Crystal Structure of Moganite and Its Anisotropic Atomic Displacement Parameters Determined by Synchrotron X-ray Diffraction and X-ray/Neutron Pair Distribution Function Analyses

The crystal structure of moganite from the Mogán formation on Gran Canaria has been re-investigated using high-resolution synchrotron X-ray diffraction (XRD) and X-ray/neutron pair distribution function (PDF) analyses. Our study for the first time reports the anisotropic atomic displacement parameters (ADPs) of a natural moganite. Rietveld analysis of synchrotron XRD data determined the crystal structure of moganite with the space group I2/a. The refined unit-cell parameters are a = 8.7363(8), b = 4.8688(5), c = 10.7203(9) Å, and β = 90.212(4)°. The ADPs of Si and O in moganite were obtained from X-ray and neutron PDF analyses. The shapes and orientations of the anisotropic ellipsoids determined from X-ray and neutron measurements are similar. The anisotropic ellipsoids for O extend along planes perpendicular to the Si-Si axis of corner-sharing SiO4 tetrahedra, suggesting precession-like movement. Neutron PDF result confirms the occurrence of OH over some of the tetrahedral sites. We postulate that moganite nanomineral is stable with respect to quartz in hypersaline water. The ADPs of moganite show a similar trend as those of quartz determined by single-crystal XRD. In short, the combined methods can provide high-quality structural parameters of moganite nanomineral, including its ADPs and extra OH position at the surface. This approach can be used as an alternative means for solving the structures of crystals that are not large enough for single-crystal XRD measurements, such as fine-grained and nanocrystalline minerals formed in various geological environments.


Introduction
Moganite (CNMMN no. 99-035) is a silica polymorph that takes the name from its locality: the Mogán formation on southern Gran Canaria in the Canary Islands, first described by Flörke et al. (1976) [1]. Moganite has been observed ubiquitously in silica sinters, volcanic rocks, carbonate turbidites and deep-sea sediments around the world and is used as an important indicator for evaporitic paleoenvironments [1][2][3][4][5][6][7]. It has been identified as a common constituent in silica varieties such as chert, agate, flint, and chalcedony and commonly coexists with fine-grained quartz [1,2,[8][9][10]. Moganite is a metastable phase that eventually transforms to quartz or dissolves preferentially during diagenesis and aging [5,11,12]. Recently, moganite has been discovered in a lunar meteorite in the form of nanocrystalline aggregates in KREEP (high potassium, rare-earth element,

Materials and Methods
Moganite samples were collected from unconsolidated powders that form rinds around a chert found within the ignimbrite lava flows of the Mogán formation on Gran Canaria, Spain ( Figure S1). The white powder in the sample was the main subject of our study. Moganite from Mogán formation has been extensively studied using various techniques such as XRD, electron probe microanalysis (EPMA), infrared spectroscopy and nuclear magnetic resonance spectroscopy [1,3,14,20,31].
EPMA specimens were prepared as carbon coated thin sections. EPMA measurements with wavelength dispersive spectrometers (WDS) were made with a CAMECA SXFive FEG electron microprobe using 20 kV and 15 nA beam current in the Geoscience Department of the University of Wisconsin-Madison. TEM specimens were prepared by depositing drops of moganite suspension on carbon-coated TEM Cu grids. High-angle annular-dark-field images, TEM images and their selected-area electron diffraction (SAED) patterns were obtained using FEI Titan 80-200 and JEOL 2010 microscopes operated at 200 keV.
High-resolution X-ray powder diffraction patterns were collected at beamline 11-BM, Advanced Photon Source (APS), Argonne National Laboratory, using a wavelength of 0.412836 Å. The finely ground powders from the moganite sample were placed into a 0.8 mm diameter polyimide tube. The XRD measurement was calibrated using a LaB 6 standard. The crystal structures and mineral phase ratios in the sample were determined using the Rietveld method with the GSASII software [32]. The structures of moganite [14], quartz [33], gypsum [34] and halite [35] were used as the initial structures for the Rietveld refinement. The crystallite sizes were determined by full width at half maximum (FWHM) and integral breadth from whole peak profile.
Synchrotron X-ray PDF experiments were conducted using a wavelength of 0.24152 Å on beamline 17-BM at the APS, Argonne National Laboratory. The moganite sample was placed into a polyimide tube with a 1 mm diameter. An amorphous silicon area detector was used to collect two-dimensional diffraction patterns in the transmission geometry. Each single exposure on the detector was set to 1 s and was repeated 300 times, totaling a collection time of 300 s. The distances between the sample and the detector and the center positions of the beams were calibrated using a LaB 6 standard. For background removal, Minerals 2021, 11, 272 3 of 12 diffraction data of the empty polyimide tube were collected using the same exposure times. GSAS-II software was used to convert diffraction images to conventional 1-D profiles (i.e., intensity versus wave vector Q). The data obtained up to a Q max of 19.6 Å −1 were then converted into PDF patterns using PdfGetX3 [36]. The instrumental resolution parameters of Q damp and Q broad were 0.045 and 0.069 Å −1 , respectively. PDF fitting and refinement were performed using the PDFGui program [37].
Neutron PDF measurements were performed on the NOMAD instrument (BL-1B beamline) at the Spallation Neutron Source (SNS), Oak Ridge National Laboratory. The powder sample was loaded into a 3 mm diameter quartz capillary. The neutron PDF pattern was calculated with the NOMAD data reduction software by the Fourier transformation of the structure function S(Q). The data obtained up to a Q max of 31.4 Å −1 were transformed into PDF patterns using the PDFgetN program [38]. The instrumental resolution parameters of Q damp and Q broad were 0.01766 and 0.01918 Å −1 , respectively. PDFGui software was used for fitting the neutron PDF data.

High-Resolution Synchrotron XRD
High-resolution synchrotron XRD reveals the presence of the (011) and (200) peaks of moganite adjacent to the (010) peak of quartz ( Figure 1). The sample contains moganite 75.3(5) wt.%, quartz 14.2(3) wt.%, gypsum 6.6(2) wt.% and halite 3.7(2) wt.% determined by Rietveld refinement (Figure 1). Previous studies also showed the occurrence of moganite (~65-85 wt. %), quartz, gypsum and halite in similar samples from the Mogán formation [2,19]. The crystallite sizes are estimated as moganite (68.6 nm), quartz (95.5 nm), gypsum (473.1 nm) and halite (749.5 nm) from the XRD pattern. The refined unit cell parameters, atomic coordinates and isotropic displacement parameters (U iso ) of these phases are presented in Table 1. Moganite has unit cell parameters of a = 8.7363(8), b = 4.8688(5), c = 10.7203(9) Å, and β = 90.212(4) • with space group I2/a (which follows the non-conventional setting to maintain the relationship with the trigonal quartz cell). The refined structure of moganite is well matched with the reported structures [3,14]. The calculated density of moganite (2.63 g/cm 3 ) is slightly lower than that of quartz (2.65 g/cm 3 ). The refined structure of nanocrystalline quartz has a slightly larger unit cell than reported ( Table 1). The refined unit cell parameters of gypsum are similar to the previously reported values [34,35]. Impurities may influence the unit cell parameters of halite and gypsum.

EPMA
The major elements of moganite areas show almost pure silica with Na, K, Mg, Ca, Al and Fe impurities at trace levels ( Table 2). The EPMA results of moganite also reveal a water content of 3.13-5.31 wt.% by directly analyzing O using EPMA and assigning the excessive O to H 2 O. Thus, its chemical formula is SiO 2 · 0.145H 2 O based on the average values listed in Table 2. Weight loss of approximately 5% of almost pure moganite was suggested by thermogravimetric analysis from 298 to 983 K [5]. Infrared spectra of moganite indicate that 2-3 wt.% of water is not a constituent of the structure [1,3,17,19]. The water in moganite is mainly in the form of silanol species (Si-OH) and free water, and the ratio H 2 O SiOH /H 2 O free is approximately 1.2 [19]. Moganite also contains a CO 2 content of~0.1-1.0 wt.% with a minor component of CO identified by mass spectroscopy [8,19]. Experimental and calculated synchrotron X-ray diffraction (XRD) patterns (overlapped black and red lines) of the studied sample consisting of moganite, quartz, gypsum and halite. The weight percentages of the mineral phases were determined using the Rietveld method. The residue (grey line) between the experimental data and calculated profile is shown below the XRD pattern. Table 1. Unit-cell parameters, atomic coordinates and thermal displacement parameters (Uiso) of moganite, quartz, halite and gypsum determined by Rietveld refinement (Figure 1). Lattice parameters: a =5.6338(7) Å Figure 1. Experimental and calculated synchrotron X-ray diffraction (XRD) patterns (overlapped black and red lines) of the studied sample consisting of moganite, quartz, gypsum and halite. The weight percentages of the mineral phases were determined using the Rietveld method. The residue (grey line) between the experimental data and calculated profile is shown below the XRD pattern. Table 1. Unit-cell parameters, atomic coordinates and thermal displacement parameters (U iso ) of moganite, quartz, halite and gypsum determined by Rietveld refinement (Figure 1).

TEM
High-angle annular dark-filed image, bright-field TEM image and SAED patterns of moganite are shown in Figure 2. The moganite shows an aggregation of plate-like nanosized crystals with thicknesses of~5 to 13 nm. The SAED patterns are from a microcrystalline quartz of chert inside the moganite rinds ( Figure 2C) and an area dominated by moganite intergrown with nanocrystalline quartz ( Figure 2D). Compared to the SAED pattern of nanocrystalline quartz, moganite shows superlattice reflections ( Figure 2D) [3]. Streaking reflections result from non-periodic intergrowths of moganite and quartz nanocrystals (or domains).

TEM
High-angle annular dark-filed image, bright-field TEM image and SAED patterns of moganite are shown in Figure 2. The moganite shows an aggregation of plate-like nanosized crystals with thicknesses of ~5 to 13 nm. The SAED patterns are from a microcrystalline quartz of chert inside the moganite rinds ( Figure 2C) and an area dominated by moganite intergrown with nanocrystalline quartz ( Figure 2D). Compared to the SAED pattern of nanocrystalline quartz, moganite shows superlattice reflections ( Figure 2D) [3]. Streaking reflections result from non-periodic intergrowths of moganite and quartz nanocrystals (or domains).

Neutron/X-ray PDF analysis
The powder sample of moganite/quartz was treated several times in deionized water to eliminate the co-existing halite and gypsum. The synchrotron XRD pattern of the posttreatment sample shows 80.7(5) wt.% of moganite and 19.3(3) wt.% of quartz ( Figure S2). The experimental results of I(Q), S(Q), F(Q) and G(r) from X-ray and neutron scattering of this sample are shown in Supplementary Figures S3 and S4. PDF patterns from 1 to 40 Å are presented in Figure 3. The first major peak at 1.61 Å corresponds to Si-O correlations

Neutron/X-ray PDF Analysis
The powder sample of moganite/quartz was treated several times in deionized water to eliminate the co-existing halite and gypsum. The synchrotron XRD pattern of the posttreatment sample shows 80.7(5) wt.% of moganite and 19.3(3) wt.% of quartz ( Figure S2). The experimental results of I(Q), S(Q), F(Q) and G(r) from X-ray and neutron scattering of this sample are shown in Supplementary Figures S3 and S4. PDF patterns from 1 to 40 Å are presented in Figure 3. The first major peak at 1.61 Å corresponds to Si-O correlations in silica tetrahedra. The second peak at 2.61-2.62 Å and the third peak at 3.07 Å are related to O-O and Si-Si correlations, respectively, within the corner-sharing SiO 4 tetrahedra. and calculated patterns, the results of PDF refinement show an acceptable agreement with the calculated model with a Rw value of 14.5% (Figure 3). For neutron PDF refinement, the unit-cell parameters, atomic coordinates and ADPs of moganite all varied, and the obtained structural parameters are listed in Table 3. The refined quartz structural parameters are listed in Supplementary Table S1. The two obtained sets of structural parameters from X-ray and neutron refinements are generally in good agreement. Since neutrons interact with the nuclei in the sample while X-rays interact with its electrons, neutron scattering is sensitive to light elements such as hydrogen and oxygen. Thus, neutron PDF refinement was also applied to refine the occupancy of O sites in moganite (Table 3), where it is related to the surface OH and silanol group (Si-OH). An excessive occupancy (1.06) of O sites in the moganite structure improved the neutron PDF fitting (Rw value decreases by 1.2%), and the result is shown in Figure S5 and Table S2. Thus, taking into account the excessive oxygen, the chemical formula of moganite is SiO2 ⸱ 0.12H2O or, SiO1.88OH0.24 (Table 3), which corresponds to 3.5 wt.% of water. The particle size of moganite is estimated as ~6 nm from the long-ranged PDF pattern based on a sudden drop in peak intensities around 5-6 nm range ( Figure S6).  PDF refinement was carried out by fitting the experimental PDF patterns (Figure 3). The initial structures of moganite and quartz for PDF refinement were the refined structures obtained from high-resolution synchrotron XRD data ( Table 1). The X-ray PDF refinement mainly focused on determination of ADPs of each atom with the unit cell parameters and atomic coordinates fixed. Based on the differences between experimental and calculated patterns, the results of PDF refinement show an acceptable agreement with the calculated model with a R w value of 14.5% (Figure 3). For neutron PDF refinement, the unit-cell parameters, atomic coordinates and ADPs of moganite all varied, and the obtained structural parameters are listed in Table 3. The refined quartz structural parameters are listed in Supplementary Table S1. The two obtained sets of structural parameters from X-ray and neutron refinements are generally in good agreement. Table 3. Unit-cell parameters, atomic coordinates and anisotropic displacement parameters of moganite derived from X-ray and neutron PDF analyses. Since neutrons interact with the nuclei in the sample while X-rays interact with its electrons, neutron scattering is sensitive to light elements such as hydrogen and oxygen. Thus, neutron PDF refinement was also applied to refine the occupancy of O sites in moganite (Table 3), where it is related to the surface OH and silanol group (Si-OH). An excessive occupancy (1.06) of O sites in the moganite structure improved the neutron PDF fitting (R w value decreases by 1.2%), and the result is shown in Figure S5 and Table  S2. Thus, taking into account the excessive oxygen, the chemical formula of moganite is SiO 2 ·0.12H 2 O or, SiO 1.88 OH 0.24 (Table 3), which corresponds to 3.5 wt.% of water. The particle size of moganite is estimated as~6 nm from the long-ranged PDF pattern based on a sudden drop in peak intensities around 5-6 nm range ( Figure S6).

Discussion
Moganite is a low-temperature precipitate that coexists with fine-grained quartz, halite and gypsum in the late in-filling of cavities, fissures and cracks at ignimbrite flows of the Mogán formation ( Figure 1 and Figure S1) [1,2,8]. The emplacement temperature of the pyroclastic flow was above 700 • C, and the volatiles would continuously escape from the flow via fumaroles during cooling [1]. Heaney (1995) suggested that high alkali and sulfate activities play an important role in the formation of moganite. Evaporitic regimes such as arid and alkaline environments were associated with high concentrations of moganite (>30%) [4,10]. Moganite occurs in young rocks with less than~100 Ma because thermodynamically unstable moganite may transform to quartz or dissolve during silicawater interactions at ambient pressure [2,4,11]. We hypothesize that moganite nanocrystal is stable with respect to quartz in halite-saturated water at low temperature ( Figure 4A). The OHsites of moganite confirmed by neutron PDF analysis could adsorb alkali cations such as Na + and K + during its formation. These cations may lower the surface energy of moganite nanocrystals in halite-saturated hypersaline water. In low salinity water, opal instead of moganite forms at low temperature [4,5]. The average size of moganite (~68.6 nm) calculated from XRD refinement is larger than the size from TEM images. The attached moganite nanocrystals with same orientation may contribute to the large average size from XRD refinement. The different methods for studying same mineral often provide different answers. For example, orthoclase shows monoclinic structure in optical microscope and powder XRD; however, TEM shows triclinic nano-domains [40][41][42]. TEM images also suggest surface-induced nucleation and growth by nanocrystals with the same or similar orientations ( Figure 4B). Determination of the detailed structure of moganite has been difficult because it typically occurs in the form of nano-sized crystals and coexists with other minerals [14,43]. In this case, the application of powder diffraction and related techniques is essential for characterizing the crystal structure [22]. Synchrotron XRD and X-ray/neutron PDF methods provide high-quality structural parameters for moganite (Tables 1 and 3). Our refined unit-cell parameters and bond distances of moganite are in general accordance with those determined by Miehe and Graetsch (1992) [3] and Heaney and Post (2001) [4] (Table 4). However, compared to previous studies, our refined Si(1) and Si(2) bond lengths are much closer to each other, suggesting more regular SiO4 tetrahedra and position of Si at the centers of regular tetrahedra (Table 4). Overall, the average structures of moganite determined by synchrotron techniques are in good agreement with the previously reported structures.
Although the crystal structures of moganite and quartz are closely related, their XRD and SAED patterns reveal that the atomic arrangement of moganite is different from that of quartz (Figures 1 and 2). The framework structures of quartz and moganite are built by linear silica tetrahedral chains that are connected via bridge tetrahedra ( Figure 5). The linear tetrahedral chains are parallel to [010] in moganite and [100] in quartz. The topological difference between the two structures is the position of the tetrahedral bridge which is responsible for the systematic displacements along 1/2 [110] direction at the unitcell scale ( Figure 5) [3,14]. Determination of the detailed structure of moganite has been difficult because it typically occurs in the form of nano-sized crystals and coexists with other minerals [14,43]. In this case, the application of powder diffraction and related techniques is essential for characterizing the crystal structure [22]. Synchrotron XRD and X-ray/neutron PDF methods provide high-quality structural parameters for moganite (Tables 1 and 3). Our refined unit-cell parameters and bond distances of moganite are in general accordance with those determined by Miehe and Graetsch (1992) [3] and Heaney and Post (2001) [4] ( Table 4). However, compared to previous studies, our refined Si(1) and Si(2) bond lengths are much closer to each other, suggesting more regular SiO 4 tetrahedra and position of Si at the centers of regular tetrahedra (Table 4). Overall, the average structures of moganite determined by synchrotron techniques are in good agreement with the previously reported structures. Although the crystal structures of moganite and quartz are closely related, their XRD and SAED patterns reveal that the atomic arrangement of moganite is different from that of quartz (Figures 1 and 2). The framework structures of quartz and moganite are built by linear silica tetrahedral chains that are connected via bridge tetrahedra ( Figure 5). The linear tetrahedral chains are parallel to [010] in moganite and [100] in quartz. The topological difference between the two structures is the position of the tetrahedral bridge which is responsible for the systematic displacements along 1/2 [110] direction at the unit-cell scale ( Figure 5) [3,14].   Table 2). The models show the displacement ellipsoids of each atom drawn with 80% probability. Blue atoms are silicon, and red atoms are oxygen.

Conclusions
The results of this study have important implications for how to determine the average and local structure of natural moganite. The combined synchrotron XRD and Xray/Neutron PDF analysis is a powerful tool to obtain high-quality structural parameters. Rietveld analysis of Bragg peaks from synchrotron XRD determines the average structure of moganite nanocrystals. The unit-cell parameters and bond distances of the refined moganite structure show consistency with the previously reported structures. On the other hand, X-ray and neutron PDF methods can provide the local structure of moganite including its ADPs. The shapes and orientations of anisotropic ellipsoids of atoms in the refined moganite structure show similar tendencies to those of the quartz structure. Neutron PDF also confirms the occupancy of O sites, suggesting surface OH and silanol (Si-OH) in moganite, which are previously determined by IR and NMR studies [17][18][19]. In nature, the monovalent cations adsorbed on moganite can lower its surface energy, which can explain why moganite nanomineral is stable with respect to quartz in halite-saturate hypersaline water. In short, the results from this combined approach can provide highquality structural parameters of fine-grained minerals such as moganite and quartz nanocrystals. This approach can be used as an alternative means for refining structures of crystals that are not large enough for single-crystal XRD measurements. The approach will be Moganite structure models from X-ray and neutron PDF analyses are projected along the b-axis ( Figure 6). The structure of moganite can be described as alternating slices of right-and left-handed quartz (or unit cell twinning) characterized by the presence of 4and 6-membered rings of SiO 4 tetrahedra ( Figure 5 and Figure S7) [3]. It is known that four-membered rings are present in other silica polymorphs, coesite and opal [44]. Petrovic et al. (1996) suggested that the structural instability of moganite may be associated with the four-membered rings of silica tetrahedra, which are not present in the quartz structure. Other moganite-type phases such as PON [15], Zn[BPO 4 (OH) 2 ] [45] and AlPO 4 [16] were synthesized at high-pressure and high-temperature conditions. For example, cristobaliteand quartz-type PON can be transformed into the moganite-type PON after being annealed at 850 • C and 2.5 GPa [15]. The unit cell twinning in moganite is similar to that in protoenstatite, whose nanocrystal is stable with respect to enstatite and clinoenstatite at low temperatures [46].  . Structural models of moganite derived from X-ray and neutron PDF analyses ( Table 2). The models show the displacement ellipsoids of each atom drawn with 80% probability. Blue atoms are silicon, and red atoms are oxygen.

Conclusions
The results of this study have important implications for how to determine the average and local structure of natural moganite. The combined synchrotron XRD and Xray/Neutron PDF analysis is a powerful tool to obtain high-quality structural parameters. Rietveld analysis of Bragg peaks from synchrotron XRD determines the average structure of moganite nanocrystals. The unit-cell parameters and bond distances of the refined moganite structure show consistency with the previously reported structures. On the other hand, X-ray and neutron PDF methods can provide the local structure of moganite including its ADPs. The shapes and orientations of anisotropic ellipsoids of atoms in the Figure 6. Structural models of moganite derived from X-ray and neutron PDF analyses ( Table 2). The models show the displacement ellipsoids of each atom drawn with 80% probability. Blue atoms are silicon, and red atoms are oxygen.
Moganite structure models from X-ray and neutron PDF analyses yielded the displacement ellipsoids of silicon and oxygen atoms ( Figure 6). The shape and orientation of the ellipsoids between X-ray and neutron sources are very similar. The anisotropic ellipsoids for the O atoms in moganite extend along the planes perpendicular to the axial direction of corner-sharing SiO 4 tetrahedra, suggesting precession-like motions. Excessive occupancy of O indicates silanol water or Si-OH on surface tetrahedra of moganite nanocrystals. In addition, the structure of moganite is compared with that of nanocrystalline quartz from X-ray PDF refinement (this study) and the previously reported quartz structure determined by single-crystal XRD [39] (Supplementary Figure S8). Both moganite and quartz structures show similar shapes and orientations of their anisotropic ellipsoids (Supplementary Figure  S8). The nanocrystalline quartz shows relatively larger unit cell and ADP parameters than those in bulk quartz (Table 1 and Supplementary Table S1), which can be attributed to surface relaxation of quartz nanocrystals. Therefore, our results confirm that X-ray and neutron PDF techniques are powerful to characterize the stoichiometry (Si/O ratio) and ADPs of moganite and provide high-quality crystalline structural information.

Conclusions
The results of this study have important implications for how to determine the average and local structure of natural moganite. The combined synchrotron XRD and Xray/Neutron PDF analysis is a powerful tool to obtain high-quality structural parameters. Rietveld analysis of Bragg peaks from synchrotron XRD determines the average structure of moganite nanocrystals. The unit-cell parameters and bond distances of the refined moganite structure show consistency with the previously reported structures. On the other hand, X-ray and neutron PDF methods can provide the local structure of moganite including its ADPs. The shapes and orientations of anisotropic ellipsoids of atoms in the refined moganite structure show similar tendencies to those of the quartz structure. Neutron PDF also confirms the occupancy of O sites, suggesting surface OH and silanol (Si-OH) in moganite, which are previously determined by IR and NMR studies [17][18][19]. In nature, the monovalent cations adsorbed on moganite can lower its surface energy, which can explain why moganite nanomineral is stable with respect to quartz in halite-saturate hypersaline water. In short, the results from this combined approach can provide high-quality structural parameters of fine-grained minerals such as moganite and quartz nanocrystals. This approach can be used as an alternative means for refining structures of crystals that are not large enough for single-crystal XRD measurements. The approach will be useful for the structural determination of other submicron sized crystals and nanominerals formed in geological environments.

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Data Availability Statement:
The data presented in this study are available on request from the corresponding author.