CO₂ adsorption in Y zeolite: a structural and dynamic view by a novel principal-component-analysis-assisted in situ single-crystal X-ray diffraction experiment

The increasing efficiency of detectors and brightness of X-rays in both laboratory and large-scale facilities allow the collection of full single-crystal X-ray data sets within minutes. The analysis of these `crystallographic big data' requires new tools and approaches. To answer these needs, the use of principal component analysis (PCA) is proposed to improve the efficiency and speed of the analysis. Potentialities and limitations of PCA were investigated using single-crystal X-ray diffraction (XRD) data collected in situ on Y zeolite, in which CO<sub>2</sub>, acting as an active species, is thermally adsorbed while cooling from 300 to 200 K. For the first time, thanks to the high sensitivity of single-crystal XRD, it was possible to determine the sites where CO<sub>2</sub> is adsorbed, the increase in their occupancy while the temperature is decreased, and the correlated motion of active species, i.e. CO<sub>2</sub>, H<sub>2</sub>O and Na<sup>+</sup>. PCA allowed identification and elimination of problematic data sets, and better understanding of the trends of the occupancies of CO<sub>2</sub>, Na<sup>+</sup> and water. The quality of the data allowed for the first time calculation of the enthalpy (ΔH) and entropy (ΔS) of the CO<sub>2</sub> adsorption by applying the van 't Hoff equation to in situ single-crystal data. The calculation of thermodynamic values was carried out by both traditional and PCA-based approaches, producing comparable results. The obtained ΔH value is significant and involves systems (CO<sub>2</sub> and Y zeolite) with no toxicity, superb stability and chemical inertness. Such features, coupled with the absence of carbonate formation and framework inertness upon adsorption, were demonstrated for the bulk crystal by the single-crystal experiment, and suggest that the phenomenon can be easily reversed for a large number of cycles, with CO<sub>2</sub> released on demand. The main advantages of PCA-assisted analysis reside in its speed and in the possibility of it being applied directly to raw data, possibly as an `online' data-quality test during data collection, without any a priori knowledge of the crystal structure.

1. Introduction

1.1. On the need for novel, efficient and fast approaches to single-crystal X-ray diffraction data analysis

The availability of faster detectors and brighter laboratory and large-scale facility X-ray sources allows the collection of a full single-crystal X-ray diffraction (XRD) data set within seconds (or even less) to minutes and the automatic collection of data sets (especially in the macromolecular crystallography field) increases dramatically the number of collected crystal structure data sets. In situ single-crystal diffraction will become far more common in the next few years, just as in situ powder diffraction has become more widespread in recent decades. Moreover, the novel approach named `serial crystallography' at X-ray free-electron laser (XFEL) facilities will further increase the amount of data and crystal structure data sets to be analysed (Standfuss & Spence, 2017 and references therein). A similar increase in the amount of data is also observed at synchrotron facilities, for macromolecular systems, where the approach of serial crystallography is becoming routine (Weinert et al., 2017). In situ single-crystal structural studies can be carried out to examine simple and slow kinetics (minutes to hours, or while studying systems at equilibrium as in the present work), also with laboratory facilities (Vergentev et al., 2015). Taking into account these considerations, the number of collected data sets will soon greatly override the capacity of structure refinement analysis by the traditional manual approach, where the human operator analyses one crystal data set at a time. It is thus evident that there is an increasing need for efficient tools to manage and analyse large single-crystal data sets coming from in situ and/or serial crystallography.

1.2. PCA as a possible complementary tool in XRD data analysis

In the present article, we propose a principal-component-analysis- (PCA) based approach which is able to answer the issues raised in Section 1.1. PCA is a blind dimensionality-reduction method used to obtain an effective representation of the system under investigation with a lower number of variables (called principal components, PCs) than in the original case (Massart et al., 1998, 1988). The loadings (weights of the original variables along the PCs) and the scores (projection of the samples on the space given by the PCs) allow the identification of relationships between the variables. PCA is widely used in analytical chemistry and in the biological and ecological fields, but has rarely been applied to material science (Rajan, 2005; Rajan et al., 2002). We recently demonstrated that PCA can unravel kinetic trends without a structural model when applied to X-ray powder diffraction (XRPD) data (Guccione et al., 2018; Palin et al., 2015, 2016) and in the present article we extend for the first time its application to single-crystal XRD data.

1.3. The scientific case

As a test case, we choose a hot topic example, i.e. the study of the adsorption of CO₂ into Y zeolite. The alarming data on climate change have prompted increasing efforts in developing methods for the reduction of CO₂ in the atmosphere (Lee & Park, 2015). Nanoporous materials such as carbon molecular sieves (Lee & Park, 2015), metal–organic frameworks (MOFs) (Kim et al., 2017) and zeolites (Pham et al., 2014; Stevens et al., 2008; Vitillo et al., 2018) are promising candidates for CO₂ capture and separation thanks to their large internal surface area and micropore volume, chemical tunability, fast adsorption/desorption kinetics and low heat of adsorption. In particular, zeolite Y is interesting for its low cost of preparation and resistance to heating and cooling cycles (Agostini et al., 2010). Understanding and tailoring the features of nanoporous materials to assess their performance in CO₂ adsorption/desorption are of paramount importance to develop efficient materials. There are reports of studies on the adsorption properties of zeolites in the literature (Sarker et al., 2017). However the kinetic and/or dynamic analysis requires the application of models (Lima et al., 2015), which can be influenced by the nature of the interaction, including eventual interference effects among sites, and these therefore need to be known. To gain insight into the inter­actions and structural dynamics of CO₂ adsorption into Y zeolites, an in situ single-crystal XRD experiment was performed, which allowed us to locate and follow the CO₂ atomic positions and occupancy at the different temperatures and the response of the framework and cations to the adsorption. Besides the classical ab initio approach of solving and refining the crystal structure from each data set taken independently, two automatic approaches were tested. At first, automatic structure refinement of the whole in situ data set was carried out using TOPAS-Academic (Coelho, 2012). Then a PCA-assisted analysis was carried out.

2. Methodology innovations

PCA is applied here for the first time to the analysis of single-crystal data; it has the advantage of processing all data sets at the same time and does not require one to solve and refine the crystal structures from each data set. It is exploited here three times with two different approaches. PCA was first applied directly on experimental (case 1) and on simulated (case 2) intensities to extract the dynamic trends within the data; in these cases the variables are the Miller indices identifying the diffraction spots and the samples are the hkl intensities in the data sets collected at different temperatures. PCA was then applied in a different way to the occupancies obtained by a structural refinement (case 3) to facilitate the interpretation of the results from a traditional crystallographic approach; the variables in this case are the atomic species, and the PCA cases are again the data sets collected at the various temperatures.

The in situ single-crystal structural approach to study CO₂ adsorption in Y zeolite is unprecedented; in the literature there are only reports of a study by XRPD (Arletti et al., 2016) and a few single-crystal studies of CO₂ adsorption on other types of zeolite performed under ex situ conditions (Fujiyama et al., 2013; Nguyen et al., 2014). Structural studies of the adsorption in Y zeolite of organic molecules can also be found in the literature (Martucci et al., 2015; Gigli et al., 2018). In this study traditional structural refinement (both manual and automatic) and PCA-based approaches are thus explored and the results compared to assess potentialities and limitations of PCA applied to single-crystal data. The manual structure refinement is able to locate extra-framework atoms in an accurate way after structure solution but requires a model structure and is very time consuming. The refinement of a data set of 50 structures takes many working hours and a protocol has to be defined in order to treat all the structures consistently. The automatic (batch) refinement is faster, but still needs the structure to be solved and careful checking of results and refined variables. In contrast, PCA can be executed on the full data set; it does not need structural information; and can provide information about the trends in the data in a few minutes. The trends extracted by PCA can be coupled with structural information obtained from one or more data sets to gain a better insight into their meaning (i.e. to link the changes to the relevant part of the structure).

Finally, the thermodynamic parameters (enthalpy and entropy of the adsorption) were calculated by the van 't Hoff equation, extending its application from in situ Fourier transform infrared spectrometry (FTIR) (Garrone et al., 2017; Garrone & Areán, 2005) to in situ XRD.

3. Experimental and data analysis details

3.1. The in situ single-crystal diffraction experiment

A suitable crystal of Y zeolite for single-crystal measurements was obtained by the hydrothermal method described in the literature (Warzywoda et al., 1999; Ferchiche et al., 2001) and detailed in the supporting information. The experiments were performed at the ESRF Synchrotron in Grenoble, on the Swiss–Norwegian Beam Line (SNBL; BM01A) equipped with a 2D Pilatus 2M detector. The single crystal was mounted on a 0.2 mm capillary and sealed inside a 0.3 mm capillary. The external capillary was connected to a gas line and a vacuum pump and left at 300 K under vacuum for the outgassing. One first data set, to test the sample and to be used as a reference, was collected under vacuum at 300 K. CO₂ was injected into the capillary to a pressure of 10 kPa and the temperature was lowered to 200 K, while measuring a complete single-crystal data set (360° φ scan with an exposure time of 2 s per frame) every 2 K. Between two data sets the dead time was 2 min to allow the cryostream to reach and stabilize at the temperature and the sample to reach its equilibrium.

3.2. Details of the data analysis

Data reduction was performed using CrysAlisPro (Rigaku, Oxford Diffraction). The data were treated at first by SHELXL (Sheldrick, 2015) with the SHELXLE interface (Hübschle et al., 2011) and then by TOPAS-Academic (Coelho, 2012) in single-crystal diffraction batch analysis mode. Simulated hkl files were generated by TOPAS giving the desired occupancies (from linear or polynomial fitting or from the refined data) as input to the structure model and obtaining the calculated profile as output. PCA of simulated, experimental data and refined occupancy values was carried out by RootProf (Caliandro & Belviso, 2014). Graphics were generated using CCDC Mercury (Macrae et al., 2008) and Vesta (Momma & Izumi, 2011). The 200 and 300 K refined crystal structures are given as CIFs in the supporting information. Their checkCIF files present a number of unavoidable C and G alerts due to the disorder of CO₂, water and Na⁺ moieties. The 300 K CIF also contains one B alert due to the larger disorder observed at the higher temperature.

4. Dynamic structural analysis

4.1. Location of extra-framework species

Individual structural refinement of in situ single-crystal data was performed using SHELX. The data revealed that the cell parameters increased while decreasing the temperature, as CO₂ was filling the pores (Fig. S1). The crystal structure was at first solved and refined from three data sets, collected at the temperatures 200, 254 and 300 K, revealing that not only CO₂, but also Na⁺ ions and a residual water molecule moved noticeably during the experiment. The refinement of all the atom positions of Na⁺, CO₂ and water is difficult to handle in a consistent way for all the data sets. Such a refinement became unstable in batch mode and the resulting atomic shifts were difficult or impossible to interpret. A structural model was then built from the SHELX refinement of one data set out of five (every 10 K), considering all positions of CO₂, water and Na⁺ atoms found from manual structure solution. Concerning CO₂ conformation, it is generally considered that CO₂ in zeolites can be found as a linear molecule, even if density functional theory (DFT) calculations (Wong-Ng et al., 2013) suggest that a bending of CO₂ (with an OCO angle of about 150°) requires a limited energy cost. On the other hand, the partial conversion of CO₂ to carbonate (OCO bond of 120°) may result in an electron density interpretable only by a bent CO₂ (Wong-Ng et al., 2013). For these reasons, the initial refinement of CO₂ was carried out without constraints on the OCO bond angle to verify CO₂ linearity.

Looking to the experimental electron density and to the unconstrained refined position, carbonate species are unlikely; moreover, any attempt at locating and refining bent CO₂ molecules or carbonate species failed or gave increased agreement factors and/or higher atomic displacement parameter (ADP) values. Only linear CO₂ molecules were then used in all the manual and sequential refinements. This evidence confirms that carbonate species are present in X zeolites only (Arletti et al., 2016; Pirngruber et al., 2010; Busca, 2017; Wong-Ng et al., 2013) and are unlikely in Y zeolite. The positions of Na atoms were treated as disordered sites, i.e. by fixing their coordinates and refining their occupancies (Fig. 1).

Figure 1 Zeolite Y structure highlighting CO2 and Na^+ sites (Si = blue; Na = yellow; O = red; C = brown).

4.2. Dynamic structural refinements

The refinement was performed manually on one data set out of five. This approach allowed tracking of the movements as a function of a single variable (occupancy) instead of three (x, y, z), facilitating the interpretation of the results (Fig. 1 and Fig. S4 in the supporting information). The agreement factors (Figs. S2 and S3) confirmed the quality of the collected data and the goodness of fit of the refinements. A sequential batch refinement of all the patterns was then performed using TOPAS in single-crystal mode. The refinement conditions used in TOPAS were set to be consistent, as much as possible, in terms of fixed parameters and constraints with the SHELX refinement. The thermal factors were refined at 254 K and kept fixed in the automatic sequential refinement. The occupancy of the CO₂ positions was refined constraining all atoms of the same molecule to have the same occupancy.

The total occupancy of Na atoms was also constrained after the first refinements. In this way, a stable refinement was obtained. Despite the different number of samples and the different software used, the manual and automatic approaches gave very similar results (Tables S1 and S2), except for the Na⁺ occupancy, which is found to be systematically larger by TOPAS (Fig. 2b). The analysis of the refined structures revealed at first a change of the Na distribution among the different positions upon CO₂ adsorption when the temperature changes from 300 to 200 K. When the CO₂ occupancy increases, Na⁺ ions in the sites I′ (from now on Na11) and II′ (from now on Na21) far from the centre of the sodalite cage and close to CO₂ increase their occupancy (Figs. 2a, 2b). At the same time, the depletion of the Na⁺ position at the centre of the hexagonal prism (site Na I, from now on Na1) is observed. This is in line with the molecular dynamics simulation performed by Plant et al. (2006). The water molecule near the centre of the sodalite cage moves towards the Na⁺ ions from position a (Ow_a at higher symmetry) to position b (Ow_b) at lower symmetry. The shift of the atoms, represented by occupancy variation between the positions, is highlighted by the animation provided as supporting information.

Figure 2 Occupancy of CO2 (C1C and C2C atoms representing the two CO2 moieties), water (Ow_a and Ow_b) and Na^+ during the thermal treatment from manual (a) and sequential (b) refinements.

4.3. PCA as a complementary tool for analysis of in situ single-crystal diffraction data

PCA was applied in three different modes, i.e. using directly hkl intensities or the refined occupancy values as the input data matrix. Cases 1, 2 and 3 as defined at the beginning of Section 2 are described in the next two subsections.

4.3.1. PCA directly applied to X-ray simulated and experimental diffraction data

Besides the above-described manual (SHELX) and automatic (TOPAS TA) traditional approaches of structure refinement and analysis, the efficiency of multivariate methods in following structural changes occurring during in situ experiments (Palin et al., 2015, 2016) was exploited by applying PCA to these single-crystal data. As a preliminary test, since the application of PCA to in situ single-crystal XRD data is unprecedented, a simulated experiment was carried out and analysed by PCA (case 1 as defined in Section 2) as described for polycrystalline samples by Palin et al. (2015, 2016). Simulated hkl data were generated starting from the refined structure and the occupancies of a subset of atoms varied. This approach allowed us to test PCA starting from an ideal data set and introducing complexity step by step, to facilitate the comprehension and interpretation of the results. Several simulations were performed as summarized in Table SI-1: in simulations 1, 2 and 3, only the occupancies of selected species were varied with simple linear trends, in simulation 4 a polynomial trend was used, while in simulation 5 all occupancy variables were varied according to the occupancies obtained from refinement on real data. The cell parameter was kept fixed in all simulations. The PCA results are shown in the supporting information (Figs. S5–S8). The PCA scores of simulation 5 (Table SI-1) are shown in Fig. 3(a), since this simulation is the most similar to the real experiment. In the simplest cases, PCA scores are able to reproduce the introduced CO₂ occupancy variations; we call the subset of varying atoms `active species'.

Figure 3 Scores of PC1 and PC2 from PCA applied to case 1, i.e. data from simulation 5 (a), case 2, i.e. experimental data (b), and case 3, the loadings obtained after the PCA giving as input the occupancies from sequential refinement (c). The scatter plot of these analyses is reported in the supporting information (Figs. S12–S14); the analysis was limited to the first two PCs, able to explain 95 and 97% of the variance in experimental and simulated data, respectively.

As a first consideration, it must be pointed out that PCA can be used to estimate the quality of the data when tracking the changes occurring during an in situ experiment. In fact, as widely discussed by Palin et al. (2015) for powder diffraction data, the PC1 versus PC2 scores must show a parabolic behaviour if an occupancy variation is observed within a data set. This is clearly also visible in simulated data (Figs. S5–S8C) for the single-crystal case. This trend is still observable in the more complex simulation, close to real data (Fig. S12), and is also observed in the real data (Fig. S13), even if the experimental errors induce deviations from the theoretical behaviour. The presence of such parabolic trends ensures a good quality of the data and a correct recovery of the dynamic trends within the in situ XRD data set. In these ideal and simple situations, PC1 scores unravel from raw hkl intensities the dynamic trend of the active species within the simulated or real experiment, i.e. the response of the sample to the applied stimulus.

In more complex cases than the real one investigated in this study, PCs mix contributions from different active species, having similar trends of occupancy variations. When PCA was applied to real in situ data (case 1 as defined in Section 2), a discontinuity in the data trend as a function of time was found (Fig. S9). It is captured by PC1 scores, which match the scale parameter obtained by the TOPAS batch refinement, and can be ascribed to a synchrotron refill which occurred during the measurements. This issue is automatically handled by SHELX and TOPAS through the scale factor, but should not be overlooked when dealing with raw data by a blind approach such as PCA. In this case, the maximum variance of the input data set is in fact the parameter known in structure refinement as the scale factor. PCA is not a priori able to recognize a scale effect from genuine structural variations. To overcome the problem, the pre-processing features of RootProf (normalization) were therefore applied to normalize the data. PCA then showed some outliers (Fig. S10), which were therefore investigated and excluded from the analyses. The data set `232 K' was collected during the refill; therefore there are discrepancies in the intensities of the peaks. The data set at 252 K also showed some anomalies and a careful inspection of the data reduction statistics revealed problems during data collection. In fact, the `absscale' parameter of this data set (Fig. S11) has a very unusual trend (the expected behaviour is a nearly flat line) with a bump in the first frames and two very negative values. These two examples highlight the potentialities of PCA in data quality control during the experiment, especially in those cases where a large number of data sets (hundreds or thousands) are collected thanks to the improved time resolution. The plots of PC1 and PC2 scores on the pre-processed normalized data are given, after excluding the two outlier data sets (232 and 252 K), in Fig. 3(b) and show very similar trends compared with those from simulated data [Fig. 3(a)]. By comparing the trends of occupancies shown in Fig. 2 and PCA results in Fig. 3, PC1 shows a trend similar to that of the occupancies of CO₂, Na 11 and Ow_b, while PC2 resembles the trend of Ow_a. Since PCA explains the variance contained in the data set, the signs of the scores and loadings of each PC are arbitrary. They can be flipped if the sign of both scores and loadings is reversed at the same time. It must be noticed that data points in Figs. 2(a) and 2(b) show different scattering between adjacent data sets. This is due to the different sampling in manual (one data set used out of five with 10 K between adjacent data sets) and batch refinement and PCA (all data sets used with 2 K data sets) analyses. The change in the structure between two adjacent data sets is smaller than the error in the batch refinement and PCA [Figs. 2(b) and 3(b), respectively] while it is larger than the error in the manual refinement [Fig. 2(a)].

4.3.2. PCA applied to occupancy values from the structural refinement

PCA was then used with a different approach, defined as case 3 in Section 2 [Fig. 3(c), Fig. 4]. PCA was performed using the atomic occupancies (instead of hkl intensities as in cases 1 and 2) versus temperatures as input. This allowed us to compare known structural features obtained by the refinement procedure, and to explain the correspondence between PCs and active species. In this way, it is possible to directly associate the species to PCA trends. A pre-processing based on standard normal variate transformation (Caliandro & Belviso, 2014) has been applied to the refined occupancy values, to account for different absolute occupancy values.

Figure 4 Plot of PC2 versus PC1 scores from PCA applied to occupancy values obtained from the sequential refinement. Each point in the plot corresponds to the site indicated by the label. The insets show the normalized trends of occupancies (found by the automatic TOPAS TA refinement given as input in PCA case 3) next to the related point in the plot, grouped according to the score plot.

By comparing the loading obtained by PCA performed on refined occupancies [Fig. 3(c)] with the scores obtained by PCA performed on raw data [Fig. 3(b)], we can see that the trends in this case are also very similar, thus demonstrating that PCA can be applied directly to raw data. It must be noted that in cases 1 and 2 the scores represent the trend of the changes, while in case 3 the loadings describe the trends. The difference depends on the fact that, in cases 1 and 2, the hkl intensities are given as input of the PCA, while in case 3 the occupancy trends (inset of Fig. 4) are given as input. In fact, by definition in the PCA procedures, the loadings are the coefficient defining the new coordinates and they therefore describe the input variables in the new basis of PC1, PC2, …, PCx. In other words, they are the projection of the input variable in the new basis. The number of PCs to be considered is chosen to explain at least 90–95% of the variance of the original data set. The scores describe the variance of the input variable. Therefore, giving hkl intensities as input (cases 1 and 2) the scores describe the structural variation within the experiment, contained in hkl variations, and we demonstrated that they represent the `occupancy trends' [Figs. 3(a), 3(b)]. Giving occupancy trends [Fig. 2(b)] as input (case 3), the loadings give back the trend described by the new basis (PC1 and PC2 in Fig. 3) while the scores (Fig. 4) represent the classification of the occupancy variations, i.e. they tell us which atoms vary with similar trends.

However, assigning a structural interpretation to the trends extracted by the PCA from raw data requires a traditional refinement approach to find the correspondence between the direct and reciprocal space. The necessity of solving and refining the structure can be avoided if a simple and evident change occurs, e.g. water elimination in porous or layered solids. In the present case study, assigning the trends observed by PCA in hkl intensities to chemical behaviour is impossible without a structural refinement. However, PCA can also be used as a tool to analyse trends in the refined occupancies [Fig. 2(b)], if these are given as input. In this case, the plot of the scores of each PC (Fig. S15) indicates which atomic species has the larger influence on that PC while the PC1 versus PC2 score scatter plot (Fig. 4) gives at first glance the similarities between the trends of different atomic species. The analysis of the scores of the PCA applied to occupancies refined by TOPAS PC1 versus PC2 loading scatter plot can thus give an overview of the variations and features of the trends [Fig. 3(c)] as a function of temperature, and connect them to a particular atom. In addition, in this case PCA is very efficient in classifying the trends coming from structural refinement. The PC2 versus PC1 score plot (Fig. 4) shows data points representing the active species positioned according to their coordinate in the new PCA basis and, next to them, the corresponding refined occupancy profiles as a function of temperature. A close position of two points in Fig. 4 implies that the corresponding refined occupancies behave in a similar manner. The closer the points, the more similar the behaviours. PCA was repeated giving as input the occupancies of each single position. This analysis highlights the peculiar trends of Na21 positions, being rather scattered in Fig. S16. This implies that each Na21 position behaves differently from the other ones, because of the different interaction with CO₂ molecules.

Of course, the information is not different from visual observation of the trends [cf. Fig. 2(b) and the insets of Fig. 4], but has the advantage of being automatic, very fast, unbiased and quantitative, with respect to the traditional comparative approaches. Moreover, the method is multivariate in the sense that trends of many variables are identified and compared at the same time. The `manual comparison' method requires an increasing amount of time comparing 10 to 100 trends and it is impossible with a larger number of different trends (consider, for instance, tracking amino-acid changes in an in situ protein XRD study). The PCA method performs the analysis reported in Fig. 4 in seconds to minutes even if more than 1000 occupancy (or other structural parameter) trends are observed.

4.3.3. Chemical considerations on observed occupancy trends

It can be observed that atoms in Fig. 4 are divided into two groups. Therefore, PC1 is able to discriminate the species that increase their occupancies with temperature (Na1, Na21 and Ow_a) from those having the opposite behaviour (i.e. the CO₂ moieties, Na11 and Ow_b) (cf. PC1 trend in Figs. 3 and 4). PC2 instead discriminates occupancies according to the shape of the occupancy variations, and distinguishes the monotonic behaviour, followed by Na atoms and the CO₂ moieties, from the more complex trend of water atoms (cf. PC2 trend in Figs. 3 and 4), which show an inversion point at about 270 K when CO₂ adsorption reaches an inflection point. The apparent increase in occupancy of water sites with temperature decrease (PC2 plot in Fig. 3) could be due to the reduction of thermal motion and to the fact that a little bit of water is desorbed shifting back from position a (in a special position) to position b (towards the side of the cage) upon CO₂ adsorption (Fig. 1). This analysis explains why PCA finds two main trends in the raw data: (i) the monotonic occupancy variations of most atoms, both increasing and decreasing with temperature, captured by PC1 (Fig. 3), and (ii) the peculiar behaviour of water molecules, which deviates from the monotonic trend for temperatures higher than 270 K, captured by the second PC (PC2) (Fig. 3).

5. Thermodynamic calculations

The calculation of the enthalpy and entropy of CO₂ adsorption was then performed, extending to in situ XRD the approach proposed by Garrone et al. for in situ FT–IR data (Garrone et al., 2017; Garrone & Areán, 2005), using the refined occupancies as an indicator of CO₂ adsorption. The calculation of these parameters is possible because the timing of the experiment, described in Section 3, allowed collection of each data set at equilibrium, without evident evolution of the system during individual measurements. This is confirmed and demonstrated by the good values of R_int and R(sigma) [see Fig. S2 (top)] of each data set (they would be higher and more irregular in the temperature range where adsorption occurs if the system were evolving within the same data set). Moreover the 2D raw data frames collected at the beginning and at the end of the data set would have given many inconsistent intensities for equivalent reflections [Fig. S2 (bottom)] if the system were evolving.

Therefore, the van 't Hoff equation can be exploited to obtain the thermodynamic parameters of the process. The equation in its linearized form [equation (2) in the supporting information] was used to build the plot in Fig. 5. The total CO₂ occupancies from Rietveld refinement were used to calculate θ, i.e. the fraction of occupied adsorption sites. The slope and the intercept, obtained from linear regression, together with their standard deviation, allowed us to calculate [see equation (2) in the supporting information] the values of ΔH = −32 ± 3 kJ mol⁻¹ and ΔS = −100 ± 10 J Kmol⁻¹, using the data from 234 to 290 K, thus eliminating the low and high temperatures where occupancies are asymptotically constant. This range was selected by visual inspection (Fig. 3) and further confirmed by the best R² value in the interpolation of the van 't Hoff equation (Fig. 5). The values are in agreement with data reported for CO₂ in MFI zeolite (Armandi et al., 2009). The corresponding plot obtained using the PC1 scores as CO₂ amount estimator is reported in Fig. 5 (after switching the sign according to a priori knowledge that adsorption is exothermic) and gives an approximate value of ΔH = −52 ± 1 kJ mol⁻¹ and ΔS = −196 ± 6 J Kmol⁻¹. The difference compared with values obtained by the occupancy data from refinement is important, but obtaining the same order of magnitude with a totally blind and much faster method, not requiring a priori information on the crystal structure, is noteworthy. PCA can thus be a very efficient tool to obtain thermodynamic parameters by PCA applied on raw data as soon as they are collected, useful as a preliminary investigation and data-quality check. In other words, when thermodynamic calculation carried out by PCA during the experiment gives unlikely results, possible problems in experiment execution can be inferred, found and solved.

Figure 5 Plot and linear regression of the linearized van 't Hoff equation. In the grey plot, θ is calculated as occCO2/occCO2max. y = 3842.6x − 12.123, R^2 = 0.8486. In the yellow plot, θ is calculated as PC1/PC1max, using PC1 scores from the analysis of real data. y = 6212.3x − 23.52, R^2 = 0.983.

6. Conclusions and perspectives

6.1. Structural and thermodynamic results

An in situ single-crystal XRD experiment, followed by an automatic and PCA-assisted data analysis, allowed an unprecedented clear and high-resolution view of structural changes during CO₂ adsorption into Y zeolite. Even if the single crystals suffer from reduced diffusion and a lack of statistical significance with respect to the typical nanometric or micrometric polycrystalline samples, the structural dynamics disclosed during cooling in a CO₂ atmosphere give a realistic starting point for interpreting the events occurring in a powder sample. Summarizing the results on the scientific case, Na atoms are `pulled' towards CO₂ during its adsorption into the zeolite channels. Water molecules are, at the same time, moved away from the centre of the cage. Changes in every site can be tracked singularly by both manual and automatic traditional crystal structure refinements. The enthalpy and entropy of CO₂ adsorption were calculated as ΔH = −32 kJ mol⁻¹ and ΔS = −100 J Kmol⁻¹, respectively. These values are consistent with those calculated from FT–IR data by Armandi et al. (2009), thus demonstrating the possibility of obtaining thermodynamic data from in situ single-crystal diffraction. The enthalpy value is significant and involves systems (CO₂ and Y zeolite) with no toxicity, superb stability and chemical inertness. The XRD experiment indicated the absence of carbonate formation and that zeolite changes are limited to Na-ion movement, with the framework unchanged before and after adsorption. The CO₂ adsorption phenomenon can thus be easily reversed, with CO₂ released on demand, with a heat recovery. The system can therefore be considered both as an efficient CO₂ and a heat tank, available on demand at temperatures close to room temperature.

6.2. Methodological innovations: potentialities and limitations of PCA in single-crystal XRD

The potentialities and limitations of automatic refinement by TOPAS and of the PCA-assisted analysis were tested on an in situ single-crystal data set. Automatic analysis by TOPAS was faster and was applied to all 50 data sets (instead of the ten manually refined data sets where only one out of five data sets is analysed). Automatic refinement was stable after some manual data set analyses were performed to optimize the automatic refinement procedure and determine the range of variation of parameters, mainly occupancies and ADPs in a gas adsorption experiment. PCA was used in two different ways. When applied to raw hkl data, it was able at first to identify problematic data sets and then to unravel the dynamic trends in the data without the knowledge of the structure and within minutes after data collection finished (we can infer for future experiments that this may also be possible with partial data sets during data collection). The results are similar to those obtained by more time-consuming traditional manual and automatic approaches (see Figs. 2 and 3). PCA can thus act as a diagnostic tool if performed during or soon after the measurements to highlight problems in the measurement related to the experimental setup and to data collection. This was shown by the data collection/reduction issues highlighted by the first analyses (Figs. S9–S11). The approach can be very useful to determine dynamic or kinetic trends in systems whose crystal structure is disordered in a portion of the experiment (maybe across a transition) so that the traditional refinement becomes impossible. PCA was in fact able to describe all the complex events that involve different atoms in the structure, grouping the atom movements by their `direction' and `timing', giving the overall kinetic information if performed on the raw data. PCA was then used in a different way to obtain insight into relationships between atom occupancy changes during CO₂ adsorption. In this case, PCA was performed using the results from the structure refinement as the input data matrix. In particular, CO₂, Na⁺ and water occupancy changes were analysed by PCA and the common trends obtained. PCA clearly indicates which atoms change their occupancies in a synchronized way. This information was obtained from the plots shown in Fig. 4. Finally, the possibility to exploit an in situ single-crystal experiment to obtain thermodynamic data by a structure-free PCA-based approach was also demonstrated. PCA was able to estimate, with a large discrepancy with respect to the traditional approach, the enthalpy and entropy of adsorption, but the trend was obtained and the order of magnitude investigated. The main limitation in this case is the difficulty of correctly scaling the data using the blind approach of PCA. A correct scaling of the data is one of the more challenging and intriguing aspects of PCA application to XRD data.

6.3. Perspective of PCA usage in single-crystal diffraction

The main limitation of the PCA-based blind approach is attributing a chemical/structural sense to the investigated data, and, in this case, the traditional (manual or automatic) approaches are superior. However, PCA can be very useful to identify the subset of the collected data set that is more interesting for data analysis, e.g. those data sets where the dynamic effect starts, reaches the maximum speed and finishes. PCA can also be very efficient in highlighting very small dynamic effects, not evident by traditional visual analysis, and also in very large data sets. A future can be envisaged in which, after collecting hundreds or thousands of single-crystal data sets within a single (in situ or serial crystallography) experiment, PCA can be used to check data quality, identify problematic data sets and diminish the number of data sets to be refined manually by traditional structure-based approaches. In this way, a huge efficiency improvement will be obtained, with respect to the alternatives of refining manually all (hundreds or thousands) data sets or refining a subset of data sets selected by arbitrary methods.

Supporting information

Computing details

For both structures, data collection: CrysAlis PRO 1.171.38.46 (Rigaku OD, 2015); cell refinement: CrysAlis PRO 1.171.38.46 (Rigaku OD, 2015); data reduction: CrysAlis PRO 1.171.38.46 (Rigaku OD, 2015); program(s) used to refine structure: SHELXL2013 (Sheldrick, 2013).

Na Zeolite Y * CO2 (200K)

Crystal data

C33.94Al0Na58.75O481.80Si192	Dx = 1.589 Mg m^−3
Mr = 14860.36	Synchrotron radiation, λ = 0.70158 Å
Cubic, Fd3m	Cell parameters from 11995 reflections
Hall symbol: -F 4vw 2vw 3	θ = 2.3–31.9°
a = 24.94919 (16) Å	µ = 0.53 mm^−1
V = 15529.9 (3) Å^3	T = 200 K
Z = 1	Block, colourless
F(000) = 7392	0.05 × 0.05 × 0.05 mm

Data collection

Dectris-CrysAlisPro-abstract goniometer imported dectris images diffractometer	1108 reflections with I > 2σ(I)
Radiation source: synchrotron	Rint = 0.055
Synchrotron monochromator	θmax = 32.3°, θmin = 2.3°
φ scans	h = −37→37
32446 measured reflections	k = −34→34
1395 independent reflections	l = −37→37

Refinement

Refinement on F^2	70 parameters
Least-squares matrix: full	2 restraints
R[F^2 > 2σ(F^2)] = 0.072	w = 1/[σ^2(Fo^2) + (0.1605P)^2 + 181.6847P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.265	(Δ/σ)max = 0.01
S = 1.10	Δρmax = 1.00 e Å^−3
1395 reflections	Δρmin = −0.83 e Å^−3

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Si1	0.53610 (3)	0.30351 (3)	0.62518 (3)	0.0148 (3)
O2	0.49721 (10)	0.25279 (10)	0.60597 (13)	0.0241 (7)
O4	0.57242 (9)	0.32234 (13)	0.57242 (9)	0.0221 (6)
O3	0.57462 (10)	0.28205 (14)	0.67538 (10)	0.0251 (7)
O1	0.5	0.35646 (10)	0.64354 (10)	0.0257 (7)
Na2A	0.5587 (7)	0.0587 (7)	0.5587 (7)	0.028*	0.140 (4)
Na2B	0.56520 (19)	0.06520 (19)	0.56520 (19)	0.028*	0.529 (4)
Na2C	0.5763 (8)	0.0763 (8)	0.5763 (8)	0.028*	0.128 (4)
Na1	0.5	0.25	0.75	0.032*	0.121 (4)
Na3A	0.5289 (13)	0.2211 (13)	0.5289 (13)	0.027*	0.078 (4)
Na3B	0.5162 (4)	0.2338 (4)	0.5162 (4)	0.02*	0.269 (4)
Na3C	0.5059 (6)	0.2441 (6)	0.5059 (6)	0.019*	0.130 (4)
Na3D	0.4862 (6)	0.2638 (6)	0.4862 (6)	0.042*	0.206 (3)
Na3E	0.4711 (14)	0.3055 (19)	0.4711 (14)	0.11*	0.098 (3)
OWA	0.5803 (13)	0.1697 (13)	0.5803 (13)	0.04*	0.19 (4)
OWB	0.5683 (10)	0.1545 (8)	0.5955 (8)	0.04*	0.205 (15)
O1C	0.4089 (6)	0.5564 (8)	0.3411 (6)	0.042*	0.211 (10)
C1C	0.375	0.5652 (19)	0.375	0.042*	0.211 (10)
O4C	0.4076 (7)	0.5178 (5)	0.5178 (5)	0.05*	0.292 (12)
C2C	0.4224 (17)	0.5488 (15)	0.4907 (15)	0.05*	0.124 (6)
O3C	0.4286 (11)	0.5805 (11)	0.4550 (11)	0.05*	0.124 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Si1	0.0139 (4)	0.0156 (4)	0.0148 (4)	−0.0002 (2)	0.0021 (2)	−0.0018 (2)
O2	0.0252 (10)	0.0252 (10)	0.0218 (14)	−0.0110 (12)	0.0028 (9)	−0.0028 (9)
O4	0.0217 (9)	0.0229 (14)	0.0217 (9)	0.0010 (8)	0.0079 (11)	0.0010 (8)
O3	0.0240 (9)	0.0273 (16)	0.0240 (9)	−0.0038 (9)	−0.0047 (11)	0.0038 (9)
O1	0.0274 (16)	0.0248 (10)	0.0248 (10)	0.0071 (9)	0.0071 (9)	0.0017 (12)

Geometric parameters (Å, º)

Si1—O1	1.6631 (14)	Na1—O3^xx	2.752 (3)
Si1—O2	1.6651 (12)	Na1—Na2B^xv	2.817 (8)
Si1—O4	1.6656 (12)	Na1—Na2B^i	2.817 (8)
Si1—O3	1.6671 (14)	Na1—Na2C^xv	3.30 (3)
Si1—Na3A	3.167 (5)	Na1—Na2C^i	3.30 (3)
Si1—Na3B	3.266 (4)	Na3A—OWA	2.22 (8)
Si1—Na2A^i	3.299 (9)	Na3A—O2^vii	2.224 (6)
Si1—Na2B^i	3.393 (3)	Na3A—O2^xxi	2.224 (6)
Si1—Na3C	3.408 (10)	Na3A—O4^vii	2.956 (5)
Si1—Na1	3.5061 (7)	Na3A—O4^xxi	2.956 (5)
O2—Si1^ii	1.6651 (12)	Na3A—Si1^iii	3.167 (5)
O2—Na3A	2.224 (6)	Na3A—Si1^vii	3.167 (5)
O2—Na3B	2.338 (6)	Na3A—Si1^xi	3.167 (5)
O2—Na3C	2.515 (13)	Na3A—Si1^xxi	3.167 (5)
O2—Na3D	3.014 (17)	Na3A—Si1^ii	3.167 (5)
O4—Si1^iii	1.6655 (12)	Na3B—O2^vii	2.338 (6)
O4—Na3A	2.956 (5)	Na3B—O2^xxi	2.338 (6)
O4—Na3B	2.969 (4)	Na3B—O4^vii	2.969 (4)
O3—Si1^iv	1.6671 (14)	Na3B—O4^xxi	2.969 (4)
O3—Na2A^i	2.333 (11)	Na3B—Si1^iii	3.265 (4)
O3—Na2B^i	2.449 (5)	Na3B—Si1^xi	3.265 (4)
O3—Na2C^i	2.70 (2)	Na3B—Si1^vii	3.265 (4)
O3—Na1	2.752 (3)	Na3B—Si1^xxi	3.265 (4)
O1—Si1^v	1.6632 (14)	Na3B—Si1^ii	3.265 (4)
Na2A—O3^vi	2.333 (11)	Na3C—O2^vii	2.515 (13)
Na2A—O3^i	2.333 (11)	Na3C—O2^xxi	2.515 (13)
Na2A—O3^vii	2.333 (11)	Na3C—Si1^iii	3.408 (10)
Na2A—Na1^i	2.54 (3)	Na3C—Si1^vii	3.408 (10)
Na2A—OWA	2.87 (3)	Na3C—Si1^xi	3.408 (10)
Na2A—OWA^i	2.87 (3)	Na3C—Si1^xxi	3.408 (10)
Na2A—OWA^viii	2.87 (3)	Na3C—Si1^ii	3.408 (10)
Na2A—Si1^ix	3.299 (9)	Na3D—O2^xxi	3.014 (17)
Na2A—Si1^i	3.299 (9)	Na3D—O2^vii	3.014 (17)
Na2A—Si1^x	3.299 (9)	Na3E—Na3E^vii	0.94 (8)
Na2A—Si1^xi	3.299 (9)	Na3E—Na3E^xxi	0.94 (8)
Na2A—Si1^vii	3.299 (9)	Na3E—O1C^xxii	2.78 (3)
Na2B—OWB^vi	2.355 (14)	Na3E—O1C^xxiii	2.78 (3)
Na2B—OWB^vii	2.355 (14)	OWA—Na2A^i	2.87 (3)
Na2B—OWB^xii	2.355 (14)	OWA—Na2A^viii	2.87 (3)
Na2B—OWB^xiii	2.355 (14)	OWB—OWB^xxi	0.96 (5)
Na2B—OWB^i	2.355 (14)	OWB—OWB^vii	0.96 (5)
Na2B—OWB	2.355 (14)	OWB—Na2B^i	2.355 (14)
Na2B—O3^vii	2.449 (5)	O1C—C1C	1.22 (2)
Na2B—O3^vi	2.449 (5)	O1C—Na3E^xxiv	2.78 (3)
Na2B—O3^i	2.449 (5)	O1C—Na3E^xxv	2.78 (3)
Na2B—Na1^i	2.817 (8)	C1C—O1C^xxvi	1.22 (2)
Na2B—Si1^i	3.393 (3)	O4C—C2C	1.09 (3)
Na2B—Si1^x	3.393 (3)	O4C—C2C^xxvii	1.09 (3)
Na2C—O3^i	2.70 (2)	O4C—O3C^xxviii	1.53 (3)
Na2C—O3^vii	2.70 (2)	O4C—O3C^xxix	1.53 (3)
Na2C—O3^vi	2.70 (2)	O4C—C2C^xxviii	1.86 (4)
Na2C—Na1^i	3.30 (3)	O4C—C2C^xxix	1.86 (4)
Na2C—Na2C^viii	3.44 (5)	C2C—C2C^xxix	1.12 (8)
Na2C—Na2C^xiv	3.44 (5)	C2C—O3C	1.20 (4)
Na2C—Na2C^i	3.44 (5)	C2C—O3C^xxix	1.47 (5)
Na1—Na2A^xv	2.54 (3)	C2C—O4C^xxx	1.86 (4)
Na1—Na2A^i	2.54 (3)	C2C—O3C^iii	1.92 (5)
Na1—O3^xvi	2.752 (3)	O3C—O3C^iii	0.93 (5)
Na1—O3^xvii	2.752 (3)	O3C—C2C^xxix	1.47 (5)
Na1—O3^xviii	2.752 (3)	O3C—O4C^xxx	1.53 (3)
Na1—O3^xix	2.752 (3)	O3C—C2C^iii	1.92 (5)
O1—Si1—O2	111.55 (13)	O3^xvi—Na1—Na2B^i	127.85 (8)
O1—Si1—O4	106.76 (15)	O3^xvii—Na1—Na2B^i	52.15 (8)
O2—Si1—O4	107.69 (15)	O3^xviii—Na1—Na2B^i	127.85 (7)
O1—Si1—O3	111.12 (15)	O3^xix—Na1—Na2B^i	52.15 (7)
O2—Si1—O3	107.94 (16)	O3^xx—Na1—Na2B^i	127.85 (8)
O4—Si1—O3	111.76 (17)	Na2B^xv—Na1—Na2B^i	180.00 (15)
O1—Si1—Na3A	133.9 (10)	O3—Na1—Na2C^xv	127.84 (8)
O2—Si1—Na3A	41.86 (11)	O3^xvi—Na1—Na2C^xv	52.15 (8)
O4—Si1—Na3A	67.3 (3)	O3^xvii—Na1—Na2C^xv	127.84 (8)
O3—Si1—Na3A	113.2 (10)	O3^xviii—Na1—Na2C^xv	52.15 (7)
O1—Si1—Na3B	124.8 (3)	O3^xix—Na1—Na2C^xv	127.85 (7)
O2—Si1—Na3B	42.86 (12)	O3^xx—Na1—Na2C^xv	52.15 (8)
O4—Si1—Na3B	64.85 (13)	O3—Na1—Na2C^i	52.16 (7)
O3—Si1—Na3B	122.8 (3)	O3^xvi—Na1—Na2C^i	127.85 (8)
O1—Si1—Na2A^i	129.0 (5)	O3^xvii—Na1—Na2C^i	52.16 (8)
O2—Si1—Na2A^i	66.32 (15)	O3^xviii—Na1—Na2C^i	127.85 (7)
O4—Si1—Na2A^i	122.8 (5)	O3^xix—Na1—Na2C^i	52.15 (7)
O3—Si1—Na2A^i	41.67 (15)	O3^xx—Na1—Na2C^i	127.85 (8)
Na3A—Si1—Na2A^i	80.7 (10)	Na2C^xv—Na1—Na2C^i	180.0 (5)
O1—Si1—Na2B^i	133.50 (17)	OWA—Na3A—O2^vii	84.9 (14)
O2—Si1—Na2B^i	65.64 (12)	OWA—Na3A—O2^xxi	84.9 (14)
O4—Si1—Na2B^i	118.44 (16)	O2^vii—Na3A—O2^xxi	119.2 (4)
O3—Si1—Na2B^i	42.85 (12)	OWA—Na3A—O2	84.9 (14)
Na3B—Si1—Na2B^i	86.1 (3)	O2^vii—Na3A—O2	119.2 (4)
O1—Si1—Na3C	117.8 (4)	O2^xxi—Na3A—O2	119.2 (4)
O2—Si1—Na3C	44.72 (17)	OWA—Na3A—O4	93.9 (11)
O4—Si1—Na3C	63.45 (14)	O2^vii—Na3A—O4	179 (3)
O3—Si1—Na3C	130.0 (4)	O2^xxi—Na3A—O4	60.61 (4)
O1—Si1—Na1	85.33 (11)	O2—Na3A—O4	60.61 (4)
O2—Si1—Na1	79.43 (11)	OWA—Na3A—O4^vii	93.9 (11)
O4—Si1—Na1	161.64 (11)	O2^vii—Na3A—O4^vii	60.61 (4)
O3—Si1—Na1	50.09 (12)	O2^xxi—Na3A—O4^vii	179 (3)
Na3A—Si1—Na1	114.3 (6)	O2—Na3A—O4^vii	60.61 (4)
Na3B—Si1—Na1	119.84 (14)	O4—Na3A—O4^vii	119.5 (3)
Na2A^i—Si1—Na1	43.7 (5)	OWA—Na3A—O4^xxi	93.9 (11)
Na2B^i—Si1—Na1	48.17 (13)	O2^vii—Na3A—O4^xxi	60.61 (4)
Na3C—Si1—Na1	123.6 (2)	O2^xxi—Na3A—O4^xxi	60.61 (4)
Si1—O2—Si1^ii	143.4 (2)	O2—Na3A—O4^xxi	179 (3)
Si1—O2—Na3A	108.17 (12)	O4—Na3A—O4^xxi	119.5 (3)
Si1^ii—O2—Na3A	108.17 (12)	O4^vii—Na3A—O4^xxi	119.5 (3)
Si1—O2—Na3B	108.16 (11)	OWA—Na3A—Si1^iii	84.5 (10)
Si1^ii—O2—Na3B	108.16 (11)	O2^vii—Na3A—Si1^iii	148.3 (8)
Si1—O2—Na3C	107.52 (12)	O2^xxi—Na3A—Si1^iii	29.97 (7)
Si1^ii—O2—Na3C	107.52 (12)	O2—Na3A—Si1^iii	89.4 (2)
Si1—O2—Na3D	105.62 (12)	O4—Na3A—Si1^iii	31.33 (4)
Si1^ii—O2—Na3D	105.62 (12)	O4^vii—Na3A—Si1^iii	149.96 (11)
Si1^iii—O4—Si1	141.3 (2)	O4^xxi—Na3A—Si1^iii	90.48 (4)
Si1^iii—O4—Na3A	81.4 (3)	OWA—Na3A—Si1^vii	84.5 (10)
Si1—O4—Na3A	81.4 (3)	O2^vii—Na3A—Si1^vii	29.97 (7)
Si1^iii—O4—Na3B	84.63 (15)	O2^xxi—Na3A—Si1^vii	148.3 (8)
Si1—O4—Na3B	84.63 (15)	O2—Na3A—Si1^vii	89.4 (2)
Si1^iv—O3—Si1	139.7 (2)	O4—Na3A—Si1^vii	149.96 (11)
Si1^iv—O3—Na2A^i	109.97 (12)	O4^vii—Na3A—Si1^vii	31.33 (4)
Si1—O3—Na2A^i	109.97 (12)	O4^xxi—Na3A—Si1^vii	90.48 (4)
Si1^iv—O3—Na2B^i	109.58 (12)	Si1^iii—Na3A—Si1^vii	169 (2)
Si1—O3—Na2B^i	109.58 (12)	OWA—Na3A—Si1^xi	84.5 (10)
Si1^iv—O3—Na2C^i	108.57 (14)	O2^vii—Na3A—Si1^xi	29.97 (7)
Si1—O3—Na2C^i	108.57 (14)	O2^xxi—Na3A—Si1^xi	89.4 (2)
Si1^iv—O3—Na1	102.22 (12)	O2—Na3A—Si1^xi	148.3 (8)
Si1—O3—Na1	102.22 (12)	O4—Na3A—Si1^xi	149.96 (11)
Na2A^i—O3—Na1	59.2 (7)	O4^vii—Na3A—Si1^xi	90.48 (4)
Na2B^i—O3—Na1	65.30 (18)	O4^xxi—Na3A—Si1^xi	31.33 (4)
Na2C^i—O3—Na1	74.3 (6)	Si1^iii—Na3A—Si1^xi	119.1 (3)
Si1—O1—Si1^v	137.0 (2)	Si1^vii—Na3A—Si1^xi	59.89 (11)
O3^vi—Na2A—O3^i	107.5 (7)	OWA—Na3A—Si1^xxi	84.5 (10)
O3^vi—Na2A—O3^vii	107.5 (7)	O2^vii—Na3A—Si1^xxi	89.4 (2)
O3^i—Na2A—O3^vii	107.5 (7)	O2^xxi—Na3A—Si1^xxi	29.97 (7)
O3^vi—Na2A—Na1^i	68.6 (7)	O2—Na3A—Si1^xxi	148.3 (8)
O3^i—Na2A—Na1^i	68.6 (7)	O4—Na3A—Si1^xxi	90.48 (4)
O3^vii—Na2A—Na1^i	68.6 (7)	O4^vii—Na3A—Si1^xxi	149.96 (11)
O3^vi—Na2A—OWA	89.2 (7)	O4^xxi—Na3A—Si1^xxi	31.33 (4)
O3^i—Na2A—OWA	150.7 (15)	Si1^iii—Na3A—Si1^xxi	59.89 (11)
O3^vii—Na2A—OWA	89.2 (7)	Si1^vii—Na3A—Si1^xxi	119.1 (3)
Na1^i—Na2A—OWA	140.7 (11)	Si1^xi—Na3A—Si1^xxi	59.49 (11)
O3^vi—Na2A—OWA^i	150.7 (15)	OWA—Na3A—Si1^ii	84.5 (10)
O3^i—Na2A—OWA^i	89.2 (7)	O2^vii—Na3A—Si1^ii	89.4 (2)
O3^vii—Na2A—OWA^i	89.2 (7)	O2^xxi—Na3A—Si1^ii	148.3 (8)
Na1^i—Na2A—OWA^i	140.6 (11)	O2—Na3A—Si1^ii	29.97 (7)
OWA—Na2A—OWA^i	66.6 (17)	O4—Na3A—Si1^ii	90.48 (4)
O3^vi—Na2A—OWA^viii	89.2 (7)	O4^vii—Na3A—Si1^ii	31.33 (4)
O3^i—Na2A—OWA^viii	89.2 (7)	O4^xxi—Na3A—Si1^ii	149.96 (11)
O3^vii—Na2A—OWA^viii	150.7 (15)	Si1^iii—Na3A—Si1^ii	119.1 (3)
Na1^i—Na2A—OWA^viii	140.7 (11)	Si1^vii—Na3A—Si1^ii	59.49 (11)
OWA—Na2A—OWA^viii	66.6 (18)	Si1^xi—Na3A—Si1^ii	119.1 (3)
OWA^i—Na2A—OWA^viii	66.6 (18)	Si1^xxi—Na3A—Si1^ii	169 (2)
O3^vi—Na2A—Si1^ix	131.2 (9)	O2^vii—Na3B—O2^xxi	110.3 (4)
O3^i—Na2A—Si1^ix	83.9 (4)	O2^vii—Na3B—O2	110.3 (4)
O3^vii—Na2A—Si1^ix	28.36 (8)	O2^xxi—Na3B—O2	110.3 (4)
Na1^i—Na2A—Si1^ix	72.5 (5)	O2^vii—Na3B—O4	154.7 (7)
OWA—Na2A—Si1^ix	103.3 (4)	O2^xxi—Na3B—O4	59.49 (7)
OWA^i—Na2A—Si1^ix	73.1 (9)	O2—Na3B—O4	59.49 (7)
OWA^viii—Na2A—Si1^ix	139.2 (10)	O2^vii—Na3B—O4^vii	59.49 (7)
O3^vi—Na2A—Si1^i	131.2 (9)	O2^xxi—Na3B—O4^vii	154.7 (7)
O3^i—Na2A—Si1^i	28.36 (8)	O2—Na3B—O4^vii	59.49 (7)
O3^vii—Na2A—Si1^i	83.9 (4)	O4—Na3B—O4^vii	118.68 (12)
Na1^i—Na2A—Si1^i	72.5 (5)	O2^vii—Na3B—O4^xxi	59.49 (7)
OWA—Na2A—Si1^i	139.2 (10)	O2^xxi—Na3B—O4^xxi	59.49 (7)
OWA^i—Na2A—Si1^i	73.1 (9)	O2—Na3B—O4^xxi	154.7 (7)
OWA^viii—Na2A—Si1^i	103.3 (4)	O4—Na3B—O4^xxi	118.68 (12)
Si1^ix—Na2A—Si1^i	57.28 (17)	O4^vii—Na3B—O4^xxi	118.68 (12)
O3^vi—Na2A—Si1^x	83.9 (4)	O2^vii—Na3B—Si1^iii	135.2 (5)
O3^i—Na2A—Si1^x	28.36 (8)	O2^xxi—Na3B—Si1^iii	28.98 (4)
O3^vii—Na2A—Si1^x	131.2 (9)	O2—Na3B—Si1^iii	85.13 (17)
Na1^i—Na2A—Si1^x	72.5 (5)	O4—Na3B—Si1^iii	30.52 (4)
OWA—Na2A—Si1^x	139.2 (10)	O4^vii—Na3B—Si1^iii	143.1 (3)
OWA^i—Na2A—Si1^x	103.3 (4)	O4^xxi—Na3B—Si1^iii	88.36 (11)
OWA^viii—Na2A—Si1^x	73.1 (9)	O2^vii—Na3B—Si1^xi	28.98 (4)
Si1^ix—Na2A—Si1^x	111.4 (4)	O2^xxi—Na3B—Si1^xi	85.13 (17)
Si1^i—Na2A—Si1^x	56.66 (16)	O2—Na3B—Si1^xi	135.2 (5)
O3^vi—Na2A—Si1^xi	28.36 (8)	O4—Na3B—Si1^xi	143.1 (3)
O3^i—Na2A—Si1^xi	131.2 (9)	O4^vii—Na3B—Si1^xi	88.36 (11)
O3^vii—Na2A—Si1^xi	83.9 (4)	O4^xxi—Na3B—Si1^xi	30.52 (4)
Na1^i—Na2A—Si1^xi	72.5 (5)	Si1^iii—Na3B—Si1^xi	113.4 (2)
OWA—Na2A—Si1^xi	73.1 (9)	O2^vii—Na3B—Si1^vii	28.98 (4)
OWA^i—Na2A—Si1^xi	139.2 (10)	O2^xxi—Na3B—Si1^vii	135.2 (5)
OWA^viii—Na2A—Si1^xi	103.3 (4)	O2—Na3B—Si1^vii	85.13 (17)
Si1^ix—Na2A—Si1^xi	111.4 (4)	O4—Na3B—Si1^vii	143.1 (3)
Si1^i—Na2A—Si1^xi	145.0 (9)	O4^vii—Na3B—Si1^vii	30.52 (4)
Si1^x—Na2A—Si1^xi	111.4 (4)	O4^xxi—Na3B—Si1^vii	88.36 (11)
O3^vi—Na2A—Si1^vii	83.9 (4)	Si1^iii—Na3B—Si1^vii	149.7 (5)
O3^i—Na2A—Si1^vii	131.2 (9)	Si1^xi—Na3B—Si1^vii	57.91 (8)
O3^vii—Na2A—Si1^vii	28.36 (8)	O2^vii—Na3B—Si1^xxi	85.13 (17)
Na1^i—Na2A—Si1^vii	72.5 (5)	O2^xxi—Na3B—Si1^xxi	28.98 (4)
OWA—Na2A—Si1^vii	73.1 (9)	O2—Na3B—Si1^xxi	135.2 (5)
OWA^i—Na2A—Si1^vii	103.3 (4)	O4—Na3B—Si1^xxi	88.36 (11)
OWA^viii—Na2A—Si1^vii	139.2 (10)	O4^vii—Na3B—Si1^xxi	143.1 (3)
Si1^ix—Na2A—Si1^vii	56.66 (16)	O4^xxi—Na3B—Si1^xxi	30.52 (4)
Si1^i—Na2A—Si1^vii	111.4 (4)	Si1^iii—Na3B—Si1^xxi	57.91 (8)
Si1^x—Na2A—Si1^vii	145.0 (9)	Si1^xi—Na3B—Si1^xxi	57.53 (8)
Si1^xi—Na2A—Si1^vii	57.28 (16)	Si1^vii—Na3B—Si1^xxi	113.4 (2)
OWB^vi—Na2B—OWB^vii	69.8 (9)	O2^vii—Na3B—Si1^ii	85.13 (17)
OWB^vi—Na2B—OWB^xii	23.5 (14)	O2^xxi—Na3B—Si1^ii	135.2 (5)
OWB^vii—Na2B—OWB^xii	52.5 (12)	O2—Na3B—Si1^ii	28.98 (4)
OWB^vi—Na2B—OWB^xiii	52.5 (12)	O4—Na3B—Si1^ii	88.36 (11)
OWB^vii—Na2B—OWB^xiii	80.6 (12)	O4^vii—Na3B—Si1^ii	30.52 (4)
OWB^xii—Na2B—OWB^xiii	69.8 (9)	O4^xxi—Na3B—Si1^ii	143.1 (3)
OWB^vi—Na2B—OWB^i	69.8 (9)	Si1^iii—Na3B—Si1^ii	113.4 (2)
OWB^vii—Na2B—OWB^i	69.8 (9)	Si1^xi—Na3B—Si1^ii	113.4 (2)
OWB^xii—Na2B—OWB^i	80.6 (12)	Si1^vii—Na3B—Si1^ii	57.53 (8)
OWB^xiii—Na2B—OWB^i	23.5 (14)	Si1^xxi—Na3B—Si1^ii	149.7 (5)
OWB^vi—Na2B—OWB	80.6 (12)	O2^vii—Na3B—Si1	135.2 (5)
OWB^vii—Na2B—OWB	23.5 (14)	O2^xxi—Na3B—Si1	85.13 (17)
OWB^xii—Na2B—OWB	69.8 (9)	O2—Na3B—Si1	28.98 (4)
OWB^xiii—Na2B—OWB	69.8 (9)	O4—Na3B—Si1	30.52 (4)
OWB^i—Na2B—OWB	52.5 (12)	O4^vii—Na3B—Si1	88.36 (11)
OWB^vi—Na2B—O3^vii	154.7 (6)	O4^xxi—Na3B—Si1	143.1 (3)
OWB^vii—Na2B—O3^vii	102.9 (6)	Si1^iii—Na3B—Si1	57.53 (8)
OWB^xii—Na2B—O3^vii	154.7 (6)	Si1^xi—Na3B—Si1	149.7 (5)
OWB^xiii—Na2B—O3^vii	102.9 (6)	Si1^vii—Na3B—Si1	113.4 (2)
OWB^i—Na2B—O3^vii	84.9 (6)	Si1^xxi—Na3B—Si1	113.4 (2)
OWB—Na2B—O3^vii	84.9 (6)	Si1^ii—Na3B—Si1	57.91 (8)
OWB^vi—Na2B—O3^vi	102.9 (6)	O2^vii—Na3C—O2^xxi	99.5 (7)
OWB^vii—Na2B—O3^vi	84.9 (6)	O2^vii—Na3C—O2	99.5 (7)
OWB^xii—Na2B—O3^vi	84.9 (6)	O2^xxi—Na3C—O2	99.5 (7)
OWB^xiii—Na2B—O3^vi	154.7 (6)	O2^vii—Na3C—Si1^iii	121.8 (8)
OWB^i—Na2B—O3^vi	154.7 (6)	O2^xxi—Na3C—Si1^iii	27.77 (8)
OWB—Na2B—O3^vi	102.9 (6)	O2—Na3C—Si1^iii	79.6 (4)
O3^vii—Na2B—O3^vi	100.4 (2)	O2^vii—Na3C—Si1^vii	27.77 (8)
OWB^vi—Na2B—O3^i	84.9 (6)	O2^xxi—Na3C—Si1^vii	121.8 (8)
OWB^vii—Na2B—O3^i	154.7 (6)	O2—Na3C—Si1^vii	79.6 (4)
OWB^xii—Na2B—O3^i	102.9 (6)	Si1^iii—Na3C—Si1^vii	135.3 (8)
OWB^xiii—Na2B—O3^i	84.9 (6)	O2^vii—Na3C—Si1^xi	27.77 (8)
OWB^i—Na2B—O3^i	102.9 (6)	O2^xxi—Na3C—Si1^xi	79.6 (4)
OWB—Na2B—O3^i	154.7 (6)	O2—Na3C—Si1^xi	121.8 (8)
O3^vii—Na2B—O3^i	100.4 (2)	Si1^iii—Na3C—Si1^xi	106.4 (5)
O3^vi—Na2B—O3^i	100.4 (2)	Si1^vii—Na3C—Si1^xi	55.27 (18)
OWB^vi—Na2B—Na1^i	138.6 (5)	O2^vii—Na3C—Si1^xxi	79.6 (4)
OWB^vii—Na2B—Na1^i	138.6 (5)	O2^xxi—Na3C—Si1^xxi	27.77 (8)
OWB^xii—Na2B—Na1^i	138.6 (5)	O2—Na3C—Si1^xxi	121.8 (8)
OWB^xiii—Na2B—Na1^i	138.6 (5)	Si1^iii—Na3C—Si1^xxi	55.27 (18)
OWB^i—Na2B—Na1^i	138.6 (5)	Si1^vii—Na3C—Si1^xxi	106.4 (5)
OWB—Na2B—Na1^i	138.6 (5)	Si1^xi—Na3C—Si1^xxi	54.91 (18)
O3^vii—Na2B—Na1^i	62.54 (18)	O2^vii—Na3C—Si1^ii	79.6 (4)
O3^vi—Na2B—Na1^i	62.54 (18)	O2^xxi—Na3C—Si1^ii	121.8 (8)
O3^i—Na2B—Na1^i	62.54 (18)	O2—Na3C—Si1^ii	27.77 (8)
OWB^vi—Na2B—Si1^i	95.2 (7)	Si1^iii—Na3C—Si1^ii	106.4 (5)
OWB^vii—Na2B—Si1^i	151.7 (6)	Si1^vii—Na3C—Si1^ii	54.91 (18)
OWB^xii—Na2B—Si1^i	117.9 (7)	Si1^xi—Na3C—Si1^ii	106.4 (5)
OWB^xiii—Na2B—Si1^i	71.4 (6)	Si1^xxi—Na3C—Si1^ii	135.3 (8)
OWB^i—Na2B—Si1^i	82.6 (6)	O2^vii—Na3C—Si1	121.8 (8)
OWB—Na2B—Si1^i	133.8 (7)	O2^xxi—Na3C—Si1	79.6 (4)
O3^vii—Na2B—Si1^i	80.20 (11)	O2—Na3C—Si1	27.77 (8)
O3^vi—Na2B—Si1^i	122.6 (3)	Si1^iii—Na3C—Si1	54.91 (18)
O3^i—Na2B—Si1^i	27.58 (3)	Si1^vii—Na3C—Si1	106.4 (5)
Na1^i—Na2B—Si1^i	68.02 (13)	Si1^xi—Na3C—Si1	135.3 (8)
OWB^vi—Na2B—Si1^x	71.4 (6)	Si1^xxi—Na3C—Si1	106.4 (5)
OWB^vii—Na2B—Si1^x	133.8 (7)	Si1^ii—Na3C—Si1	55.27 (18)
OWB^xii—Na2B—Si1^x	82.6 (6)	O2^xxi—Na3D—O2^vii	79.1 (5)
OWB^xiii—Na2B—Si1^x	95.2 (7)	O2^xxi—Na3D—O2	79.1 (5)
OWB^i—Na2B—Si1^x	117.9 (7)	O2^vii—Na3D—O2	79.1 (5)
OWB—Na2B—Si1^x	151.7 (6)	Na3E^vii—Na3E—Na3E^xxi	60.00 (2)
O3^vii—Na2B—Si1^x	122.6 (3)	Na3E^vii—Na3E—O1C^xxii	140.1 (9)
O3^vi—Na2B—Si1^x	80.20 (11)	Na3E^xxi—Na3E—O1C^xxii	80.3 (9)
O3^i—Na2B—Si1^x	27.58 (3)	Na3E^vii—Na3E—O1C^xxiii	80.3 (9)
Na1^i—Na2B—Si1^x	68.02 (13)	Na3E^xxi—Na3E—O1C^xxiii	140.1 (9)
Si1^i—Na2B—Si1^x	54.94 (6)	O1C^xxii—Na3E—O1C^xxiii	138.9 (18)
O3^i—Na2C—O3^vii	88.3 (8)	Na3A—OWA—Na2A^i	109.9 (11)
O3^i—Na2C—O3^vi	88.3 (8)	Na3A—OWA—Na2A^viii	109.9 (11)
O3^vii—Na2C—O3^vi	88.3 (8)	Na2A^i—OWA—Na2A^viii	109.1 (11)
O3^i—Na2C—Na1^i	53.5 (6)	Na3A—OWA—Na2A	109.9 (11)
O3^vii—Na2C—Na1^i	53.5 (6)	Na2A^i—OWA—Na2A	109.1 (11)
O3^vi—Na2C—Na1^i	53.5 (6)	Na2A^viii—OWA—Na2A	109.1 (11)
O3^i—Na2C—Na2C^viii	135.9 (4)	OWB^xxi—OWB—OWB^vii	60.001 (7)
O3^vii—Na2C—Na2C^viii	135.9 (4)	OWB^xxi—OWB—Na2B	133.8 (7)
O3^vi—Na2C—Na2C^viii	91.2 (6)	OWB^vii—OWB—Na2B	78.2 (7)
Na1^i—Na2C—Na2C^viii	144.737 (4)	OWB^xxi—OWB—Na2B^i	78.2 (7)
O3^i—Na2C—Na2C^xiv	91.2 (6)	OWB^vii—OWB—Na2B^i	133.8 (7)
O3^vii—Na2C—Na2C^xiv	135.9 (4)	Na2B—OWB—Na2B^i	127.3 (12)
O3^vi—Na2C—Na2C^xiv	135.9 (4)	C1C—O1C—Na3E^xxiv	138 (3)
Na1^i—Na2C—Na2C^xiv	144.737 (2)	C1C—O1C—Na3E^xxv	138 (3)
Na2C^viii—Na2C—Na2C^xiv	60	Na3E^xxiv—O1C—Na3E^xxv	19.5 (18)
O3^i—Na2C—Na2C^i	135.9 (4)	O1C—C1C—O1C^xxvi	159 (5)
O3^vii—Na2C—Na2C^i	91.2 (6)	C2C—O4C—C2C^xxvii	140 (5)
O3^vi—Na2C—Na2C^i	135.9 (4)	C2C—O4C—O3C^xxviii	99 (3)
Na1^i—Na2C—Na2C^i	144.7360 (10)	C2C^xxvii—O4C—O3C^xxviii	66 (3)
Na2C^viii—Na2C—Na2C^i	60	C2C—O4C—O3C^xxix	66 (3)
Na2C^xiv—Na2C—Na2C^i	60	C2C^xxvii—O4C—O3C^xxix	99 (3)
Na2A^xv—Na1—Na2A^i	180.0 (6)	O3C^xxviii—O4C—O3C^xxix	35 (2)
Na2A^xv—Na1—O3	127.84 (8)	C2C—O4C—C2C^xxviii	112 (3)
Na2A^i—Na1—O3	52.16 (8)	C2C^xxvii—O4C—C2C^xxviii	33 (3)
Na2A^xv—Na1—O3^xvi	52.16 (7)	O3C^xxviii—O4C—C2C^xxviii	40.0 (14)
Na2A^i—Na1—O3^xvi	127.84 (8)	O3C^xxix—O4C—C2C^xxviii	68.2 (17)
O3—Na1—O3^xvi	93.70 (11)	C2C—O4C—C2C^xxix	33 (3)
Na2A^xv—Na1—O3^xvii	127.84 (8)	C2C^xxvii—O4C—C2C^xxix	112 (3)
Na2A^i—Na1—O3^xvii	52.16 (7)	O3C^xxviii—O4C—C2C^xxix	68.2 (17)
O3—Na1—O3^xvii	86.30 (11)	O3C^xxix—O4C—C2C^xxix	40.0 (14)
O3^xvi—Na1—O3^xvii	180.00 (8)	C2C^xxviii—O4C—C2C^xxix	81 (3)
Na2A^xv—Na1—O3^xviii	52.15 (7)	O4C—C2C—C2C^xxix	115 (5)
Na2A^i—Na1—O3^xviii	127.85 (7)	O4C—C2C—O3C	166 (4)
O3—Na1—O3^xviii	93.70 (11)	C2C^xxix—C2C—O3C	78 (4)
O3^xvi—Na1—O3^xviii	86.29 (11)	O4C—C2C—O3C^xxix	72 (3)
O3^xvii—Na1—O3^xviii	93.71 (11)	C2C^xxix—C2C—O3C^xxix	53 (3)
Na2A^xv—Na1—O3^xix	127.85 (7)	O3C—C2C—O3C^xxix	116 (3)
Na2A^i—Na1—O3^xix	52.15 (7)	O4C—C2C—O4C^xxx	139 (3)
O3—Na1—O3^xix	86.30 (11)	C2C^xxix—C2C—O4C^xxx	32 (3)
O3^xvi—Na1—O3^xix	93.71 (11)	O3C—C2C—O4C^xxx	55 (2)
O3^xvii—Na1—O3^xix	86.29 (11)	O3C^xxix—C2C—O4C^xxx	85 (2)
O3^xviii—Na1—O3^xix	180.00 (14)	O4C—C2C—O3C^iii	159 (4)
Na2A^xv—Na1—O3^xx	52.15 (7)	C2C^xxix—C2C—O3C^iii	78 (4)
Na2A^i—Na1—O3^xx	127.85 (8)	O3C—C2C—O3C^iii	22.4 (16)
O3—Na1—O3^xx	180.00 (7)	O3C^xxix—C2C—O3C^iii	127 (3)
O3^xvi—Na1—O3^xx	86.29 (11)	O4C^xxx—C2C—O3C^iii	47.7 (13)
O3^xvii—Na1—O3^xx	93.71 (11)	O3C^iii—O3C—C2C	128 (2)
O3^xviii—Na1—O3^xx	86.29 (11)	O3C^iii—O3C—C2C^xxix	112.4 (18)
O3^xix—Na1—O3^xx	93.71 (11)	C2C—O3C—C2C^xxix	48 (3)
O3—Na1—Na2B^xv	127.84 (7)	O3C^iii—O3C—O4C^xxx	72.3 (10)
O3^xvi—Na1—Na2B^xv	52.15 (8)	C2C—O3C—O4C^xxx	85 (3)
O3^xvii—Na1—Na2B^xv	127.85 (8)	C2C^xxix—O3C—O4C^xxx	42.7 (16)
O3^xviii—Na1—Na2B^xv	52.15 (7)	O3C^iii—O3C—C2C^iii	29.5 (15)
O3^xix—Na1—Na2B^xv	127.85 (7)	C2C—O3C—C2C^iii	99 (4)
O3^xx—Na1—Na2B^xv	52.15 (8)	C2C^xxix—O3C—C2C^iii	94 (3)
O3—Na1—Na2B^i	52.16 (7)	O4C^xxx—O3C—C2C^iii	64.1 (16)

Symmetry codes: (i) x, −y+1/4, −z+5/4; (ii) −y+3/4, −x+3/4, z; (iii) z, y, x; (iv) −z+5/4, y, −x+5/4; (v) −x+1, −z+1, −y+1; (vi) −z+5/4, x−1/2, −y+3/4; (vii) −y+3/4, −z+3/4, x; (viii) −x+5/4, −y+1/4, z; (ix) −y+3/4, x−1/2, −z+5/4; (x) −z+5/4, −y+1/4, x; (xi) x, −z+3/4, −y+3/4; (xii) y+1/2, z−1/2, x; (xiii) z, x−1/2, y+1/2; (xiv) −x+5/4, y, −z+5/4; (xv) −x+1, y+1/4, z+1/4; (xvi) y+1/4, −z+1, x+1/4; (xvii) −y+3/4, z−1/2, −x+5/4; (xviii) z−1/4, x−1/4, −y+1; (xix) −z+5/4, −x+3/4, y+1/2; (xx) −x+1, −y+1/2, −z+3/2; (xxi) z, −x+3/4, −y+3/4; (xxii) y, z, x; (xxiii) −z+3/4, −x+3/4, y; (xxiv) −y+3/4, z, −x+3/4; (xxv) z, x, y; (xxvi) −x+3/4, y, −z+3/4; (xxvii) x, z, y; (xxviii) −y+1, −z+1, −x+1; (xxix) −y+1, −x+1, −z+1; (xxx) −z+1, −x+1, −y+1.

Na Zeolite Y * CO2 (300K)

Crystal data

C0.34Al0Na0.36O2.57Si	Dx = 1.692 Mg m^−3
Mr = 81.54	Synchrotron radiation, λ = 0.70158 Å
Cubic, Fd3m	Cell parameters from 10763 reflections
Hall symbol: -F 4vw 2vw 3	θ = 2.3–31.9°
a = 24.86059 (15) Å	µ = 0.55 mm^−1
V = 15365.1 (3) Å^3	T = 300 K
Z = 192	Block, colourless
F(000) = 7784	0.05 × 0.05 × 0.05 mm

Data collection

Dectris-CrysAlisPro-abstract goniometer imported dectris images diffractometer	1083 reflections with I > 2σ(I)
Radiation source: synchrotron	Rint = 0.060
Synchrotron monochromator	θmax = 32.4°, θmin = 2.3°
φ scans	h = −37→37
32086 measured reflections	k = −34→34
1382 independent reflections	l = −36→37

Refinement

Refinement on F^2	75 parameters
Least-squares matrix: full	2 restraints
R[F^2 > 2σ(F^2)] = 0.064	w = 1/[σ^2(Fo^2) + (0.1086P)^2 + 202.8124P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.227	(Δ/σ)max = 0.036
S = 1.15	Δρmax = 0.94 e Å^−3
1382 reflections	Δρmin = −0.6 e Å^−3

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Si1	0.53602 (3)	0.30336 (3)	0.62556 (3)	0.0168 (3)
O2	0.49715 (10)	0.25285 (10)	0.60539 (13)	0.0265 (7)
O4	0.57383 (10)	0.32195 (14)	0.57383 (10)	0.0280 (7)
O3	0.57245 (11)	0.28172 (15)	0.67755 (11)	0.0311 (7)
O1	0.5	0.35713 (10)	0.64287 (10)	0.0292 (7)
Na2A	0.5580 (9)	0.1920 (9)	0.6920 (9)	0.041 (8)*	0.156 (4)
Na2B	0.5681 (4)	0.1819 (4)	0.6819 (4)	0.029 (2)*	0.358 (4)
Na2C	0.585 (4)	0.165 (4)	0.665 (4)	0.08 (4)*	0.049 (4)
Na1	0.5	0.25	0.75	0.032 (3)*	0.393 (4)
Na3A	0.5201 (6)	0.2299 (6)	0.5201 (6)	0.019 (5)*	0.160 (4)
Na3B	0.5113 (3)	0.2387 (3)	0.5113 (3)	0.025 (2)*	0.450 (4)
Na3C	0.5025 (7)	0.2475 (7)	0.5025 (7)	0.033 (7)*	0.176 (4)
Na3E	0.4703 (11)	0.3109 (14)	0.4703 (11)	0.185 (19)*	0.205 (4)
OWA	0.5839 (5)	0.1661 (5)	0.5839 (5)	0.075*	0.55 (2)
O1C	0.4023 (13)	0.5517 (19)	0.3477 (13)	0.13*	0.224 (13)
C1C	0.375	0.567 (6)	0.375	0.17*	0.224 (13)
O4C	0.410 (2)	0.5156 (17)	0.5156 (17)	0.115*	0.18 (2)
C2C	0.404 (2)	0.536 (2)	0.478 (2)	0.158*	0.280 (11)
O3C	0.4188 (13)	0.5702 (13)	0.4528 (12)	0.17*	0.280 (11)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Si1	0.0156 (4)	0.0184 (4)	0.0165 (4)	−0.0005 (2)	0.0027 (2)	−0.0019 (2)
O2	0.0285 (10)	0.0285 (10)	0.0226 (14)	−0.0106 (12)	0.0023 (9)	−0.0023 (9)
O4	0.0277 (10)	0.0287 (16)	0.0277 (10)	0.0001 (9)	0.0096 (12)	0.0001 (9)
O3	0.0316 (11)	0.0301 (17)	0.0316 (11)	−0.0047 (10)	−0.0092 (14)	0.0047 (10)
O1	0.0284 (16)	0.0296 (10)	0.0296 (10)	0.0078 (9)	0.0078 (9)	−0.0018 (13)

Geometric parameters (Å, º)

Si1—O4	1.6588 (13)	Na1—O3^vi	2.666 (4)
Si1—O2	1.6618 (13)	Na1—O3^xiii	2.666 (4)
Si1—O1	1.6656 (16)	Na1—O3^v	2.666 (4)
Si1—O3	1.6673 (15)	Na1—O3^xi	2.666 (4)
Si1—Na3A	3.220 (6)	Na1—Na2B^xi	2.931 (15)
Si1—Na2A	3.269 (11)	Na1—Si1^i	3.4830 (7)
Si1—Na3B	3.322 (5)	Na1—Si1^xiv	3.4830 (7)
Si1—Na2B	3.422 (6)	Na3A—O2^xv	2.269 (7)
Si1—Na3C	3.462 (13)	Na3A—O2^xvi	2.269 (7)
Si1—Na1	3.4830 (7)	Na3A—OWA	2.75 (3)
O2—Si1^i	1.6618 (13)	Na3A—O4^xv	2.968 (4)
O2—Na3A	2.269 (7)	Na3A—O4^xvi	2.968 (4)
O2—Na3B	2.392 (7)	Na3A—Si1^ii	3.220 (6)
O2—Na3C	2.565 (16)	Na3A—Si1^xv	3.220 (6)
O4—Si1^ii	1.6588 (13)	Na3A—Si1^xvii	3.220 (6)
O4—Na3A	2.968 (4)	Na3A—Si1^xvi	3.220 (6)
O3—Si1^iii	1.6673 (15)	Na3A—Si1^i	3.220 (6)
O3—Na2A	2.287 (15)	Na3B—O2^xv	2.392 (7)
O3—Na2B	2.486 (9)	Na3B—O2^xvi	2.392 (7)
O3—Na1	2.666 (4)	Na3B—Si1^ii	3.322 (5)
O3—Na2C	2.94 (12)	Na3B—Si1^xv	3.322 (5)
O1—Si1^iv	1.6656 (16)	Na3B—Si1^xvii	3.322 (5)
Na2A—O3^v	2.287 (15)	Na3B—Si1^i	3.322 (5)
Na2A—O3^vi	2.287 (15)	Na3B—Si1^xvi	3.322 (5)
Na2A—Na1	2.50 (4)	Na3C—O2^xv	2.565 (16)
Na2A—OWA	2.84 (3)	Na3C—O2^xvi	2.565 (16)
Na2A—OWA^vii	2.84 (3)	Na3C—Si1^ii	3.462 (13)
Na2A—OWA^viii	2.84 (3)	Na3C—Si1^xv	3.462 (13)
Na2A—Si1^v	3.269 (11)	Na3C—Si1^xvii	3.462 (13)
Na2A—Si1^iii	3.269 (11)	Na3C—Si1^xvi	3.462 (13)
Na2A—Si1^ix	3.269 (11)	Na3C—Si1^i	3.462 (13)
Na2A—Si1^vi	3.269 (11)	Na3E—Na3E^xv	1.09 (6)
Na2A—Si1^i	3.269 (11)	Na3E—Na3E^xvi	1.09 (6)
Na2B—O3^vi	2.486 (9)	Na3E—O1C^xviii	2.79 (5)
Na2B—O3^v	2.486 (9)	Na3E—O1C^xix	2.79 (5)
Na2B—OWA	2.499 (14)	Na3E—C2C^xx	2.83 (6)
Na2B—OWA^viii	2.499 (14)	Na3E—C2C^xxi	2.83 (6)
Na2B—OWA^vii	2.499 (14)	Na3E—O4C^xx	2.93 (7)
Na2B—Na1	2.932 (15)	OWA—Na2C^viii	2.01 (10)
Na2B—Si1^v	3.422 (6)	OWA—Na2C^vii	2.01 (10)
Na2B—Si1^iii	3.422 (6)	OWA—Na2B^viii	2.499 (14)
Na2B—Si1^i	3.422 (6)	OWA—Na2B^vii	2.499 (14)
Na2B—Si1^vi	3.422 (6)	OWA—Na2A^viii	2.84 (3)
Na2B—Si1^ix	3.422 (6)	OWA—Na2A^vii	2.84 (3)
Na2C—OWA	2.01 (10)	O1C—C1C	1.03 (7)
Na2C—OWA^vii	2.01 (10)	O1C—Na3E^xxii	2.79 (5)
Na2C—OWA^viii	2.01 (10)	O1C—Na3E^xx	2.79 (5)
Na2C—Na2C^vii	2.8 (3)	C1C—O1C^xxiii	1.03 (7)
Na2C—Na2C^x	2.8 (3)	O4C—C2C	1.08 (5)
Na2C—Na2C^viii	2.8 (3)	O4C—C2C^xxiv	1.08 (5)
Na2C—O3^v	2.94 (12)	O4C—Na3E^xix	2.93 (7)
Na2C—O3^vi	2.94 (12)	C2C—O3C	1.12 (5)
Na2C—Na1	3.66 (18)	C2C—C2C^xxiv	2.04 (10)
Na1—Na2A^xi	2.50 (4)	C2C—Na3E^xix	2.83 (6)
Na1—O3^xii	2.666 (4)	O3C—O3C^ii	1.19 (6)
O4—Si1—O2	107.83 (16)	O3—Na1—O3^xii	93.25 (12)
O4—Si1—O1	106.33 (16)	Na2A—Na1—O3^vi	52.47 (8)
O2—Si1—O1	111.83 (13)	Na2A^xi—Na1—O3^vi	127.53 (8)
O4—Si1—O3	112.52 (18)	O3—Na1—O3^vi	86.75 (12)
O2—Si1—O3	107.82 (16)	O3^xii—Na1—O3^vi	180.00 (9)
O1—Si1—O3	110.53 (16)	Na2A—Na1—O3^xiii	127.53 (8)
O4—Si1—Na3A	66.18 (16)	Na2A^xi—Na1—O3^xiii	52.47 (8)
O2—Si1—Na3A	41.78 (12)	O3—Na1—O3^xiii	93.25 (12)
O1—Si1—Na3A	126.8 (4)	O3^xii—Na1—O3^xiii	86.75 (12)
O3—Si1—Na3A	121.0 (5)	O3^vi—Na1—O3^xiii	93.25 (12)
O4—Si1—Na2A	122.2 (6)	Na2A—Na1—O3^v	52.47 (8)
O2—Si1—Na2A	67.04 (17)	Na2A^xi—Na1—O3^v	127.53 (8)
O1—Si1—Na2A	129.7 (7)	O3—Na1—O3^v	86.75 (12)
O3—Si1—Na2A	40.9 (2)	O3^xii—Na1—O3^v	93.25 (12)
Na3A—Si1—Na2A	87.3 (6)	O3^vi—Na1—O3^v	86.75 (12)
O4—Si1—Na3B	64.95 (13)	O3^xiii—Na1—O3^v	180.00 (15)
O2—Si1—Na3B	43.01 (12)	Na2A—Na1—O3^xi	127.53 (8)
O1—Si1—Na3B	120.6 (2)	Na2A^xi—Na1—O3^xi	52.47 (8)
O3—Si1—Na3B	127.4 (3)	O3—Na1—O3^xi	180.00 (9)
O4—Si1—Na2B	115.5 (3)	O3^xii—Na1—O3^xi	86.75 (12)
O2—Si1—Na2B	65.95 (13)	O3^vi—Na1—O3^xi	93.25 (12)
O1—Si1—Na2B	136.7 (3)	O3^xiii—Na1—O3^xi	86.75 (12)
O3—Si1—Na2B	43.25 (15)	O3^v—Na1—O3^xi	93.25 (12)
Na3B—Si1—Na2B	88.1 (3)	O3—Na1—Na2B^xi	127.53 (8)
O4—Si1—Na3C	64.09 (14)	O3^xii—Na1—Na2B^xi	52.47 (8)
O2—Si1—Na3C	44.79 (19)	O3^vi—Na1—Na2B^xi	127.53 (8)
O1—Si1—Na3C	114.9 (5)	O3^xiii—Na1—Na2B^xi	52.47 (8)
O3—Si1—Na3C	133.4 (5)	O3^v—Na1—Na2B^xi	127.53 (8)
O4—Si1—Na1	160.13 (12)	O3^xi—Na1—Na2B^xi	52.47 (8)
O2—Si1—Na1	80.26 (11)	O3—Na1—Na2B	52.47 (8)
O1—Si1—Na1	86.45 (12)	O3^xii—Na1—Na2B	127.53 (8)
O3—Si1—Na1	47.80 (13)	O3^vi—Na1—Na2B	52.47 (8)
Na3A—Si1—Na1	118.4 (3)	O3^xiii—Na1—Na2B	127.53 (8)
Na2A—Si1—Na1	43.2 (6)	O3^v—Na1—Na2B	52.47 (8)
Na3B—Si1—Na1	121.87 (13)	O3^xi—Na1—Na2B	127.53 (8)
Na2B—Si1—Na1	50.2 (2)	Na2B^xi—Na1—Na2B	180
Na3C—Si1—Na1	124.8 (2)	Na2A—Na1—Si1^i	63.809 (13)
Si1^i—O2—Si1	142.0 (2)	Na2A^xi—Na1—Si1^i	116.191 (13)
Si1^i—O2—Na3A	109.02 (11)	O3—Na1—Si1^i	74.53 (3)
Si1—O2—Na3A	109.01 (11)	O3^xii—Na1—Si1^i	152.40 (2)
Si1^i—O2—Na3B	108.71 (11)	O3^vi—Na1—Si1^i	27.60 (2)
Si1—O2—Na3B	108.71 (11)	O3^xiii—Na1—Si1^i	69.74 (7)
Si1^i—O2—Na3C	108.06 (12)	O3^v—Na1—Si1^i	110.26 (7)
Si1—O2—Na3C	108.05 (12)	O3^xi—Na1—Si1^i	105.47 (3)
Si1—O4—Si1^ii	143.2 (2)	Na2B^xi—Na1—Si1^i	116.191 (13)
Si1—O4—Na3A	83.06 (19)	Na2B—Na1—Si1^i	63.809 (13)
Si1^ii—O4—Na3A	83.06 (19)	Na2A—Na1—Si1^xiv	116.191 (13)
Si1^iii—O3—Si1	137.6 (2)	Na2A^xi—Na1—Si1^xiv	63.809 (13)
Si1^iii—O3—Na2A	110.54 (15)	O3—Na1—Si1^xiv	105.47 (3)
Si1—O3—Na2A	110.55 (15)	O3^xii—Na1—Si1^xiv	27.60 (2)
Si1^iii—O3—Na2B	109.39 (13)	O3^vi—Na1—Si1^xiv	152.40 (2)
Si1—O3—Na2B	109.39 (13)	O3^xiii—Na1—Si1^xiv	110.26 (7)
Si1^iii—O3—Na1	104.60 (13)	O3^v—Na1—Si1^xiv	69.74 (7)
Si1—O3—Na1	104.60 (13)	O3^xi—Na1—Si1^xiv	74.53 (3)
Na2A—O3—Na1	59.9 (9)	Na2B^xi—Na1—Si1^xiv	63.809 (13)
Na2B—O3—Na1	69.3 (3)	Na2B—Na1—Si1^xiv	116.191 (13)
Si1^iii—O3—Na2C	107.1 (6)	Si1^i—Na1—Si1^xiv	180
Si1—O3—Na2C	107.1 (6)	O2^xv—Na3A—O2^xvi	114.0 (5)
Na1—O3—Na2C	82 (2)	O2^xv—Na3A—O2	114.0 (5)
Si1—O1—Si1^iv	134.7 (2)	O2^xvi—Na3A—O2	114.0 (5)
O3^v—Na2A—O3^vi	106.4 (10)	O2^xv—Na3A—OWA	75.5 (6)
O3^v—Na2A—O3	106.4 (10)	O2^xvi—Na3A—OWA	75.5 (6)
O3^vi—Na2A—O3	106.4 (10)	O2—Na3A—OWA	75.5 (6)
O3^v—Na2A—Na1	67.6 (9)	O2^xv—Na3A—O4^xv	59.90 (9)
O3^vi—Na2A—Na1	67.6 (9)	O2^xvi—Na3A—O4^xv	161.2 (11)
O3—Na2A—Na1	67.6 (9)	O2—Na3A—O4^xv	59.90 (9)
O3^v—Na2A—OWA	148.4 (14)	OWA—Na3A—O4^xv	85.7 (5)
O3^vi—Na2A—OWA	92.1 (6)	O2^xv—Na3A—O4^xvi	59.90 (9)
O3—Na2A—OWA	92.1 (6)	O2^xvi—Na3A—O4^xvi	59.90 (9)
Na1—Na2A—OWA	144.0 (6)	O2—Na3A—O4^xvi	161.2 (11)
O3^v—Na2A—OWA^vii	92.1 (6)	OWA—Na3A—O4^xvi	85.7 (5)
O3^vi—Na2A—OWA^vii	148.4 (14)	O4^xv—Na3A—O4^xvi	119.44 (13)
O3—Na2A—OWA^vii	92.1 (6)	O2^xv—Na3A—O4	161.2 (11)
Na1—Na2A—OWA^vii	144.0 (6)	O2^xvi—Na3A—O4	59.90 (9)
OWA—Na2A—OWA^vii	61.1 (10)	O2—Na3A—O4	59.90 (9)
O3^v—Na2A—OWA^viii	92.1 (6)	OWA—Na3A—O4	85.7 (5)
O3^vi—Na2A—OWA^viii	92.1 (6)	O4^xv—Na3A—O4	119.44 (13)
O3—Na2A—OWA^viii	148.4 (14)	O4^xvi—Na3A—O4	119.44 (13)
Na1—Na2A—OWA^viii	144.0 (6)	O2^xv—Na3A—Si1^ii	139.9 (7)
OWA—Na2A—OWA^viii	61.1 (10)	O2^xvi—Na3A—Si1^ii	29.20 (6)
OWA^vii—Na2A—OWA^viii	61.1 (10)	O2—Na3A—Si1^ii	87.0 (2)
O3^v—Na2A—Si1^v	28.53 (9)	OWA—Na3A—Si1^ii	77.6 (4)
O3^vi—Na2A—Si1^v	130.7 (12)	O4^xv—Na3A—Si1^ii	145.9 (5)
O3—Na2A—Si1^v	83.7 (5)	O4^xvi—Na3A—Si1^ii	89.05 (14)
Na1—Na2A—Si1^v	72.9 (6)	O4—Na3A—Si1^ii	30.76 (5)
OWA—Na2A—Si1^v	136.4 (10)	O2^xv—Na3A—Si1^xv	29.20 (6)
OWA^vii—Na2A—Si1^v	75.6 (4)	O2^xvi—Na3A—Si1^xv	139.9 (7)
OWA^viii—Na2A—Si1^v	103.6 (4)	O2—Na3A—Si1^xv	87.0 (2)
O3^v—Na2A—Si1^iii	83.7 (5)	OWA—Na3A—Si1^xv	77.6 (4)
O3^vi—Na2A—Si1^iii	130.7 (12)	O4^xv—Na3A—Si1^xv	30.76 (5)
O3—Na2A—Si1^iii	28.53 (9)	O4^xvi—Na3A—Si1^xv	89.04 (14)
Na1—Na2A—Si1^iii	72.9 (6)	O4—Na3A—Si1^xv	145.9 (5)
OWA—Na2A—Si1^iii	103.6 (4)	Si1^ii—Na3A—Si1^xv	155.2 (9)
OWA^vii—Na2A—Si1^iii	75.6 (4)	O2^xv—Na3A—Si1^xvii	29.20 (6)
OWA^viii—Na2A—Si1^iii	136.4 (10)	O2^xvi—Na3A—Si1^xvii	87.0 (2)
Si1^v—Na2A—Si1^iii	57.4 (2)	O2—Na3A—Si1^xvii	139.9 (7)
O3^v—Na2A—Si1^ix	28.53 (9)	OWA—Na3A—Si1^xvii	77.6 (4)
O3^vi—Na2A—Si1^ix	83.7 (5)	O4^xv—Na3A—Si1^xvii	89.04 (14)
O3—Na2A—Si1^ix	130.7 (12)	O4^xvi—Na3A—Si1^xvii	30.76 (5)
Na1—Na2A—Si1^ix	72.9 (6)	O4—Na3A—Si1^xvii	145.9 (5)
OWA—Na2A—Si1^ix	136.4 (10)	Si1^ii—Na3A—Si1^xvii	115.5 (3)
OWA^vii—Na2A—Si1^ix	103.6 (4)	Si1^xv—Na3A—Si1^xvii	58.40 (11)
OWA^viii—Na2A—Si1^ix	75.6 (4)	O2^xv—Na3A—Si1^xvi	87.0 (2)
Si1^v—Na2A—Si1^ix	56.8 (2)	O2^xvi—Na3A—Si1^xvi	29.20 (6)
Si1^iii—Na2A—Si1^ix	111.8 (6)	O2—Na3A—Si1^xvi	139.9 (7)
O3^v—Na2A—Si1^vi	83.7 (5)	OWA—Na3A—Si1^xvi	77.6 (4)
O3^vi—Na2A—Si1^vi	28.53 (9)	O4^xv—Na3A—Si1^xvi	145.9 (5)
O3—Na2A—Si1^vi	130.7 (12)	O4^xvi—Na3A—Si1^xvi	30.76 (5)
Na1—Na2A—Si1^vi	72.9 (6)	O4—Na3A—Si1^xvi	89.05 (14)
OWA—Na2A—Si1^vi	103.6 (4)	Si1^ii—Na3A—Si1^xvi	58.41 (11)
OWA^vii—Na2A—Si1^vi	136.4 (10)	Si1^xv—Na3A—Si1^xvi	115.5 (3)
OWA^viii—Na2A—Si1^vi	75.6 (4)	Si1^xvii—Na3A—Si1^xvi	58.53 (11)
Si1^v—Na2A—Si1^vi	111.8 (6)	O2^xv—Na3A—Si1^i	87.0 (2)
Si1^iii—Na2A—Si1^vi	145.9 (13)	O2^xvi—Na3A—Si1^i	139.9 (7)
Si1^ix—Na2A—Si1^vi	57.4 (2)	O2—Na3A—Si1^i	29.20 (6)
O3^v—Na2A—Si1^i	130.7 (12)	OWA—Na3A—Si1^i	77.6 (4)
O3^vi—Na2A—Si1^i	28.53 (9)	O4^xv—Na3A—Si1^i	30.76 (5)
O3—Na2A—Si1^i	83.7 (5)	O4^xvi—Na3A—Si1^i	145.9 (5)
Na1—Na2A—Si1^i	72.9 (6)	O4—Na3A—Si1^i	89.04 (14)
OWA—Na2A—Si1^i	75.6 (4)	Si1^ii—Na3A—Si1^i	115.5 (3)
OWA^vii—Na2A—Si1^i	136.4 (10)	Si1^xv—Na3A—Si1^i	58.53 (11)
OWA^viii—Na2A—Si1^i	103.6 (4)	Si1^xvii—Na3A—Si1^i	115.5 (3)
Si1^v—Na2A—Si1^i	145.9 (13)	Si1^xvi—Na3A—Si1^i	155.2 (9)
Si1^iii—Na2A—Si1^i	111.8 (6)	O2^xv—Na3B—O2^xvi	105.4 (4)
Si1^ix—Na2A—Si1^i	111.8 (6)	O2^xv—Na3B—O2	105.4 (4)
Si1^vi—Na2A—Si1^i	56.8 (2)	O2^xvi—Na3B—O2	105.4 (4)
O3^vi—Na2B—O3^v	94.9 (4)	O2^xv—Na3B—Si1^ii	128.7 (5)
O3^vi—Na2B—O3	94.9 (4)	O2^xvi—Na3B—Si1^ii	28.28 (4)
O3^v—Na2B—O3	94.9 (4)	O2—Na3B—Si1^ii	82.72 (19)
O3^vi—Na2B—OWA	96.2 (3)	O2^xv—Na3B—Si1^xv	28.28 (4)
O3^v—Na2B—OWA	163.6 (7)	O2^xvi—Na3B—Si1^xv	128.7 (5)
O3—Na2B—OWA	96.2 (3)	O2—Na3B—Si1^xv	82.72 (19)
O3^vi—Na2B—OWA^viii	96.2 (3)	Si1^ii—Na3B—Si1^xv	142.5 (5)
O3^v—Na2B—OWA^viii	96.2 (3)	O2^xv—Na3B—Si1^xvii	28.28 (4)
O3—Na2B—OWA^viii	163.6 (7)	O2^xvi—Na3B—Si1^xvii	82.72 (19)
OWA—Na2B—OWA^viii	70.6 (8)	O2—Na3B—Si1^xvii	128.7 (5)
O3^vi—Na2B—OWA^vii	163.6 (7)	Si1^ii—Na3B—Si1^xvii	110.2 (2)
O3^v—Na2B—OWA^vii	96.2 (3)	Si1^xv—Na3B—Si1^xvii	56.45 (9)
O3—Na2B—OWA^vii	96.2 (3)	O2^xv—Na3B—Si1^i	82.72 (19)
OWA—Na2B—OWA^vii	70.6 (8)	O2^xvi—Na3B—Si1^i	128.7 (5)
OWA^viii—Na2B—OWA^vii	70.6 (8)	O2—Na3B—Si1^i	28.28 (4)
O3^vi—Na2B—Na1	58.3 (3)	Si1^ii—Na3B—Si1^i	110.2 (2)
O3^v—Na2B—Na1	58.3 (3)	Si1^xv—Na3B—Si1^i	56.57 (9)
O3—Na2B—Na1	58.3 (3)	Si1^xvii—Na3B—Si1^i	110.2 (2)
OWA—Na2B—Na1	138.2 (5)	O2^xv—Na3B—Si1^xvi	82.72 (19)
OWA^viii—Na2B—Na1	138.2 (5)	O2^xvi—Na3B—Si1^xvi	28.28 (4)
OWA^vii—Na2B—Na1	138.2 (5)	O2—Na3B—Si1^xvi	128.7 (5)
O3^vi—Na2B—Si1^v	117.2 (5)	Si1^ii—Na3B—Si1^xvi	56.45 (9)
O3^v—Na2B—Si1^v	27.36 (5)	Si1^xv—Na3B—Si1^xvi	110.2 (2)
O3—Na2B—Si1^v	77.8 (2)	Si1^xvii—Na3B—Si1^xvi	56.58 (9)
OWA—Na2B—Si1^v	146.3 (4)	Si1^i—Na3B—Si1^xvi	142.5 (5)
OWA^viii—Na2B—Si1^v	107.56 (16)	O2^xv—Na3B—Si1	128.7 (5)
OWA^vii—Na2B—Si1^v	77.1 (4)	O2^xvi—Na3B—Si1	82.72 (19)
Na1—Na2B—Si1^v	66.0 (2)	O2—Na3B—Si1	28.29 (4)
O3^vi—Na2B—Si1^iii	117.2 (5)	Si1^ii—Na3B—Si1	56.57 (9)
O3^v—Na2B—Si1^iii	77.8 (2)	Si1^xv—Na3B—Si1	110.2 (2)
O3—Na2B—Si1^iii	27.36 (5)	Si1^xvii—Na3B—Si1	142.5 (5)
OWA—Na2B—Si1^iii	107.56 (16)	Si1^i—Na3B—Si1	56.45 (9)
OWA^viii—Na2B—Si1^iii	146.3 (4)	Si1^xvi—Na3B—Si1	110.2 (2)
OWA^vii—Na2B—Si1^iii	77.1 (4)	O2^xv—Na3C—O2^xvi	95.8 (8)
Na1—Na2B—Si1^iii	66.0 (2)	O2^xv—Na3C—O2	95.8 (8)
Si1^v—Na2B—Si1^iii	54.65 (11)	O2^xvi—Na3C—O2	95.8 (8)
O3^vi—Na2B—Si1^i	27.36 (5)	O2^xv—Na3C—Si1^ii	117.3 (9)
O3^v—Na2B—Si1^i	117.2 (5)	O2^xvi—Na3C—Si1^ii	27.15 (10)
O3—Na2B—Si1^i	77.8 (2)	O2—Na3C—Si1^ii	77.6 (4)
OWA—Na2B—Si1^i	77.1 (4)	O2^xv—Na3C—Si1^xv	27.15 (10)
OWA^viii—Na2B—Si1^i	107.56 (16)	O2^xvi—Na3C—Si1^xv	117.3 (9)
OWA^vii—Na2B—Si1^i	146.3 (4)	O2—Na3C—Si1^xv	77.6 (4)
Na1—Na2B—Si1^i	66.0 (2)	Si1^ii—Na3C—Si1^xv	130.6 (9)
Si1^v—Na2B—Si1^i	131.9 (5)	O2^xv—Na3C—Si1^xvii	27.15 (10)
Si1^iii—Na2B—Si1^i	104.5 (3)	O2^xvi—Na3C—Si1^xvii	77.6 (4)
O3^vi—Na2B—Si1^vi	27.36 (5)	O2—Na3C—Si1^xvii	117.3 (9)
O3^v—Na2B—Si1^vi	77.8 (2)	Si1^ii—Na3C—Si1^xvii	103.8 (5)
O3—Na2B—Si1^vi	117.2 (5)	Si1^xv—Na3C—Si1^xvii	54.0 (2)
OWA—Na2B—Si1^vi	107.56 (16)	O2^xv—Na3C—Si1^xvi	77.6 (4)
OWA^viii—Na2B—Si1^vi	77.1 (4)	O2^xvi—Na3C—Si1^xvi	27.15 (10)
OWA^vii—Na2B—Si1^vi	146.3 (4)	O2—Na3C—Si1^xvi	117.3 (9)
Na1—Na2B—Si1^vi	66.0 (2)	Si1^ii—Na3C—Si1^xvi	54.0 (2)
Si1^v—Na2B—Si1^vi	104.5 (3)	Si1^xv—Na3C—Si1^xvi	103.8 (5)
Si1^iii—Na2B—Si1^vi	131.9 (5)	Si1^xvii—Na3C—Si1^xvi	54.1 (2)
Si1^i—Na2B—Si1^vi	54.02 (11)	O2^xv—Na3C—Si1^i	77.6 (4)
O3^vi—Na2B—Si1^ix	77.8 (2)	O2^xvi—Na3C—Si1^i	117.3 (9)
O3^v—Na2B—Si1^ix	27.36 (5)	O2—Na3C—Si1^i	27.15 (10)
O3—Na2B—Si1^ix	117.2 (5)	Si1^ii—Na3C—Si1^i	103.8 (5)
OWA—Na2B—Si1^ix	146.3 (4)	Si1^xv—Na3C—Si1^i	54.1 (2)
OWA^viii—Na2B—Si1^ix	77.1 (4)	Si1^xvii—Na3C—Si1^i	103.8 (5)
OWA^vii—Na2B—Si1^ix	107.56 (16)	Si1^xvi—Na3C—Si1^i	130.6 (9)
Na1—Na2B—Si1^ix	66.0 (2)	O2^xv—Na3C—Si1	117.3 (9)
Si1^v—Na2B—Si1^ix	54.02 (11)	O2^xvi—Na3C—Si1	77.6 (4)
Si1^iii—Na2B—Si1^ix	104.5 (3)	O2—Na3C—Si1	27.16 (10)
Si1^i—Na2B—Si1^ix	104.5 (3)	Si1^ii—Na3C—Si1	54.1 (2)
Si1^vi—Na2B—Si1^ix	54.65 (11)	Si1^xv—Na3C—Si1	103.8 (5)
OWA—Na2C—OWA^vii	92 (6)	Si1^xvii—Na3C—Si1	130.6 (9)
OWA—Na2C—OWA^viii	92 (6)	Si1^xvi—Na3C—Si1	103.8 (5)
OWA^vii—Na2C—OWA^viii	92 (6)	Si1^i—Na3C—Si1	54.0 (2)
OWA—Na2C—Na2C^vii	46 (3)	Na3E^xv—Na3E—Na3E^xvi	60.002 (12)
OWA^vii—Na2C—Na2C^vii	46 (3)	Na3E^xv—Na3E—O1C^xviii	78.7 (7)
OWA^viii—Na2C—Na2C^vii	91 (4)	Na3E^xvi—Na3E—O1C^xviii	138.2 (7)
OWA—Na2C—Na2C^x	91 (4)	Na3E^xv—Na3E—O1C^xix	138.2 (7)
OWA^vii—Na2C—Na2C^x	46 (3)	Na3E^xvi—Na3E—O1C^xix	78.7 (7)
OWA^viii—Na2C—Na2C^x	46 (3)	O1C^xviii—Na3E—O1C^xix	140.4 (16)
Na2C^vii—Na2C—Na2C^x	60.0010 (10)	Na3E^xv—Na3E—C2C^xx	128.6 (11)
OWA—Na2C—Na2C^viii	46 (3)	Na3E^xvi—Na3E—C2C^xx	169.4 (12)
OWA^vii—Na2C—Na2C^viii	91 (4)	O1C^xviii—Na3E—C2C^xx	49.9 (11)
OWA^viii—Na2C—Na2C^viii	46 (3)	O1C^xix—Na3E—C2C^xx	91.8 (15)
Na2C^vii—Na2C—Na2C^viii	59.9970 (10)	Na3E^xv—Na3E—C2C^xxi	169.4 (11)
Na2C^x—Na2C—Na2C^viii	59.997 (4)	Na3E^xvi—Na3E—C2C^xxi	128.6 (11)
OWA—Na2C—O3^v	170 (7)	O1C^xviii—Na3E—C2C^xxi	91.8 (15)
OWA^vii—Na2C—O3^v	95.2 (16)	O1C^xix—Na3E—C2C^xxi	49.9 (11)
OWA^viii—Na2C—O3^v	95.2 (16)	C2C^xx—Na3E—C2C^xxi	42 (2)
Na2C^vii—Na2C—O3^v	140.8 (15)	Na3E^xv—Na3E—O4C^xx	149.92 (9)
Na2C^x—Na2C—O3^v	99 (2)	Na3E^xvi—Na3E—O4C^xx	149.92 (9)
Na2C^viii—Na2C—O3^v	140.8 (15)	O1C^xviii—Na3E—O4C^xx	71.2 (7)
OWA—Na2C—O3^vi	95.2 (16)	O1C^xix—Na3E—O4C^xx	71.2 (7)
OWA^vii—Na2C—O3^vi	170 (7)	C2C^xx—Na3E—O4C^xx	21.5 (10)
OWA^viii—Na2C—O3^vi	95.2 (16)	C2C^xxi—Na3E—O4C^xx	21.5 (10)
Na2C^vii—Na2C—O3^vi	140.8 (15)	Na2C^viii—OWA—Na2C^vii	88 (6)
Na2C^x—Na2C—O3^vi	140.8 (15)	Na2C^viii—OWA—Na2C	88 (6)
Na2C^viii—Na2C—O3^vi	99 (2)	Na2C^vii—OWA—Na2C	88 (6)
O3^v—Na2C—O3^vi	77 (4)	Na2B—OWA—Na2B^viii	106.4 (6)
OWA—Na2C—O3	95.2 (16)	Na2B—OWA—Na2B^vii	106.4 (6)
OWA^vii—Na2C—O3	95.2 (16)	Na2B^viii—OWA—Na2B^vii	106.4 (6)
OWA^viii—Na2C—O3	170 (7)	Na3A—OWA—Na2A^viii	106.5 (6)
Na2C^vii—Na2C—O3	99 (2)	Na3A—OWA—Na2A^vii	106.5 (6)
Na2C^x—Na2C—O3	140.8 (15)	Na2A^viii—OWA—Na2A^vii	112.3 (6)
Na2C^viii—Na2C—O3	140.8 (15)	Na3A—OWA—Na2A	106.5 (6)
O3^v—Na2C—O3	77 (4)	Na2A^viii—OWA—Na2A	112.3 (6)
O3^vi—Na2C—O3	77 (4)	Na2A^vii—OWA—Na2A	112.3 (6)
OWA—Na2C—Na1	124 (4)	C1C—O1C—Na3E^xxii	151 (9)
OWA^vii—Na2C—Na1	124 (4)	C1C—O1C—Na3E^xx	151 (9)
OWA^viii—Na2C—Na1	124 (4)	Na3E^xxii—O1C—Na3E^xx	22.6 (14)
Na2C^vii—Na2C—Na1	144.74 (2)	O1C^xxiii—C1C—O1C	138 (10)
Na2C^x—Na2C—Na1	144.737 (9)	C2C—O4C—C2C^xxiv	142 (9)
Na2C^viii—Na2C—Na1	144.74 (2)	C2C—O4C—Na3E^xix	74 (5)
O3^v—Na2C—Na1	46 (2)	C2C^xxiv—O4C—Na3E^xix	74 (5)
O3^vi—Na2C—Na1	46 (2)	O4C—C2C—O3C	143 (7)
O3—Na2C—Na1	46 (2)	O4C—C2C—C2C^xxiv	19 (5)
Na2A—Na1—Na2A^xi	180	O3C—C2C—C2C^xxiv	159 (4)
Na2A—Na1—O3	52.47 (8)	O4C—C2C—Na3E^xix	84 (5)
Na2A^xi—Na1—O3	127.53 (8)	O3C—C2C—Na3E^xix	132 (4)
Na2A—Na1—O3^xii	127.53 (8)	C2C^xxiv—C2C—Na3E^xix	68.9 (11)
Na2A^xi—Na1—O3^xii	52.47 (8)	C2C—O3C—O3C^ii	128 (4)

Symmetry codes: (i) −y+3/4, −x+3/4, z; (ii) z, y, x; (iii) −z+5/4, y, −x+5/4; (iv) −x+1, −z+1, −y+1; (v) −z+5/4, −x+3/4, y+1/2; (vi) −y+3/4, z−1/2, −x+5/4; (vii) −x+5/4, y, −z+5/4; (viii) x, −y+1/4, −z+5/4; (ix) x, z−1/2, y+1/2; (x) −x+5/4, −y+1/4, z; (xi) −x+1, −y+1/2, −z+3/2; (xii) y+1/4, −z+1, x+1/4; (xiii) z−1/4, x−1/4, −y+1; (xiv) y+1/4, x−1/4, −z+3/2; (xv) −y+3/4, −z+3/4, x; (xvi) z, −x+3/4, −y+3/4; (xvii) x, −z+3/4, −y+3/4; (xviii) −z+3/4, −x+3/4, y; (xix) y, z, x; (xx) z, x, y; (xxi) y, x, z; (xxii) −y+3/4, z, −x+3/4; (xxiii) −x+3/4, y, −z+3/4; (xxiv) x, z, y.