Extraordinary structural complexity of ilmajokite: a multilevel hierarchical framework structure of natural origin.

The crystal structure of ilmajokite, a rare Na-K-Ba-Ce-titanosilicate from the Khibiny mountains, Kola peninsula, Russia, has been solved using single-crystal X-ray diffraction data. The crystal structure is based on a 3D titanosilicate framework consisting of trigonal prismatic titanosilicate (TPTS) clusters centered by Ce3+ in [9]-coordination. Four adjacent TPTS clusters are linked into four-membered rings within the (010) plane and connected via ribbons parallel to 101. The ribbons are organized into layers parallel to (010) and modulated along the a axis with a modulation wavelength of csinβ = 32.91 Å and an amplitude of ∼b/2 = 13.89 Å. The layers are linked by additional silicate tetrahedra. Na+, K+, Ba2+ and H2O groups occur in the framework cavities and have different occupancies and coordination environments. The crystal structure of ilmajokite can be separated into eight hierarchical levels: atoms, coordination polyhedra, TPTS clusters, rings, ribbons, layers, the framework and the whole structure. The information-based analysis allows estimation of the complexity of the structure as 8.468 bits per atom and 11990.129 bits per cell. According to this analysis, ilmajokite is the third-most complex mineral known to date after ewingite and morrisonite, and is the most complex mineral framework structure, comparable in complexity to paulingite-(Ca) (11 590.532 bits per cell). © Zolotarev et al. 2020.

Introduction

Minerals constitute a distinct group of crystalline materials formed by natural geochemical or biogeochemical processes without any anthropogenic influence. Approximately 5500 different mineral species are known today with more than 100 new species discovered every year. Many of these minerals have their synthetic counterparts, but there are many minerals that have no artificial analogs (Khomyakov, 1994 ▸). Their existence and formation under natural conditions represent a serious challenge for both mineralogists and material scientists looking for new structural architectures with interesting physical and chemical properties. Recently, a number of highly complex minerals has been characterized with structural features never before seen in synthetic materials. In particular, the crystal structures of charoite and denisovite are based on different kinds of silicate nanotubules (Rozhdestvenskaya et al., 2009 ▸, 2010 ▸, 2017 ▸), and ewingite (Olds et al., 2017 ▸) and morrisonite (Kampf et al., 2016 ▸) contain novel types of nanoscale heteropolyhedral clusters.

One interesting group of minerals with unique and important properties are titanosilicates. Due to their microporosity and catalytic activity, titanosilicates continue to attract considerable attention in the fields of materials science and nanochemistry (Rocha & Anderson, 2000 ▸; Noh et al., 2012 ▸; Milyutin et al., 2017 ▸; Oleksiienko et al., 2017 ▸; Přech, 2018 ▸; Cuko et al., 2018 ▸; Figueiredo et al., 2018 ▸). At the same time, they are of great interest from the viewpoint of mineralogy and geochemistry given their large diversity mostly in alkaline rocks such as those occurring in the alkaline massifs of the Kola peninsula, Russia, and Mont-Saint-Hilaire, Quebec, Canada (Cámara et al., 2017 ▸; Sokolova et al., 2017 ▸; Sokolova & Cámara, 2017 ▸; Selivanova et al., 2018 ▸; Zolotarev et al., 2018 ▸; Andrade et al., 2018 ▸; Lykova et al., 2018 ▸; Pakhomovsky et al., 2018 ▸; Pekov et al., 2019 ▸; Zhitova et al., 2019 ▸). Indeed, most titanosilicate materials used in industry were found as minerals before their unique properties were recognized. For instance, ETS-4 (Engelhardt titanosilicate-4; Kuznicki et al., 2001 ▸) is a synthetic analog of zorite, first described by Soviet mineralogists in the Kola peninsula in 1973 (Mer’kov et al., 1973 ▸). The ion-exchanger UOP-910, which is used for the removal of Cs-137 from radioactive-waste solutions (Anthony et al., 1994 ▸), is a natural counterpart of sitinakite, a microporous titanosilicate from hydrothermal veins of the Khibiny massif, Kola peninsula, Russia (Sokolova et al., 1989 ▸; Men’shikov et al., 1992 ▸). Another family of recently described microporous titanosilicates, the ivanyukite-group minerals (Yakovenchuk et al., 2009 ▸), have the pharmacosiderite-type structure, well known as a useful synthetic material since the 1990s (Harrison et al., 1995 ▸). There are many other unique natural titanosilicates with interesting structures that have no precedents among synthetic materials. For instance, yuksporite is based on nanoscale porous titanosilicate tubes that have never been prepared under laboratory conditions to date (Krivovichev et al., 2004 ▸).

Herein we report on the structural and chemical features of ilmajokite, a rare titanosilicate from the Lovozero tundra, Kola peninsula, Russia. The mineral occurs in the ‘Yubileynaya’ pegmatite vein, Karnasurt Mountain, near the river Ilmajok and lake Ilma. Ilmajokite is found as crystals and crystalline crusts on the surfaces of voids in natrolite (Bussen et al., 1972 ▸). The fresh crystals are yellowish and transparent. In air, they slowly become cloudy and fragment into separate plates and fibers. The chemical formula, determined by wet chemical analysis, was given as (Na8.8Ba0.5 REE 0.7)Σ = 10(Ti4.99(Fe,Al,Nb)0.01)Σ = 5(Si13.9Al0.01)Σ = 14O22(OH)44·nH2O (the formula was proposed by I. D. Borneman-Starynkevich). The admixture of nahcolite, NaHCO3, was mentioned, which significantly increased the observed amount of Na. Ilmajokite has a large quantity of H2O (24.54 wt%), which is released on heating; the mineral loses up to 12.7% at 175°C, although 6.5% is still retained at 320°C. Release of H2O starts as low as 60°C but it is not complete until 760°C (Bussen et al., 1972 ▸). H-speciation was determined by infra-red (IR) spectroscopy based on broad absorptions at 1618 and 3389–2889 cm−1.

The instability of ilmajokite crystals under atmospheric conditions prevented detailed crystallographic study for a long time. Bussen et al. (1972 ▸) determined the mineral to be probably monoclinic with unit-cell parameters a ≃ 23, b ≃ 24.4, c ≃ 37 Å. A later study by Goiko et al. (1974 ▸) on fresh material held hermetically after extraction from the pegmatite confirmed the monoclinic symmetry and determined the unit-cell parameters to be a = 39.80, b = 29.5, c = 29.83 Å, β = 96.63°, V = 34788 Å3, possible space groups C2/c or Cc. Cámara et al. (2010 ▸) investigated single crystals of ilmajokite provided by E. I. Semenov in 2004 (sample ILM01). The study at room temperature gave a C-centered monoclinic cell with a = 35.774 (4), b = 27.407 (3), c = 31.131 (5) Å, β = 95.66 (1)°, V = 30374 (7) Å3. The R int value was very high (∼32%) and no model could be obtained from these data. A low-temperature data collection at 125 K slightly enhanced the data quality, but no solution could be found. The cell refinement confirmed a C-centered cell with a = 35.32 (16), b = 26.93 (12), c = 30.68 (14) Å, β = 95.84 (2)°, V = 29034 (403) Å3. A further study was done later by some of the authors (FC, LB, FCH and ES) on another crystal provided by C. Ferraris (Muséum National d’Histoire Naturelle, Paris, France; catalog number 197.68) in 2010 (ILM02), extracted from a sample deposited at the National School of Mines, Paris, France. This time, a high-performing BRUKER APEX II ULTRA single-crystal diffractometer was used (Turbo X-ray source coupled with the HELIOS Mo optics provides up to 60 times more intense data from small crystals) at the Department of Geological Sciences of the University of Manitoba, Canada. The results were very similar to the previous ones [refined unit cell: a = 36.084 (18), b = 27.726 (13), c = 31.248 (15) Å, β = 98.051 (5)°, V = 30953 (45) Å3] but with a better internal agreement factor (R int ≃ 5%). Yet again, systematic absences were compatible with space groups C2/c or Cc, but no model could be obtained from these data as they were very weak at d < 2.3 Å (Fig. S1 of the supporting information), and show high mosaicity. Interestingly, mosaicity begins at lower resolution along [Fig. S1(b)].

Considerable attempts have been made by separate groups to obtain the structure model for ilmajokite, but with no success. Recently, the first author (AAZ) found a single crystal of ilmajokite in the collections of the Fersman Mineralogical Museum of the Russian Academy of Sciences (Moscow, Russia) which allowed data collection good enough to resolve the atomic arrangement of this unusual mineral. The good quality of the crystal was due to the fact that it was covered by lacquer soon after extraction of the sample from the host rock.

Materials and methods

Sample description

The holotype sample was obtained from the Fersman Mineralogical Museum of the Russian Academy of Sciences (Moscow, Russia), where it is stored under catalog number 86969. The sample originates from the Yubileinaya pegmatite (Karnasurt Mountain, Lovozero, Kola Peninsula) (Pekov, 2001 ▸) where it is one of the latest primary minerals. We checked several single crystals and we were able to obtain acceptable X-ray diffraction data for one of them. The crystal selected for data collection was a yellowish transparent plate was 0.15 × 0.08 × 0.04 mm in size.

Chemical composition

The chemical composition of ilmajokite was determined on ilmajokite crystals from the sample ILM02 using a CAMECA SX-100 electron-microprobe at the Department of Geological Sciences of the University of Manitoba, Canada, operating in wavelength-dispersion mode with an accelerating voltage of 15 kV, a specimen current of 5 nA, a beam size of 15 µm and count times on peak and background of 20 and 10 s, respectively. The results are reported in Table S1 of the supporting information. Even with such a large beam, the material showed significant beam damage (Fig. S2) and Na loss (see, for instance, analyses 5, 8, 9 and 10, Table S1). Overlap of BaLβ on CeLα and CeMζ on FKα were accounted for. The elements Zn, Sr, Gd and U were sought but not detected. Data were reduced using the PAP procedure by Pouchou & Pichoir (1985 ▸).

Analyses show Na loss even under mild conditions (5 nA and 15 µm defocalized beam) with a progressive loss of Na. Also, the formation of cracks on the surface denotes volatilization under vacuum (typical for micro and mesoporous hydrated phases). Totals decrease from 90 wt% to ca 86 wt%. Fluorine is absent. Normalization on the basis of 218 charges (see Section 3.4 crystal-chemical formula) using the average of points 1, 2, 3, 4 and 11 (in a separate fragment) gave the empirical formula (Na9.55K1.09Ba0.84Ca0.08Th0.08)Σ11.64(REE 1.99Y0.01)2(Ti11.98Ta0.05Nb0.01Mn0.01Mg0.01Fe2+ 0.01Zr0.01)Σ12.08[Si37.72Al0.03]O109, with REE = Ce0.99La0.59Nd0.27Pr0.10Sm0.03Dy0.01.

Single-crystal X-ray diffraction

Single-crystal X-ray diffraction study of ilmajokite was done at the Resource Center ‘X-ray Diffraction Methods’ of St Petersburg State University using the Bruker Kappa APEX DUO diffractometer (microfocus tube) equipped with a CCD area detector. The study was done using monochromatic Mo Kα X-radiation (λ = 0.71073 Å), with frame widths of 0.5° in ω and 30 s counting time for each frame. The intensity data were reduced and corrected for Lorentz, polarization and background effects using the Bruker software APEX2 (Bruker-AXS, 2014 ▸). A semiempirical absorption-correction based upon the intensities of equivalent reflections was applied using SADABS (Sheldrick, 2007 ▸). The structure was solved and refined in the space group C2/c to R 1 = 0.081 (wR 2 = 0.233) for 14 797 unique observed reflections with I ≥ 2σ(I) using the SHELX program package (Sheldrick, 2015 ▸) within the Olex2 shell (Dolomanov et al., 2009 ▸). Crystal data, data collection information and refinement details are given in Table 1 ▸.

Table 1

Crystal data and structure refinement for ilmajokite

Crystal data
Chemical formula	Ba0.45H44.25Ce1.04K0.55Na5.62O76.74Si18.76Ti6
M r	2445.37
Crystal system, space group	Monoclinic, C2/c
Temperature (K)	296
a, b, c (Å)	35.908 (5), 27.784 (3), 33.126 (4)
β (°)	96.494 (3)
V (Å3)	32836 (7)
Z	16
Radiation type	Mo Kα
μ (mm−1)	1.79
Crystal size (mm)	0.15 × 0.08 × 0.04
Data collection
Diffractometer	Bruker Kappa APEX DUO
Absorption correction	Multi-scan
No. of measured, independent, observed [I > 2σ(I)] reflections	108441, 21527, 14797
R int	0.130
θmax (°)	22.7
(sin θ/λ)max (Å−1)	0.543
Refinement
R[F 2 > 2σ(F 2)], wR(F 2), S	0.081, 0.264, 0.97
No. of parameters	1847
No. of restraints	18
H-atom treatment	H-atom parameters not defined
	w = 1/[σ2(F o 2) + (0.1738P)2 + 608.3564P] where P = (F o 2 + 2F c 2)/3
Δρmax, Δρmin (e Å−3)	1.89, −2.80

The unit-cell parameters of ilmajokite determined in our study correspond well with those reported by Cámara et al. (2010 ▸) for their room-temperature study. The most significant difference is for the c parameter, which in our study is about 2 Å longer than that determined by Cámara et al. (2010 ▸). It is most likely that this difference is due to the different hydration states of the two samples, which also explains the lower quality of the diffraction data for the crystal with the smaller c parameter (see Fig. S1).

Results

Atom coordination

The crystal structure of ilmajokite contains 236 symmetrically independent sites, including 1 Ba, 2 REE (rare-earth elements, with Ce as the dominant component), 12 Ti, 41 Si, 15 Na, 3 K, 84 O, 38 OH and 40 H2O sites. Cation coordination numbers, average bond lengths and their variations, and bond-valence sums are given in Table 2 ▸. The coordination of Ti4+ and Si4+ cations is octahedral and tetrahedral, as is typical for many other natural and synthetic titanosilicates (Krivovichev, 2005 ▸). The low coordination numbers and bond-valence sums for several alkali-metal (Na, K) sites are due to their low occupancies (up to 0.22). Of 84 O sites, 38 are bridging between adjacent Si atoms; 44 are bridging between Si and Ti atoms; 5 are bonded to Si, Ti and Ce atoms; 6 are bonded to two Ti and one Ce atoms each; one is bonded to two Ti and one Si atoms. Of 38 OH groups, 4 are bonded to two Ti atoms, and the remaining 34 are terminal (silanol) groups of SiO4 tetrahedra. The bond-valence sums for the O atoms, OH and H2O groups (without contributions from the H atoms) are in the ranges 1.73–2.28, 0.89–1.42 and 0.0–0.58, respectively. The most significant deviations from the expected values (2.00, 1.20 and 0–0.40, respectively) are observed for disordered cation sites that cannot be estimated correctly.

Table 2

Coordination numbers (CNs) of cations, average bond lengths and their variations (Å), and bond-valence sums (BVS, in valence units, v.u.) for the crystal structure of ilmajokite

Bond valence units were calculated using parameters from Gagné & Hawthorne (2015 ▸).

Atom	CN	Bond lengths		BVS
		Average	Range (min–max)
Ba	10	2.899	2.818–2.968	1.91
K	6, 7	2.816	2.403–3.308	1.03–1.27
Na	3, 5, 6, 7, 8	2.555	1.999–3.022	0.42–1.10
Ce	9	2.543	2.481–2.626	3.00
Ti	6	1.955	1.853–2.105	3.99–4.17
Si	4	1.621	1.512–1.671	3.87–4.27

Local topological features

The crystal structure of ilmajokite is based on a titanosilicate framework of unprecedented complexity. Analysis of the local topological features of the SiO4 tetrahedra shows that they belong to ten different types, from Q 2 (two-connected) to Q 5 groups [herein, Q indicates a tetrahedron that shares its O corners with n adjacent coordination polyhedra (only Si and Ti polyhedra are taken into account)]. The Q 5 type is not typical for silicate frameworks of corner-sharing tetrahedra (Liebau, 1985 ▸), but occurs in octahedral–tetrahedral frameworks. In ilmajokite, it corresponds to the Si10O4 tetrahedron that shares three of its corners with three adjacent tetrahedra and one corner with two TiO6 octahedra sharing a common edge (see below). In order to distinguish between silicate tetrahedra of the same type but with different chemical environments, we use the notation Q , where m + k = n. For instance, there are three types of Q 3 tetrahedra in ilmajokite, Q 3 Ti + 2Si, Q 3 3Si and Q 3 2Ti + Si. The complete local topological classification of silicate tetrahedra in ilmajokite is given in Table 3 ▸. It is noteworthy that all Q 2 2Si tetrahedra are only partly occupied with site occupancies less than 0.5.

Table 3

Topological types of Si tetrahedra in the crystal structure of ilmajokite

General type	Specific type	Si Sites
Q 2	Q 2 Si + Ti	3, 21
	Q 2 2Si	17†, 37†, 38†, 39†, 40†, 41†
	Q 2 2Ti	36
Q 3	Q 3 2Si + Ti	2, 8, 9, 14, 19, 29, 33, 35
	Q 3 3Si	5, 13, 24, 25
	Q 3 2Ti + Si	20, 31
Q 4	Q 4 2Ti + 2Si	1, 4, 6, 12, 15, 16, 18, 22, 23, 26, 27, 28, 32, 34
	Q 4 4Ti	7
	Q 4 3Si + Ti	11, 30
Q 5	Q 5 3Si + 2Ti	10

Partially occupied sites.

Structural organization

The projection of the crystal structure of ilmajokite along the c axis is shown in Fig. 1 ▸. The titanosilicate framework has a complex organization that can be described as follows. Two TiO6 octahedra share a common edge to form a [Ti2O10] dimer. Three dimers with parallel orientation form a trigonal prism centered by Ce3+ in [9]-coordination. The triple-dimer titanate structure is surrounded by SiO4 tetrahedra to form a trigonal prismatic titanosilicate cluster, further denoted as a TPTS cluster. There are two symmetrically different TPTS clusters centered by the Ce1 and Ce2 atoms [Figs. 2 ▸(a) and 2(c)]. For further description of the structural topology of the framework, we adopt a nodal representation, where each Ti and Si polyhedron is symbolized by a node of respective color and two nodes are linked by an edge if the two corresponding polyhedra share a common O atom. This approach is widely used for the description of complex topologies observed in zeolite-type tetrahedral (Baerlocher et al., 2007 ▸; Smith, 2000 ▸) and heteropolyhedral (Krivovichev, 2005 ▸; Krivovichev et al., 2005 ▸) frameworks. The nodal representation of the two independent TPTS clusters in ilmajokite is given in Figs. 2 ▸(b) and 2(d).

Figure 1

Projection of the crystal structure of ilmajokite along the c axis. Legend: Si tetrahedra – yellow, Ti octahedra – blue; H2O molecules, Na, K, Ba and Ce atoms are shown as red, light-blue, green, brown and orange spheres, respectively.

Figure 2

TPTS clusters in the crystal structure of ilmajokite shown in (a) and (c) polyhedral and (b) and (d) nodal representations. The numbering scheme corresponds to the numbering of Si and Ti atoms from the experiment. The Ce-centered Ti6 trigonal prism is highlighted in yellow. The legend follows that of Fig. 1 ▸.

Four adjacent TPTS clusters are linked via the Si9–Si19 links and the Si7O4 tetrahedron (note that this is the only Q4 4Ti tetrahedron in the crystal structure) to form a four-membered ring (Fig. 3 ▸). The rings are arranged within the (010) plane [Fig. 4 ▸(a)] and linked via partly occupied Si39, Si40 and Si41 polyhedra (Q 2 2Si type) into ribbons parallel to [Fig. 4 ▸(b)]. A schematic description of the topology of the chain is given in Fig. 5 ▸. The ribbons are organized into layers parallel to (010). The view of the layers along the a axis [Fig. 6 ▸(a)] shows that they are modulated with a modulation wavelength of csinβ = 32.91 Å and an amplitude of ∼b/2 = 13.89 Å. The layers are linked via Si14, Si14 and Si31 tetrahedra; with the first two partly occupied (the Q 2 2Si type) and the last fully occupied (the Q 3 2Ti + Si type). Thus the most condensed unit in the titanosilicate framework is the four-membered ring of the TPTS clusters, whereas the linkage of the rings proceeds via Si14, Si31, Si37, Si38, Si39, Si40 and Si41 tetrahedra; with only Si31 fully occupied, whereas the others are less than half-occupied.

Figure 3

Four-membered ring of the TPTS clusters shown in (a) polyhedral and (b) nodal representations. Legend and numbering scheme follow that of Fig. 1 ▸.

Figure 4

(a) Arrangement of the four-membered rings of the TPTS clusters within the (010) plane and (b) their linkage through additional Si39, Si40 and Si41 nodes into ribbons.

Figure 5

Schematic representation of the topology of ribbons formed by TPTS (CeTi6Si17) clusters in ilmajokite (four-membered rings are highlighted in gray).

Figure 6

(a) Arrangement of layers of ribbons of TPTS clusters along the b axis and (b) their linkage into a 3D framework via Si14, Si31 and Si37 nodes.

Na+, K+, Ba2+ and H2O groups occur in the framework cavities and have different occupancies and coordination environments (Table 2 ▸).

It is noteworthy that the mosaicity observed in the ILM02 crystal has lower resolution in the direction of the ribbons, reflecting damage in the structure of that crystal, probably related to amorphization by dehydration.

Crystal-chemical formula

The crystal-chemical formula determined from the structure refinement is Na11.24K1.10Ba0.90Ce2Ti12Si37.52O94(OH)30.38·(H2O)29.06, in close agreement between the sums of the positive (+218.22) and negative (−218.38) charges, which is remarkable in view of the difficulties associated with the structure refinement. There is also a very good agreement with the results of the electron-microprobe analysis (see Section 2.2), particularly considering the difficulty due to dehydration and Na migration under the beam. Assuming that the selected points with less Na are closer to the actual H2O content, the formula is in accordance with 14 H2O groups per formula unit and the following empirical formula: (Na9.55K1.09Ba0.84Ca0.08Th0.08)Σ11.64(REE 1.99Y0.01)2(Ti11.96Ta0.05Nb0.01Mn0.01Mg0.01Fe2+ 0.01Zr0.01)Σ12.06[Si37.68Al0.03]O94(OH)30·(H2O)14.18, with REE = Ce0.99La0.59Nd0.27Pr0.10Sm0.03Dy0.01.

Taking into account the presence of the titanosilicate framework and its silicate sub-framework, the detailed crystal-chemical formula of ilmajokite may be written as Na11.24K1.10Ba0.90〈Ce2{Ti12[Si37.52O88(OH)26.38]O6(OH)4}〉·(H2O)29.06, where square, curly and angular brackets denote silicate, titanosilicate and rare-earth-titanosilicate substructures. On the basis of both chemical and structural data, the ideal crystal-chemical formula of ilmajokite can be written as Na11KBaCe2Ti12Si37.5O94(OH)31 .29H2O, which requires SiO2 46.06, TiO2 19.60, Ce2O3 6.69, BaO 3.14, Na2O 6.97, K2O 0.96, H2O 16.58 (total 100 wt%). The amount of H2O in the crystal-chemical formula disagrees with the value of 24.54 wt% reported by Bussen et al. (1972 ▸), which could be due to the possibility of variable hydration states frequently observed for microporous framework minerals. The two-step dehydration described by Bussen et al. (1972 ▸) may correspond to the loss of zeolitic H2O and the complete dehydration associated with the hydroxyl groups.

The ideal formula of the silicate sub-framework, assuming full occupancy of the partly occupied Si and associated OH sites, and excluding the Si37–Si38 disorder, can be written as [Si40O88(OH)32]48− or [Si5O11(OH)4]6− with the amazingly simple Si:O ratio of 1:3. It is interesting to note that the Si:O 1:3 ratio has previously been reported for other rather complex silicate minerals such as hyttsjöite, Pb18Ba2Ca5Mn2 2+Fe2 3+[Si30O90]Cl(H2O)6 (Grew et al., 1996 ▸); aerinite, Ca6FeAl(Fe,Mg)2(Al,Mg)6[Si12O36](OH)12H)(H2O)12(CO3) (Rius et al., 2004 ▸, 2009 ▸); and sveinbergeite, (H2O)2(Ca(H2O))(Fe6 2+Fe3+)Ti2[Si4O12]2O2(OH)4((OH)H2O)) (Khomyakov et al., 2011 ▸). We note that the silicate subframework found in the crystal structure of ilmajokite is new and has not been observed previously in any mineral or inorganic compound (Pushcharovsky et al., 2016 ▸).

Discussion

Hierarchical analysis

The economist and Nobel laureate Herbert Simon once noted that ‘hierarchy… is one of the central structural schemes that the architect of complexity uses’ (Simon, 1962 ▸). The high number of hierarchical levels of structural organization (hierarchical depth) reflects the high degree of complexity of a system. As has been noted previously [see, e.g. Makovicky (1997 ▸); Ferraris et al. (2004 ▸); Hawthorne (2014 ▸)], the crystal structures of minerals and inorganic compounds have a hierarchical organization [see Krivovichev (2017 ▸) for a detailed discussion and examples]. From this point of view, the crystal structure of ilmajokite possesses a multilevel hierarchical structure (Fig. 7 ▸). The first (lowest) level consists of atoms that are grouped into coordination polyhedra (second level). The TiO6 octahedra are linked to form dimers (third level). The dimers together with SiO4 tetrahedra and centering Ce3+ cations comprise TPTS clusters (fourth level). The clusters are linked to form four-membered rings (fifth level), which are further interlinked to form ribbons (sixth level). The ribbons are united into a three-dimensional octahedral–tetrahedral framework (seventh level), which, together with alkali metal, Ba2+ cations and H2O molecules complete the structure organization (eighth level). The subdivision of the structure into eight levels reflects its high complexity which is considered in the next section.

Figure 7

Hierarchial organization of the crystal structure of ilmajokite separated into eight hierarchy levels (highlighted in gray).

Complexity analysis

The complexity of the crystal structure of ilmajokite can be quantitatively estimated using information-based complexity measures recently proposed by Krivovichev (2012 ▸, 2013 ▸, 2014 ▸). Since the positions of the H atoms were not determined from the single-crystal diffraction experiment, the procedure of H-correction was applied as described by Pankova et al. (2018 ▸). The resulting parameters are as follows: the number of atoms per reduced unit cell, v, is equal to 1416; the amount of Shannon information per atom, I G, is 8.468 bits; and the amount of Shannon information per unit cell, I G, total, is 11 990.129 bits. The parameters without H-corrections are v = 972, I G = 7.925 bits per atom, I G, total = 7702.918 bits per cell, which means that hydration is responsible for ca 36% of the total structural complexity. The total value of Shannon information places ilmajokite as the third-most complex mineral known to date after ewingite, Mg4Ca4(UO2)12(CO3)15O2(OH)6·69H2O [23 477.507 bits per cell with H-correction and 12 684.86 bits per cell without H-correction (∼46% of total complexity is due to H atoms); Olds et al. (2017 ▸)] and morrisonite, Ca11(As3+V2 4+V10 5+As6 5+O51)2·78H2O [13 588.350 bits per cell with H-correction and 7553.229 bits per cell after H-correction (H atoms are responsible for ∼44% of structural complexity); Kampf et al. (2016 ▸)]. Since both ewingite and morrisonite contain nanoscale clusters, ilmajokite is the most complex with a framework structure, and in terms of its complexity, is very close to paulingite-(Ca), Ca5(Al10Si32O84)·34H2O [11 590.532 bits per cell with H-correction and 6766.998 bits per cell after H-correction (∼42% complexity is due to H atoms); Passaglia et al. (2001 ▸)].

Conclusions

Under natural conditions, ilmajokite forms as one of the latest minerals of hydrothermal activity, which includes several stages and a range of precursor phases that precede the crystallization of the mineral. The extreme complexity of ilmajokite is the result of a combination of a number of factors, including its high chemical complexity and seggregation of chemically different elements (Na, K, Ba, Ce, Ti, Si) into their own crystallographic sites (the most interesting is the absence of any detectable K–Ba substitution), the presence of polynuclear TPTS clusters of nanoscale size (the diameter of the cluster is around 1.4 nm), condensation of the TPTS clusters into larger four-membered units, the high hydration state, etc.

Crystal structure: contains datablock(s) I. DOI: 10.1107/S2052252519016622/lt5023sup1.cif

Structure factors: contains datablock(s) I. DOI: 10.1107/S2052252519016622/lt5023Isup2.hkl

Supplementary data. DOI: 10.1107/S2052252519016622/lt5023sup3.pdf

CCDC reference: 1971431