Synthesis, revised crystal structures, and refractive indices of ABW-type CsMTiO<subscript>4</subscript> (M = Al, Fe, Ga) and ANA-type CsTi<subscript>1.10</subscript>Si<subscript>1.90</subscript>O<subscript>6.50</subscript>, and the determination of the electronic polarizability of 4-coordinated Ti<superscript>4+</superscript>

Single crystals of ABW-type CsAlTiO₄ (CAT), CsFeTiO₄ (CFT), CsGaTiO₄ (CGT), and ANA-type CsTi_1.1Si_1.9O_6.5 (CST) were grown and characterized by electron microprobe analyses, single-crystal X-ray diffraction, thermal analyses, and spindle-stage optical investigations to determine the electronic polarizability of 4-coordinated Ti⁴⁺, α(^[4]Ti⁴⁺). The crystal structure of CAT was confirmed to crystallize in the highest possible topological symmetry Imma (a = 8.9677(2) Å, b = 5.7322(1) Å, c = 9.9612(3) Å) with tetrahedrally coordinated Al and Ti equally distributed on Wyckoff position 8i. Twinning by reticular merohedry with a twin index of 2 was observed for most of the crystals resulting in a hexagonal twin lattice (a = 11.487(3) Å, c = 8.968(2) Å) with Laue symmetry 6/mmm. Refractive indices measured by immersion methods on an untwinned specimen are n_x = 1.716(5), n_y = 1.725(2), and n_z = 1.727(1) with 2V_z = 127.1(6)°. The diffraction patterns of CFT and CGT clearly showed superstructure reflections causing a symmetry lowering of index 4 with a transformation according to 2a, b, c from Imma to Pmab with a = 18.3054(7) Å, b = 5.8083(2) Å, c = 9.9938(4) Å for CFT, and a = 18.2921(6) Å, b = 5.7636(2) Å, c = 9.9210(3) Å for CGT. Refractive indices for CGT are n_x = 1.750(3), n_y = 1.772(3), and n_z = 1.776(2) with 2V_z = 132(1)°. The crystal structure of the ANA-type CsTi_1.1Si_1.9O_6.5 was confirmed to crystallize in space group Ia 3 ¯ $\overline{3}$ d (a = 13.8333(4) Å). The extra 0.5 O atoms are needed for charge compensation and to allow the sum of electronic polarizabilities to give a total electronic polarizability calculated from the refractive index n = 1.718(4). The electronic polarizability of ^[4]Ti⁴⁺ was calculated from the difference between the observed total polarizabilities (derived from the mean refractive indices of CAT and CGT) and the sum of electronic polarizabilities of cations and anions omitting the polarizability of Ti resulting in α(^[4]Ti⁴⁺) = 5.15(5) ų.

Keywords: ABW-type CsMTiO4; ANA-type CsTiSi2O6.5; crystal growth; crystal structure; electronic polarizabilities; refractive indices

CsMTiO4 compounds with M = Al, Fe, Ga belong to the structural family with the zeolite framework type code ABW [[1]], [[2]]. CsAlTiO4 (CAT Compound designations are given in bold-face letters not to be confused with framework-type codes.) was first described by Gatehouse [[3]] who stated that Roth and Waring [[4]] first mentioned this compound, but there is no specific information given in reference [[4]]. It was identified in the ternary system Cs2O–Al2O3–TiO2 by Solomah and Odoj [[5]] having orthorhombic lattice parameters, and its crystal structure was solved by Gatehouse [[3]] in space group Imma. Thus, it represents the highest possible topological symmetry of all ABW-type materials [[1]], [[2]], [[6]]. The structure is formed by six-membered rings of corner-sharing (Al,Ti)O4 tetrahedra with Al and Ti statistically distributed on the tetrahedral site. Figure 1 shows the characteristic six-rings with three tetrahedra pointing up (U) and three pointing down (D) in a UUUDDD manner of the ABW aristotype structure assuming an idealized hypothetical SiO2 framework from distance least squares calculations [[1]], [[7]]. The three-dimensional connection results in the formation of eight-rings parallel to [010] in the Imma setting. Little is known about the other two compounds with M = Fe and Ga. CsFeTiO4 (CFT) was described in space group Pc21n [[8]] as an analog to CsFeSiO4 having an ordered Si/Fe distribution [[9]]. CsGaTiO4 (CGT) was described in space group Imma [[10]] based on the results of X-ray diffraction Rietveld refinements, representing a second example together with CAT with the highest possible topological symmetry.

Graph: Figure 1: The [100] projection of the ABW-type framework in the highest possible topological symmetry Imma [[1]], [[7]] drawn with S TRUPLO [[11]].

CsTiSi2O6.5 (CST) was found by Balmer and Bunker [[12]] as a synthesis product in their investigations of possible exchange materials for the removal of radioactive Cs and Sr from wastes. Park et al. point out that CST has shown favorable Cs leach rates compared to those of pollucite [[13]]. CST was identified to have a pollucite-like crystal structure [[14]] and thus belongs to the ANA (analcime) framework type of zeolite-type compounds [[1]], [[2]]. The crystal structure was refined by Balmer et al. [[15]], [[16]] in space group Ia $3¯$ d. Compared with pollucite (ideal anhydrous composition CsAlSi2O6) Al3+ is replaced by Ti4+ and consequently 0.5 O (eight per unit cell) are needed for charge compensation. These O atoms are statistically distributed over two general 96h [[17]] positions with low occupancies. Some unreasonably short distances and rather high displacement parameters indicate some problems in the refinement. The additional O atoms yield a partial 5-coordination of Ti and 13-coordinated Cs not present in pollucite. The 5-coordinated Ti was confirmed by X-ray absorption spectroscopy (XANES) with an edge-sharing geometry determined by the analysis of the extended X-ray absorption fine structure (EXAFS) [[18]], [[19]] and confirmed by Raman spectroscopy [[18]], [[20]]. It was shown that the pollucite-type compounds can be synthesized by sol-gel methods in a complete solid-solution series CsTixAl1−xSi2O6+0.5x with 0 ≤ x ≤ 1 [[19]], [[21]].

All these compounds (CsMTiO4, CsTiSi2O6.5) have 4-coordinated Ti as a common feature. This prompted us to synthesize single crystals to determine the electronic polarizability of [4]Ti4+ not determined in [[22]] because of the paucity of compounds with 4-coordinated Ti suitable for refractive-index measurements.

CsAlTiO4 (CAT) was synthesized by a solid-state reaction as described by Gatehouse [[3]]. The synthesis was carried out over a period of 28 days at 1500 °C in a sealed platinum tube filled with a stoichiometric powder mixture. Crystals of sufficient size (up to 1 mm) for optical investigations and single-crystal X-ray diffraction were synthesized. The crystals, which were mostly twinned, had an irregular shape with rounded or plate-like habit and small isolated inclusions. The twin domains were intergrown and could be separated for the investigations. A small amount of a secondary phase could be identified as CsAl- or CsTi-hollandite.

Starting materials for CsGaTiO4 (CGT) and CsFeTiO4 (CFT) experiments were produced by powder synthesis. Since no data on the melting behavior of CGT and CFT were available, a simultaneous thermal analysis was performed on both compounds. Powder samples of 0.05 g with a grain size of 2–3 microns were analyzed on a Netzsch STA 449 Jupiter instrument using DSC and TG.

The measurements were made in platinum crucibles under nitrogen atmosphere in the temperature range of 25–1500 °C and a heating rate of 10 °C/min. The DSC measurements showed melting points of 1337.6 °C for CGT and 1231.5 °C for CFT (see Figure 2) and crystallization points of 1292.9 and 1087.5 °C. Moderate weight loss due to evaporation of Cs2O in the liquid state was obtained during TG measurements (see Figure 3). In CFT, a thermal anomaly occurs at about 1200 °C (marked green in Figure 2). This can most likely be attributed to a minor secondary phase Cs2Ti6O13 [[23]] which was present in the starting material. Its melting point roughly coincides with the observed anomaly.

Graph: Figure 2: DSC curves showing the endothermic reactions (melting) observed for CFT and CGT. The green highlighted peak can be attributed to a secondary phase Cs2Ti6O13 [[23]]. Arrows indicate instrumental artifacts.

Graph: Figure 3: TG curves showing the weight loss in CFT and CGT. Arrows indicate melting point and crystallization point corresponding to the onsets in the DSC curves in Figure 2.

The relatively low melting points, large supercooling regions, and the congruent melting behavior allowed the direct synthesis of both CGT and CFT from their melt. A series of cooling experiments was carried out in the temperature range of 1370–1000 °C in 20 ml platinum crucibles. Extra Cs2O was added to compensate for the outgassing of volatile Cs2O. The amount of Cs2O was derived from preliminary experiments recording the weight loss. Maximum crystal size (up to 4 mm length) with good optical quality could be obtained with a cooling rate of 10 °C/h with conditions listed in Table 1.

Table 1: Synthesis conditions.

CGT formed colorless, translucent crystals of isometric to tabular habitus. CFT crystals were dark red, translucent, and formed compact plate-like pieces. Minor amounts of secondary phases crystallized from the melt for both compounds. They were identified by X-ray powder diffraction as CsTi-hollandites and Fe/Ga oxides.

CsMTiO4 (M = Al, Fe and Ga) compounds are not water soluble or hygroscopic and remain stable in hot diluted nitric acid.

The synthesis of CsSi2TiO6.5 was carried out by a flux method using CsVO3 as solvent as described by Balmer et al. [[15]], [[16]]. A powder mixture of CsVO3 and pre-synthesized CST in a molar ratio of 1:1 was heated to 1100 °C in a sealed platinum tube and then cooled to 650 °C at a rate of 2.7 °C/h. The melt batch was then treated with hot diluted HNO3, and the crystallization products were isolated by polarization optics. The synthesized CST crystals were colorless, translucent, and partially faceted, and reached sizes of 0.1–1 mm. Synthesis conditions are listed in Table 1.

All samples were investigated with a Cameca SX 100 electron microprobe equipped with five WDX spectrometers. The measurements were carried out with a 15 kV acceleration voltage, 15 nA beam current, and a focused beam (1 µm). Raw data were corrected with the software "Peak Sight" and "PAP" matrix [[24]]. The following standards were used for calibration: kyanite for Al, wollastonite for Si, rutile for Ti, hematite for Fe, gallium phosphide for Ga, and pollucite for Cs. Counting time for each element was 10 s. The analytical results are listed in Table 2 and the resulting chemical compositions in Table 3.

Table 2: Electron microprobe analyses of CMTs and CST given in weight percent or labeled below detection limit (b.d.l.).

Table 3: Chemical compositions.

Data collection was carried out with a Bruker D8 venture Kappa-diffractometer using Mo Kα radiation (Kα1, λ = 0.7093 Å; Kα2, λ = 0.7136 Å), PHOTON 100 area detector, and TRIUMPH monochromator. Crystal data and data collection parameters are listed in Table 4. Unit-cell determination was carried out with the Bruker A PEX3 software suite. The orientation of the unit cells representing the different domains of the twinned CAT crystal was determined using the program C ELL N OW [[25]]. Structure refinements were done with the program S HELX-97 [[26]], [[27]] as part of the W INGX suite [[28]]. Crystal structure projections were drawn with the program S TRUPLO [[11]].

Table 4: Crystal data, data collection parameters, and structure refinement details.

1 $R=\frac{{{\displaystyle \sum }}^{\text{}}}{\left|}$ , $wR=\sqrt{\frac{{{\displaystyle \sum }}^{\text{}}}{\left|}}$ , $\text{GoF}=\sqrt{\frac{{{\displaystyle \sum }}^{\text{}}}{\mathit{w}}}$ , $R_{\text{int}}=\frac{{{\displaystyle \sum }}^{\text{}}}{|}$ .

The orientation of the indicatrices of the two anisotropic crystals, CFT and CGT, were determined recording the extinction curves on a spindle stage mounted on a petrographic microscope. The procedure is described in detail by Bloss [[29]]. Our improved microrefractometer spindle stage (described by Medenbach [[30]]) is equipped with a second spindle, where a smithsonite crystal (ne = 1.8489, no = 1.6213) was mounted as internal refractometer for the exact determination of refractive indices when the match between object crystal and immersion is reached. Extinction curves were recorded by rotating the object spindle in steps of 10° and reading the microscope stage angles for extinction under crossed polarizers. The resulting curves are presented in Figure 4. The program E XCALIBRW [[31]] was used for plotting the extinction curves to determine the orientation of the principal axes of the indicatrix and to calculate the optical angle 2V.

Graph: Figure 4: Extinction curves for CAT and CGT. AB, acute bisectrix; OB, obtuse bisectrix; ON, optical normal; OA1 and Oa2 are the optical axes.

It was not possible to measure CFT because its refractive indices were higher than 1.8 where the Cargille immersion oils showed crystalline precipitations (see [[32]]) blurring the liquid and covering the CFT crystal in such a way that the Becke line could no longer be observed.

The total electronic polarizabilities of minerals and compounds with bonding characters intermediate between covalent and ionic can be derived from the mean refractive indices of these compounds using the Anderson–Eggleton relationship [[33]], [[34]] ${\alpha }_A=\frac{(}{n^2}$

Graph

(1)with the total electronic polarizability αAE (Å3), the molar volume Vm (Å3) of the formula unit, the mean refractive index n at 589.3 nm, with 2.26 representing the electronic overlap factor [[22]], [[35]]. The total electronic polarizability can also be calculated from the sum of the individual contributions αcat of cations and αan of anions in the respective compounds. The individual polarizabilities of cations and anions are taken from Tables 4 and 5 in ref. [[22]]. If the value of a certain ion is missing in this compilation, it can be derived from the difference between the observed total polarizability (calculated from the mean refractive index using Equation (1)) and the sum of the polarizabilities of the remaining ions. In CsAlTiO4, e.g., the electronic polarizabilities of Cs, Al, and O are known and therefore α([4]Ti4+) can be calculated according to α(Ti) = αtot − (α(Cs) + α(Al) + 4α(O)) with αtot calculated from the mean refractive index using Equation (1).

Table 5: Atomic coordinates, Wyckoff positions, site occupancies (occ), equivalent isotropic displacement parameter Ueq (Å2), and anisotropic displacement parameters Uij (Å2) of CsAlTiO4 (first line) compared with the results from [[3]] (second line, italics). T represents mixed occupancy of Al and Ti on one site.

2 The isotropic displacement parameter U eq is defined as one-third of the trace of the orthogonalized U ij tensor. Coefficients U ij of the anisotropic displacement factor tensor of the atoms are defined by: $-2{\pi }^2[{\left(}^h{U}_{11}+\cdots +2hk{a}^{\ast }{b}^{\ast }{U}_{12}+\cdots ]$ .

Close inspection of the X-ray diffraction intensities confirmed space group Imma found by Gatehouse [[3]]. Some apparent superstructure reflections could be explained by λ/2 contributions in the X-ray spectrum of the primary beam. Thus, the crystal structure is expected to have a statistical distribution of Al and Ti on one site as described in [[3]]. The atom parameters from the final refinement with initial parameters taken from Gatehouse are listed in Table 5 and interatomic distances in Table 6.

Table 6: Interatomic distances and angles of CsAlTiO4 (CAT) (first line) compared with the results from [[3]] (second line).

A crystal-structure projection is shown in Section 5.1.2. Most of the CAT crystals were twinned by reticular merohedry with a twin index of 2 by two mirror planes (011) and (013). The resulting twin lattice is hexagonal with a = b = 11.487(3) Å, c = 8.968(2) Å, and Laue symmetry 6/mmm as observed for RbSiAlO4 [[36]]. The corresponding precession image is shown in Figure 5.

Graph: Figure 5: Precession image (2kl) showing the three individual unit cells and the resulting hexagonal twin lattice.

In contrast to CAT, a careful analysis of the diffraction patterns of CFT and CGT using the program J ana2006 [[37]] clearly showed superstructure reflections which could not be explained by λ/2 contributions, multiple diffraction (Renninger) effects, or twinning. This caused a doubling of the a lattice parameter compared to CAT with reflection conditions indicating a primitive lattice. Assuming that the crystal structures represent superstructures which can be derived from CAT, the following orthorhombic space groups would allow for a doubling of a: (numbers in parentheses represent the space group numbers in the International Tables for Crystallography [[17]]): P2221 (17), P2212 (17), P21221 (18), P21212 (18), Pmm2 (25), Pm21b (26), Pma2 (28), P2mb (28), P21ab (29), Pn2b (30), P2an (30), Pnm21 (31), Pm21n (31), P21mn (31), Pna21 (33), Pn2n (34), Pmmb (51), Pnan (52), Pnmb (53), Pman (53), Pmab (57), Pnmn (58), Pmmn (59), Pnab (60).

Exploring systematic extinctions in the set of X-ray reflections clearly indicated an a glide plane in the second viewing direction. The symmetry analysis showed a slight preference for the acentric space group Pma2 with the lowest number of violations of the reflection conditions. Alternatively, the monoclinic centrosymmetric space group P121/a1, which is on the same level of symmetry reduction as Pma2 with an index of 8 relative to Imma, shows a similarly good agreement with the reflection conditions. Refinements in both space groups yielded essentially identical results within 0.07 Å maximum deviation between corresponding atoms, i.e., the crystal structure intrinsically combines the symmetry elements of both space groups which would be accommodated by space groups Pmab and Pman as supergroups of both Pma2 and P121/a1. We decided on Pmab because of the significantly higher number of violations of reflection conditions in Pman resulting from the n glide plane.

Starting parameters for the refinement of the CFT structure were derived from the atomic parameters of the CAT structure in Imma according to the scheme shown in Figure 6. Final atom parameters are listed in Table 7 and selected distances and angles in Table 8. The crystal structure is shown in Figure 7. Similar results are obtained for the CGT structure where the superstructure reflections also indicated a doubling of unit-cell parameter a.

Graph: Figure 6: Atomic site relationships for CFT and CGT. The type of symmetry reduction is listed (t = translationengleich, k = klassengleich) together with its index representing the number of cosets derived from the supergroup. In addition, the set of basis vectors is given describing the transformation of the unit cell to its subgroup. For further details see [[1]], [[6]].

Table 7: Atomic coordinates, Wyckoff positions (Wyck.), site occupancies (Occ.), and equivalent isotropic displacement parameters Ueq (Å2). First line CFT, second line CGT (italics).

3 For definition of U eq see Table 5.

Table 8: Selected interatomic distances and angles for CFT (first line) and CGT (second line, italics). T refers to (Fe, Ga, Ti).

Graph: Figure 7: Crystal-structure projections of CFT projected parallel a (left) and parallel b (right). T11O4-tetrahedra are green, T12O4-tatrahedra are blue, Cs11 atoms are gray, and Cs12 atoms are pink. For crystal-structure projection of CGT see Figure 9 in Section 5.1.2.

Figure 6 also contains another branch of symmetry lowering to monoclinic symmetry represented by some ABW-type phosphates and sulfates discussed in Section 5.2.

CST is cubic, crystallizing in space group Ia $3¯$ d, and accordingly it appears optically istotropic under the polarizing microscope with crossed polarizers. Its crystal structure was described by Balmer et al. [[16]] and McCready et al. [[14]] to have a cubic ANA type framework derived from the mineral analcime. The mineral pollucite is its Cs analog usually containing some Na as, e.g., in Cs11Na5Al16Si32O96 · 5H2O [[38]]. Na-free pollucite, Cs16A116Si32O96 is anhydrous retaining the cubic ANA type structure [[39]], [[40]], but it is also described with tetragonal symmetry in I41/a at room temperature [[41]] or, at low temperature, after a phase transition in I41/acd [[40]]. The symmetry relationships are described in [[1]]. If Al3+ is replaced by Ti4+, we get a neutral framework. Charge compensation for Cs can be achieved by introducing additional oxygen located close to the TiO4 tetrahedra, thus extending the coordination of one half of the Ti atoms to 5-coordinated Ti, as assumed by Balmer et al. [[16]]. Consequently, the chemical composition results in CsTiSi2O6.5 or Cs16Ti16Si32O104 in terms of the unit-cell content. This could be rearranged to Cs16[Ti16Si32O96]O8 indicating the excess oxygen that is not part of the TO2 framework (T = Si4+, Ti4). The formation of hydroxyls for achieving charge balance according to (CsOH)16[Ti16Si32O96] can be ruled out because of the anhydrous synthesis conditions in a sealed platinum tube at 1100 °C. Similarly, it is unlikely that Ti4+ would be reduced to Ti3+ yielding Cs+16[Ti3+16Si4+32O96]. The best model we present here is the one described in [[16]] including an excess of 8 O atoms per unit cell for charge compensation.

Electron microprobe analysis clearly indicated a Ti/Si ratio different from 1 yielding the chemical composition CsTi1.1Si1.9O6.5. Initial atom parameters for the refinements were taken from [[16]] omitting the extra O atoms needed for charge compensation. Refinement of Cs and framework atoms with Si and Ti statistically distributed on the T site yielded R1 = 4.96% with anisotropic displacement parameters for all atoms, with a residual electron density is 0.76 e/Å3. This represents the final results based on usual criteria for evaluating refinements. However, 16 Cs+ ions are not charge balanced, assuming that all Ti is fully oxidized to Ti4+, and therefore additional O atoms are introduced following the model presented in [[16]]. Introducing O2 and O3 with an occupancy constrained to a sum of 8 O atoms as extra oxygen and refined with isotropic displacement parameters lowered R1 to 4.70%, and to 4.24% after refinement of extinction coefficient and applying the two-term weighting scheme suggested by S HELX. The final parameters are listed in Table 9 and selected distances and angles in Table 10. Crystal structure projections are shown in Figure 8.

Table 9: Atomic coordinates, Wyckoff positions (Wyck.), site occupancies (Occ.), and equivalent isotropic displacement parameters Ueq (Å2) of CST. First line this work, second line ref. [[16]] X-ray diffraction refinement (italics).

• 4 aSum constrained to 0.0833 corresponding to 8 O atoms per unit cell.
• 5 bRefined isotropically.
• 6 cFixed in the refinement.

Table 10: Selected interatomic distances and angles for CST. T refers to (Si,Ti). First line this work, second line ref. [[16]] X-ray diffraction refinement (italics).

• 7 aEvery second Ti is assumed to have a fifth distance statistically distributed to one of the possible distances to O2 or O3.
• 8 bAll Cs atoms are assumed to have a 13th distance to one of the possible distances to O2 or O3.

Graph: Figure 8: Crystal structure projections of CST. Left: View parallel [001], Right: View parallel [111]. O1 is red, O2 is yellow, O3 is green.

Refractive indices were measured for CAT, CGT, and CST crystals after determination of the orientation of the optical indicatrix of CAT and CGT by recording the extinction curves shown in Figure 4. CFT could not be measured as explained in Section 2.4. The resulting refractive indices are listed in Table 11. The observed optical angle 2Vzobs is derived from the extinction curves by the program E XCALIBRW [[31]] compared with the corresponding value calculated from the refractive indices according to $\cos V_Z=\frac{n_x}{n_y}\sqrt{\frac{(}{n_y}}$ [[42]]. The observed and calculated values are in excellent agreement with each other considering that 2Vzcalc is very sensitive to small changes in the refractive indices. A small variation within fractions of the error margins yields a perfect agreement (see second line for CAT and CGT). It is also a measure of the accuracy of the refractive-index determination.

Table 11: Refractive indices nx, ny, nz with mean value <n>, optical angle 2Vz, and birefringence Δ. Measurements were done at 589.3 nm.

9 aMean value of four measurements on different crystals.

After the determination of the mean refractive indices, the electronic polarizability of [4]Ti4+ can be calculated from the difference between the total electronic polarizability αobs and the sum of the electronic polarizabilities of Cs, Al or Ga, Ti, and O. The total electronic polarizability αobs of the respective compound is calculated according to Equation (1) with n taken from Table 11. The sum of the electronic polarizabilities of the cations is calculated from the values listed in Table 4 in ref. [[22]]. The electronic polarizability of O is calculated according to Equation (6) in ref. [22]. The corresponding values are listed in Table 12. Results are obtained using the program P OLARIO [[43]].

Table 12: Electronic polarizabilities. αobs is calculated from Equation (1), electronic polarizabilities for the cations are taken from Table 4 in ref. [22], and parameters for calculating the O polarizabilities are taken from Table 5 in ref. [[22]]. Bold entry corresponds to chemical composition used here.

• 10 *Calculation of Σ α and α ([4]Ti).
• 11 CAT and CGT : Σ α  =  α (Cs) +  α (M) + 4* α (O), α ([4]Ti) =  α obs − Σ α.
• 12 CST with [4]Ti and [5]Ti: Σ α  =  α (Cs) + 2* α (Si) + 0.5* α ([5]Ti)+ 6.5* α (O), α ([4]Ti) = 2*(α obs − Σ α).
• 13 CST with [4]Ti only: Σ α  =  α (Cs) + 2* α (Si) + 6.5* α (O), α ([4]Ti) =  α obs − Σ α.
• 14 CST with Ti:Si = 1.10:1.90: Σ α  =  α (Cs) + 1.9* α (Si) + 6.5* α (O), α ([4]Ti) = (α obs − Σ α)/1.1.
• 15 CST with CsOH: Σ α  =  α (Cs) +  α (OH) + 1.9* α (Si) + 6* α (O), α ([4]Ti) = (α obs − Σ α)/1.1.
• 16 **CAT and CGT only.

Because of the uncertainties in the chemical composition and the crystal structure of CST the mean value for α([4]Ti) is calculated from CAT and CGT only, yielding 5.15 Å3 as the electronic polarizability of 4-coordinated Ti4+. For further details see discussion Sections 5.1.3 and 5.3.

Crystal-structure refinements confirmed the results obtained by Gatehouse [[3]] of a zeolite-type crystal structure with framework type code ABW. Equal fractions of Al and Ti are randomly distributed over the T-site on Wyckoff position 8i. CAT represents the aristotype structure with the highest possible symmetry in the orthorhombic space group Imma (or Imam in its standardized setting used in ref. [[1]] and [[6]]; see Section 5.2 for further details). The mean (Al,Ti)–O distance of 1.76 Å (Table 6) agrees well with the mean value of 1.77 Å calculated from Al–Omean = 1.736 Å [[44]] and [4]Ti–O = 1.816 Å calculated from 13 TiO4 tetrahedra of the compounds listed in Table 13, not considering spinels with defect structures [[45]], [[46]] The crystal-structure projection is presented in Figure 9.

Table 13: Mean Ti–O distances in TiO4 tetrahedra.

Graph: Figure 9: Comparison of the crystal structures of CGT (left) with CAT (right). Red lines indicate twice the rotation angle.

As described in Section 4.1.2, the X-ray diffraction intensities clearly indicated a superstructure with 2a, b, c relative to the aristotype structure of CAT. Out of 24 space groups representing possible subgroups of Imma (see Section 4.1.2), Pmab was chosen as the space group with highest symmetry fulfilling both reflection conditions and subgroup criteria. This is in contrast to the findings in [[8]] and [[10]] where space groups Pc21n and Imma were assigned to CFT and CGT, respectively. It cannot be ruled out that the true symmetry might be even lower. Refinements in a lower symmetry failed because of high correlations. It is remarkable that the symmetry lowering obviously is not caused by an ordering of Fe and Ti (as proposed in [[8]]), or Ga and Ti on the T sites. The deviations of atom positions from the CAT structure listed in Table 14, representing the deviation from the aristotype symmetry, clearly show that mainly the O atoms are primarily responsible for the symmetry lowering. This is derived by calculating the interatomic distances between corresponding atoms of the CAT and the CFT structure superimposed on each other.

Table 14: Deviation of atom positions of CFT from the corresponding positions in CAT.

It is especially O2 and O3 which cause the symmetry lowering. The cations essentially conform to the aristotype structure. This is shown in Figure 9 comparing the high (Imma) and low (Pmab) symmetry structures. Consequently, the lowering of symmetry is caused by a rotation of the TO4 tetrahedra about the a axis. Twice the rotation angle (projected parallel a) is indicated in Figure 9 by the red lines in the upper left (Ga,Ti)O4 tetrahedron. The total rotation angle (see Figure 9) is 31.3° for CGT and 37.0° for CFT which is considered to be a significant deviation from the aristotype structure. Still, an uncertainty remains that the refinement could have been done in an unnecessarily low symmetry as discussed in [[57]], [[58]], but the superstructure reflections unequivocally indicate a symmetry reduction and therefore support the choice of space group Pmab for the crystal structures of CFT and CGT. This shows that the symmetry lowering is not caused by an ordering of Ti and Fe (or Ti and Ga) as it is the case for, e.g., CsNiPO4 [[59]], CsCoPO4 [[60]], CsZnPO4 [[61]], and LiNH4SO4 [[62]], [[63]] all crystallizing in space group P121/a1 with doubled lattice parameter a which is a subgroup of Pmab. Different from CFT and CGT, all these structures include pairs of framework cations with large differences in ionic radii which possibly may be the primary driving force for ordering in those structures.

The crystal structure of CST is closely related to the ANA type compound pollucite CsAlSi2O6 with a substitution of Al3+ by Ti4+requiring additional negative charges introduced by 8 O atoms corresponding to 0.5 O per formula unit. This model was determined from neutron powder diffraction and single crystal X-ray diffraction studies [[16]], described in [[14]], [[64]], and confirmed by XAS [[18]], 29Si MAS NMR [[15]], XANES, EXAFS, and Raman spectroscopy [[19]]. Ba-substituted compounds with chemical compositions according to CsxBa(1−x)/2TiSi2O6.5 were described in [[13]], [[65]]. Xu et al. [[21]] showed that there is a complete solid solution between CST and pollucite: CsTixAl1−xSi2O6+0.5x. Still, the extra O atoms needed for charge compensation are introduced here as well as by Balmer et al. [[16]] without a definite proof in the crystal structure refinement. As stated in the results section, the refinement converged at reasonable residuals with just framework atoms and Cs lowering R1 to 4.96% and to 4.70% after inserting two possible O atoms. Here, the atom parameters were refined in contrast to [[16]] where they were fixed on positions reasonably close to Cs and T atoms. In addition, the independently refined occupancies of the two O atoms yielded 8.1(6) O atoms, which correspond almost exactly to the expected number of O atoms. Further evidence for extra oxygen is presented by the analysis of the electronic polarizability of [4]Ti (see Table 12). Applying various possible models for charge compensation, the chemical composition of Cs[4]Ti1.10Si1.90O6.50 yielded the best result for the electronic polarizability of Ti in the range obtained from CAT and CGT. Here, it is assumed that all Ti atoms are 4-coordinated whereas the distance calculations might indicate a fifth O atom coordinated to TiO4. However, this configuration can be considered to represent predominantly a 4-coordination for following reasons: (1) The distances within the regular tetrahedron range between 1.64 and 1.67 Å, whereas the additional bonds to O2 and O3 have much larger distances between 1.95 and 2.19 Å, yielding much weaker bonding than within the tetrahedron. (2) Only every second Ti is involved in the extended coordination; the others remain 4-coordinated together with Si. (3) O2 and O3 have occupancies of approximately 4% on each site, i.e., only four out of 96 possible positions are occupied, and consequently less than one O2 and less than one O3 can be bonded to a Ti atom as candidate for a 5-coordinated Ti. This might explain why physically all Ti act as 4-coordinated cations. This might be even overinterpreted considering that all T and O1 positions consist of SiO4 and TiO4 tetrahedra superimposed on each other. There must be a local distortion of the tetrahedral geometry when O2 and O3 atoms are close to the Ti atom yielding distances too short to the O1 atoms for simultaneous occupancies (1.40(6) Å to O3 in this work, 1.695(7) Å to O2 in [[16]]). This can only be explained by a local rearrangement of the O atoms about the central Ti which cannot be determined in the refinement. (4) For 5-coordinated Ti we would expect a configuration with a short Ti–O bond and four longer ones [67] which is not accomplished here (Figure 10).

Graph: Figure 10: Coordination of Ti with additional O atoms. O1 in regular tetrahedron (red), O2 (yellow), O3 (green). Labels represent distances between Ti and O [Å]. Distances shown in red color belong to the (Ti,Si)O4 tetrahedron.

The lowering of the symmetry of CFT and CGT represents a new branch in the symmetry relationships of ABW type compounds [[6]]. All subgroups are derived from the aristotype symmetry in space group setting Imam to conform with the setting of numerous representatives of ABW types. Therefore, space group Pmab of CFT and CGT is transformed here to its standard Pmca setting according to a, c, b. The resulting branch in the Bärnighausen-tree [[66]] is shown in Figure 11 including the derivation of all maximal subgroups.

Graph: Figure 11: Group/subgroup relationships among ABW-type compounds with new branch 3. Space groups listed in frames represent actually observed symmetries, others represent intermediate steps for symmetry reduction. The type of symmetry reduction is listed (t = translationengleich, k = klassengleich) together with its index representing the number of cosets derived from the supergroup. In addition, the set of basis vectors is given describing the transformation of the unit cell to its subgroup. For further details see [[1]], [[6]]. The new subgroup Pmca is highlighted in a gray field.

As explained in chapter 3 and shown in chapter 4, the electronic polarizability of 4-coordinated Ti4+ was calculated from the mean refractive indices of CAT and CGT (see Table 12) yielding α([4]Ti4+) = 5.15 Å3. Using this value and solving Equation (1) for n, we can now predict the mean refractive indices of compounds known to contain 4-coordinated Ti as listed in Table 15.

Table 15: Mean total polarizabilities and mean refractive indices of compounds containing 4-coordinated Ti. References are given for the structural data. Optical parameters are calculated using electronic polarizabilities from [[22]], α([4]Ti4+) = 5.15 Å3 from this work, and applying Equation (1) solved for n.

Plotting the electronic polarizabilities of 4-, 5-, and 6-coordinated Ti versus the coordination number (CN) in Figure 12 shows that these values do not follow the typical trend of cations with smoothly decreasing polarizabilities as a function of CN. This is attributed to a special bonding situation of Ti in TiO5 with one short bond to oxygen as discussed in Shannon and Fischer [67]. The electronic polarizability of 5-coordinated Ti with α = 4.35 Å3 represents a minimum between α([4]Ti) = 5.15 Å3 and α([6]Ti) = 5.01 Å3.

Graph: Figure 12: Electronic polarizabilities plotted versus coordination numbers.

With the successful synthesis of single crystals of CsAlTiO4 (CAT), CsGaTiO4 (CGT), and CsTi1.1Si1.9O6.5 (CST), all having 4-coordinated Ti4+, it was possible to determine the electronic polarizability α of [4]Ti4+ from their refractive indices measured by immersion methods and calculating the total electronic polarizability using the Anderson-Eggleton relationship (Equation 1). In this context, we have redetermined the crystal structures of CGT and its Fe analog CsFeTiO4 (CFT). For the first time, superstructure reflections were observed in single-crystal diffraction patterns of these compounds causing a symmetry lowering from Imma to Pmab with doubled lattice parameter a. We adopted the crystal structure model of CST from [[16]] with two disordered O atoms partly extending the coordination of Ti and Cs. This configuration is strongly distorted with SiO4, TiO4, and TiO5 superimposed on each other in the unit cell representing average positions in the crystal-structure refinements.

CFT could not be used for the determination of α([4]Ti4+) because of its high refractive index difficult to measure by immersion methods. The electronic polarizability α([4]Ti4+) = 5.15 Å3 determined from CAT, CGT, and CST is slightly higher than α([6]Ti4+) = 5.01 Å3 which follows the general trend of a monotonic polarizability decrease with increasing coordination number. Here, α([5]Ti4+) = 4.35 Å3 is a lower value than that predicted from a monotonic decreasing polarizability between α([4]Ti4+) and α([6]Ti4+). We attribute this low polarizability value [[67]] to unusual bonding behavior in TiO5 polyhedra having one short bond, sometimes referred to as a "titanyl" bond.

We thank the Deutsche Forschungsgemeinschaft (DFG) for funding this project under grant FI442/21-2, Anne Hübner (Bremen) for the EMPA preparation, Olaf Medenbach (Bochum) for providing optical equipment, and Ruth C. Shannon (Boulder) and two anonymous referees for their comments on the manuscript.