Structural properties of β-metal(II) hydroxides: Combined XAS and Raman spectroscopic studies on lattice stability

Temperature-dependent x-ray absorption (XAS) and high-pressure (HP) Raman spectroscopy results on two prominent β-metal(II) hydroxides, viz. β-Ni(OH)2 and β-Co(OH)2 are presented. Raman data at ambient conditions show the β-Co(OH)2 phonons to be softer than the β-Ni(OH)2 ones. Analysis of the extended x-ray absorption fine structure data at metal K-edge as a function of temperature reveals the Einstein frequencies of the metal-oxygen and the metal-metal bonds to be, respectively, 309 and for β-Co(OH)2 and the same to be 385 and for β-Ni(OH)2. In both the β-metal(II) hydroxides, up to about 10 GPa, HP Raman spectroscopy show a continuous hardening of the phonon modes associated with the metal-oxygen sub-lattices, whereas a systematic frequency softening is displayed by the hydroxyl symmetric stretching mode. These contrasting behaviours imply a gradual development of lattice instability with pressure mainly due to the displacement of H atoms around the metal-oxygen axis. The presented data allow a direct comparison of the local-lattice behaviour by quantifying the strength (XAS) and anharmonicity (RAMAN) of the atomic bonds in the two systems.

The β-Ni(OH) 2 and β-Co(OH) 2 exist in hexagonal symmetry with space group P3m1 (number 164). The metal, oxygen and hydrogen atoms occupy positions (0, 0, 0), (1/3, 2/3, z) and (1/3, 2/3, u), respectively, where z and u are system-specific. Note that the metal occupies the Wyckoff position 1a and O and H occupy the Wyckoff position 2d [12,13]. The metal (M) atoms are sandwiched between two layers of oxygen atoms, resulting in an MO 6 octahedron. The OH bonds are oriented along the threefold axis perpendicular to these layers. Previously, there have been several attempts to elucidate the structural and dynamical properties of these two β-metal(II) hydroxides using x-ray diffraction (XRD) [14][15][16], infrared and Raman spectroscopy [14,[17][18][19][20] and neutron scattering [17,18,[21][22][23]. Due to its unique ability to provide site-specific information about the local electronic and lattice structure (like oxidation state, coordination, numbers and identity of neighbours), x-ray absorption spectroscopy (XAS) provides direct information on atomic 66002-p1 bond strength and dynamics and is thus an ideal tool to characterize these compounds. In our recent work [24], we reported the local structural and electronic properties of β-Ni(OH) 2 deduced by a combined XAS and Raman spectroscopic investigation under high pressure (0-16 GPa). Our results revealed the onset of a weak structural/electronic instability in the high-pressure regime. In the present paper we extend our investigation to β-Co(OH) 2 and compare the results with that of β-Ni(OH) 2 . We further use temperature-dependent (77-377 K) XAS data probing the local structure around the metal site of the two systems for further comparison. These data enable a direct comparison between the stability of the two β-metal(II) hydroxides on the basis of the inter-atomic distances and the related Debye-Waller factors, and the phonon frequencies.
Materials and experimental procedure. -For the temperature-dependent XAS measurements, commercial β-Ni(OH) 2 and β-Co(OH) 2 powders, from Sigma Aldrich, have been diluted in an inert matrix (BN) and pressed to a form of pellet. Transmission EXAFS measurements at Ni (8333 eV) and Co (7709 eV) K-edges were performed in q-EXAFS mode at the CLAESS beamline [25] of the Spanish National Light Source, (ALBA Synchrotron, Barcelona, Spain), using a Si 311 double-crystal monochromator. The incoming and outgoing photon fluxes were measured by ionization chambers filled with appropriate mixtures of N 2 and Kr gases. The sample was inserted into a liquidnitrogen cryostat and the temperature was varied between 77 and 377 K, controlled by a feedback loop electric heater. For the pressure-dependent Raman measurements, pure powder of β-Co(OH) 2 has been compacted in the sample chamber of a membrane-driven diamond anvil cell (DAC), equipped with type-2A low-fluorescence diamonds. Since the bulk modulus of β-Co(OH) 2 is quite small (49 GPa, as reported in [14]), no hydrostatic medium has been used since the non-hydrostatic effect can be considered to be negligible. Raman spectra have been acquired by means of a confocal-microscope Raman spectrometer, equipped with a 20× objective, a 32 mW He-Ne laser (632.8 nm wavelength), and a 1800 lines/mm grating monochromator, coupled with a Peltier cooled CCD detector. Data have been collected in the backscattering geometry and a notch filter was used to reject the elastic contribution. The low-frequency cutoff of the notch filter limits the collection of reliable spectra below 130 cm −1 . Under these conditions, a few tens of micron diameter laser spot on the sample and a spectral resolution of about 3 cm −1 could be achieved. To complement these results, HP x-ray diffraction (HP-XRD) measurements [24] were carried out, using the Xpress beamline of the Elettra-Sincrotrone Trieste.

Temperature-dependent
XAS measurements. Temperature-dependent extended x-ray absorption fine structure (EXAFS) spectra and the corresponding Fourier transforms (FT) magnitudes for β-Co(OH) 2 and β-Ni(OH) 2 , extracted from the respective metal K-edge XAS are presented in fig. 1 (panels (a), (b), (e) and (f)). The continuous Cauchy wavelet transform (CCWT) analysis method enables the visualization of the EXAFS spectra in three dimensions by decomposing the k-space and R-space signals [26]. Panels (c) and (d) of fig. 1 present the CCWT modulus at 77 K respectively for β-Co(OH) 2 and β-Ni(OH) 2 . The visualized CCWT signals allow the identification of those local structural details which are difficult to be identified in a one-dimensional decomposition such as the Fourier transform of the EXAFS signal [27]. Peaks in the CCWT map can be identified by the theoretical calculation of χ(k) based on the structural parameters [12,13] using the FEFF8 code [28]. In both maps, the CCWT modulus presents three different structures. In each map, the intensities of these structures are quite different, simplifying the identification of scattering from heavy and light atom groups. The closest shape (appearing around 1.8Å and centred around 6Å −1 ) is associated with the metal-OH octahedron (1st shell), whereas the second one (located at 2.7Å and centred near 8Å −1 ) is due to the 6 next-nearest-neighbour metal atoms (2nd shell). Above this contribution, a region of positive and destructive interference is clearly visible; indicating the presence of 66002-p2 Table 1: Results from EXAFS analysis on β-metal(II) hydroxides as a function of temperature.  (4) counterphased multiple scattering signals. Finally, the weaker structure located around 6Å and centred near 8Å −1 represents a higher-order shell, originating from the single scattering signal from OH groups belonging to other octahedra. It is worth noticing that the signal is generally stronger in β-Co(OH) 2 than in β-Ni(OH) 2 , thus suggesting that the structure of Co-hydroxide is more ordered than the Ni-one. HP-XRD data at the lowest pressure showing a narrower Bragg peak for β-Co(OH) 2 than for β-Ni(OH) 2 is in line with this.
The temperature increase causes a damping of the EX-AFS oscillations due to the increase in the atomic thermal fluctuations, and this is reflected in the decrease in intensity of the FT peaks ( fig. 1(b) and (f)). To obtain quantitative information from the measured data, EXAFS analysis has been performed [29] according to the standard equation: where R j is the distance between the photoabsorber and the neighbouring j-atoms, N j is the number of neighbouring atoms, S 2 0 is the passive electrons' amplitude reduction factor, f j (k, R j ) is the backscattered amplitude, λ is the photoelectron mean free path, δ j (k) is the phase shift, and σ 2 j is the correlated Debye-Waller (DW) factor measuring the mean square relative displacement (MSRD) between photoabsorber and backscatterer [30]. The EXAFS data were fitted using the Artemis program (version 0.9.20) of the IFFEFIT package [31]. In the model curve, f j (k, R j ), λ, and δ j (k) were calculated using the FEFF-8 code [28].
We included only the first two shells: the first one corresponding to the OH backscattering and the second one associated with M-M scatter groups, for the EXAFS modelling to obtain reliable quantitative information.
Recall that the maximum number of independent fitting parameters, n, is given by the formula n = (2 × Δk × ΔR)/π, where Δk and ΔR are the windows used in the fit. In the present study Δk = 14Å −1 and ΔR = 2.1Å, limiting the maximum number of free parameters to be ∼13. In order to minimize n, we kept all the coordination numbers constant as obtained from the diffraction data. Distances and Debye-Waller (DW) factors have been grouped. One distance and a corresponding DW factor have been fitted for each shell -the first shell taking into account the M-OH interaction and the second shell dealing with the M-M interaction. No multiple scattering paths were considered since their rank is relatively low compared to single scattering paths (see also CCWT maps). Finally, two other adjustable parameters (S 2 0 and E 0 ) have been introduced to account for the amplitude and common phase of the χ(k). The analysis results are summarized in table 1 and the DW factors for the M-OH group and M-M groups are plotted as a function of temperature in fig. 2.
The temperature evolution of the DW factors shows different slopes for the different bonds and systems, thus corresponding to different atomic bond strengths for M-OH and M-M in the two β-metal(II) hydroxides. In a temperature-dependent study it is possible to separate the static and dynamic DW factor contributions. In particular using the correlated Einstein model, the temperaturedependent Debye-Waller factor [32] can be fitted to where μ i is the reduced mass of the atomic pair and ω Ej is the corresponding Einstein frequency. The best-fit curves are shown in fig. 2    We observe that the static disorder, σ 2 0 , is almost the same in the two β-metal(II) hydroxides for the M-M backscattering (∼0.004Å −2 ), while it changes for the M-OH. Recall that the atomic masses of Co (58.933195(5) u) and Ni (58.6934(2) u) are very close. Passing from Co to Ni, the strength of the bonds (k) in the hydroxide strongly increases, most likely because of the difference in the electronic configuration of the absorber, which is indeed seen in the x-ray absorption near-edge structure (XANES) data shown in fig. 3(d). Note that the β-metal(II) hydroxides are isostructural and allow the same number and kind of phonon modes (see the following section).

Pressure-dependent Raman measurements.
Raman spectra of β-Co(OH) 2 and β-Ni(OH) 2 after subtraction of the diamond fluorescence signal, are compared in fig. 3 at selected pressures. For both the samples, the group theory analysis of the zone-center phonon modes of brucitetype hydroxides demonstrates that the total irreducible representation is Γ = 2A 1g + 3A 2u + 2E g + 3E u . Four Raman active modes are allowed, three of which are lattice modes and one is a symmetric OH stretching vibration. According to the literature, the lowest-frequency lattice modes can be assigned to E g (liberation) and A 1g (stretching), respectively. Higher-energy modes are associated with A 2u and E g stretching and liberation of the M-O sublattice [14,20,24]. We note that the A 2u mode analysis is affected by the diamond fluorescence (see the shaded region in fig. 3(a)). The A 1g O-H internal stretching modes [14,20] are observed above 3000 cm −1 (see fig. 3(b)). While in β-Ni(OH) 2 a weak shoulder appears on the high energy side, in β-Co(OH) 2 , no shoulder of the main A 1g peak has been observed (see fig. 3(b)), consistent with earlier reports [14]. Although the two β-metal(II) hydroxides are isostructural, the strikingly larger FWHM of the A 1g O-H internal stretching mode at the lowest pressure indicates a varying local ordering consistent with the varying XANES features (edge and near-edge) observed at the metal K-edge in β-Co(OH) 2 and β-Ni(OH) 2 . At ambient pressure as well as at higher pressures, the β-Co(OH) 2 phonons look generally softer than the β-Ni(OH) 2 ones. The ambient pressure case is in agreement with the EX-AFS results (table 2).
No new phonon modes are observed in the Raman spectra of the β-Co(OH) 2 systems up to 10 GPa, indicating the absence of any evident structural phase transition, similarly to the β-Ni(OH) 2 case. This is indeed confirmed by the HP-XRD data ( fig. 3(d)). With the application of pressure, a regular hardening of the low-energy phonon frequencies (related to M-O displacements) is observed ( fig. 3(a)), while the high-frequency region shows a clear softening of the O-H internal stretching mode ( fig. 3(b)). As a general feature, with an increase in pressure the Raman spectrum loses intensity and exhibits a considerable broadening of all the features. These findings can be interpreted as the result of an increase in disorder, which 66002-p4  is further supported by the broadening of the diffraction peaks. To get quantitative information, the measured Raman spectra were fitted with a standard model curve [33] given by the sum of the phonon contributions, each described by a damped harmonic oscillator. Phonon frequencies (ω) and full width at half-maximum (FWHM) for β-Co(OH) 2 obtained using the described fitting procedure are shown in fig. 4, along with the corresponding values for β-Ni(OH) 2 taken from ref. [24]. The two hydroxides show very similar behaviour under pressure. However, a few subtle differences can be pinpointed. If we apply linear approximation to the pressure dependence of the phonon frequencies, we can calculate the slope as dω/dP . Values for dω/dP are reported in table 3. Larger values of |dω/dP | indicate a stronger anharmonicity of the phonon mode. We notice that the |dω/dP | values for β-Ni(OH) 2 are higher than those for β-Co(OH) 2 , i.e., higher in the system characterized by stronger elastic constants of M-O and M-M atomic bonds (see table 2). The FWHM of the OH stretching peak (see fig. 4(d)) is seen to increase with a discontinuous pressure rate in both compounds. This result is in disagreement with recent investigations reported in [14], but it is consistent with previous spectroscopic studies [34,35], where the authors speculate about a "partial amorphization" of the OH sub-lattice. We observe that the threshold values (separating the two regimes observed in FWHM) occur at different pressures. For β-Co(OH) 2 and β-Ni(OH) 2 these values are found to be around 2 and 4-5 GPa, respectively. We remark that higher pressure values (at which the anomaly occurs) are found in the compound characterized by stronger elastic constants (i.e., in Ni(OH) 2 ). The observed findings suggest the presence of a nonlinear mechanism of disorder of the O-H bonds in the two hydroxides as a result of lattice compression.
Conclusions. -In conclusion, we have presented a temperature-dependent x-ray absorption spectroscopy study of β-M-hydroxide (M = Co, Ni) together with a pressure-dependent Raman spectroscopic investigation over the same systems. The metal K-edge EXAFS analysis has allowed for the characterization of the local environment around the absorber atom. Distances, DW factors and elastic constants for both M-O and M-M atomic bonds have been calculated. Raman spectra collected at ambient condition confirm general softer bonds for the β-Co(OH) 2 once compared with the β-Ni(OH) 2 compound. High-pressure Raman investigation of the phonon spectra of β-Co(OH) 2 has been compared with the previously published results for β-Ni(OH) 2 [24]. In both cases, while the M-O vibrations experience a hardening of the phonon modes, the hydroxyl stretch mode shows a linear softening. However, the lattice response is different for the two systems, which are characterized by a different anharmonicity that appears indirectly proportional to the estimated lattice constants from the temperature-dependent XAS study. Moreover, the FWHM of the high-energy mode increases at a discontinuous rate with a threshold pressure close to 2 and 4-5 GPa for β-Co(OH) 2 and β-Ni(OH) 2 , respectively. Overall, the Raman results suggest that the M-O sublattices remain essentially intact as a function of pressure though some minor anomalies occur as indicated by a progressive broadening (i.e., pressure increases probably only the static disorder of the systems); while the H sublattice undergoes some subtle structural rearrangement. We believe this anomalous behaviour is related to the intrinsic local properties, and in particular to the different local bond force strengths detected in the β-Co(OH) 2 and β-Ni(OH) 2 systems. * * * One of us (BJ) acknowledges the IISc-ICTP fellowship from IISc Bangalore and ICTP Trieste.