are restricted to 8 data points. A fit according to a thirdorder Birch-Murnaghan (BM-3) formalism [32] yields K 0 = 53.0 ± 1.7 GPa with dK/dP = 5.7 ± 1.8, which fits into the series of values being greater than 4, thus confirming equivalent compression behavior for the C2/c α-form of the kieserite-type compounds. The re-evaluation of the volume data of α-NiSO 4 ·H 2 O shows 65.9 ± 6.7 GPa with dK/dP = 2.3 ± 4.6 for an unconstrained equivalent BM-3 fit, whereas it yields 60.1 ± 1.0 GPa for dK/dP set to 6.5. The unconstrained fit to the data of α-MgSO 4 ·H 2 O provides K 0 = 48.1 ± 0.5 GPa with dK/dP = 8.1 ± 0.6. The comparable values obtained in this way also correspond to the Anderson-Anderson relationship [33], with indirectly proportional relationships between the volume compressibility and the molar volume within an isostructural series. Even if the absolute numbers for the individual crystallographic directions are subject to somewhat greater fluctuations, a comparable behavior is also proven for the compressional anisotropy. The a-axis is the stiffest, while along the directions of the crystallographic b-and c-axes the compressibilities are more or less similar for each of the four representatives ( Table 2).
The elastic properties of the lattice of the high-pressure polymorph (β-CoSO 4 ·H 2 O) offer a similar picture, both in terms of volume compressibility and anisotropy ( Table 2). It is noteworthy that dK/dP for the β-phase of all representatives is much closer to the value K′ = 4. Moreover, the anisotropy is once again similar, and more or less the same in comparison to the α-phase, which is not surprising, since the two structures have identical bond topologies with different symmetries. The high-pressure range beyond 7 GPa deserves special attention, since subtle deviations from linear developments have been seen as an indication of the existence of a further phase, namely the γ-form of the Ni(II)-kieserite analogue [18], comprising a disordered O2B hydrogen bond acceptor position (cf. Figure 3) and hence a further diversified hydrogen bonding system. Despite all the similarities that are evident in many respects, especially between the Co(II) and Ni(II) analogue phases, a comparably significant deviation could not be observed. As a result from the findings in this study, we refrain from postulating the existence of an equivalent γ-CoSO 4 ·H 2 O polymorph within the investigated pressure range.

Crystal structure of the β-CoSO 4 ·H 2 O polymorph
In-situ high-pressure crystal structure investigations on CoSO 4 ·H 2 O were performed at 3.0 and 4.9 GPa from a bicrystal mount in a DAC, in addition to single-crystal data collection at ambient pressure from a sample mounted on a glass fibre. While the 1-bar structure was refined in C2/c according to [12] (matching the recent refinement by [13] very closely), all high-pressure crystal structures were refined in P1 in the setting of the reduced cell according to [16][17][18]. The final refinements confirm the space-group symmetries, which have also been reported earlier for the analogue phases and polymorphs of Mg(II), Fe(II) and Ni(II). Details of the intensity data collections and the results of refinements are summarized in Table 3, the resulting positional parameters and refined displacement parameters are listed in Table 4, and selected interatomic distances are summarized in Table 5. Selected sections of the crystal structures of αand β-CoSO 4 ·H 2 O are compared in Figure 3. While the S atoms occupy a single position in both space groups, the Co atoms are located on two individual sites (i.e. CoA and CoB) in P1. The same applies to the O1 and O2 sites, which both split into two independent sites (O1A, O1B, and O2A, O2B), while the Ow position maintains a single site both in C2/c and P1. The sulfate tetrahedron loses its former point symmetry 2 in the triclinic highpressure polymorph.
The SO 4 group behaves as rather rigid unit over the full investigated pressure range, whereas mean Co-O distances and volumes of both Co(A/B)O 6 octahedra steadily decrease with pressure, albeit in a somewhat different way for the A and B site in the high-P polymorph ( Table 5, see also next section). As the kieserite-type structure topology remains the same across the phase transition, the structure accommodates increasing densification by mutual polyhedral tiltings and rotations. The bond angles at the   bridging oxygen atoms (O1 and O2 both linking an octahedron with a tetrahedron, and the water molecule with Ow providing the link within the octahedral chains) undergo significant changes to generally smaller values, thus substantially reducing the volume of interpolyhedral voids. This results, as the most striking feature, in a partial modification of the hydrogen bonding scheme: In the monoclinic α-form, two symmetrically equivalent Ow-H···O2 hydrogen bonds (Figure 3(a)  given as respective average and shortest values for water molecules) contribute to the linkage between adjacent octahedral chains; in the triclinic β-phase, an additional weaker Ow-H2···O1B bond (2.94 Å at 4.88 GPa) is formed and a minor diversification of the further strengthened Ow-H(1/2)···O2 (A/B) bonds occurs (Table 5, Figure 3(b)). This rearrangement was also assumed to be a major driving force for the pressureinduced αto β-transformation in other kieserite-type compounds [16][17][18] A and B) show the highest relative compressibilities, despite the comparatively small ionic radius and short ambient <Mg-O> of 2.078 Å [13], even exceeding the compressibility of the clearly larger FeO 6 octahedra. The polyhedral modulus K oct of the Mg octahedra is only ∼65-70 GPa, which corresponds to a compressibility approximately twice as large compared to the values usually found for MgO 6 in any oxide and silicate (∼150 GPa [36]). On the other hand, the smallest octahedron around Ni exhibits, as expected, the highest stiffness within this group. The polyhedral connectivity through shared corners and the presence of H 2 O ligands explains the generally high octahedral as well as bulk volume compressibilities of this structure type. In cases where the compressibilities of A and B octahedra differ significantly and consistently (i.e. Mg and Ni), the B octahedron is the more compressible one. For all four compounds, the octahedral bond length distortions decrease more or less in a similar fashion, with the respective angular distortions increasing steadily (Figure 4(c)).
A closer look at the individual M-O distances in Figure 4(a) reveals that the longest bonds to the Ow water molecules shorten the strongest, whereas the M-O1 bonds, oriented roughly along the monoclinc a-axis, are the stiffest ones, thus contributing to the observed high respective axial moduli M a ( Table 2). As illustrated in Figure 4(d), these differences also change the type of octahedral distortion with increasing pressure from a clearly elongated [4+2]-coordination (with a tendency towards [2+2+2] in FeSO 4 ·H 2 O, as discussed by [14]) to a rather regular proper [6]-fold coordination for the A-octahedra of Co and Ni, and to even a [2+4]-type for Fe(A), whereas the B-octahedra tend to keep the former shape within the α-phases. However, only the MgO octahedra both maintain the distinct [4+2]-elongation present at ambient conditions.
In contrast, the sulfate tetrahedron behaves as a rather rigid unit within limits of error in all four compounds and over the full pressure ranges investigated. A tendency from the expected overall mean <S-O> bond length of 1.473 Å [37] at ambient pressures towards marginally smaller values with pressure is hardly significant (especially considering that the ambient data were obtained without Table : Crystal data and details of the intensity data collections and structure refinements for CoSO  ·H  O at  − , . and . GPa.   Wyck. Wyck. the DAC), neither in the four kieserites nor in limited data on high-pressure single crystal structure investigations on sulfates from the literature; e.g. for kainite, KMg(SO 4 )Cl· 3H 2 O [38], a reduction by only 1% within ∼12 GPa was found, and in gypsum [39], Ca(SO 4 )·2H 2 O, as well as in blödite [40], Na 2 Mg(SO 4 ) 2 ·4H 2 O, the <S-O> distances remain almost unchanged up to 4 and 10 GPa, respectively. In spite of its incompressibility, the SO 4 group plays an important role for the structural changes in the kieseritetype compounds with pressure. On the one hand, interpolyhedral M-O-S angles at the linking oxygen atoms O1 and O2 decrease with pressure ( Figure 5(a)). This also applies to the octahedral chain angle M-Ow-M, indicating enhanced tilting and folding to reduce the interpolyhedral voids with increasing pressure. While the angles at Ow and O1(A/B) continue this trend across the phase transition, there is a strong differentiation between O2A versus O2B in the β-phases. Here it has to be mentioned that also under pressure these angles remain larger in the Mg phase compared to the other M(II) representatives, which has been attributed by [13] to the respective absence or presence of partly filled 3d orbitals and related differences in Values at P c are interpolated from the bracketing data points in the αand β-phase. For errors see the underlying structural data in [16][17][18] and Tables 3-5.  On the other hand, Figure 5(b) illustrates that only the loss of the twofold symmetry of the SO 4 tetrahedron at the phase transition allows really substantial tetrahedral rotations especially of the O1-O2 edges, as well as (in part counteracting) edge tiltings, as indicated in Figure 3(b). These edge tiltings are particularly strong and eye-catching in case of the O1A-O1B edge, which in the monoclinic α-phases is forced by symmetry to lie strictly perpendicular to the b-axis. In case of the title compound shown in Figure 3, O1A-O1B is tilted by 7.6°at 4.9 GPa, increasing up to 11.5°in the Fe-phase at 9.2 GPa. In our opinion, the symmetry breaking of the SO 4 tetrahedron at the critical pressure is the decisive driving mechanism of the phase transition. The significantly higher P c in the Fe-compound might then be attributed to the larger and thus more flexible FeO 6 octahedron with its tendency towards a [2+2+2]coordination already at ambient conditions, which is pursued by the other compounds with increasing pressure (Figure 4(d)).
A further argument to assign the change in the hydrogen bonding scheme, depicted in Figures 3 and 5(c), rather to a side effect than to the driving mechanism of the phase transitions is found in the evolution of the bond valences at the acceptor oxygen atoms with pressure. As Figure 5(d) shows, the 'new' acceptor oxygen O1B exhibits the respective highest bond valence sums of all oxygen atoms in the respective β-phases, i.e. there seems to be no 'need' for O1B to act as acceptor to satisfy its bonding requirements (note thatin order to reduce bias due to the comparatively high uncertainties in the S-O bond lengthsthe respective values at 10 −4 GPa were used at all pressures for the calculation of bond valences according to [41]).

Conclusion
The kieserite-type compound α-CoSO 4 ·H 2 O undergoes a ferroelastic phase transition at 2.40(3) GPa from a monoclinic C2/c to a triclinic P1 phase, in analogy to those observed already for the respective compounds of Mg, Fe, and Ni. A further transition to a disordered γ-phase, as detected for NiSO 4 ·H 2 O, could not be observed within the experimentally accessible pressure range. The most significant structural change under compression is a modification of the hydrogen bonding scheme from two equivalent Ow-H···O2 bonds at ambient conditions to include an additional weaker Ow-H2···O1B bond in the β-phase. This has also been assumed so far as the main driving mechanism of the C2/c to P1 phase transition. However, the present comparison of topological and crystal chemical data including bond valence calculations suggests that the loss of point symmetry 2 of the sulfate tetrahedra, allowing symmetrically unrestricted tetrahedral rotations and edge tiltings, could be the actual driving mechanism of the phase transition. Moreover, it appears that among the series of isotypic kieserite-type (c) hydrogen bond lengths Ow···O2/O1; (d) bond valence sums for oxygen atoms (without contribution of H atoms). The critical pressures P c of the C2/c to P1 phase transitions are indicated by vertical lines. Values at P c are interpolated from the bracketing data points in the αand β-phase. For errors see the underlying structural data in [16][17][18] and Tables 3-5. compounds, specific peculiarities of the Mg-compound (e.g. larger angles at linking oxygen atoms) and Fecompound (e.g. deviating style of octahedral distortion) are maintained also in their respective high-pressure β-phases.