Identifying and explaining vibrational modes of sanbornite (low-1 BaSi 2 O 5 ) and Ba 5 Si 8 O 21 : A joint experimental and theoretical study

ABSTRACT


Introduction
Barium silicates are extensively studied for their excellent material properties and device performance in a range of important technological applications [1][2][3][4][5][6][7] Sanbornite (low-BaSi2O5) is a uncommon mineral found in Big Creek, California (USA), and its hydrous analogue bigcreekite (BaSi2O5•4H2O) are rare examples where Ba is concentrated in a silicate phase [8][9][10].On the other hand, Ba5Si8O21 is a synthetic phase, displaying the rare characteristic of being an anhydrous phase containing ribbons (quadruple zweier chains) of silica tetrahedra surrounded by Ba cations which stabilize the stretched chains.Each ribbon is composed of two types of SiO4 units that can be distinguished by the number of inter-tetrahedral linkages they contain.These can be described as Q n species where n is the number oxygens bonded to adjacent Si cations.In Ba5Si8O21, the tetrahedra along the edges of the ribbons are only bonded to two adjacent tetrahedra, Q 2 species, whereas the tetrahedra which form the interior of the ribbon are connected to three adjacent tetrahedra, Q 3 species.Ultimately, Ba5Si8O21 is distinct from sanbornite in the presence of the Q 2 species but comparable in that ribbon and sheets are dominantly composed of Q 3 species.Both structures have been discussed in considerable detail by Liebau and colleagues [11][12][13][14].
Sanbornite and Ba5Si8O21 have received considerable attention in recent years due to their desirable formation as acicular aggregates, leading to a considerable strengthening of the glassceramics produced and due to their high thermal expansion, which has led to their wide investigation for solid-oxide fuel cell sealant materials [5,15].In particular, sanbornite-based glasses display volume nucleation and thus have long been of interest to researchers looking into the fundamental process of crystallization [16][17][18][19][20][21][22].When doped with rare-earth elements, these materials can be used as light emitting diode materials [23,24].Although interesting behaviors have been shown, there is a lack of clarity regarding the origin and significance of the vibrational modes and their transitions during crystallization processes [21,[25][26][27][28].
Vibrational spectroscopy is one of the most versatile techniques used in the investigation of the structure of oxides and oxide glasses.For the low symmetry materials, there may be several bands calculated to lie near the position of a single observed feature.In such cases it is impossible to make an unambiguous assignment if the calculated intensities are so model-dependent that they cannot be used as an aid.Quantum-chemical computations predicting frequencies and spectral intensities are essential to complement the interpretation of experimental spectra, particularly for complex materials where the high density of states results in spectral complexity [26].
Despite the long history of using Raman and infrared spectroscopy, as well as the employ ab initio quantum mechanical methods [29,30], as appropriate tools to investigate the vibrational behavior and related properties (e.g.heat capacity), few crystalline phases of silicates have had detailed determination of their vibrational modes.Early studies have been subject to the limitations and ad hoc assumption used to determine the dominant spectral features [29].
The temperature effect on the phonon properties of both sanbornite (low-BaSi2O5) and Ba5Si8O21 is unknown yet, and it is of great interest to study their vibrational properties at hightemperature.In this context, this work investigates the vibrational modes of these systems related with the phases presented in the BaO-SiO2 system.The experimental results are correlated with first-principle calculations, at the density functional theory (DFT) level, which allows not only the classification of the vibrational modes up to 1150˚C, but also to obtain information and structural changes undergone by these materials.The application of the described strategy allowed us to reliably describe the low-BaSi2O5 and Ba5Si8O21 materials.

Experimental and theoretical procedures 2.1. Sample preparation
High-purity reagents, BaCO3 and SiO2 (Sigma-Aldrich, >99.9%),where used to synthesize both low-BaSi2O5 and Ba5Si8O21.Due to the impurities resulting from the stable phases differing by only ~3% BaO, the solid-state reaction procedure was followed.This entails grinding the powders in a highly vibrating mill (to ensure fine and evenly distributed grain sizes) and compression into tablets and then heat-treated for 30 h at 1340 and 1410°C for low-BaSi2O5 and Ba5Si8O21, respectively.Prior to heat treatment the polycrystalline tablets were calcined for 1h at 1000°C.Both phases have been confirmed by X-ray diffraction (XRD) measurements using Cu Kα radiation operating at 40 kV and a current of 20 mA in continuous scanning mode (0.5° min -1 ) with a 2θ step of 0.02° between 10° ≤ 2θ ≤ 80° on a Rigaku Ultima IV diffractometer.Rietveld refinement of the resulting patterns were done using the GSAS program [32,33].A LabRAM on the sample.Spectra where taken using a 100x visible objective, a 100 µm pinhole, an 1800 gr/mm grating resulting in a frequency and lateral spatial resolution of ~0.5 cm -1 and <2 μm, respectively.Spectra are the average of 12 scans of a dwell time of five seconds.Spectra have been intensity normalized to the high frequency stretching region, although raw spectra have roughly equal intensity.Measured Raman active modes were curve fit using Lorentzian lineshapes to determine individual peak parameters.High temperature measurements were carried out on 40-60 mg polycrystalline monolithic chips heated using a Linkam stage and a 50x SLWD objective.
Slightly longer spectra (10 second dwell time and 16 spectra were averaged) were taken as the furnace window cuts the measured intensity to roughly a third of ambient condition spectra.

Computational methods
DFT calculations of the lattice parameters and vibrational modes were done using Becke's three-parameter hybrid non-local exchange functional, combined with a Lee-Yang-Parr gradientcorrected correlation functional (B3LYP), implemented in the CRYSTAL17 package [34].The atoms were centered and described using pseudopotential databases; [35], 88-31G* [36] and 8-411d11G [37] (all-electron) for Ba, Si and O, respectively.Regarding the diagonalization of the density matrix, the reciprocal space net was described by a shrinking factor of 4, generated according to the Monkhorst-Pack scheme.The accuracy of the evaluation of the Coulomb and exchange series was controlled by five thresholds, whose adopted values were 10 −7 , 10 −7 , 10 −7 , 10 −7 , and 10 −14 .The vibrational frequencies calculation was performed at the Γ point within the harmonic approximation, and the dynamic matrix was computed by the numerical evaluation of the first derivative of analytical atomic gradients.

XRD analysis
The XRD patterns of the synthesized samples are shown in Fig. 1.The crystal structure parameters are in agreement with the literature results, Table 1.The Rietveld refinement results are comparable to published results having a goodness-of-fit (χ 2 ) close to unity and R values below 10% [38].The cell volumes for the measured and calculated structures of low-BaSi2O5 and Ba5Si8O21 are less than 1% and 4% of the published values [11,12,15], respectively.
Therefore, the simulations show a very good agreement with the experimental results of the measured structures.Sanbornite is a phyllosilicate composed of two layers: one of Q 3 species and one of BaO9 polyhedra (Figure 2).Each of the Q 3 species are connected to adjacent tetrahedra via bridging oxygens (BO) at the O1 and O3 sites whereas the O2 oxygen is a non-bridging oxygen (NBO) which is only bonded to one Si and three Ba atoms.Topologically, sanbornite can be described as a 6 3 net or an infinite layer of six-membered tetrahedral rings [39].The large size of the Ba cations distorts each sheet such that the NBO are sticking out towards the Ba cations.This results in a relationship between the layers were one BaO9 polyhedron sits atop of two silica tetrahedra, and vice versa.
Ba5Si8O21 has 18 crystallographic sites (Figure 3) and as a consequence has a large number of Raman modes (Table 3).This phase is a rare silicate composed of quadruple zweier chains that form ribbons that can be described topologically as 2 T2 3 T6 ribbons [40].In the Ba5Si8O21 structure, the edge of each ribbon has Q 2 species at the Si1 site.The remaining Si sites (Si2-Si4) are Q 3 species, all of which have three BO and one NBO.The Q n species display distinct vibrational frequencies.3 and colors follow those in figure 2. The directions defined by the a and c lattice parameters are drawn.

Low-BaSi2O5
The primitive cell of sanbornite (Pmcn) contains 32 atoms and therefore, 96 normal modes including the three acoustic translations (B1u, B2u & B3u) (Figure 2).The correlation method [41] allows for the determination of the vibrational modes at the center of the Brillouin zone, There is no known published evaluation of the vibrational spectra despite the multiple Raman studies involving sanbornite [27,28,42].However, theoretical results reproduce the experimental vibrational modes with an absolute mean deviation of <6 cm -1 , and the high degree of overlap in the measured peaks and the displacement from unity in the calculated frequencies yields a small potential for ambiguity.For example, the measured modes numbering 12 (148.5 cm -1 ) through 17 (267 cm -1 ) could correspond to the calculated modes at 182.7 through 278.0 cm -1 .The overall agreement found between measured and simulated frequencies suggests that the spectrum can be divided into four regions according to the predominant symmetry character of the modes: the essentially rigid rotational motions occur below 100 cm -1 ; bending modes involving Ba-O polyhedral from 100-400 cm -1 ; intra-or inter-tetrahedral bending modes (O-Si-O, Si-O-Si), with varying degree of Ba participation, at the range 400-760 cm -1 ; the stretching mode region found >800 cm -1 .However, there are several stretching modes around 118 and 160 cm -1 and bending modes in the stretching region.Modes described as lattice involve significant movement of both the BaO9 and SiO4 sublattices.The complete list of mode symmetries and cations involved are reported in Table 2.
An analysis of the theoretical results of Table 2 shows that there is no distinction in either the relative intensities, the linewidths, or symmetry of modes involving a particular site (whether Si or Ba).Apart from the frequency distinctions there is no physically measurable parameter that distinguishes modes involving Si from Ba, nor distinguishing BO from NBO behavior.

Ba5Si8O21
The primitive cell of Ba5Si8O21 (C2/c) contains 68 atoms and consequently 204 normal modes including the acoustic modes (Au + 2Bu).The vibrational modes at Brillouin zone center can be composed as:   5821 = 49   + 50   + 51   + 51   .The theoretical results reproduce the experimental observed modes slightly better than for sanbornite with a lower absolute mean deviation of <5.1 cm -1 .It is important to remark that numerous vibrational modes leave some ambiguity, especially at lower frequencies where many modes overlap.Note that the Ba3 and O11 sites (Figure 3) are found at the Wycoff sites 4a and 4e, respectively, and consequently, the correlation method would infer that the Ba3 is not Raman active and that O11 site would only contribute to three modes.Fortunately, our simulation shows that this inference is somewhat misleading.An analysis of the results of Table 3 renders that the Ba3 site contributes to at least six modes whereas the O11 site contributes to multiple modes included several pure Si4-O11 stretching modes with values larger than 1100 cm -1 .This result highlights the necessity of ab initio simulations in determining the origin of the Raman modes.As with sanbornite, the spectra can be divided into four regions with small shifts in the limits (Figure 4).The essentially rigid rotational motions occur below 100 cm -1 ; bending modes involving Ba-O polyhedral from 100-370 cm -1 ; intra-or inter-tetrahedral bending modes (O-Si-O, Si-O-Si), with varying degree of Ba participation, found from 370-780 cm -1 ; the stretching mode region found >900 cm -1 .
The same caveats noted above apply to our analysis of Ba5Si8O21, however, given the complexity of the spectra we emphasize that the agreement is excellent.The above modes are discussed in more detail below along with some correlations to their crystal chemical properties.

Temperature dependence of Raman modes
In general, as temperature increases, a thermal expansion takes place with concomitant increase of the crystal volume by lengthening bonds and increasing the inter-tetrahedral angles.
These changes should be recorded in the frequencies of the vibrational modes.Twenty of the 33 measured modes found for sanbornite (Table 2) have been consistently identified up to 1150˚C, and therefore, can be related to its thermal expansion.Table 4 includes the ambient position center (ν0) and linewidth (W0) and their temperature dependences (δν/δT and δW/δT, respectively) as well as a confidence indicator whether regression well (R 2 > 0.9) to weakly describes the mode trend.Modes not included in this table were not well constrained or too weak to follow as the temperature increases.
Raman modes are related to specific bonds, and/or groups of bonds, that can be characterized by their crystal chemical properties.For instance, the Ba-O2 bonds are solely responsible for vibrational modes at 55.0, 71.9, 148.5, and 315.7 cm -1 , however, not all are well defined.Using the thermal expansion data of Gorelova et al., [15], combined with our in situ high temperature data reported here allows us to determine the mode dependence on various crystal structure parameters.
In Figure 4, representative spectra at room temperature and 800˚C were chosen to show the temperature dependence of the modes.At higher temperatures, >800˚C, the distinctions between overlapping modes are lost due to homogeneous broadening.The vibrational modes with very low values of frequency at 55.0 (ν1) and 71.9 cm -1 (ν3) are well defined, and become increasingly so, at higher temperatures (Figure 4a).The low frequency bands are related to rigid motions of the Ba-O2 bonds and, therefore relate directly to the bond length and indirectly to the volume of the BaO9 polyhedron (Figure 5).Although they both have slightly different dependencies, they are similar at roughly ~1.5 cm -1 for bond length change of 0.01 Å (Fig. 6a).A difference quite easily measured given the resolution of our Raman spectrometer.Likewise, the 1077.9cm -1 (ν45) stretching mode of the O1 away from the central Si atom shows an even stronger correlation with the bond length (Fig. 6c).This stretching mode is much more sensitive to a changing bond length in that for every 0.01 Å the frequency shifts by -9.8 cm -1 .This bond length shift is very similar but even more strongly correlated than that found for the Si-O stretching modes and bond lengths in forsterite (Mg2SiO4) [30].Another intense mode is found at 535.5 cm -1 (ν32) at ambient temperatures.This mode is related predominantly to the bending motion of the Si perpendicular the face joined by adjacent bridging (two O3) and non-bridging (O2) oxygens.Ultimately, this vibrational mode can be correlated to the overall volume of the SiO4 tetrahedron (Fig. 3b).In this case, a 1% volume change corresponds to a 1.9 shift in wavenumbers.Further generalization of these relationships may permit Raman spectroscopy to be used in situ to probe crystal chemical properties, especially, during chemical reactions (e.g.crystallization), where the origin of the vibrational mode is known.

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The Ba5Si8O21 spectra has a high number of vibrational modes which has the advantage of permitting quite well-constrained temperature dependence of the peak positions.However, the corollary is that this co-dependence becomes a disadvantage when one mode in a series of overlapping mode becomes poorly constrained such that it degrades the fit of all overlapping modes.Ultimately, of the 70 modes observed at ambient conditions, 28 were reliable characterized to temperatures above 800˚C (see Table 5).The temperature-dependent Raman study of the Ba5Si8O21 was performed to obtain information on structural changes induced by temperature, and the wavenumber versus temperature plots are presented in Figure 7.We can observe that the Raman spectra remain nearly unchanged during the heating of the sample.Notable among these modes are those that are similar to those in sanbornite, specifically those centered at 57, ~500, 900-1070 cm -1 , which are related to Si-O-Ba bending, and Ba-O and Si-O stretching motions, respectively.Unlike sanbornite, Ba5Si8O21 does not have modes predominantly associated with specific Ba-oxygen bonding.The mode at 56.6 cm -1 (ν2) involves rigid motion of the Ba2 site combined with the two opposing oxygens, O2 and O10, on adjacent tetrahedral ribbons.The linear correlation to the Ba2-O* distance is weaker (Fig. 8a) than observed for sanbornite (Fig. 6a).This is explained by the overlap of ν2 mode with adjacent ν1 and ν3 modes.
Likewise, the remaining modes involve more than one oxygen and often both Si and Ba.For instance, the bending modes at 468.5 (ν59) and 501.8 cm -1 (ν62) involve Si4-O10-Ba2 and Si3-O6-Ba2, respectively (Table 3).Both should therefore be sensitive to the twisting of the adjacent tetrahedra with thermal expansion which is concentrated along the ribbon length rather than perpendicular to it [15].Figure 8b shows the frequency dependence of these modes correlated to their respective Si-O and Ba-O bond lengths.They show excellent correlation in either case.This change is significant, because often shifts in bending modes are associated with changes in bond angles, however, in this case, the Si4-O10-Ba2 and Si3-O6-Ba2 angles change less than 1 degree between room temperature and 1000˚C, whereas these modes show large frequency displacements, both approximately -1 cm -1 for every 100˚C.These bending mode correlations are stronger than recent correlations found for orthoenstatite [29].Ultimately, however, knowing the pressure dependence as well as the temperature dependence reported here would provide a more rigorous understanding of the volume dependence and consequently the thermodynamics of these phases.Finally, the stretching modes at 928.1 (ν83) and 1066.6 (ν95) cm -1 are uniquely associated with the Si1 (Q 2 ) and adjacent Si2 (Q 3 ) sites, respectively, and clearly persist to the highest temperatures investigated here (Fig. 4, 7).The Si1 mode involves both stretching of both adjacent oxygens, O1 and O2, away from the central silicon, whereas, the Si2 mode localized to the O5-Si2 bond.Both of these peaks overlap with adjacent modes although the ν95 mode suffers more from this issue.The high frequency Bg modes are quite sensitive to orientation, however, as this experiment was conducted on the same site, we can be certain that the same ν95 mode was followed throughout our high-temperature experiment.In the Si1 case, the average of the short, Si1-O1, and the long, Si1-O2, bond lengths are plotted against the frequency shift (Figure 8c).The strong correlations in both the peak center and linewidth affirm this interpretation (Table 5).In both cases, there is a strong correlation between the bond length and the frequency of these modes.Although not identical, nor should they be expected to be identical, they are similar.They indicate that a 0.01 Å change in bond length corresponds to a shift of 10 ± 2 cm -1 .

Conclusions
The prominent phases of silicate: sanbornite and Ba5Si8O21 have become ever more important for industrial applications and hold promise in understanding crystal nucleation and growth processes.Though widely used, Raman spectroscopy remains limited by an inability to make detailed mode assignments and consequently, clear and confident interpretations remain few and far between.This issue is largely overcome with ab initio calculations of vibrational frequencies, as done here.The vibrational mode assignments and their relation to the structural features has been reported in detail for both sanbornite and Ba5Si8O21.
In addition, we report the temperature dependence of the Raman modes.Given the detailed mode assignments, associated to specific Ba or Si sites or bonding configurations have been revealed.Several examples, particularly of the stretching modes which are localized to specific Si-O bonds show strong correlations with the bond length changes up to 1100˚C.These relationships should be pursued to high pressures so that a complete thermodynamic model can be made.Finally, if the frequency dependence on some of these crystal chemical parameters can be generalized more broadly, in situ Raman experiments may lead to critical insights into in situ reactions, including crystallization and catalysis.Finally, we hope that this type of research can be considered a clear example of how the joint use of first principle calculations and experimental measurements of vibrational modes is an appropriate strategy to disclose the structure of complex oxide-based materials.

Figure 2 :
Figure 2: A schematic representation of the sanbornite crystal structure.Ba are large yellow spheres (colour online).Blue Si-centered tetrahedra show dark red BO and lighter pink NBO.Site labels refer to those in table 2. The directions defined by the a and c lattice parameters are drawn.

Figure 3 :
Figure 3: A schematic representation of the unit cell showing structural features of Ba5Si8O21.Site labels refer to those in Table3and colors follow those in figure2.The directions defined by the a and c lattice parameters are drawn.

Figure 5 :
Figure 5: Spectra of sanbornite and Ba5Si8O21 at 25ªC and 800 ºC.A) the low frequency region and B) the high frequency stretching modes.Arrows highlight the vibrational modes.

Figure 8 :
Figure 8: Temperature dependence of vibrational modes for Ba5Si8O21 highlighting the A) low frequency, B) middle frequency, and C) high frequency mode behavior.