- © 2012 Mineralogical Society of America
First-principles calculations based on density-functional theory (DFT) and low-T IR spectroscopy were performed to gain more insight into the structure of the so-called 3.65 Å phase, a high-pressure phase of the composition MgSi(OH)6. DFT-calculations predict a monoclinic symmetry with ordered sixfold-coordinated Mg and Si and six unique hydrogen sites as the most stable structure. Adapting the structural parameters of the DFT-determined lowest-energy configuration and assuming (MgSi)-ordering, a new Rietveld refinement of the powder XRD pattern of the 3.65 Å phase was performed, which resulted in excellent refinement statistics and successful assignment of X-ray reflections that were unassigned in former structural models with orthorhombic symmetry. A configuration with ordered Mg and Si at the octahedral positions causes a small monoclinic distortion of the network of strongly tilted octahedra and thus leads to space group P21. The structural refinement yields the following unit-cell parameters: a = 5.1131(3), b = 5.1898(3), c = 7.3303(4) Å, β = 90.03(1)°, V = 194.52(2) Å3, space group: P21, Z = 2, ρ = 2.637 g/cm3. The structure of the 3.65 Å phase can be considered as a modified A-site defective perovskite with a unique network of corner-sharing alternating Mg(OH)6 and Si(OH)6 octahedra and is probably related to the structure of stottite group minerals. Low-T IR spectroscopy confirms the presence of 6 different H-positions in the proposed structure. Measured IR-spectra and computed spectra compare favorably, which further supports the computed structure as the correct model for the 3.65 Å phase.
Dense hydrous magnesium silicates (DHMS) are important potential carriers of water into deep parts of the Earth’s mantle due to their high-pressure stability and large hydrogen content. They can play an especially relevant role for the water cycle in regions related to deep subduction. Therefore, knowledge of their structure, stability, and physical properties is necessary to constrain the hydrogen budget in the Earth’s interior.
The DHMS 3.65 Å phase is named after the d-value of its most prominent X-ray reflection and was first synthesized by Sclar and Morzenti (1971) at 9 GPa and temperatures below 500 °C. Recently, Wunder et al. (2011) determined the composition of the 3.65 Å phase to be MgSi(OH)6, characterized its IR and Raman properties, phase relations, and structure. The crystals of the 3.65 Å phase are too small for structure determination by single-crystal X-ray diffraction analyses. Therefore, constraints were placed on its structure by Rietveld refinement with powder XRD, using the structure of δ-Al(OH)3 (Dachille and Gigl 1983; Komatsu et al. 2007; Matsui et al. 2011) as a starting model, and replacing the octahedral Al by Mg and Si according to the substitution 2Al3+ = Mg2+ + Si4+. Accordingly, its structure can be considered as a modified hydrous A-site defective perovskite. From crystal chemical considerations the structure of the 3.65 Å phase is of great interest, as it represents the second DHMS with exclusively sixfold-coordinated Si beside phase D. Wunder et al. (2011) suggested two different structural models for the 3.65 Å phase: (1) in the first, by analogy with δ-Al(OD)3 after Komatsu et al. (2007) four different H exist, which are arranged in the empty A-site positions of perovskite. This structural model with disordered H-positions has the symmetry of space group Pnam. (2) The second model with space group P212121, is derived from the structure determination of δ-Al(OD)3 after Matsui et al. (2011). In this structural model, hydrogen atoms are ordered and occupy three different positions within the vacant A site of perovskite. Octahedral tilt angles differ strongly in the two models. Wunder et al. (2011) assumed disordered (MgSi) configuration at the octahedral positions of both these structures. Rietveld refinements could not resolve the ambiguity about (MgSi) ordering.
In this study, we present results of DFT-calculations that were performed to constrain the symmetry and the positions of the hydrogen atoms of the 3.65 Å phase from lattice energy minimization. Furthermore, we performed low-T IR spectroscopy and computed the frequency-dependent dielectric response function as an independent verification of the proposed crystal structure. Adapting the structural parameters of the DFT-determined low-energy configuration we improved significantly the previous Rietveld refinement of the powder XRD pattern of the 3.65 Å phase.
Electronic structure calculations in the framework of density-functional theory (DFT) were performed using the planewave code ABINIT (Gonze et al. 2009). The planewave basis set was expanded up to an energy of 1000 eV and norm-conserving pseudpotentials were used (Fuchs and Scheffler 1999). Two sets of calculations were performed, one using the local density approximation (LDA) and the other using the generalized gradient approximation (GGA) according to Perdew et al. (1996) (PBE) for the exchange-correlation functional. The Brillouin zone of the unit cells (containing 28 atoms) was sampled by a 2 × 2 × 2 Monkhorst-Pack grid. The initial simulation cells were set up according to the experimental lattice constants and atomic positions of the two orthorhombic structure models, Pnam and P212121 (Wunder et al. 2011). Due to electrostatic considerations, Si and Mg cations were assumed to order at low temperatures. Hence, they were placed on alternating positions in all three Cartesian directions. Hydrogen atoms of the original Pnam phase have only an occupancy of 0.5. Therefore, half of the crystallographically possible hydrogen atoms were removed under the constraints that (1) very short H-H distances and (2) two O-H bonds to the same oxygen were not allowed. As a consequence of this setup, the symmetry of both initial structures was lowered to P21. Full geometry optimizations were performed to obtain the lattice energies, cell parameters, and atomic positions of the unit cells at zero pressure and temperature, which approximates ambient conditions.
The lowest-energy structure from the GGA calculations was used in a second step to compute the dielectric response and the vibrational spectra. Γ point phonons, Born effective charges, and displacement vectors were calculated using density-functional perturbation theory (Gonze and Lee 1997) as implemented in the ABINIT code (Gonze et al. 2009). For these calculations a higher energy cutoff (1900 eV) was needed to ensure convergence of the frequencies. A larger k-point set (4 × 4 × 4) did not lead to a significant change in the results. The low-frequency dielectric permittivity tensor, εij(ω), relates the macroscopic displacement field to the macroscopic electric field and is computed from the above properties according to Gonze and Lee (1997) with a damping factor of 2 cm−1 (see e.g. Balan et al. 2001). The imaginary part of εij(ω), Im[εij(ω)], provides a first approximation to the IR spectrum. As we deal with powder samples, an average over the three diagonal elements, Im[εii(ω)], is computed to obtain a scalar quantity, Im[ε (ω)].
The starting material for the T-dependent IR analyses and powder XRD measurements for new Rietveld refinement was the solid synthesis product of run MA304 presented in Wunder et al. (2011). The synthesis was performed at 10 GPa and 425 °C in a 77 h multi-anvil experiment using a gel of equal Mg and Si fraction plus water in excess as starting materials. The product contained about 90 wt% of the 3.65 Å phase and 10 wt% of the 10 Å phase as result from a quantitative phase analysis of the former Rietveld refinement (Wunder et al. 2011). The chemical composition of the 3.65 Å phase of run MA304 and its spectroscopic properties at ambient conditions were determined by EMP, transmission electron microscope (TEM), IR and Raman spectroscopy (see Wunder et al. 2011).
T-dependent IR measurement
IR spectra on 1–2 μm thin films of the 3.65 Å phase were collected on a Bruker Vertex 80v FTIR spectrometer connected to a Hyperion microscope at room temperatures and at −190 °C using a Linkam FTIR600 freezing stage cooled with liquid nitrogen. The film preparation method is described in detail in Hofmeister (1995). Prior to this procedure the 10 Å phase was successfully separated from the sample by handpicking under a binocular microscope. Important components of the spectrometer were a Globar light source, a KBr beam splitter, an InSb detector (used for the region of the OH-stretching vibrations), and a HgCdTe detector (used for the region of the lattice vibrations). The spectra were collected with a resolution of 2 cm−1 and averaged over 256 scans in the OH-stretching region between 2500 and 4000 cm−1 and in the mid-infrared (MIR) region between 600 and 1500 cm−1. For the MIR region, we utilized both windows of the freezing stage and sample holder made of ZnSe. In the OH-stretching region, the sample was placed on a sapphire sample holder. The spectra were fitted with the program PeakFit by Jandel Scientific using the second-derivative zero algorithm for the background and a mixed Lorentzian and Gaussian lineshape for the component bands.
Powder XRD diffraction with Rietveld refinement
Recording of the XRD powder diffraction of the product of run MA304 has already been described in Wunder et al. (2011). As a start for the refinement of the 3.65 Å phase in monoclinic space group P21 we used the structural data of the lowest energy configuration as derived from the DFT-calculations (see later). For the 10 Å phase, structural data were taken from Comodi et al. (2005). Unit-cell parameters, other structural parameters and phase proportions were refined using the GSAS software package for Rietveld refinement (Larson and Von Dreele 1987). Neither the H positions nor its isotropic displacement factors were refined (all Uiso of H were fixed at the value of 0.001 Å2). Isotropic displacement factors of all O as well as Mg and Si were combined and a single value was refined. The refinements were done in the following sequence: scale factor, background (fitted with a real-space correlation function, which is capable of modeling the diffuse background from the amorphous foil and glue used for sample preparation), zero-point correction, phase fractions, peak shape [defined as pseudo-Voigt with variable Gaussian (U, V, W) and Lorentzian (X, Y) character], lattice parameters, preferred orientation, atomic positions, and isotropic temperature displacement factors.
The DFT optimized lattice parameters and atomic positions are listed in Table 1. The cell volumes of the structures derived from the Pnam and from the P212121 phases using the same functional are very similar. In all cases, the monoclinic distortion is smaller than 0.15°. Due to the known systematic errors of LDA and GGA functionals, the LDA cell parameters turn out to be somewhat smaller and the GGA cell parameters somewhat larger than the experimental values. The total energy of the structure derived from the P212121 phase is lower than that derived from Pnam by 15 kJ/mol in the LDA and 11 kJ/mol in the GGA calculation, respectively. Looking at the atomic positions, this difference seems to be mainly caused by the different hydrogen positions. The hydrogen positions of the original P212121 structure were ordered, whereas the hydrogen sublattice of the Pnam phase was disordered. However, the reduction to P21 due to (MgSi) ordering in both cases leads to some flexibility in the hydrogen structure without affecting the overall space group. The close similarity between the two derived structures including their lattice energies and cell volumes suggests that no other structural differences besides the hydrogen positions should be present.
As input for the Rietveld refinement of the 3.65 Å phase in P21 (see below) we chose the optimized parameters of the lowest-energy phase derived from the original P212121 structure using the GGA-PBE functional, which provides a cell volume that is more consistent to experiment than LDA. Some distances of the computed structure are listed in Table 2.
The dielectric response function, Im[ε(ω)], is computed using the GGA-PBE functional from the same GGA optimized structure as GGA is usually considered to provide more realistic frequencies than LDA. The resulting spectra are shown in Figure 1a in the frequency range of the OH-stretching modes and in Figure 1b in the range of lattice vibrations between 1500 and 750 cm−1. For the 6 H atoms in the unit cell of the P21 phase, 12 distinct vibrational modes are predicted in the OH-stretching region between 3462 and 3096 cm−1 (Fig. 1a). The displacement vectors of the individual modes reveal coupling between OH vibrations. While the modes at 3462 and 3389 cm−1 (3455 and 3382 cm−1) are due to stretching vibrations of O2-H2 (O1-H1) essentially in the x-y plane, the bands at 3300 and 3278 cm−1 can be assigned to in-phase and out-of-phase O5-H5 vibrations in . The remaining 6 modes at lower frequencies involve more coupled motions of the other 3 H atoms in the structure, H3, H4, and H6. The strongest components of the displacement vector are vibrations of O6-H6 at 3231 and 3096 cm−1, O4-H3 at 3205 and 3180 cm−1, and O3-H4 at 3175 and 3099 cm−1.
T-dependent IR spectra
Figures 1c and 1d show the IR spectra in the OH-stretching region and MIR region between 730 and 1500 cm−1 taken at 25 and −190 °C. At 25 °C we observe six broad OH bands at 3188, 3216, 3235, 3321, 3418, and 3460 cm−1, which we assigned to OH-stretching vibrations involving the six crystallographically non-equivalent hydrogen atoms (Table 4) (Wunder et al. 2011). However, the new spectrum at −190 °C reveals that the IR pattern in the OH-stretching region is much more complex and at least 8 OH bands can be distinguished (Fig. 1c). Four of them at lower wavenumber (3134–3305 cm−1) are still relatively broad even at −190 °C and may be deconvoluted in even more bands as observed for the two bands at higher wavenumbers, each of which split into two bands at −190 °C. This splitting cannot be explained by partial disorder of the structure as the band separation would be too small. Moreover the same splitting occurs in the calculated spectrum based on a completely ordered structure and can be assigned to coupled OH motions (see above). The MIR spectrum in Figure 1d at −190 °C is also in excellent agreement with the calculated spectra in Figure 1b.
Powder XRD diffraction with Rietveld refinement
Table 3 presents the structural data and fit statistics of the Rietveld refinement performed using the DFT-derived low-energy structure with space group P21 as a starting model. The new refinement is compared with the corresponding results for refinements in Pnam and P212121 after Wunder et al. (2011). Quantitative phase analyses of the powder XRD pattern of run MA304 resulted in 90 wt% of 3.65 Å phase and 10 wt% of 10 Å phase for the refinement in space group P21, which is identical to refinements in Pnam and P212121 (Wunder et al. 2011). Considering the different settings, the cell dimensions a, b, c as well as the unit-cell volume V are within 2σ uncertainties identical for all three different space groups. This is due to the very small deviation of 0.03(1)° for the monoclinic angle in P21, which is consistent with the DFT-calculations, and the same number of formula units per unit cell (Z = 2) in the three different space groups.
In the refinement in space group Pnam, two reflections at d = 4.234 Å (~20 °2Θ, CuKα1-radiation) and 4.192 Å (~21.2°) could not be assigned to either 10 Å phase or to 3.65 Å phase (Fig. 2). The reflection at 4.234 Å could be assigned to (110) of 3.65 Å phase in the space group P212121, but with significant difference between measured and calculated intensity; the reflection at 4.192 Å remained unassigned (Fig. 2). Thus, the refinement statistics for P212121 are slightly better than that for Pnam (Table 3). In the refinement in P21 these two reflections could be assigned to (011) and (101) of the 3.65 Å phase and measured and calculated intensities for these two reflections fit perfectly. As a result of this, the quality of refinement statistics for P21 is significantly better than for both, P212121 and Pnam (Table 3). The atomic coordinates and isotropic displacement parameters for the 3.65 Å phase refined in P21 are listed in Table 4. Because of the limitations of the powder XRD measurement and the Rietveld method, the derived values for the isotropic displacement parameters are at best only rough approximations.
In analogy to the structure of perovskite, the 3.65 Å phase forms a framework of corner-linked octahedra in this new structural model (Fig. 3). In the three-dimensional array, clusters of six Mg octahedra surround a Si octahedral, and vice versa. Thus, Mg and Si are ordered in two symmetrically distinct cation positions. (MgSi) ordering has been proposed based on the broad asymmetric O-Mg,Si-O bending modes observed in the MIR absorption spectra of the 3.65 Å phase (Wunder et al. 2011). The polyhedra are strongly tilted with respect to the crystallographic axes. The Mg and Si octahedra are significantly distorted with long Mg-O bond lengths along the b-axis (Mg-O4 and Mg-O6, Table 2) and long Si-O distances along the a-axis (Si-O5, Table 2). Tilting and distortion of octahedra, accompanied by structural ordering of Mg and Si induces a symmetry reduction to monoclinic P21 from orthorhombic P212121 or Pnam. Symmetry reduction has already been assumed from the occurrence of a sharp Raman band at 269 cm−1 (Wunder et al. 2011, their Fig. 2c) and is strongly supported by the DFT calculations and the new Rietveld refinement, which resulted in excellent refinement statistics and the successful assignment of reflections that were unassigned in Pnam and P212121 structure models (Fig. 2).
The six DFT-derived H-positions of the 3.65 Å phase were not refined during the Rietveld analyses. The individual O-H, O-H···O and O···H distances (in the GGA-PBE-model) give realistic values and range from 0.976 to 0.991 Å, 2.714 to 2.971 Å, and 1.726 to 1.999 Å (Table 2), respectively. As none of the H-H distance is shorter than 2.2 Å (Table 2), no critical proton-proton repulsion is evident for H positions in the determined structure of the 3.65 Å phase.
The peak frequencies and relative intensities in the measured IR spectra and the computed dielectric response function (Figs. 1a–1d) compare favorably and provide additional confidence in the proposed structure model for the 3.65 Å phase. All features observed in the IR spectra are reproduced by the DFT calculations. These include the apparent splitting of the two highest frequency bands around 3450 and 3400 cm−1. This is explained by stretching vibrations of O2-H2 and O1-H1, which have the shortest and very similar O-H distances (Table 2). On the contrary, the lowest frequency modes can be assigned to O4-H3, O3-H4, and O6-H6, which experience the longest O-H bond lengths and consequently the strongest hydrogen bonding.
The computed spectrum of the higher energy P21 structure obtained from Pnam, which has similar lattice parameters (Table 1), shows strongly shifted peaks (most of them shifted to higher wavenumbers). This underlines the much higher sensitivity of vibrational spectroscopy as compared to X-ray diffraction to the distribution of hydrogen in the crystal structure.
The large interstices that are defined by eight octahedra, are not filled by large A cations as in the perovskite structure, but are occupied by hydrogen atoms. Due to this open framework structure, the density of the 3.65 Å phase, ρ = 2.637 g/cm3, is unusually low for a high-pressure phase. There are six unique oxygen sites in the 3.65 Å phase, all of which participate in hydrogen bonding. Thus, the 3.65 Å phase is composed of corner-sharing alternating Mg(OH)6 and Si(OH)6 octahedra. It represents the third known phase besides the mineral thaumasite, Ca3Si(OH)6(CO3)(SO4)·12H2O (Effenberger et al. 1983), and synthetic phase D, MgSi(OH)2O4 (Yang et al. 1997), to contain fully hydrated silica octahedra. However, in contrast to the 3.65 Å phase, in both these phases the Si-octahedra are edge-shared to other polyhedra. Much stronger structural analogies exist to minerals of the stottite group (I.I. Ross et al. 1988; N.L. Ross et al. 2002), which consist of a framework of corner-sharing octahedra in ordered configuration with fully protonated O atoms. Our preliminary attempts in refining the structure of the 3.65 Å phase by using the structure of stottite, FeGe(OH)4 (I.I. Ross et al. 1988) as a starting model, yielded problems in the assignment of some (weak) reflections. However, Rietveld refinements of powder XRD data are probably not the appropriate method to solve possible analogies to the various cubic and tetragonal varieties of the stottite-group phases. Single-crystal structure data of the 3.65 Å phase are strongly needed.
S.J. was supported by DFG grant JA 1469/4-1.
We thank L. Ehm for effective editorial handling of the manuscript. The suggestions and comments of two anonymous reviewers significantly improved the manuscript.
- Manuscript Received October 10, 2011.
- Manuscript Accepted February 23, 2012.