Hydrothermal synthesis and structural study on Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O, a tobermorite related compound

Abstract

The hydrothermal treatment of a glass with a molar ratio of Rb₂O:CaO:SiO₂ = 1:4:6 at 400 °C and 500 bar resulted in the formation of single-crystals of Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O or {Ca₄Si₆O₁₅[O_0.855(OH)_0.145]₂}·(Rb_1.71·2H₂O). The basic crystallographic data of this phase at room conditions are as follows: space group P 2₁/m, a = 6.7766(4), b = 22.3162(10), c = 6.7782(4) Å, β = 114.056(7)°, V = 936.02(8) ų, Z = 2. A striking feature of the crystals is a polysynthetic twinning, clearly observable under a petrographic microscope. The diffraction patterns of all investigated samples can be explained as a superposition of two reciprocal lattices, with a two-fold axis parallel to [101] being the twin element. Synchrotron radiation was used to determine the crystal structure from a data set collected at the X06DA beamline of the Swiss Light Source, Paul Scherrer Institute. Least-squares refinements resulted in a residual of R(|F|) = 0.073 for 1712 reflections and 163 parameters. According to Liebau’s crystal chemical classification, the compound can be described as an unbranched dreier double chain silicate. The bands run parallel to [101] and are formed by the condensation of two wollastonite-type single-chains. The two calcium cations within the asymmetric unit are coordinated by seven ligands each. The [CaX₇]-groups (X: O²⁻, OH⁻, H₂O) are linked into layer-like units parallel to (010) by sharing common edges. Adjacent layers are connected by the silicate ribbons, resulting in a negatively charged heteropolyhedral network enclosing tunnel-like cavities. The rubidium atoms are distributed among a total of four partially occupied and mutually exclusive extra-framework positions within these channels. Each of the monovalent cation positions is coordinated by eight ligands, providing additional direct linkage between the network-forming polyhedra. The crystal structure of Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O is closely related to natural paratobermorite, a hydrous calcium silicate of the tobermorite supergroup of minerals. The paper will cover the common features of both phases and the differences between the compounds, including aspects of OD-theory.

INTRODUCTION

According to Biagioni et al. (2015) and the subsequently published data by Pekov et al. (2022), the tobermorite supergroup of minerals comprises the following hydrous calcium silicates: plombièrite [Ca₅Si₆O₁₆(OH)₂·7H₂O], tobermorite (Ca₅Si₆O₁₇·5H₂O), kenotobermorite [Ca₄Si₆O₁₅(OH)₂·5H₂O], clinotobermorite (Ca₅Si₆O₁₇·5H₂O), and paratobermorite [Ca₅AlSi₅O₁₆(OH)·5H₂O]. In this context, riversideite [Ca₅Si₆O₁₆(OH)₂] is considered to be of questionable status. This is due to its incomplete structural description and uncertainties regarding its occurrence in nature. Notably, the chemical formulas provided in parentheses are simplified representations of the compositions. Biagioni et al. (2015) also gave an excellent overview of the trials and tribulations in the nomenclature of tobermorites and its development over the years. In addition, the authors summarized alternatively used classification schemes, focusing on (i) aspects of polytypism, a phenomenon common in this mineral supergroup or (ii) the value of the d-spacing of the Bragg peak, which is the first to be observed in a powder diffraction pattern. The latter approach is more frequently used in materials science. For example, tobermorite sensu stricto has also been called tobermorite-11Å, for which several polytypes exist, such as tobermorite-2M.

From a petrological perspective, the group members generally form by hydrothermal processes from limestones that have undergone contact metamorphism and metasomatism. Furthermore, they can be found in vesicles, vugs and cavity fillings in basalts or rodingite-type rocks. Calcite, ettringite, portlandite, and various zeolites can occur as accompanying minerals (Anthony et al., 1995; Bonaccorsi and Merlino, 2005; Pekov et al., 2022).

While the various members of the tobermorite family represent rather exotic species within the mineral kingdom, their synthetic counterparts are of importance for applied mineralogy because they are used as model structures for the calcium silicate hydrates or C-S-H phases which represent the major binding compounds in concrete. They form during the hydration reaction of Ca₃SiO₅ and Ca₂SiO₄, representing the main silicate phases in Portland cement clinker (Taylor, 1997), which is by far the most important inorganic binder. In 2022, for instance, the global cement production was approximately 4.2 billion tons (Ige et al., 2024) and is expected to reach 8.2 billion tons by 2030 (Tkachenko et al., 2023), making the C-S-H phases one of the most produced inorganic compounds of technical relevance.

Despite the challenges associated with the structural characterization of the industrial C-S-H phases, including their X-ray amorphous nature, their flexible chemical composition, and the absence of phase pure samples (Taylor, 1997), there are compelling indications that they can be derived from members of the tobermorite supergroup such as plombièrite (tobermorite-14Å) or clinotobermorite, through the introduction of defects (Richardson, 2014).

At present, only limited crystallographic information is available concerning the incorporation of alkali cations into tobermorite-related phases. This is somehow surprising because these compounds are known to exhibit high cation exchange capacities for these monovalent ions (Tsuji and Komarneni, 1989; Miyake et al., 1989; Coleman, 2005). For instance, Mitsuda (1970) and Organova et al. (2002) studied combined potassium and aluminium substituted tobermorites. While Mitsuda obtained his samples from a mild hydrothermal treatment of a clinoptilolite-lime mixture, the latter authors investigated natural specimens from three different, as yet undisclosed locations. According to a hypothetical structure model proposed by Organova et al. (2002), an exchange of calcium by potassium may involve a higher degree of condensation of the silicate anions. In contrast, Kahlenberg (2025) recently demonstrated, that under dry synthesis conditions, cesium cations can substitute for the calcium ions inside the channel-like cavities of a clinotobermorite-related phase with composition Cs₂Si₄Si₆O₁₇ without causing a drastic re-arrangement of the surrounding network, which is formed by two characteristic structural elements: (i) bands of silicate tetrahedra and (ii) layers of well-defined [CaO_6-7]-polyhedra. Finally, Ferreira et al. (2003) and Zanardi et al. (2006) reported the hydrothermal synthesis of two tobermorite-like compounds (Na_2.16K_1.0Eu_2.28Si₆O₁₇·3.56H₂O and Na_2.7K_1.0Bi_2.25Si₆O₁₇·3H₂O), where the sodium ions are incorporated into the aforementioned layers, while the potassium cations occupy extra-framework positions.

The present contribution is the first to report on the synthesis and characterization of a rubidium-containing phase related to those of the tobermorite supergroup that was crystallized under hydrothermal conditions involving only Rb⁺, Ca²⁺, and Si⁴⁺ cations.

EXPERIMENTAL DETAILS

Synthesis

Single crystals were obtained by a hydrothermal synthesis route. The starting material for the experiments was a glass with a Rb₂O:CaO:SiO₂ molar ratio of 1:4:6 (or Rb₂Ca₄Si₆O₁₇), the preparation of which was based on the following educts: Rb₂CO₃ (Aldrich, 99.8%), CaCO₃ (calcite, Merck, >99.9%), and SiO₂ (quartz, AlfaAesar, 99.995%). Prior to weighing on an analytical balance, the reagents were dried at 300 °C for a period of 24 h. In addition to removing physically adsorbed water, this step is important because rubidium carbonate is known to be hygroscopic. The components were pre-homogenized with a spatula and then transferred to a 20 cm³ grinding jar of a planetary ball mill. Three 10 mm diameter agate grinding beads were added and the entire sample was covered with ethanol. Grinding was repeated three times for 15 min at 600 rpm. The slurry was then poured into an open glass laboratory bowl, dried for 24 h at 60 °C to completely evaporate the alcohol, and filled into a 50 ml platinum crucible, which was finally covered with a platinum lid. The container was heated in a box furnace in air from room temperature to 1300 °C at a rate of 6 °C/min and annealed for 60 min at the maximum temperature. The sample was removed from the furnace and quenched to ambient conditions by dipping the bottom of the crucible into a water bath. The glass that had formed was transparent and showed cracks as well as some trapped gas bubbles. The whole container was then stored in an evacuated dessicator. Weight loss was determined from the differences in mass before and after heating. The observed value was 0.4% greater than the predicted value (based on CO₂ release from the disintegration of the carbonates), indicating that losses due to evaporation of the Rb₂O component were small. After mechanical separation of the glass from the crucible, it was crushed in an agate mortar. Small fragments weighing approximately 25 mg in total were loaded into a gold capsule (3.8/4.0 mm inner/outer diameter and 30 mm long) together with 10 µl of a freshly prepared 2 M Rb₂CO₃ solution and welded shut. The high-P-T synthesis was performed in an externally heated Tuttle-type hydrothermal pressure vessel using water as the pressure medium. At room temperature, the sample was first pressurized to 500 bar and subsequently isobarically heated to 400 °C. After 14 days of operation, the sample was quenched to room conditions. Weighing of the sample before and after the experiment showed no evidence of capsule leakage. Following the opening of the capsule, the product was extracted with a micro pincer and a dissection needle, which was then analyzed using a polarizing binocular. The optical inspection revealed the presence of a larger number of transparent, colorless, and birefringent crystals (with a diameter of up to 120 µm) showing thin plate or lath-shaped morphology, along with a glassy optically isotropic matrix with conchoidal fracture. All the crystals exhibited a more or less distinct undulous extinction or even polysynthetic twinning under crossed nichols. Furthermore, a pronounced cleavage was observed when stress from a scalpel blade was applied. The more platy samples showed a tendency to fracture into needle-shaped fragments, suggesting that the structure contains chain-like structural motifs.

Chemical analysis

In the next step of characterization, we tried to determine the chemical composition of the crystals by electron microprobe analysis (EMPA) using a JEOL JXA8100 instrument operated with 15 kV acceleration voltage and 10 nA beam current. To prevent a possible hydration during sample preparation, the crystals were measured ‘as is’ without any additional polishing. Therefore, three crystals were mounted on double-sided sticky carbon tape and subsequently coated with carbon. An attempt was made to keep the prominent face of each platy crystal as parallel as possible to the surface of the adhesive tape. Due to the unavailability of appropriate Rb-standards for wavelength dispersive spectroscopy, an energy-dispersive analysis was performed, which yielded an average element ratio (normalized to 1 Rb atom) of Rb:Ca:Si = 1:2.45(7):3.60(3).

Single-crystal X-ray diffraction

A total of 10 crystal fragments with maximum diameters between 90 and 110 µm were mounted on the tip of thin glass fibers with epoxy resin and subsequently screened on a laboratory single-crystal diffractometer using MoKα radiation. However, the resulting diffraction patterns clearly showed the superposition of multiple reciprocal lattices with broad and partially overlapping reflections, thereby precluding the use of these samples for further structural analysis. Consequently, we finally decided to focus on the fraction of smaller crystals or fragments with maximum diameters of about 20-30 µm and to collect single-crystal diffraction data at the X06DA beamline of the Swiss Light Source, Paul Scherrer Institute, Villigen, Switzerland. The application of synchrotron radiation offers not only much higher photon fluxes when compared with laboratory instruments but also superior resolution which is a definite advantage when dealing with potentially intergrown samples. At last, a crystal was found that consisted of only two species with clearly separated reciprocal lattices. Both individuals could be indexed with the same type of unit cell (see below). As a result of the previously mentioned excellent spatial resolution, both diffraction patterns were virtually free from overlaps. For further analysis, we concentrated on the data set with higher average intensities. It is noteworthy, that many of the reflections of both species were still radially spread out.

Diffraction experiments were performed at 25 °C using the DA+ acquisition software (Wojdyla et al., 2018) and a Pilatus 2M-F detector in shutterless operation mode. The wavelength was adjusted to 0.70848 Å (= 17.5 keV). The detector was placed 80 mm from the sample without a vertical offset, resulting in a maximum resolution of 0.7 Å. 1800 frames were recorded using fine-sliced (0.1°) ω-scans with 0.1 s per frame. Table 1 contains a summary of the conditions pertaining to data collection. The CrysAlis^PRO software package (Rigaku Oxford Diffraction, 2020) was employed for indexing, integration, and data reduction including Lorentz and polarization as well as an empirical absorption correction based on spherical harmonics.

Table 1. Crystal data and structure refinement

Empirical formula	Rb1.71Ca4{Si6O15[O0.855(OH)0.145]2}2H2O
Formula weight	783.287
Temperature	293(2) K
Wavelength	0.70848 Å
Crystal system	monoclinic
Space group	P 21/m
Unit cell dimensions	a = 6.7766(4) Å	α = 90°
	b = 22.3162(10) Å	β = 114.056(7)°
	c = 6.7782(4) Å	γ = 90°
Volume	936.02(8) Å3
Z	2
Density (calculated)	2.772 Mg/m3
Absorption coefficient	6.05 mm−1
F(000)	763
Crystal size	9 × 23 × 28 µm3
Theta range for data collection	3.28 to 25.26°
Index ranges	−8 <= h <= 7, −26 <= k <= 25, −8 <= l <= 8
Reflections collected	4037
Independent reflections	1712 [R(int) = 0.0409]
Observed reflections [I > 2σ(I)]	1516
Completeness to theta = 25.26°	97.8%
Refinement method	Full-matrix least-squares on F2
Data / restraints / parameters	1712 / 0 / 163
Goodness-of-fit on F2	1.050
Final R indices [I > 2σ(I)]	R1 = 0.0727, wR2 = 0.2024
R indices (all data)	R1 = 0.0786, wR2 = 0.2080
Extinction coefficient	0.010(3)
Largest diff. peak and hole	1.375 and −0.947 e.Å−3

The diffraction pattern could be indexed with the following C-centered orthorhombic unit cell: a = 11.372, b = 7.377, and c = 22.316 Å. Additional non-integral systematic absences of the type 00l: l = 2n + 1 pointed the presence of a 2₁-screw axis parallel [001]. In the next step of data analysis, the reflections were merged in the orthorhombic Laue group mmm. The resulting internal residual R_int had a comparatively high value of 0.114. Therefore, a possible symmetry reduction was considered. In particular, merging the data in the monoclinic Laue symmetry 112/m gave a much lower R_int value of 0.043. The combination of these findings pointed to the presence of a twinning by pseudo-merohedry (Parsons, 2003), wherein the reciprocal lattices of two monoclinic pseudo-orthorhombic structures with space groups C 1 1 2₁ or C 1 1 2₁/m (non-standard settings) are superimposed. Provided that the twinning hypothesis is true, the observed value for R_int(mmm) indicates, that the volume fractions α and (1 − α) of the two twin domains in the crystal are significantly, but not extremely different from 0.5 each. Otherwise, the difference between R_int(mmm) and R_int(112/m) would be much more pronounced. The existence of twinning by merohedry or pseudo-merohedry can be verified by statistical tests, under the assumption that α ≠ 0.5 (Britton, 1972). Therefore, the program TWIN3.0 (Kahlenberg and Messner, 2001) was employed, where the procedure after Britton is implemented as one possible test option. A two-fold rotation axis 2_[010] was assumed to be the twin element. The test results confirmed the hypothesis of the presence of twinning by pseudo-merohedry, and the volume fractions for the two twin-related orientations were estimated to 0.33 and 0.67, respectively.

In order to avoid dealing with non-standard settings of space groups, we finally decided to continue our analysis with a data set transformed to a monoclinic primitive cell (second setting) with half the volume. The corresponding transformation matrix from the C-centered to the new primitive cell is as follows:

  

\begin{equation*} \begin{pmatrix} \boldsymbol{a}_{P} & \boldsymbol{b}_{P} & \boldsymbol{c}_{P} \end{pmatrix} = \begin{pmatrix} \boldsymbol{a}_{C} & \boldsymbol{b}_{C} & \boldsymbol{c}_{C} \end{pmatrix} \cdot \begin{pmatrix} -\text{½} & 0 & \text{½} \\ \text{½} & 0 & \text{½} \\ 0 & 1 & 0 \end{pmatrix} \end{equation*}

The resulting transformed lattice parameters are a = 6.777, b = 22.316, c = 6.777 Å, β = 114.06°. With respect to the new setting, the twin element corresponds to 2_[101]. After indexing in the new monoclinic primitive cell, the diffraction pattern was re-integrated.

Structure solution was initiated in space group P 1 2₁/m 1 using direct methods (program SIR2004, Burla et al., 2005). A partial model containing the Si-, Ca-, and the O-atoms was obtained, which was subsequently refined by least-squares calculations (program SHELXL-97, Sheldrick, 2015). The scattering curves and anomalous dispersion coefficients were obtained from the International Tables for Crystallography, Vol. C (Prince, 2004). The examination of the resulting difference Fourier map revealed the presence of four additional maxima of electron density, located on the mirror planes within the tunnel-like cavities of the structure. While the distances between the individual maxima and the surrounding oxygen atoms were acceptable for Rb-O bonds (Gagné and Hawthorne, 2016), the distances between some of them were as low as 1.88, 1.98, or 2.46 Å. The simultaneous full occupation of all these positions by Rb-atoms is therefore mutually exclusive.

Extending the model to an anisotropic description of the thermal motion of the atoms and including a Larson-type extinction correction resulted to a residual of R1 = 0.156 (162 parameters). Upon introducing the aforementioned twin model and the volume fraction α of the smaller domain as an additional parameter, the calculations converged to R1 = 0.0727. The largest shift/esd in the final cycles was <0.001. Notably, α was refined to 0.311(5), which is in good agreement with the value estimated from the a priori statistical test. Final unconstrained site population refinements indicated rubidium occupancies on the four positions between 33 and 57%. The resulting total Rb content corresponds to 3.42(2) atoms per unit cell.

Additional information regarding data collection and refinement parameters can be found in Table 1. Table 2 presents the fractional atomic coordinates, along with equivalent isotropic displacement factors. Anisotropic displacement factors and selected bond distances and bond angles, as well as polyhedral distortion parameters for the [SiO₄]-tetrahedra, are reported in Tables 3 and 4, respectively. The distortion parameters (quadratic elongation: QE, angle variance: AV) were evaluated according to Robinson et al. (1971). The parameter sets of Gagné and Hawthorne (2015) for Ca-O, Si-O, and Rb-O interactions were employed to calculate bond valence sums (BVS), which are summarized in Table 5. Figures showing structural features were prepared using the program VESTA3 (Momma and Izumi, 2011). For the illustration of the three-dimensional representation surface of the compositional strain tensor the program WinTensor, version 1.5 was employed (Kaminsky, 2014).

Table 2. Atomic coordinates (×10⁴) and equivalent isotropic displacement parameters (Ų × 10³) for Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O

	Wyckoff-position	Occupancy (%)	x	y	z	U(eq)
Ca1	4f		5042(3)	5413(1)	2510(3)	27(1)
Ca2	4f		102(3)	5501(1)	7405(3)	26(1)
Si1	4f		1804(5)	8217(1)	5766(5)	24(1)
Si2	4f		9718(4)	9086(1)	2049(5)	25(1)
Si3	4f		5538(5)	9047(1)	7888(5)	24(1)
O1	2e		1820(20)	7500	5530(30)	55(4)
O2	4f		8863(12)	9489(3)	3472(14)	26(2)
O3	4f		7685(10)	8808(3)	9920(12)	29(2)
O4	4f		6199(13)	9425(3)	6223(14)	29(2)
O5	4f		4043(11)	9449(3)	8681(14)	28(2)
O6	4f		1293(14)	9460(4)	1256(15)	39(2)
O7	4f		868(14)	8472(4)	3286(13)	42(2)
O8	4f		4336(12)	8402(3)	6826(13)	35(2)
O9	4f	14.5 OH and 85.5 O	482(13)	8437(3)	7072(15)	41(2)
O10	4f	100 H2O	4820(30)	6650(5)	2450(30)	56(7)
Rb1	2e	57.2(10)	7045(11)	7500	757(9)	100(3)
Rb2	2e	32.6(8)	8646(14)	7500	9050(15)	66(3)
Rb3	2e	46.4(8)	6761(6)	7500	5080(8)	59(2)
Rb4	2e	34.8(10)	1834(17)	7500	584(15)	98(4)

U(eq) is defined as one third of the trace of the orthogonalized U_ij tensor. Unless otherwise specified, all positions are fully occupied. O9 is a mixed anion position containing O²⁻ and (OH)-groups. O10 corresponds to a water molecule.

Table 3. Anisotropic displacement parameters (Ų × 10³) for Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O

	U11	U22	U33	U23	U13	U12
Ca1	13(1)	38(1)	28(2)	−1(1)	7(1)	2(1)
Ca2	14(1)	32(1)	31(2)	2(1)	8(1)	0(1)
Si1	23(1)	17(1)	31(2)	1(1)	10(1)	0(1)
Si2	17(1)	31(2)	27(2)	1(1)	9(1)	1(1)
Si3	18(1)	30(1)	25(2)	−2(1)	8(1)	−2(1)
O1	51(8)	4(4)	111(14)	0	36(8)	0
O2	19(4)	22(3)	33(5)	−1(3)	5(3)	2(3)
O3	16(3)	31(4)	35(5)	−1(3)	4(3)	0(3)
O4	25(4)	33(4)	31(5)	9(4)	15(3)	8(4)
O5	11(3)	31(3)	40(5)	−7(3)	8(3)	−6(3)
O6	23(4)	65(5)	29(5)	1(4)	12(3)	−16(4)
O7	48(5)	48(5)	23(4)	5(4)	8(4)	25(4)
O8	29(4)	35(4)	40(5)	−11(3)	13(3)	−7(3)
O9	36(4)	37(4)	67(7)	7(4)	38(4)	3(4)
O10	94(16)	19(5)	102(19)	12(8)	89(16)	6(8)
Rb1	181(7)	33(2)	95(4)	0	67(4)	0
Rb2	95(6)	34(3)	95(6)	0	66(5)	0
Rb3	36(2)	64(3)	77(4)	0	25(2)	0
Rb4	128(9)	107(7)	75(6)	0	59(6)	0

The anisotropic displacement factor exponent takes the form: −2π²[h²a*²U₁₁ + … + 2 h k a* b* U₁₂].

Table 4. Selected bond lengths (Å) and angles (°) for Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O

Bond distances
Ca1-O4	2.338(9)	Ca1-O6	2.345(8)
Ca1-O2	2.409(8)	Ca1-O5	2.421(9)
Ca1-O5	2.464(7)	Ca1-O4	2.625(7)
Ca1-O10	2.764(11)
Ca2-O6	2.400(9)	Ca2-O9	2.404(8)
Ca2-O4	2.437(8)	Ca2-O2	2.447(9)
Ca2-O5	2.452(7)	Ca2-O2	2.508(6)
Ca2-O6	2.796(9)
Si1-O9	1.573(7)	Si1-O1	1.609(3)
Si1-O8	1.620(8)	Si1-O7	1.638(8)
<Si1-O>	1.613
QE	1.004	AV	18.67
Si2-O2	1.590(7)	Si2-O6	1.609(7)
Si2-O7	1.629(8)	Si2-O3	1.657(8)
<Si2-O>	1.632
QE	1.005	AV	20.12
Si3-O5	1.601(7)	Si3-O4	1.613(7)
Si3-O3	1.632(7)	Si3-O8	1.665(8)
<Si3-O>	1.631
QE	1.005	AV	21.34
Rb1-O10	2.934(10) x 2	Rb1-O3	3.038(7) x 2
Rb1-O8	3.246(9) x 2	Rb1-O7	3.277(10) x 2
Rb2-O9	3.013(8) x 2	Rb2-O3	3.099(7) x 2
Rb2-O8	3.357(11) x 2	Rb2-O7	3.420(11) x 2
Rb3-O10	2.568(16) x 2	Rb3-O8	3.121(9) x 2
Rb3-O9	3.127(9) x 2	Rb3-O1	3.317(13)
Rb3-O1	3.482(13)
Rb4-O10	2.685(16) x 2	Rb4-O9	3.017(10) x 2
Rb4-O7	3.077(9) x 2	Rb4-O1	3.354(18)
Rb4-O1	3.425(18)
Bond angles
O9-Si1-O1	113.3(6)	O9-Si1-O8	114.4(5)
O1-Si1-O8	104.4(6)	O9-Si1-O7	113.4(5)
O1-Si1-O7	105.0(7)	O8-Si1-O7	105.3(4)
O2-Si2-O6	111.4(4)	O2-Si2-O7	112.3(4)
O6-Si2-O7	111.3(5)	O2-Si2-O3	111.1(4)
O6-Si2-O3	109.4(5)	O7-Si2-O3	100.8(4)
O5-Si3-O4	109.6(4)	O5-Si3-O3	111.6(4)
O4-Si3-O3	110.8(4)	O5-Si3-O8	111.4(4)
O4-Si3-O8	112.1(5)	O3-Si3-O8	101.2(4)
Si1-O1-Si1	168.1(11)	Si3-O3-Si2	138.7(5)
Si2-O7-Si1	136.4(5)	Si1-O8-Si3	130.9(5)

QE, quadratic elongation; AV, angle variance.

Table 5. Bond-valence calculations in valence units (v.u.) for Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O

Site	Ca1	Ca2	Si1	Si2	Si3	Rb1	Rb2	Rb3	Rb4	Σ
O1			1.04×1↓×2→				0.03,0.02	0.02,0.02		2.17
O2	0.29	0.27,0.23		1.09						1.88
O3				0.92	0.98	0.06×2↓×1→	0.03×2↓			1.99
O4	0.35,0.17	0.27			1.03					1.82
O5	0.28,0.26	0.26			1.06					1.87
O6	0.34	0.30,0.11		1.04						1.80
O7			0.96	0.99		0.04×2↓×1→	0.02×2↓×1→		0.04×2↓×1→	2.04
O8			1.01		0.90	0.04×2↓×1→	0.02×2↓×1→	0.04×2↓×1→		2.01
O9=(O,OH)		0.30	1.14				0.04×2↓×1→	0.04×2↓×1→	0.04×2↓×1→	1.56
O10=H2O	0.12					0.08×2↓×1→		0.14×2↓×1→	0.08×2↓×1→	0.42
Σ	1.82	1.74	4.15	4.04	3.97	0.45	0.21	0.50	0.35

Percentages refer to the occupancy of the Rb-sites as determined by structure analysis. They have been used as weighting factors for the contributions of the rubidium ions.

RESULTS

The crystal structure of the present compound belongs to the group of band silicates. According to Liebau’s crystal chemical classification the compound can be described as an unbranched dreier double chain silicate (Liebau, 1985). The bands run parallel to [101] and are formed by the condensation of two wollastonite-type single-chains with translation periods of 7.377 Å (see Figs. 1 and 2). The mean plane of the double chains defined by the Si atoms is parallel to (−1 0 1). Similar chains have been encountered in the crystal structures of tobermorite-11Å, clinotobermorite or xonotlite, for example (Biagioni et al., 2015). In more detail, the double-chains are located on mirror planes m_[010] at y = ¼ and y = ¾. They contain one tertiary (Q³, Si1) and two binary (Q², Si2 and Si3) tetrahedra. Linkage between the individual chains is provided by the oxygen atoms O1 residing on the special Wyckoff-position 2e. Moreover, the bands enclose eight-membered rings of silicate tetrahedra in ddssddss or uussuuss conformation (d: down, u: up, s: side). The ellipticity e of the rings, defined as the ratio between the minimum and maximum diameters of the rings, has a value of 0.79 (see Fig. 1).

Figure 1. Graphical representation of a single dreier double chain of silicate tetrahedra in Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O. The chain is illustrated in a projection perpendicular to its direction. Oxygen atoms are shown as red spheres. [SiO₄]-tetrahedra are presented in blue.

Figure 2. Graphical representation of a single dreier double chain of silicate tetrahedra in Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O. The chain is illustrated in a projection parallel to its direction. Oxygen atoms are shown as red spheres. [SiO₄]-tetrahedra are presented in blue.

Each of the three silicon atoms resides on a general Wyckoff-position. The individual Si-O bond distances vary between 1.573 and 1.665 Å, falling within the normal range observed for oxosilicate structures (Liebau, 1985). The shortest bond distances occur between silicon and the non-bridging oxygen atoms (O2, O4, O5, O6, O9). This phenomenon can be explained by the stronger attraction of the oxygen atoms to the silicon atoms than to the other surrounding cations (Ca, Rb) and has been encountered in numerous crystalline silicates (Liebau, 1985). The distortion of the tetrahedra is also reflected in the O-Si-O angles, which range from 100.8 to 114.4°, respectively. It is noteworthy, that the distortion parameters QE and AV of the three symmetrically independent tetrahedra exhibit comparatively small values, and that the differences between the binary and tertiary [SiO₄]-groups are not very pronounced. Most of the inter-tetrahedral Si-O-Si angles vary between 130 and 139°. They are slightly lower than the value of 140° that is assumed to correspond to an unconstrained Si-O-Si angle (Liebau, 1985). In contrast, the value occurring at the O1 atom connecting the two wollastonite chains is significantly larger (168°).

The stretching factor f_S (Liebau, 1985) is a convenient measure of the deviation of silicate chains from linearity. It is defined as follows: f_S = l_c/(l_T·P). In this equation, l_c denotes the translation period along the chain, l_T denotes the length of the edge of a tetrahedron (both in Å), and P is the periodicity of the chain (in this case: P = 3). A reference value of 2.7 Å has been proposed for l_T, which is derived from the chains observed in the mineral shattuckite {Cu₅[Si₂O₆(OH)]₂}, which have the most stretched chains observed to date. For the chains in the present compound, a value of f_S = 0.911 can be calculated.

The two calcium cations within the asymmetric unit are coordinated by seven ligands each (see Table 4). Site population refinements indicated full occupancy of the corresponding sites. Very similar coordination environments for Ca²⁺ have been observed, for example, in several members belonging to the tobermorite supergroup of minerals (Biagioni et al., 2015). In particular, Hoffmann and Armbruster (1997) described these polyhedra that occur in clinotobermorite as being composed of ‘a pyramidal part on one side and a dome part on the other side joining the equatorial oxygen atoms’. Although it is not absolutely correct, the polyhedra could also be designated as distorted monocapped trigonal prisms. By sharing common edges parallel to [1 0 −1], the strictly alternating [Ca1X₇]- and [Ca2X₇]-groups (X: O²⁻, OH⁻, H₂O) are connected into rows running along [101] (see Fig. 3), where the ‘apical’ ligands all point to the same side. It is noteworthy, that the individual rows show a pseudo translation along [101] with a magnitude of approximately 3.69 Å, which corresponds to half of the translation period along this direction. All Ca-X bond distances have values below 2.8 Å. A detailed description of the assignment of the individual nature for each of the symmetrically independent X-sites will be presented in the following Discussion section. In the next step of condensation neighboring rows are linked into layer-like units parallel to (010) (see Fig. 3). Within a single layer, each Ca-centered polyhedron shares six edges with its direct neighbors.

Figure 3. Side view of a single layer of edge-sharing CaX₇-polyhedra around Ca1 (blue) and Ca2 (red), respectively. Small spheres represent oxygen atoms (red), mixed oxygen/hydroxyl containing sites (light green) and water molecules (light blue).

Adjacent layers are connected by the silicate ribbons, resulting in a negatively charged heteropolyhedral network. In more detail, the capping ligands of the monocapped prisms around Ca2 also belong to the [SiO₄]-tetrahedra around Si1. Furthermore, the remaining two symmetrically independent tetrahedra each share one edge with the CaX₇-polyhedra. This means that the length of these specific edges is constrained by the dimensions of the rigid tetrahedral units. Consequently, these edges have the smallest values.

The rubidium atoms are distributed among a total of four partially occupied extra-framework positions. All of them are located on the mirror planes at y = ¼ and y = ¾ running through the central parts of the channels. They are coordinated by eight ligands each (see Figs. 4a to 4d). These ‘soft’ cations occupy voids of variable size offered by the silicate double chains and the layers of the CaX₇-groups. They provide additional direct linkage between neighboring silicate ribbons and the adjacent Ca-containing sheets. While the <Rb-X> bonds for Rb3 and Rb4 compare well with the average data for Rb^[8]-O bonds given by Gagné and Hawthorne (2016), the corresponding values for Rb1 and Rb2 are larger by about 0.1 and 0.2 Å, respectively. A projection of the whole crystal structure parallel to [101] is shown in Figure 5a.

Figure 4. Coordination environments of the four symmetrically independent rubidium positions (a)-(d) Rb1-Rb4.

Figure 5. Projections of (a) Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O and (b) paratobermorite (Pekov et al., 2022) parallel to the directions of the dreier double chains. The partially occupied Rb- and Ca-positions within the channels are presented in pink and dark green, respectively. Water molecules are shown in light blue. Bicolored spheres indicate partially vacant sites. The sizes of the colored segments refer to the percentages as determined from the site-occupancy refinements.

DISCUSSION

The BVS data for the three silicon atoms are very close to the expected value of 4 valence units (v.u.). Both calcium cations show slightly larger (negative) deviations from the expected value of 2 v.u. This ‘underbonding’ suggests that the Ca-ions are a little bit too small for their coordination environments. Similar trends have been observed for other members of the tobermorite supergroup, where the calcium atoms reside in the center of identical [CaX₇]-polyhedra (Merlino et al., 1999; Pekov et al., 2022).

The final assignment of the symmetrically independent O-sites to O²⁻-ions, (OH)-groups, or water moieties included the results of BVS calculations (see Table 5). It should be noted at this point, that previous site population refinements based on oxygen atoms indicated full occupancies for all ten anion positions. The majority of the oxygen sites exhibit sums which conform to the theoretical 2.0 v.u. within ±10%. However, O9 (BVS = 1.56 v.u.) and particularly O10 (BVS = 0.42 v.u.) show significantly lower values. While O9 belongs to the tetrahedron around Si1, O10 is only bonded to Ca1 as well as to the Rb-cations inside the tunnel-like cavities. We interpret this result as a strong indication that O10 actually corresponds to a H₂O position. BVS values ranging from 0.40 to 0.44 v.u. for the oxygen atoms of water molecules (without considering the contributions of the hydrogens) have been already documented, as evidenced in the case of lakebogaite [CaNaFe₂³⁺H(UO₂)₂(PO₄)₄(OH)₂(H₂O)₈, Mills et al., 2008], zemannite [Mg_0.5ZnFe³⁺(Te⁴⁺O₃)·3(3 + n)H₂O, Missen et al., 2019], or jonesite {Ba₂(K,Na)[Ti₂(Si₅Al)O₁₈(H₂O)](H₂O)_n, Krivovichev and Armbruster, 2004}. O9, on the other hand, is likely to represent a partially hydroxylated anion site where oxygen anions and hydroxyl groups share the same position. It is noteworthy that the pronounced disorder of the structure resulted in unsuccessful efforts to locate the missing hydrogen positions from a difference Fourier map.

The 3.42(2) Rb, 8 Ca, and 12 Si cations inside the unit cell represent a total of 67.42 positive charges. Therefore, achieving a charge-neutral composition would require substituting 14.5% of the oxygen atoms at the O9 position with (OH)-groups. The existence of silanol [Si-(OH)] groups in the tetrahedra of various tobermorite-related phases has been described by Merlino et al. (1999, 2000), for example.

In summary, we suggest the following idealized chemical formula for the compound under investigation: Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O or Rb_1.71Ca₄Si₆O_16.71(OH)_0.292H₂O (Z = 2). According to the recommendation of Biagioni et al. (2015), which separates the framework and the extra-framework part of structures, the corresponding structural chemical formula can be written as {Ca₄Si₆O₁₅[O_0.855(OH)_0.145]₂}·(Rb_1.71·2H₂O).

The resulting element ratio of the cations of 1.71:4:6 or 1:2.34:3.51 (normalized) is in satisfactory agreement with the outcome of the EDX analysis.

Merlino and Bonaccorsi (2008) as well as Kahlenberg (2025) compared dreier double chains that have been observed in several members of the tobermorite supergroup of minerals and other natural silicates. The sequence of directedness of the tetrahedra within the eight-members rings, the ellipticity of the rings, as well as the degree of corrugation of the bands in Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O are very similar to features encountered in Al-free tobermorite-11Å [Ca_4+xSi₆O_15+2x(OH)_2−2x·5H₂O with 0 ≤ x ≤ 1, Biagioni et al., 2015] or in natural paratobermorite [Ca₅(Al_0.5Si_0.5)₂Si₄O₁₆(OH)·5H₂O, Pekov et al., 2022]. Moreover, these two phases contain similar networks formed by the abovementioned tetrahedral chains and layers of [CaX₇]-polyhedra.

The structural relationship between the present phase and paratobermorite (PM) is particularly interesting, because both compounds adopt the same monoclinic space group type with comparable lattice parameters: a_PM = 6.7149(2), b_PM = 22.9441(8), c_PM = 6.7162(3) Å, β = 113.358(4)°. If the fact that one of the tetrahedra in paratobermorite exhibits a disorder is neglected, the networks in both compounds can be analyzed using the program COMPSTRU (de la Flor et al., 2016). First, the sub-structure including the [SiO₄]-tetrahedra and [CaX₇]-polyhedra in paratobermorite was transformed into the most similar configuration of the present compound. Subsequently, the shifts between the relevant atom pairs in both structures were calculated. The results are summarized in Supplementary Table S1 (Supplementary Table S1 is available online from https://doi.org/10.2465/jmps.250415). Since the atoms were labelled differently, this table also simplifies the identification of the corresponding atoms. The calculations revealed that the displacements range from 0.054 Å (Ca1) to 0.334 Å (O10). The arithmetic mean of the differences between the atomic positions of matching atoms is 0.145 Å. In summary, it can be noted that the mixed polyhedral frameworks in both compounds are isostructural.

The main structural difference between paratobermorite and the present compound is due to the charge compensating extra-framework cations in the central part of the wide channels. In paratobermorite, only two partially occupied calcium sites located off the mirror planes provide the required positive charges. Additionally, five water positions (50% occupancy) are located on the m planes, which contribute to the coordination environment of the aforementioned Ca cations. It is precisely these water molecules that are absent in the Rb-containing compound (see Figs. 5a and 5b).

A closer look at the individual lattice parameters in Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O and paratobermorite reveals two opposing trends. While the b-axis direction in the Rb-phase decreases by about 0.63 Å, the c-axis and the a-axis both increase by 0.06 Å. This indicates an extremely anisotropic response of the frameworks to the different ions and/or molecules occupying the tunnel-like cavities. Additionally, the β-angle increases by about 0.7°.

Not surprisingly, for low symmetry compounds a complex interplay between chemical composition and structural changes related to individual deformations of the coordination polyhedra is to be expected. To obtain a more holistic picture of the distortion patterns, the evaluation of the so-called compositional strain tensor can be a helpful tool. The derivation of the components of this second-rank tensor from two sets of lattice parameters corresponding to two different compositions of (almost) isostructural phases has been described by Ohashi and Burnham (1973) as well as Kahlenberg et al. (2021), for example. The necessary calculations were performed with the program Win_Strain 4.11 (Angel, 2011). Using a finite Eulerian strain formalism referred to an orthonormal coordinate system {x, y and z} with z // c, x // a* and y = z × x, the following components of the 3 × 3 matrix for the compositional strain tensor $\varepsilon_{ij}^{\text{C}}$ were derived: $\varepsilon_{11}^{\text{C}}$ = −0.00372(9); $\varepsilon_{22}^{\text{C}}$ = 0.02774(6); $\varepsilon_{33}^{\text{C}}$ = 0.00919(7); $\varepsilon_{12}^{\text{C}}$ = 0; $\varepsilon_{13}^{\text{C}}$ = 0.00607(7) and $\varepsilon_{23}^{\text{C}}$ = 0. The superscript ‘C’ refers to the compositional character of the strain. With respect to the Cartesian coordinate system of the principal axes {e₁, e₂ and e₃}, the following three principal strains are obtained: $\varepsilon_{1}^{\text{C}}$ = −0.01311(7); $\varepsilon_{2}^{\text{C}}$ = 0.0002(1); $\varepsilon_{3}^{\text{C}}$ = 0.02774(6) indicating an extreme anisotropy of the compositional strain. In fact, $\varepsilon_{2}^{\text{C}}$ is almost negligible, that is, the compositionally induced strain is nearly planar. With the help of the symmetrical $\varepsilon_{ij}^{\text{C}}$ tensor, the relevant strain values can be calculated for any direction defined by a vector q whose three components are the direction cosines q₁, q₂, and q₃, i.e., the cosines of the angles between q and the three axes of the Cartesian reference system. By plotting the individual values as a function of q, one obtains a geometric representation of the tensor in form of a surface in three-dimensional space. As illustrated in Figure 6, the visualization of the corresponding surface provides concise information about the distribution of expanding and shrinking directions, when the present compound as the reference state is compared with paratobermorite.

Figure 6. Representation surfaces of the compositional strain tensor determined from the comparison between the lattice parameters of Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O and paratobermorite. The surface plot is referred to principal axes. While the e₃-direction coincides with b, e₂ and e₃ differ from a and c of the monoclinic coordinate system. Blue and red colored parts of the surface represent regions of positive and negative values.

As can be anticipated for the monoclinic crystal system, only one principal axis is related to the directions of the crystallographic coordinate system along a, b, and c. Using the aforementioned program Win_Strain, the following angles between the eigenvectors and the crystallographic axes have been derived. The values given in parentheses refer to the corresponding angles with a, b, and c, respectively: e₁: (146.2°; 90°; 32.9°); e₂: (123.8°; 90°; 122.9°); e₃: (90°; 180°; 90°). Finally, the components of the principal axes in the crystallographic coordinate system have been calculated and the corresponding vectors analyzed together with specific elements of the structure using the program VESTA3 (Momma and Izumi, 2011). The direction of the largest (positive) principal axis of expansion ($\varepsilon_{3}^{\text{C}}$) is perpendicular to the layers containing the CaX₇-polyhedra. The negative eigenvalue $\varepsilon_{1}^{\text{C}}$ corresponds to the direction perpendicular to the mean plane of the of the dreier double chains. The expansion along e₃ is about twice as large as the shrinkage along e₁. The strain along the chains ($\varepsilon_{2}^{\text{C}}$) is almost negligible, reflecting the very rigid character of the silicate units parallel to the bands with respect to the extra-framework content.

A different understanding of the structural connections between tobermorite-11Å, paratobermorite and the compound under investigation can be obtained from the application of concepts related to order-disorder (OD) theory. It is known that tobermorite presents OD character and displays a sequence of structural layers exhibiting C2m(m) symmetry (one of the 80 possible layer groups). These layers have translation vectors a and b, along with a third vector c₀ (not a translation vector). The values for the magnitudes of these vectors are a = 11.3, b = 7.35, and c₀ = 11.3 Å) (see also Fig. 1 in Merlino et al., 2000).

The fundamental principles of OD theory are outlined in the Appendix of the paper by Merlino and Bonaccorsi (2008) and will not be repeated here. According to OD theory, for a layer with C2m(m) symmetry, there exist two distinct possible sets of σ-operations (i.e., operations that relate adjacent layers) that are compatible with the symmetry operations of the single layer (λ-operations) (Dornberger-Schiff, 1964; Dornberger-Schiff and Fichtner, 1972; Ferraris et al., 2004). The two sets can be denoted as follows:

$\begin{matrix} \begin{matrix} C & 2 \end{matrix} & \begin{matrix} m & (m) \end{matrix} \\ \begin{matrix} & \{2_{s} \end{matrix} & \begin{matrix} n_{2,s} & n_{s,r}\} \end{matrix} \end{matrix}$

$\begin{matrix} \begin{matrix} C & 2 \end{matrix} & \begin{matrix} m & (m) \end{matrix} \\ \begin{matrix} & \{n_{r,2} \end{matrix} & \begin{matrix} 2_{r} & (2_{2})\} \end{matrix} \end{matrix}$

The first configuration, characterized by values of ½ for both s and r parameters, yields the OD family symbol

  

\begin{equation*} \begin{array}{llll} C & \phantom{\{}2 & m & (m) \\ & \{2_{\text{½}} & n_{2,\text{½}} & (n_{\text{½},\text{½}})\} \end{array} \end{equation*}

This result enables the derivation of the real structure of tobermorite and the definition of its two primary polytypes (maximum degree of order or MDO-structures). A detailed discussion of the procedure can be found in Merlino et al. (1999, 2000) and Biagioni et al. (2015). Merlino and Bonaccorsi (2008) investigated the second distinct set of σ-operations, that are compatible with the layer group symmetry C2m(m). By setting r = ½, a new OD groupoid family was derived:

  

\begin{equation*} \begin{array}{llll} C & 2 & m & (m) \\ & \{n_{\text{½},2} & 2_{\text{½}} & (2_{2})\} \end{array} \end{equation*}

The layers that follow each other are related by [n_½,2 - -] or [n_−½,2 - -]. Ordered sequences of the two operations give rise to various possible polytypes. It was found that the new family of OD structures also presents two main polytypes. The first one, MDO₁, is obtained through the constant application of the σ-operation n_½,2 normal to a, namely [n_½,2 - -]. This polytype conforms to the non-standard space group F2/d11, with a = 11.3, b = 7.35, c = 45.2 Å, α = 90° (parameters are estimated from those given above for the structural layer of tobermorite). The other main polytype, MDO₂, is obtained through the regular alternation of the operations [n_½,2 - -] and [n_−½,2 - -], resulting in a translation c = 2·c₀. The C-centering and the symmetry plane [- - m] of the layer are now valid operations for the entire structure (total operations). [- - 2₂] becomes a total operation 2₁ parallel to c in a structure presenting the non-standard space group C 1 1 2₁/m, with a = 11.3, b = 7.35, c = 22.6 Å, γ = 90°. The unit cell dimensions, space group, and structural arrangement of the MDO₂ polytype closely correspond to those reported for paratobermorite, as well as to those of the initial pseudo-orthorhombic cell found for the present compound. After applying of the transformation matrix mentioned in the diffraction section of this paper, one obtains the monoclinic P cell that was finally employed for the structural description of paratobermorite and for Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}(H₂O)₂.

CONCLUDING REMARKS

The present contribution exemplifies the predictive power of OD-theory. It is noteworthy, that the principal structure arrangement realized in Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O and in paratobermorite was first suggested as a hypothetical model (Merlino and Bonaccorsi, 2008). This result was achieved by exploiting the benefits of a full description of the underlying layers and their structural parameters in terms of the concepts of order-disorder theory.

We are aware of the fact that the final residual value obtained during the refinements (R|F| = 0.073) is inferior to the results that can normally be obtained with crystals of sufficient quality. Unfortunately, such a sample was not available in this specific case. In addition, compounds of the tobermorite-supergroup are notoriously known to exhibit a rather poor, strongly disturbed long-range order due to their OD character. In this respect, the above-mentioned R value is quite comparable with those of other studies, some of which also had synchrotron diffraction data available, such as paratobermorite [R(|F|) = 0.084, laboratory data, Pekov et al., 2022] or the MDO₁ and MDO₂ polytypes of tobermorite-11Å [R(|F|) = 0.128, 0.089, and 0.110, laboratory data and synchrotron radiation, Merlino et al., 2000]. Moreover, the exclusion of the hydrogen atoms from the model (see above) will be reflected in a higher residual as well.

Notably, the recently synthesized crystal structure of Cs₂Ca₄Si₆O₁₇ (Kahlenberg, 2025) which is closely related to clinotobermorite, formed crystals of excellent quality without exhibiting the ‘problematic’ diffraction features usually observed for other tobermorite-like phases. This observation can be explained by the presence of two different types of Ca-centered polyhedra within the layers. Specifically, the CaO₆ - and CaO₇ - units alternate strictly along the rows, from which the layers are formed. Consequently, the aforementioned pseudo translational symmetry observed in Rb_1.71Ca₄{Si₆O₁₅[O_0.855(OH)_0.145]₂}2H₂O is broken, which is a pre-requisite for the formation of OD-structures.

This finding also highlights the structural importance of the presence (or absence) of different types of anions/molecules on the apical positions of the calcium polyhedra. Future research activities should include synthesis experiments under dry conditions to test whether or not a phase with the nominal composition Rb₂Ca₄Si₆O₁₇ exists.

ACKNOWLEDGMENTS

The authors thank the staff members of beamline X06DA at the Paul Scherrer Institute (Swiss Light Source) for assistance in data collection.

SUPPLEMENTARY MATERIAL

Supplementary Table S1 is available online from https://doi.org/10.2465/jmps.250415.

REFERENCES

• Angel, R.J. (2011) Win_Strain 4.11 https://www.rossangel.com/home.htm, accessed 3rd November 2020.
• Anthony, J.W., Bideaux, R.A., Bladh, K.W. and Nichols, M.C. (1995) Handbook of Mineralogy, Volume II, Part 2 Silica, Silicates. pp. 904, Mineral Data Publishing, Tucson, Arizona, USA.
•  Biagioni,  C.,  Merlino,  S. and  Bonaccorsi,  E. (2015) The tobermorite supergroup: a new nomenclature. Mineralogical Magazine, 79, 485-495.
•  Bonaccorsi,  E. and  Merlino,  S. (2005) Modular microporous minerals: cancrinite - davyne group and C-S-H phases. Reviews in Mineralogy and Geochemistry, 57, 241-290.
•  Britton,  D. (1972) Estimation of twinning parameter for twins with exactly superimposed reciprocal lattices. Acta Crystallographica, A28, 296-297.
•  Burla,  M.C.,  Caliandro,  R.,  Camalli,  M.,  Carrozzini,  B., et al (2005) SIR2004: an improved tool for crystal structure determination and refinement. Journal of Applied Crystallography, 38, 381-388.
•  Coleman,  N.J. (2005) Synthesis, structure and ion exchange properties of 11 Å tobermorites from newsprint recycling residue. Materials Research Bulletin, 40, 2000-2013.
•  de la Flor,  G.,  Orobengoa,  D.,  Tasci,  E.,  Perez-Mato,  J.M. and  Aroyo,  M.I. (2016) Comparison of structures applying the tools available at the Bilbao Crystallographic Server. Journal of Applied Crystallography, 49, 653-664.
• Dornberger-Schiff, K. (1964) Grundzüge einer Theorie von OD-Strukturen aus Schichten. Abhandlungen der Deutschen Akademie der Wissenschaften zu Berlin Klasse für Chemie, Geologie und Biologie, 3, 1-107.
•  Dornberger-Schiff,  K. and  Fichtner,  K. (1972) On the symmetry of OD structures consisting of equivalent layers. Kristall und Technik, 7, 1035-1056.
• Ferraris, G., Makovicky, E. and Merlino, S. (2004) Crystallography of modular materials. pp. 370, Oxford University Press, New York.
•  Ferreira,  A.,  Ananias,  D.,  Carlos,  L.D.,  Morais,  C.M. and  Rocha,  J. (2003) Novel microporous Lanthanide silicates with tobermorite-like structure. Journal of the American Chemical Society, 125, 14573-14579.
•  Gagné,  O.C. and  Hawthorne,  F.C. (2015) Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen. Acta Crystallographica, B71, 562-578.
•  Gagné,  O.C. and  Hawthorne,  F.C. (2016) Bond-length distributions for ions bonded to oxygen: alkali and alkaline-earth metals. Acta Crystallographica, B72, 602-625.
•  Hoffmann,  C. and  Armbruster,  T. (1997) Clinotobermorite, Ca₅[Si₃O₈(OH)₂]·4H₂O-Ca₅[Si₆O₁₇]·5H₂O, a natural C-S-H(I) type cement mineral: determination of the substructure. Zeitschrift für Kristallographie, 212, 864-873.
•  Ige,  O.E.,  Kallon,  D.V.V. and  Desai,  D. (2024) Carbon emissions mitigation methods for cement industry using a systems dynamic model. Clean Technologies and Environmental Policy, 25, 579-597.
•  Kahlenberg,  V. (2025) Clinotobermorite-related Cs₂Ca₄Si₆O₁₇ - the first cesium calcium Silicate. Mineralogy and Petrology. doi:10.1007/s00710-025-00918-0.
•  Kahlenberg,  V. and  Messner,  T. (2001) TWIN3.0 - a program for testing twinning by merohedry. Journal of Applied Crystallography, 34, 405.
•  Kahlenberg,  V.,  Krüger,  H. and  Tribus,  M. (2021) Structural systematics of SFCA-I type solid-solutions in the system CaO-Fe₂O₃-FeO-Al₂O₃. Physics and Chemistry of Minerals, 48, 25.
• Kaminsky, W. (2014) WinTensor, version 1.5, Department of Chemistry, University of Washington.
•  Krivovichev,  S.V. and  Armbruster,  T. (2004) The crystal structure of jonesite, Ba₂(K,Na)[Ti₂(Si₅Al)O₁₈(H₂O)](H₂O)_n: A first example of titanosilicate with porous double layers. American Mineralogist, 89, 314-318.
• Liebau, F. (1985) Structural chemistry of silicates. pp. 347, Springer Verlag, Berlin.
•  Merlino,  S.,  Bonaccorsi,  E. and  Armbruster,  T. (1999) Tobermorites: their real structure and order-disorder (OD) character. American Mineralogist, 84, 1613-1621.
•  Merlino,  S.,  Bonaccorsi,  E. and  Armbruster,  T. (2000) The real structures of clinotobermorite and tobermorite 9 Å: OD character, polytypes, and structural relationships. European Journal of Mineralogy, 12, 411-429.
•  Merlino,  S. and  Bonaccorsi,  E. (2008) Double wollastonite chains: topological/conformational varieties, polytypic forms, isotypic compounds. Zeitschrift für Kristallographie, 223, 85-97.
•  Mills,  S.J.,  Birch,  W.D.,  Kolitsch,  U.,  Mumme,  W.G. and  Grey,  I.E. (2008) Lakebogaite, CaNaFe₂³⁺H(UO₂)₂(PO₄)₄(OH)₂(H₂O)₈, a new uranyl phosphate with a unique crystal structure from Victoria, Australia. American Mineralogist, 93, 691-697.
•  Missen,  O.P.,  Mills,  S.J.,  Spratt,  J.,  Birch,  W.D. and  Grugger,  J. (2019) Crystal chemistry of zemannite-type structures: I. A re-examination of zemannite from Moctezuma, Mexico. European Journal of Mineralogy, 31, 519-527.
•  Mitsuda,  T. (1970) Synthesis of tobermorite from zeolite. Mineralogical Journal, 6, 143-158.
•  Miyake,  M.,  Komarneni,  S. and  Roy,  R. (1989) Kinetics, equilibria and thermodynamics of ion exchange in substituted tobermorites. Materials Research Bulletin, 24, 311-320.
•  Momma,  K. and  Izumi,  F. (2011) VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data. Journal of Applied Crystallography, 44, 1272-1276.
•  Ohashi,  Y. and  Burnham,  C.W. (1973) Clinopyroxene lattice deformations: the roles of chemical substitution and temperature. American Mineralogist, 58, 843-849.
•  Organova,  N.I.,  Koporulina,  E.V.,  Ivanova,  A.G.,  Trubkin,  N.V., et al (2002) Structure model of Al,K-substituted tobermorite and structural changes upon heating. Crystallography Reports, 47, 950-956.
•  Parsons,  S. (2003) Introduction to twinning. Acta Crystallographica, D59, 1995-2003.
•  Pekov,  I.V.,  Zubkova,  N.V.,  Chukanov,  N.V.,  Merlino,  S., et al (2022) Paratobermorite, Ca₄(Al_0.5Si_0.5)₂Si₄O₁₆·2H₂O·(Ca·3H₂O), a new tobermorite-supergroup mineral with a novel topological type of the microporous crystal structure. American Mineralogist, 107, 2272-2281.
• Prince, E. (2004) International Tables for Crystallography, Vol. C: Mathematical, physical and chemical tables, 3^rd edition. pp. 1040, Kluwer Academic Publishers, Dordrecht, Boston, London.
•  Richardson,  I.G. (2014) Model structures for C-(A)-S-H(I). Acta Crystallographica, B70, 903-923.
• Rigaku Oxford Diffraction (2020) CrysAlisPRO, version 1.171.40.84a.
•  Robinson,  K.,  Gibbs,  G.V. and  Ribbe,  P.H. (1971) Quadratic elongation: a quantitative measure of distortion in coordination polyhedra. Science, 172, 567-570.
•  Sheldrick,  G.M. (2015) Crystal structure refinement with SHELXL. Acta Crystallographica, C71, 3-8.
• Taylor, H.F.W. (1997) Cement chemistry. 2nd edition. pp. 457, Thomas Telford Publishing, London.
•  Tkachenko,  N.,  Tang,  K.,  McCarten,  M.,  Reece,  S., et al (2023) Global database of cement production assets and upstream suppliers. Scientific Data, 10, 696.
•  Tsuji,  M. and  Komarneni,  S. (1989) Alkali metal ion exchange selectivity of Al-substituted tobermorite. Journal of Materials Research, 4, 698-703.
•  Wojdyla,  J.A.,  Kaminski,  J.W.,  Panepucci,  E.,  Ebner,  S., et al (2018) DA+ data acquisition and analysis software at the Swiss Light Source macromolecular crystallography beamlines. Journal of Synchrotron Radiation, 25, 293-303.
•  Zanardi,  S.,  Carati,  A.,  Cruciani,  G.,  Bellussi,  G., et al (2006) Synthesis, characterization and crystal structure of new microporous bismuth silicates. Microporous Mesoporous Materials, 97, 34-41.