High-Pressure Behavior of Nickel Sulfate Monohydrate: Isothermal Compressibility, Structural Polymorphism, and Transition Pathway.

Single crystals of synthetic nickel sulfate monohydrate, α-NiSO4·H2O (space-group symmetry C2/c at ambient conditions), were subject to high-pressure behavior investigations in a diamond-anvil cell up to 10.8 GPa. By means of subtle spectral changes in Raman spectra recorded at 298 K on isothermal compression, two discontinuities were identified at 2.47(1) and 6.5(5) GPa. Both transitions turn out to be apparently second order in character, as deduced from the continuous evolution of unit-cell volumes determined from single-crystal X-ray diffraction. The first structural transition from α- to β-NiSO4·H2O is an obvious ferroelastic C2/c-P1̅ transition. It is purely displacive from a structural point of view, accompanied by symmetry changes in the hydrogen-bonding scheme. The second β- to γ-NiSO4·H2O transition, further splitting the O2 (hydrogen bridge acceptor) position and violating the P1̅ space-group symmetry, is also evident from the splitting of individual bands in the Raman spectra. It can be attributed to symmetry reduction through local violation of local centrosymmetry. Lattice elasticities were obtained by fitting second-order Birch-Murnaghan equations of state to the p-V data points yielding the following zero-pressure bulk moduli values: K0 = 63.4 ± 1.0 GPa for α-NiSO4·H2O, K0 = 61.3 ± 1.9 GPa for β-NiSO4·H2O, and K0 = 68.8 ± 2.5 GPa for γ-NiSO4·H2O.

Introduction

Hydrated sulfate salts and their behavior under extreme conditions are the subject of intensive research, as they are widespread on surfaces of planets, their moons, and presumably even exoplanets.[1−6] The extreme temperature (T) oscillations on planetary surfaces and the extraordinary pressures (p), along with high-p/high-T variations inside the icy satellites, may lead to structural instabilities and phase transitions. This may include changes of the hydration state, as exemplified by the p-induced dehydration reactions and described for the MgSO4·nH2O (0 ≤ n ≤ 11) series.[7−10] However, it can also involve incongruent melting[11] or polymorphism with associated structural phase transitions.[12] The Ni-enrichment in solid phases[5] in the ternary system NiSO4–MgSO4–H2O together with high Ni concentrations in the sulfate-rich soluble fraction of natural meteorite samples[13] emphasize the particular importance of nickel sulfate components, which are also known as the rare terrestrial hydrate minerals morenosite (n = 7), retgersite (n = 6), and dwornikite (n = 1).[14]

The monohydrates of divalent cations have received particular attention, since they apparently represent considerably stable solids. They have been observed on Mars and Jovian moons Ganymede and Callisto, preferably as the monohydrated magnesium sulfate mineral kieserite. Their large structural flexibility leads to the existence of various end-member representatives (M2+SO4·H2O with M2+= Mg, Mn, Fe, Co, Ni, Zn)[15,16] and their solid solutions.[17−19] This also includes selenates,[20] and in rare cases even phosphates such as Mn3+PO4·H2O.[21,22] The structure type has already been determined in space group C2/c by Leonhard and Weiss.[23] It can be described as a three-dimensional heterodesmic framework, which consists of continuous octahedral chains of corner-sharing [MO4(H2O)2]6– units running along the [001] direction, and which are cross-linked through the tetrahedral SO4 units. Within the given C2/c symmetry, the M and S atoms each occupy a single crystallographic site. The barycenter of the water molecule (Ow) is also located on a unique site. Due to the site symmetry of the Ow atoms on this position, the hydrogen bonding system exhibits 2-fold symmetry with two Ow-H···O hydrogen bonds of medium strength,[15,24,25] as well as two further intermolecular O···O contacts, not involved in the H-bonding scheme under ambient conditions.

Apart from the kieserite aristotype compounds with C2/c symmetry, CdSO4·H2O was found to crystallize in a different monoclinic space-group symmetry,[26] i.e., in the maximal nonisomorphic subgroup P21/n, which was attributed to the relatively larger size of the Cd2+ atoms located on the octahedral site. Moreover, the Jahn–Teller effect of Cu2+ was found to be responsible for a cooperative lattice distortion resulting in the triclinic space group P1̅ in CuSO4·H2O.[16,25] Recent investigations on MgSO4·H2O and FeSO4·H2O under hydrostatic compression revealed a ferroelastic phase transition following the translationsgleiche C2/c-P1̅ group–subgroup relation and being apparently second order in its thermodynamic character.[27,28] Any of the symmetry changes follow a pattern of atom displacements related to the changes within the hydrogen bonding systems, whereas the topology of the heterodesmic frameworks remains unchanged, apart from distortion originating from symmetry breaking. In this context, synthetic NiSO4·H2O single crystals are investigated in this study with respect to the occurrence of an equivalent structural polymorphism. In particular, we examine how the critical size and the electronic configuration of the cations on the M site influence the stability of the low-symmetry polymorphs to better understand the mechanism and pathway of structural transitions. Investigation of the high-p behavior of the Ni end member of this type of sulfate is essential from the cosmochemical point of view, given the potential presence and distribution of hydrated sulfates inside icy planetary bodies.

Materials and Methods

Synthesis

Sample crystals were grown under low hydrothermal conditions using a similar technique to that described by Talla and Wildner[29] within a temperature range between room temperature and 210 °C at moderate autogenous vapor pressures using polytetrafluoroethylene (PTFE)-lined autoclaves. Subeuhedral crystals formed from a supersaturated aqueous solution of sulfuric acid (∼0.25–0.75 mL concentrated H2SO4 (98%) + ∼0.5 mL H2O) added to ∼0.3 g of NiSO4·7H2O (Alfa Aesar, p.a.) inside the PTFE reaction chambers with ∼3–4 cm3 volume capacity. It was kept at T = 220 °C for 14 days and then cooled down to RT. The solid products were finally washed with pure H2O and ethanol and then dried overnight at T = 75 °C (cf. Supporting Information for more data).

High-Pressure Sample Environment

Selected crystals were loaded into ETH-type(30) diamond-anvil cells (DAC) equipped with either standard brilliant-cut or Böhler Almax-type[31] type-I diamond anvils using culet faces of ⌀ = 600 μm. Pressure chambers with ⌀ ≈ 250 μm were prepared using stainless steel gaskets preindented to ∼90–100 μm thickness. A 4:1 methanol–ethanol mixture was used as a p-transmitting medium for the single-crystal X-ray diffraction (scXRD) 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, following the calibration of Scheidl et al.[32] and Jacobsen et al.,[33] respectively. The estimated standard deviations (ESDs) of the p values obtained by the internal quartz standard were determined from the ESDs of the measured p-dependent unit-cell volume (V). The ESDs of the p obtained from the R1-line shift of the ruby luminescence spectra were estimated to be ±0.06 GPa after averaging repeated measurements.

Raman Spectroscopy

In-situ high-p Raman spectroscopy was carried out on several crystals (40 × 60 × 15 μm3, 110 × 95 × 20 μm3, 80 × 80 × 40 μm3, 40 × 50 × 40 μm3), together with ruby spheres as pressure calibrants,[34,35] all compressed in dense liquefied Ar. Spectra were collected by means of a confocal Horiba Jobin Yvon LabRAM-HR 800 spectrometer using a red He–Nd laser source emitting a beam with a wavelength of 632.8 nm and 20 mW, an Olympus BX41 microscope, and a mercury–cadmium–telluride detector. An Olympus LMPlanFL N 50× objective with a long working distance of 10.6 mm enabled focus of the laser beam onto the sample crystal inside the p chamber. A diffraction grating with 600 lines per millimeter was used for the measurements. High-p spectra were acquired using the software LabSpec 6 (HORIBA Scientific) in the spectral range from the 35 to 1190 cm–1 shift with an exposure time of 60 s and two accumulations. 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.).

Precise Measurement of Lattice Parameters

Sample crystals were compressed in a conventional methanol–ethanol mixture together with a quartz single crystal serving as the p reference. XRD Bragg peak positions were measured on a Stoe AED II and Huber 5042 diffractometer using a conventional scintillation counter and nonmonochromatized Mo radiation, with the peak centering procedure being controlled through the SINGLE(36) software. For each hydrostatic p point, 16 to 23 individual Bragg reflections were measured in the 8-position centering mode[37] to refine the respective unit-cell volumes. Lattice parameters were refined in a first step without any symmetry constraints in order to identify possible deviations in metrics and were finally constrained to monoclinic symmetry, if applicable. The equations of state (EoS) were fitted by applying weighted least-squares techniques using the software EoSFit7.[38] Normalized pressure-strain analyses were carried out in order to determine the relevant order of truncation of the Birch–Murnaghan (BM) EoS.

High-Pressure Crystallography

The scXRD intensity data collections were performed on a sample crystal (∼140 × 70 × 40 μm3) loaded in a methanol–ethanol mixture (see Supporting Information, Figure S1). The data sets were measured on a Stoe StadiVari X-ray diffractometer using a DECTRIS Pilatus 300 K detector with a 450 μm silicon layer and an air-cooled Incoatec IμS molybdenum high-brilliance microfocus tube source (50 kV, 1 mA, beam size ≈ 110 μm) at p = 0.6(1), 2.3(1), 4.5(1), and 8.4(1) GPa. 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(39) code. Indexing of the reconstructed reciprocal space yielded monoclinic lattice metrics for the measurements at 0.6(1) and 2.3(1) GPa, while at 4.5(1) and 8.4(1) GPa triclinic metrics were found. Initial positional parameters for the refinements were assigned according to those reported by Meusburger et al.[28] All refinements were carried out using scattering curves from the International Tables for Crystallography[40] and isotropic displacement parameters for all atoms using SHELXL(41) and the graphical user interface ShelXle.[42]

Results and Discussion

Evidence for Transformations in Raman Spectra

A sequence of, in total, 17 Raman spectra of NiSO4·H2O, as recorded in situ under hydrostatic high-p conditions between 0.46(6) and 10.80(6) GPa, is displayed in the Figures and 2 for the Raman shift range 35–1190 cm–1. Any attempt to measure the vibrational response related to the H2O molecule for the Raman shift range 2600–3500 cm–1 failed because of luminescence contributions from the sample and the diamond anvils. A focus on the internal modes in the ranges 35–690 cm–1 (Figure ) and 970–1190 cm–1 (Figure ) revealed the most prominent bands as described for isostructural MgSO4·H2O and FeSO4·H2O.[27−29,43] These are the external lattice vibrational modes with wavenumbers (as determined at 1 bar) assigned to 129 and 138 cm–1 (lattice vibrations); 200, 246, 265, and 295 cm–1 (translational modes of either the octahedrally coordinated M position or the H2O ligand); 419 and 518 cm–1 (ν2 mode of SO4); 622 and 629 cm–1 (ν4 of SO4); 1021 cm–1 (ν1 of SO4); and 1040, 1076, and 1095 cm–1 (ν3 of SO4). For a further detailed description, see Talla et al.[44] The high-p spectra reveal the typical average blueshifts with Δν̅/Δp values ranging between 2.42(7) and 7.45(8) cm–1 GPa–1 (Figure ).

Figure 1

Sequence of high-pressure Raman spectra obtained from a NiSO4·H2O single crystal under hydrostatic compression, indicating a phase transition occurring between 2.30(6) and 2.94(6) GPa.

Figure 2

A close-up of the sulfate stretching bands of NiSO4·H2O. The emerging shoulder on the low-energy side of the marked Raman band, evident in all Raman spectra at p > 6.4 GPa, indicates the second phase transition with a critical transition point between 6.36(6) and 7.41(6) GPa.

Figure 3

Pressure dependence Δν̅/Δp of selected Raman bands as obtained from in situ high-pressure Raman spectra of NiSO4·H2O. Specific data point colors help to interpret the correlation matrix and PCA plot (Figure S3).

The spectral evolution and the lack of drastic changes with respect to band positions, numbers, and intensities of modes suggest that the structural topology should be largely retained across the recorded p range. Nevertheless, subtle and more or less pronounced changes in the Δν̅/Δp rates can be observed, which suggests two intervals of potential structural changes, i.e., between 2.30(6) and 2.94(6) GPa (Figure ) and between 6.36(6) and 7.41(6) GPa (Figure ). Apart from an emerging shoulder followed by a significant splitting of the ν1(SO4) mode located at 1021 cm–1 (at 1 bar), new weak modes in the low-frequency range similar to those reported for MgSO4·H2O and FeSO4·H2O[27,28] have not been observed. This can be simply explained as the arbitrary orientation of samples does not necessarily allow all modes to be recognizable with comparable intensities. Compared to Meusburger et al.,[27,28] in NiSO4·H2O there is evidence for a second potential structural change within the experimentally accessible p regime. The first is represented by a potential soft mode, which is just within the measurable range around 58 cm–1 (at 1 bar, Figure ). Taking a closer look at the splitting of the Raman band attributed to the ν1(SO4) mode indicates that there is more than one crystallographic independent sulfate group in the structure. The careful analysis of the spectra (Figure ) shows that the second band component starts emerging at p ≥ 7.41(6) GPa, and thus these spectral changes coincide with the second supposed discontinuity as described above. Considering that for the earlier reported C2/c-P1̅ transition in isostructural compounds[27,28] the structures of both polymorphs exhibit just one single S position, the second structural change must be accompanied by continued symmetry breaking, leading to the diversification of more than one S site. The current observation may thus be a possible indication of another structural change, which has not yet been recognized so far. In decompression, the second Raman band component seems to vanish at p ≤ 5.60(6) GPa (Figure S4), which means that the second potential transformation in contrast to the first one would show a hysteresis of about 1.8 GPa.

A detailed analysis of the fitted pressure-dependent Raman band shifts (Figure ) in addition to a correlation matrix of these band positions especially in the region between 240 and 525 cm–1 (see the Supporting Information, Figure S3) support the observation of two distinct structural transitions in NiSO4·H2O, especially with a subsequent principal component analysis (PCA) of these data (Figure S3, top right). This technique was for example previously successfully applied on Raman and powder X-ray diffraction data for the detection of subtle second order phase transitions in lawsonite.[45] However, only the second phase transition between 6.36(6) and 7.41(6) GPa could clearly be identified by a subsequent hierarchical cluster analysis (see dendrogram in the Supporting Information, Figure S2). The first two clusters, separated between 2.94(6) and 4.30(6) GPa, are most likely influenced by the relatively larger pressure steps facilitated under low pressure conditions. Tentative clusters were shown in the PCA plot (Figure S3, top right) using three ellipses. In some Raman band shift correlations, however, this separation is more obvious as manifested by a sudden discontinuity located between 2.30(6) and 2.94(6) GPa.

Lattice Properties under Isothermal Compression

Precise unit-cell parameters and unit-cell volumes were determined at 18 individual pressure points within the pressure range 10–4 to 8.67(1) GPa by means of single-crystal diffraction and applying unconstrained refinements of metric parameters (see Table S1 in the Supporting Information). In order to facilitate the comparison between monoclinic and triclinic lattices, the lattice parameters are provided in addition to the standard monoclinic C2/c setting in that of the reduced cell (with ared = bred ≠ cred, αred = βred ≠ γred for a monoclinic metric, see Supporting Information, Table S2). Plotting the cell parameters (Figure ) and lattice angles (Figure ) as a function of p, there is clear evidence of an obvious lattice distortion from monoclinic (ared = bred, αred = βred) to triclinic symmetry (ared ≠ bred, αred ≠ βred) at ∼2.66(1) GPa. The character of lattice distortion is identical to what has been observed for the isostructural compounds of Mg[28] and Fe,[27] and hence it can be assumed that it is the equivalent C2/c–P1̅ transformation. The evolution of all three lattice angles α, β, and γ with p (Figure ) provides again a clear proof in α and β for this first discontinuity, which starts between 2.38(1) and 2.66(1) GPa. This is less obvious for the refined base vector c (Figure ). While a and b reveal a clear disproportionation of their values in the setting of the reduced cell, the c axis appears to shrink continuously even across the first discontinuity following the typical trend of nonlinear length change with pressure.

Figure 4

Pressure-dependent evolution of the unit-cell basis vectors a, b, and c. The red and gray lines correspond to fits of BM-2 EoS up to 2.5 GPa, with the respective parameters for the axial moduli as quoted in Table .

Figure 5

Pressure-dependent evolution of the unit-cell angles in the basis-vector setting of the reduced cell. The red and gray lines correspond to linear fits including the data points up to 2.5 GPa.

Table 1

Least-Square Fitted BM-EoS Parameters of the Unit-Cell Volume and Lattice Parameters for Various End Member MSO4·H2O Polymorphs

phase, p range (GPa)	X0	K0, M0 (GPa)	K′, M′	phase P range (GPa)	X0	K0, M0 (GPa)	K′, M′
α-FeSO4·H2Oa	V0 = 365.2(3)	K0 = 45.2(2)	K′ = 6.7(1)	α-NiSO4·H2O	V0 = 342.3(1)	K0 = 63.4(1.0)	K′ = 4b
10–4 – 5.94	a0 = 7.082(1)	M0 = 496(9)	M′ =1.3(3.2)	10–4 – 2.30	a0 = 6.826(1)	M0 = 401(12)	M′ =12b
	b0 = 7.553(1)	M0 = 109(2)	M′ = 36(2)		b0 = 7.598(1)	M0 = 175(4)	M′ = 12b
	c0 = 7.779(1)	M0 = 93.8(7)	M′ = 13.1(4)		c0 = 7.403(1)	M0 = 200(4)	M′ = 12b
β-FeSO4·H2Oa	V0 = 367.0(4)	K0 = 45.1(6)	K′ = 5.4c	β-NiSO4·H2O	V0 = 342.1(6)	K0 = 61.3(1.9)	K′ = 4b
6.15–8.40	a0 = 7.087(4)	M0 = 471(19)	M′ = 3.0c	4.00–6.00	a0 = 6.838(4)	M0 = 332(16)	M′ = 12b
	b0 = 7.54(1)	M0 = 112(7)	M′ = 36.8c		b0 = 7.576(6)	M0 = 191(7)	M′ = 12b
	c0 = 7.784(4)	M0 = 102(1)	M′=9.1c		c0 = 7.414(6)	M0 = 169(6)	M′=12b
α-MgSO4·H2Oa	V0 = 355.5(4)	K0 = 48.1(5)	K′ = 8.1(6)	γ-NiSO4·H2O	V0 = 339.5(8)	K0 = 68.4(2.0)	K′ = 4b
10–4 – 2.50	a0 = 6.909 (1)	M0 = 297(12)	M′ = 21(14)	6.50–9.00	a0 = 6.850(6)	M0 = 301(12)	M′ = 12b
	b0 = 7.628(1)	M0 = 142(4)	M′ = 30(5)		b0 = 7.523(6)	M0 = 264(9)	M′ = 12b
	c0 = 7.642(1)	M0 = 94.1(1.3)	M′ = 13.1(4)		c0 = 7.405(7)	M0 = 177(6)	M′ = 12b
β-MgSO4·H2Oa	V0 = 355.8(1.8)	K0 = 49.3(5.5)	K′ = 4.8(1.0)
4.75–8.40	a0 = 6.911(1)	M0 = 383(27)	M′ = −6(2)
	b0 = 7.649(1)	M0 = 83.5(5.5)	M′ = 45.9(5.5)
	c0 = 7.615(14)	M0 = 122(11)	M′ = 8.0(1.5)

Data for Mg and Fe polymorphs from Meusburger et al.[27,28]

Fixed value due to fit with BM-2 EoS.

c.f. Meusburger et al.[27]

As the Raman spectra reveal several hints for the occurrence of a second subtle structural change, the evolution of the lattice parameters was carefully inspected with respect to changes in the p interval around the second critical pressure between 6.36(6) and 7.41(6) GPa. There is no conspicuous deviation or any significant discontinuity recognizable in the p dependencies of the base vectors. It requires a very careful inspection to recognize very subtle deviations as exemplified in Figure . This plot shows the differences of the c-axis values in the two possible settings of the reduced cell, thus exhibiting a distinct change in the Δc/Δp rate of the linear trends with both lines intersecting around 2.4 GPa. The second linear trend line, as fitted to the data in the p interval 2.7–6 GPa, matches perfectly the linear relationship for the data points above the first discontinuity up to a pressure around 6.7 GPa. At this point, the last four data points clearly deviate by following another third linear trend at a deliberately lower Δc/Δp rate, thus falling slightly below the second trendline. The onset point for the second change (6.7 GPa) perfectly coincides with the pressure range between 6.36(6) and 7.41(6) GPa as determined from Raman spectroscopy, at which the splitting of the ν1(SO4) band has been observed.

Figure 6

Pressure dependent evolution of Δc between the two possible reduced cell settings mutually related by the transformation matrix (1̅00/01̅0/111). It clearly shows the first phase transformation in NiSO4·H2O at 2.4 GPa and a possible second discontinuity (visible in enlarged section) starting around 6.7 GPa.

A similar deviation can be observed for evaluating the spontaneous strain components e1 and e2, which can be expected to be proportional to the order parameter for a continuous second order phase transition from monoclinic to triclinic symmetry (Figure ). The values of the spontaneous strain components e1, e2, and e3 were calculated from the lattice parameters of the triclinic reduced cell using the extrapolated fits shown in Figures and 5 and derived from eqs –3) discussed in Carpenter et al.[46] for phase transitions between two triclinic forms (with β* and β0* being the corresponding reciprocal lattice angles).

Figure 7

Components e1, e2, and e3 of the spontaneous strain arising for the ferroelastic transition in NiSO4·H2O. Values are derived from Carpenter et al.[46] from extrapolated EoS fits provided in Figures and 5 using the lattice parameters of the reduced cell. Red lines correspond to fitted power law functions with an ideal critical exponent β = 0.5. Vertical dotted lines represent the supposed transition pressures and reveal recognizable discrepancies for e1 and e2 components above 6.5 GPa.

The plot in Figure shows nonzero values starting at 2.66(1) GPa, which clearly follow a nonlinear Δ ∝ |p–pcrit|β trend. The critical exponent β was found to be very close to 1/2, such as found for both isostructural phases MgSO4·H2O and FeSO4·H2O, thus suggesting the C2/c–P1̅ being proper second order from the point of view of Landau theory.[27,28] The equivalent fits onto the spontaneous strain values with β constrained to 1/2 reveal clear deviations starting around 6.5 GPa. The values for the critical pressure pc obtained from the fits (= 2.47 and 2.46 GPa) confirm the pressure of the monoclinic-to-triclinic transition with an uncertainty of 0.05–0.01 GPa. The critical pressure for the second transition at 6.5 GPa can only be specified with a considerably greater inaccuracy of ±0.5 GPa.

Comparative Lattice Elasticities of Polymorphs

Changes of individual lattice parameters and the unit-cell volume (V) follow the typical nonlinear trend lines on compression. On the basis of the small uncertainties obtained for V, for both the quartz calibrant and the NiSO4·H2O sample crystal (see Table S3 in the Supporting Information), it is possible to determine accurate values for the parameters of the empirical equations of state (EoS). Therefore, Birch–Murnaghan (BM) equations of state[47] were fitted to V, trying to fit third- and second-order truncations. Evaluating the p–V data (Figure a), it is noticeable that despite the two suspected phase transformations, the evolution of V does not show any discontinuity, thus evidently excluding any of the transitions being first order in character. The fit for the pressure interval relevant for the monoclinic phase (hereinafter referred to as α-NiSO4·H2O) revealed a bulk modulus K0 = 65.9 ± 6.7 GPa and its pressure derivative K′ = 2.3 ± 4.6 for a third-order BM-EoS. Considering the error of K0 and K′ as too large, due to the limited number of data points, and K′ being too small due to elastic softening effects, K0 turns to 63.4 ± 1.0 GPa on fitting the data to second-order BM-EoS. Extrapolating the obtained EoS beyond the 2.5 GPa, it can clearly be seen that the V data at higher p deviate between −0.5 Å3 and +1.3 Å3 (cf. Figure a). The values for the β-NiSO4·H2O polymorph in the range 2.5 to 6.0 GPa correspond to K0 = 44.5 ± 9.4 GPa and K′ = 8.2 ± 3.2, with a relatively high value for K′ due to obvious elastic softening effects as reported for the isostructural phases.[27,28] When the p range is restricted between 4.0 and 6.0 GPa, the fit yields a 500% error value for K0 and K′ for BM-3 EoS and K0 = 61.3 ± 1.9 GPa for BM-2 EoS. The refinement of p–V data in the area of the supposed transition to γ-NiSO4·H2O was also not possible with BM-3 EoS and provides values of K0 = 68.4 ± 2.0 GPa for BM-2 EoS, which are higher than those obtained for α- and β-NiSO4·H2O. The bulk moduli for the α- and β-forms of NiSO4·H2O are as expected and follow the Anderson–Anderson relationship[48] comparably to the α- and β-forms of MgSO4·H2O and FeSO4·H2O. The same finding as for the evolution of the volume property can be observed for the individual crystallographic axes (Figure b–d), in particular for the b- and c-axes, which show similar p dependencies to those of the volume. The a-axis (Figure b) shows an increasing compressibility as evidenced by the increasing rate for Δa/Δp, which would be equivalent to a negative M′ value, if all data points were fitted according to a BM-3 formalism with an axial modulus M0 = 423.4 ± 5.3 GPa and M′ = −2.4 ± 0.8. The M′ value would also be negative if only the data points above 2.5 GPa were used for fitting the EoS of the β-form of NiSO4·H2O (M0 = 437 ± 25 GPa, M′ = −3.9 ± 2.9). This development is remarkable as it is different in comparison to the other phases (cf. Table ) and might be indicative for the structural instability of the phase at even higher pressures beyond the maximum p within this experimental series.

Figure 8

Evolution of the unit-cell parameters of NiSO4·H2O in the C2/c base-vector setting: (a) volume, (b) lattice parameter a, (c) lattice parameter b, and (d) lattice parameter c. Plots correspond to the data provided in Table S2. Red lines correspond to fits of BM-2 EoS with the respective parameters as quoted in the text.

High-Pressure Crystal Structures

The scXRD intensity data were collected at p = 0.6(1), 2.3(1), 4.5(1) ,and 8.4(1) GPa in order to extract structural information for all three potential phases. The results of the refinements are given together with details of the data collection in Table , and the resulting parameters (fractional coordinates and isotropic displacement parameters) of the structure models are summarized in the Supporting Information (Tables S4). The refinement at 0.6(1) GPa was performed in C2/cUiso constrained only for the two H atoms, at 2.3(1) GPa in addition, the Uiso’s for the three O atoms were constrained. For the refinements in P1̅ at 4.5(1) and 8.4(1) GPa, the H positions were constrained to fixed values in addition to the fixed Uiso’s. An attempt for a refinement in P1 (at 8.4(1) GPa) was performed with positional constraints according to local 1̅ symmetry for all atoms. This symmetry was stepwise released for each atom, testing for split positions. However, there was no displacement above the three-sigma limit, apart from O2B, which was then accounted into the disordered P1̅ structure (Table S4).

Table 2

Parameters of the scXRD Data Collection and Results of the Structure Refinements of NiSO4·H2O

pressure (GPa)/T = 298(1) K	0.6(1)	2.3(1)	4.5(1)	8.4(1)	8.4(1)
space group	C2/c (15)	C2/c (15)	P1̅(2)	P1̅(2)	P1̅ (2) disordered
a (Å)	6.814(1)	6.786(1)	cf. a*	cf. a*	cf. a*
b (Å)	7.569(1)	7.502(1)	cf. b*	cf. b*	cf. b*
c (Å)	7.418(1)	7.329(1)	cf. c*	cf. c*	cf. c*
aa (Å)	5.093(1)	5.059(1)	4.950(1)	4.850(1)	4.850(1)
ba (Å)	5.092(1)	5.060(1)	5.080(1)	5.063(1)	5.063(1)
ca (Å)	7.418(1)	7.329(1)	7.233(1)	7.093(1)	7.093(1)
α (deg)	90	90	cf. α*	cf. α*	cf. α*
β (deg)	117.72(1)	117.67(1)	cf. β*	cf. β*	cf. β*
γ (deg)	90	90	cf. γ*	cf. γ*	cf. γ*
αa (deg)	108.14(1)	108.13(1)	108.07(1)	108.10(1)	108.10(1)
βa (deg)	108.13(1)	108.14(1)	108.44(1)	108.53(1)	108.53(1)
γa (deg)	96.00(1)	95.74(1)	95.38(1)	95.20	95.20
V (Å3)	338.7(1)	330.4(1)	160.3(1)	153.5(1)	153.5(1)
Z	4	4	2	2	2
no. runs/frames	20/1520	20/1520	20/1520	20/1520	20/1520
scan time (sec)	50	50	80	100	100
no. measured reflns	1550	1332	1359	1316	1316
no. unique reflns (obs/all)	184, 195	156, 159	277, 295	263, 282	263, 282
max. 2θ (deg)	73.10	72.66	72.06	72.96	72.96
Rint, Rsigma (%)	2.61, 1.12	2.41, 1.00	3.29, 1.73	3.29, 1.91	3.29, 1.91
R1(obs/all) (%)	3.25, 3.44	2.93, 2.97	2.85, 3.09	2.62, 2.81	2.46, 2.66
wR2 (%)	8.55	7.48	7.80	6.94	6.45
GoF	1.12	1.13	1.08	1.13	1.06
refined/constrained parameters	18/0	16/3	24/5	24/5	27/6
weight parameters, a and bb	0.059, 1.282	0.046, 1.894	0.050, 0.372	0.036, 0.423	0.047, 0.305
max/min electron density (e–Å–3)	0.512, −0.479	0.463, −0.350	0.439, −0.358	0.363, −0.314	0.300, −0.282

Lattice parameters of the reduced cell

w = 1/{σ 2(Fo2) + [a × P]2 + b × P}; P = ([max(0,Fo2)] + 2 × Fc2)/3].

Applying the three-dimensional reconstruction of the reciprocal space from a series of collected frames, the data collections corresponding to α-NiSO4·H2O reveal an untwinned single reciprocal lattice of monoclinic symmetry with systematic Bragg peak extinctions corresponding to C2/c symmetry. Above 2.5 GPa, the reciprocal lattice points show a distinct splitting (cf. Figure ), which is characteristic of a nonmerohedral twinning corresponding to the symmetry reduction from monoclinic to triclinic lattice metrics. Integration of Bragg peak intensities was achieved either for untwinned single-domain samples or, if twinned, at higher angles where peak separation was large enough. In addition, weak diffraction peaks (Figure ), which were forbidden in C2/c, were observed when the samples transformed to triclinic symmetry, confirming the assumed symmetry change. While the changes for the α-to-β transition around 2.5 GPa are obvious and the reflection conditions support the equivalent C2/c-to-P1̅ transition, such as reported for FeSO4·H2O,[27] there is no apparent evidence from the diffraction pattern for the supposed β-to-γ transition. With respect to hints from the Raman spectra that the S atoms could be located at different crystallographically independent sites, the reciprocal space of the 8.4(1) GPa measurement was deliberately investigated for the existence of superstructure reflections or satellites as would be expected for a commensurately or incommensurately modulated structure, e.g., Ende et al.[49] Despite adequate attention and careful inspection, neither additional Bragg peaks nor satellite reflections could be detected, despite having applied adequate exposure times for recording the diffraction patterns.

Figure 9

Layers of reconstructed reciprocal space derived from measured frames using the C2/c cell setting. Arrows indicate the appearance of diffraction peaks, which are forbidden in space group C2/c. Moreover, the reconstructed hk5 layer of the measurement at 4.5 GPa shows split components of individual twin domains following nonmerohedral twinning accompanying the monoclinic-to-triclinic transition.

Once any kind of superordinate modulation of the structure could be ruled out, all that remains to be considered is a transformation to acentric P1 related to a nonisosymmetric structural change. A refinement of a structural model in P1 was achieved by stepwise releasing the symmetry constraints of the inversion center of individual atoms between corresponding atoms in P1̅. The refinement of various soft-constrained models finally leads to a significant improvement of the reliability indices (Table ) only if the O2B was split into two components (O2B1 and O2B2) as done for a proposed P1̅ structure with disordered O2B position.

According to the findings from vibrational spectroscopy, the structure is retained without any changes in the bonding topology of the heterodesmic framework, which is composed of octahedral NiO6 and tetrahedral SO4 units as described by Giester.[25] The evolution of bond distances is independent of symmetry and does not provide any significant change that could be responsible for the transitions (Tables and 4). This is in complete agreement what has been reported for the C2/c-to-P1̅ transition from the ambient α- to the high-p β-polymorph of FeSO4·H2O.[27] In accordance with the displacive changes observed in this isostructural compound, a tendency of the framework to fold up can be anticipated for NiSO4·H2O as well, as could be observed on the bond angles on the bridging oxygen atoms. There is a general decrease of Ni–O–Ni and Ni–O–S angles as a consequence of the compacting folding, together with the diversification of Ni–O2–S angles (126° vs 133° at 4.5 GPa) in the same manner as reported for FeSO4·H2O upon exceeding the α-to-β transition point. Looking more closely at the development at the second critical point around 6.5 GPa, it can be seen that two resulting sulfate tetrahedra actually reveal different bond-length distortions with respect to their individual S–O bond lengths (e.g., S1–O2B1 = 1.56(4) Å, S1–O2B2 = 1.44(3) Å at 8.4(1) GPa). However, the true crystallographic symmetry of the main framework is yet not beyond doubt P1̅. The shown model has to be assumed to be an approximated model. One can prove beyond doubt the development of crystallographically different sites, which is just most pronounced in the case of the O2B positions. Within the obtained uncertainties from the structure refinement, the symmetry lowering recognizable from the Raman spectra beyond 7 GPa can be confirmed.

Table 3

Interatomic Distances (Å) of the NiO6 and SO4 Units in NiSO4·H2O, According to the Crystallographic Data Given in the Supporting Information (Table S4)a

pressure/atoms	10–4 GPab	0.6 GPa	2.3 GPa	4.5 GPa	8.4 GPa (P1̅)		8.4 GPa (P1̅) disordered
Ni1(A)–O1(A)	2.035(2)	2.032(6)	2.027(7)	2.028(5)	2.021(5)		2.021(5)
Ni1B–O1B				2.018(5)	1.998(5)		1.999(4)
Ni1(A)–O2(A)	2.032(2)	2.030(3)	2.019(4)	2.013(6)	2.002(6)		2.003(6)
Ni1B–O2B				1.998(7)	1.984(7)	O2B1	1.936(26)	O2B2	2.017(24)
Ni1(A)–O3	2.115(1)	2.105(2)	2.088(2)	2.065(9)	2.029(9)		2.035(8)
Ni1B–O3				2.071(9)	2.046(9)		2.042(8)
S1–O1(A)	1.459(1)	1.465(3)	1.465(3)	1.458(4)	1.453(7)		1.459(7)
S1–O1B				1.470(7)	1.458(4)		1.461(4)
S1–O2(A)	1.484(2)	1.467(6)	1.469(8)	1.481(5)	1.476(5)		1.478(5)
S1–O2B				1.488(13)	1.490(13)	O2B1	1.56(4)	O2B2	1.44(3)

The O2B positions is split into two positions (O2B1 and O2B2) for the disordered model of the P1̅ structure at 8.4 GPa.

Data from Giester and Wildner.[15]

Table 4

Bond Angles (deg) in NiSO4·H2O According to the Crystallographic Data Given in the Supporting Information (Table S4)a

pressure/atoms	10–4 GPab	0.6 GPa	2.3 GPa	4.5 GPa	8.4 GPa (P1̅)	8.4 GPa (P1̅) disordered
Ni1(A)–O3–Ni1(B)	123.61(1)	123.5(2)	122.68(1)	121.9(4)	121.0(4)	120.9(3)
Ni1A–O1A–S1	136.82(9)	136.3(3)	134.6(3)	132.1(3)	130.8(4)	130.4(3)
Ni1B–O1B–S1				133.0(4)	130.9(4)	130.9(4)
Ni1A–O2A–S1	130.80(9)	131.0(2)	130.7(2)	125.9(3)	123.0(3)	122.8(3)
Ni1B–O2B(1/2)–S1				132.6(5)	133.6(5)	131.5(1.8)	134.3(1.7)

Constraints in P1̅ (disordered) as stated for Table .

Data from Giester and Wildner.[15]

Hydrogen Bonding under Pressure

While the transformations do not cause virtually any changes with respect to the main structural units of the framework, with the exception of some polyhedral tilting leading to higher compaction, the hydrogen bonding system reveals notable changes at the critical transition points. Due to the loss of the local 2-fold axis associated with the C2/c-to-P1̅ transition, the symmetry equivalent pair of O3···O2 hydrogen bonds (O3···O2 distance: 2.647(6) Å at 2.3(1) GPa) as well as a further pair of intermolecular O3···O1 distances (3.296(5) Å at 2.3(1) GPa) become distinguishable as four symmetry-independent distances (Table ). As in MgSO4·H2O[28] and FeSO4·H2O,[27] the lattice distortion causes one of the O3···O1 distances to be drastically shortened (from 3.296(5) Å at 2.3(1) GPa to 2.851(6) Å at 8.4(1) GPa) thus becoming potentially involved in the hydrogen-bonding system (Figure ). These changes confirm the mechanism reported for the α-to-β transition in the analogous ferrous compound with the development of three short O3···O contacts suitable as relevant hydrogen bonds with O3 being the donator oxygen. As found in the isostructural compounds, the O3···O1 contacts show a significant diversification with respect to their interatomic distances, i.e., the significant shortening of O3···O1B from 3.296(5) Å (at 2.3(1) GPa) to 3.016(7) Å (at 4.5(1) GPa) while the O3···O1A distance even increases in length (to 3.436(8) Å at 4.5(1) GPa) upon crossing the critical transition point around 2.5 GPa. As the voids, in which the hydrogen atoms are positioned, are oriented along the a and b axes, their different pressure-dependent compression behavior starting around 2.5 GPa is manifested in noticeably different void sizes (O2···O2 distances) visible in Figure .

Table 5

Interatomic O···O Distances and O2–H Bond Distance (Å) of the Relevant Hydrogen Bonds in NiSO4·H2O According to the Crystallographic Data Given in Supporting Information (Table S4)a

pressure/atoms	10–4 GPab	0.6 GPa	2.3 GPa	4.5 GPa	8.4 GPa (P1̅)	8.4 GPa (P1̅) disordered
O3···O2(A)	2.673(2)	2.674(5)	2.647(6)	2.617(9)	2.592 (9)	2.577(9)
O3···O2B(1/2)				2.616(7)	2.579(6)	2.529(37)	2.556(18)
O3···O1(A)	3.374(2)	3.357(5)	3.296(5)	3.436(8)	3.470(8)	3.470 (7)
O3···O1B				3.016(7)	2.852(7)	2.851(6)
O2(A)–H	1.96(3)	1.71(14)	1.80(13)	1.76(7)	1.757(6)c	1.756(6)c
O2B(1/2)–H				1.67(7)	1.901(7)c	1.895(25)c	1.895(25)c

Constraints in P1̅ (disordered) as stated for Table .

Data from Giester and Wildner.[15]

Low shown error, due to fixed hydrogen position.

Figure 10

Hydrogen-bonding system and polyhedral connections in the α, β, and γ forms of NiSO4·H2O at 2.3(1), 4.5(1), and 8.4(1) GPa. For each form, two directions are shown, one perpendicular (upper part) and the other parallel (lower part) to the octahedral-chain units. In the triclinic forms, the voids around the hydrogen atoms form series along the a and b axes, which show different pressure-dependent compression behavior starting around 2.5 GPa. Therefore, different void sizes (as determined by the O2···O2 distances) can be recognized with respect to the hydrogen bonds parallel to the different axes.

Of particular interest are the changes in the hydrogen-bonding system when the second transformation point is exceeded around 6.5 GPa. There, the relevant O···O distances are subject to only minor changes, and the bond-length differences are only relatively small (e.g., O3···O2 = 2.53(4) and 2.56(2) Å). It is therefore obvious that the second structural change is not primarily due to the hydrogen-bonding system and apparently only adapts to the small changes arising from the framework as discussed above. However, similar to the first transition, the second one is mostly affecting the size of the voids hosting the hydrogen atoms (Figure ). It even affects them in the same fashion by further increasing the long O2···O2 distances (which are oriented along the a axis), while the short O2···O2 distances (which are oriented along the b-axis direction) decrease (O2A···O2B2: 3.306(24) Å vs O2A···O2B1: 3.115(24) Å and O2B1···O2A: 4.032(23) Å vs O2B2···O2A: 3.859(22) Å, Figure ).

Conclusions

The in situ high-p investigations on nickel sulfate monohydrate reveal two apparent structural instabilities accompanied by transformations under isothermal hydrostatic compression. While the first transition observed in NiSO4·H2O occurs at 2.47(1) GPa, showing all features equivalent to the ferroelastic transformations reported in isostructural MgSO4·H2O (pc = 2.72 GPa) and FeSO4·H2O (pc = 6.15 GPa), this study reveals a second subtle structural change in NiSO4·H2O at 6.5(5) GPa. The ferroelastic C2/c-to-P1̅ transition at 2.47 GPa is identical in its character to those described so far for the isostructural compounds. In particular, the type of lattice changes as described by the settings in C2/c and its reduced cell are more or less identical, such as the interatomic distances of the O···O contacts within the hydrogen-bonding system, which change in the same fashion. Comparing the high-p behavior of the three known kieserite-type representatives and their critical transition pressures pc (2.47, 2.72, 6.15 GPa), the unit-cell volumes (342.3, 355.5, 365.2 Å3), and the bulk moduli K0 (63.4, 48.1 45.2 GPa) with respect to the ionic radii[50] of the particular M2+ cations (0.69, 0.72, 0.78 Å), NiSO4·H2O reveals the lowest pc and the highest value for K0. This could be expected since it is the compound with the smallest M2+ cation and thus the smallest unit-cell volume of the α-phase. Although the bulk modulus is affected by the large uncertainty and might be overestimated due to the fact that the available pressure interval is the shortest among all representatives, it follows more or less the Anderson–Anderson relationship[48] (i.e., V0 × K0 ≈ constant) with 21 702, 17 099, and 16 507 Å3·GPa for the Ni, Mg, and Fe end members, respectively.

When comparing the compressibilities along the different lattice directions, it is striking that the a-axis shows a noticeable negative compressibility (M′ = −3.9 ± 2.9, BM-3 all data points above 2.5 GPa) for the β-phase of NiSO4·H2O, which has not been observed for the other two compounds. Negative values for the pressure derivatives of axial moduli have been found in many cases to indicate a structural instability, which in turn might act as the precursor of the β-to-γ transition around 6.5 GPa. In this respect, it is not surprising that a further transformation was indeed observed. The second transition is evident from results of independent analytical techniques, on the one hand by the splitting of the Raman band attributed to the ν1(SO4) mode and on the other hand by observing higher values for the reliability indices for the structure refinement of data sets measured beyond 6.5 GPa. Although weak satellite reflections could not be observed within the data sets of this study, the true symmetry of the γ-phase and the existence of a superstructure cannot be completely ruled out, especially if it is based only on slight changes in the oxygen and hydrogen positions. Therefore, the relevant Bragg peak intensities are possibly far below the detectable signal-to-noise ratio in our DAC measurement. Nevertheless, the presented model of the structure at 8.4(1) GPa reveals pseudocentrosymmetry of the heavy atoms when refining in P1 global symmetry, where the symmetry coupling of centrosymmetric positions was released stepwise for each pair of atoms. Only the oxygen atoms indicated deviations from centrosymmetry with the effect being most significant for the O2 positions. The differences between a proper refinement in P1̅ and with local symmetry constraints in P1 are evident (Table ) and provide an additional proof for the existence of a third polymorph. The transition pathway is determined by the symmetry relationship with monoclinic C2/c (α-NiSO4·H2O) and triclinic P1̅ (β-NiSO4·H2O) and a disordered O2B position in P1̅ (γ-NiSO4·H2O).

Polymorphism of M2+SO4·H2O is an important topic in astrophysics and planetary geology with respect to the monohydrate sulfates being an abundant component on the surface of icy moons (cf. Comodi et al.[51] and McCord et al.[52]). α-MgSO4·H2O and β-MgSO4·H2O have recently been considered for the interior of Callisto,[28] where the maximum pressure corresponds to around 5 GPa. Considering the significant Ni contents in the soluble sulfate fraction in C1/C2 carbonaceous chondrites believed to be chemically similar to the rocky cores of the icy moons (e.g., Ivuna and Orgueil) and meteorites with up to 13.6 wt % NiO,[13] NiSO4·H2O can be considered as an important component in natural monohydrate sulfates. According to previously reported findings, there is a tendency of the enrichment of Ni relative to Mg during the crystallization of solid nickel–magnesium sulfate from aqueous Mg–Ni-containing solutions.[5] As the first critical transition in NiSO4·H2O occurs at even lower pressure than in kieserite itself, the occurrence of the high-p β-form is therefore very likely wherever Ni substitution occurs.