Introduction

Borates and borosilicates represent the main source for boron in the Earth’s Crust. Besides the average low concentration of B in the Crust (~ 11 wt ppm, Rudnick and Gao 2014), its distribution in various lithic reservoirs is highly anisotropic, leading to massive mineral deposits often governed by the high solubility in moderate-to-high temperature (> 270 K) aqueous fluids. Therefore, B can behave as a “fugitive” element, with a consequent redistribution under conditions in which aqueous fluids are present, as commonly seen in hydrothermal or evaporitic-lacustrine deposits (Anovitz and Grew 1996; Smith and Medrano 1996). Hydrous borates are the dominant B-bearing minerals in hydrothermal or lacustrine deposits. It is worth to mention the rapid increase of the B demand over the last decades, which doubled in the last twenty years reaching at present about 10 Mtons/y (source: U.S.G.S. 2000–2021). Such a demand reflects the long series of technological processes and utilizations of boron, among those in, e.g., glass technology, ceramics, metallurgy, cosmetics, fertilizers and chemicals. More recently, natural borates are also being used for the fabrication of radiation-shielding concretes, used in nuclear energy plants and nuclear medicine applications, due to the elevated ability of 10B to absorb thermal neutrons (Carter et al. 1953; Yarar and Bayülken 1994; Palmer and Swihart 1996; Kinno et al. 2002; Rauch and Waschkowski 2002; Okuno et al. 2009, 2013; Gatta et al. 2010, 2013, 2023; Korkut et al. 2010; Uysal et al. 2018).

Inderite, a hydrous borate named after the type locality (Inder Lake, Atyrau Region, Kazakhstan), occurs as colourless or white long prismatic crystals (even up to 20–30 cm), dominated by {110}, {120}, and {001}, or as aggregates of minute needles, or even as reniform nodules. Its ideal chemical formula is usually reported as MgB3O3(OH)5·5H2O (or even Mg2B6O11·15H2O in old literature; Boldyreva 1937). Inderite was firstly discovered by Boldyreva (1937) from Inder, Kazakhstan. However, Frondel and Morgan (1956) and Frondel et al. (1956) found the same mineral species in California, giving it the new name “lesserite”. An additional source of confusion was the discovery of the triclinic polymorph “kurnakovite”, found in the same Inder district by Godlevsky (1940). Only several years later, Schaller and Mrose (1960) proved that inderite and kurnakovite were actually dimorphs, and that “lesserite” corresponded to inderite firstly discovered by Boldyreva (1937), with a final discreditation of the mineral name “lesserite”.

The first H-free structural model of inderite was provided by Ashirov et al. (1962) and then improved by Rumanova and Ashirov (1963), based on single-crystal X-ray diffraction data collected with a Weissemberg camera and applying the direct methods to the intensity data. The structure was solved in the space group P21/a with the following unit-cell geometry: a ~ 12.02, b ~ 13.12, c ~ 6.84 Å, β ~ 104°40′. Later, a structural re-investigation of inderite was performed by Corazza (1976), by single-crystal X-ray intensity data collected with a four-circle diffractometer equipped with a point-detector, and described in the space group P21/c with a = 6.8221(3), b = 13.1145(13), c = 12.0350(9) Å, and β = 104.552(8)°, with the location also of 15 independent H sites. The structural model of Corazza (1976) is, to the best of our knowledge, the last one based on experimental data and reported in the literature. More recently, a model based on density functional theory (DFT) calculations was reported by Zhou et al. (2012). It is worth to note that the materials used by Rumanova and Ashirov (1963) and Corazza (1976) were not chemically analysed: their composition was assumed. Surprisingly, there is no data in the literature, based on modern standards, on the chemical composition of inderite, especially for minor and trace elements, so that the nature of potential substituents for Mg, B and OH-group is completely unknown.

In the framework of a long-term project on the high-pressure and high-temperature crystal-chemistry of hydrous borates, especially to select new B-bearing aggregates as potential radiation-shielding materials (Lotti et al. 2019; Comboni et al. 2020a,b, 2021, 2022), we have reinvestigated the crystal structure and the chemical composition (including the B isotopic signature) of inderite by single-crystal neutron diffraction, electron microprobe analysis in wavelength-dispersive mode (EPMA-WDS), and laser ablation—inductively coupled plasma—mass spectrometry (LA-ICP-MS) and LA- multi collectors (MC-)ICP-MS, in order to provide: (1) a structural model with the unambiguous location of all the H sites and their vibrational regime, along with the description of the complex H-bonding scheme expected in inderite structure, (2) the chemical composition of this hydrous borate mineral, in terms of major, minor and trace elements, and its B isotopic signature. The occurrence of millimetric gem-quality crystals of inderite from the Kramer Borate Deposit, California (USA), along with its high B and H content (ideally: B2O3 37.3 wt% and H2O 48.3 wt%), make this mineral as a good candidate for a neutron diffraction investigation. The results of this study are pivotal to describe the thermal and compressional behaviour of inderite, on which in-situ experiments are in progress, and the first experimental findings on the compressional behaviour of inderite have been published in Comboni et al. (2023).

Materials and experimental methods

Mineralogical description and chemical characterisation

The sample of inderite here investigated was kindly provided by the late Dr. Renato Pagano (Italy). The specimen consists of few colourless, prismatic, millimetric crystals from the “Boron Open Pit”, Kramer Borate Deposit, Boron, Kern County, California, USA, in which inderite coexists with other borates (e.g., borax, colemanite, inyoite, kernite, kurnakovite, meyerhofferite, probertite, sassolite, tincalconite, ulexite), carbonates (e.g., calcite, rhodochrosite), silicates (mainly clay minerals and zeolites) and some sulphides (e.g., pyrrhotite, realgar, smythite, stibnite). The geological studies of the area indicate that borates were deposited (probably within the Middle Miocene) in a small basin, fed from volcanic springs rich in boron (Gale 1946; Christ and Garrels 1959; Barnard and Kistler 1961).

The chemical composition of two millimetric crystals of inderite from the Kramer deposit, in terms of major and minor elements, was first investigated by EPMA-WDS using a JEOL 8200 Super Probe system, at the University of Milan. The following operating conditions were used: 15 kV and 5 nA, 10 μm beam diameter, 30 s of counting times on the peaks and 10 s on the backgrounds. A set of minerals was employed as standards: omphacite (Na), K-feldspar (K), sanbornite (Ba), celestine (Sr), forsterite-154 (Mg), fayalite-143 (Fe), grossular (Al, Si, Ca), apatite (F). Despite the large beam diameters, a modest degeneration of the crystals was observed under the electron beam, as previously observed for other hydrous borates (Gatta et al. 2022a, 2023). The raw data were corrected for matrix effects using the ZAF routine implemented in the JEOL suite of programs. The two crystals of inderite under investigation were found to be homogeneous. Only Mg and Ca concentrations were measured at a significant level. The measured weight fractions of Mg was virtually identical to the ideal one within the e.s.d.. The paucity of sample did not allow any thermal analysis of the mineral. The unit formula calculated on the basis of 3O + 5OH apfu and assuming 3B apfu, according to the experimental findings of the neutron structural refinement (as discussed later), is: (Mg1.016Ca0.008)B3O3(OH)5·5H2O or, at a first approximation, (Mg1.02Ca0.01)B3O3(OH)5·5H2O. As it will be shown later, the correct form should be (Mg1.02Ca0.01)[B3O3(OH)5](H2O)4·H2O.

The in-situ trace element concentrations were determined at the Geochemistry, Geochronology, and Isotope Geology laboratory (University of Milan) using a laser ablation system (Analyte Excite ArF excimer 193 nm, Teledyne Photon Machines) connected to a single collector quadrupole inductively coupled plasma mass spectrometer (ICP-MS, iCAP RQ from Thermo Fisher Scientific). The laser microprobe is equipped with a double volume chamber (HelEx II) and He was used as carrier gas of the ablated materials with fluxes of ~ 0.5 and ~ 0.2 l/min in the ablation cell and in the HelEx II cup, respectively. The laser spot size was set to 65 µm and a laser fluence of 2.0 J/cm2, with a repetition rate of 7 Hz, was used. Each spot was analyzed for a total of 120 s, including 40 s of gas blank acquisition (comprising 10 s of laser warm up), 60 s of laser ablation measuring isotope peak intensity followed by 20 s of wash time. The NIST SRM 610 synthetic glass (Jochum et al. 2011) and 43Ca (from EPMA) were used as external and internal standards, respectively. Quality control was achieved analyzing the USGS reference basaltic glass GSD-2 g (Wilson 2018), the NIST SRM 612 synthetic glass (Jochum et al. 2011), and the IAEA-B6 obsidian (Tonarini et al. 2003) together with the unknown. Precision and accuracy are better than 5% and 10%, respectively, for most of the elements. Data reduction was carried out using the Glitter software package (Griffin et al. 2008). Data are reported in Table 1.

Table 1 Trace element concentrations (given in wt ppm, 1σ) and B isotope composition (in ‰, 2σ) of the inderite of this study, based on the LA-ICP-MS and LA-MC-ICP-MS data
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The in-situ B isotope composition of the Kramer inderite was measured coupling the same laser microprobe system used for the determination of trace element to a double focusing multi collector (MC-)ICP-MS (Neptune XT, Thermo Fisher Scientific) hosted at the at the Geochemistry, Geochronology, and Isotope Geology laboratory of the University of Milan. Instrumental setup and analytical conditions were the same as reported in Gatta et al. (2023). The results are reported in the common delta(δ)-notation as permil (‰) and expressed relative to the isotopic ratio of the NIST SRM 951 boric acid (11B/10B = 4.04362 ± 0.00137, 2σ; Catanzaro et al. 1970). The IAEA-B4 tourmaline (schorl, Tonarini et al. 2003) was employed as primary bracketing standard to correct instrumental isotope fractionation. Assessment of accuracy was achieved by analyzing two dravitic tourmalines (Marschall et al. 2006) and the B-rich synthetic andesitic glass ARM-2 (10,500 wt. ppm of B, Wu et al. 2021) in the same analytical run with the Kramer inderite. The measured δ11B are accurate within uncertainties with published values (see Gatta et al. 2023 for further details). The B isotopic composition of the Kramer inderite is reported in Table 1.

Single-crystal neutron diffraction and structure refinement

Neutron diffraction data on an inderite crystals of size 1.1 × 2.8 × 4.2 mm were collected at 10 and 280 K on the single-crystal diffractometer SXD (Keen et al. 2006) at the ISIS spallation neutron source (UK), which is equipped with an array of eleven 2D position-sensitive detectors statically placed around the sample positon. At each temperature, a series of 7 orientations of the sample around the vertical axis of the instrument were used, with a counting time of ~ 6 h each. Data at 280 K were initially indexed with the unit cell available from the X-ray measurement. Integrated intensities were extracted for both datasets using the 3D-profile fitting method implemented in the SXD2001 software (Gutmann 2017) and corrected for the Lorentz effect. An absorption correction was applied to all the data with an in-house software package that reconstructs the three-dimensional shape of the crystal via image-processing of a 360° panoramic, and calculates the exact path-length of neutrons through the crystal for characteristic diffraction shape nodes (de Meulenaer and Tompa 1965). The transmission factor is, then, calculated via analytic solution of the integral of diffraction centers across the whole crystal volume, according to diffraction angles and neutron wavelengths (Leonardi and Capelli 2022, in preparation). Final unit cell parameters were refined against the fitted positions of the Bragg peaks after the 3D profile integration.

The structural refinement of inderite, based on the data collected at 280 K, was performed starting from the (H-free) X-ray model reported by Corazza (1976). The refinement was conducted by full matrix least squares on F2, using the SHELXL-2018/3 software (Sheldrick 2008, 2014). The secondary isotropic extinction effect was corrected adopting the Larson’s formalism (Larson 1967). The neutron scattering lengths of Mg, B, O and H were taken from Sear (1986). The first cycles of refinement were conducted with isotropic displacement parameters for all the atomic site. When convergence was achieved, a series of minima in the Fourier-difference maps of the nuclear density function were observed, all assigned to H sites for the H’s negative neutron scattering length. The newly assigned 15 independent H sites were located near O sites, with bond distances all compatible with O–H groups (of hydroxyls or H2O molecules). Convergence was then rapidly achieved and, in the last cycles of refinement, all atomic sites occupied by Mg, O and H were modelled anisotropically, with a significant improving of the figures of merit (Table 2). At the end of the refinement, no significant correlations among the refined variables were found in the variance–covariance matrix, with all the principal mean-square atomic displacement parameters positive, H included (Tables 2, 3 and 4). However, a careful inspection of the difference-Fourier maps of the nuclear density showed evidence of a positional disorder of the O9w site. An additional test refinement was then performed assuming a split configuration of this oxygen site in two subsites (labelled as O9w and O9w’, Tables 2 and 3), only ~ 0.4 Å apart, with partial site occupancies and, therefore, mutually exclusive (Table 3). The final model obtained with the split O9w-O9w’ sites was found to be consistent, in terms of bond distances and angles, being O9w and O9w’ oxygen sites of a H2O molecule (Fig. 1, Tables 2, 3 and 5).

Table 2 Details of the neutron data collection and refinement of inderite
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Table 3 Refined fractional atomic coordinates and equivalent/isotropic displacement factors (Å2), based on the neutron structure refinement
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Table 4 Refined displacement parameters (Å2) in the expression: -2π2[(ha*)2U11 + … + 2hka*b*U12 + … + 2klb*c*U23], based on the neutron structure refinements
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Fig. 1
figure 1

(Top left) The principal building unit of the structure of inderite, i.e., Mg(OH2)4B3O3(OH)5, and (right) a view of the structure down to [100], based on the model derived by the neutron structure refinement of this study at 280 K. (Bottom left) Detail of the structure model with the split (and mutually exclusive) O9w-O9w’ sites. Displacement ellipsoid probability factor: 80%

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Table 5 Relevant bond distances (Å) and angles (°) based on the neutron structure refinements (*distances corrected for riding motion effect, according to Busing and Levy 1964; <  > indicates the average bond distances of a given polyhedron)
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A second refinement was conducted with the intensity data collected at low temperature (10 K), starting with the structure model obtained at 280 K. The best figures of merit were obtained with a model in which all the fifteen H sites were refined anisotropically, while the other sites (i.e., Mg, B and O sites) were left isotropic (Table 4). At this temperature, no evidence of the O9w-O9w’ split sites was found, with only one unique site position (Table 3).

Further details pertaining to the structural refinements at both 280 and 10 K are given in Table 2. Atomic coordinates and displacement parameters are listed in Tables 3 and 4, whereas a series of selected interatomic distances and angles are given in Table 5. CIF is available as supplementary electronic material.

Results and discussion

The experimental findings obtained in this study confirm the ideal formula of inderite previously reported in the literature: MgB3O3(OH)5·5H2O (or Mg[B3O3(OH)5](H2O)4·H2O). The only potential substituents of Mg is Ca, though for less than 0.01 apfu, whereas no substituents for B are found at a significant level (Table 1). Potential substituents of the hydroxyl group (e.g., F or Cl) are not measured at a significant level. Excluding B, inderite does not contain any other industrially-relevant element (e.g., Li concentration is lower than 2.5 wt ppm, Be or REE lower than 0.1 wt ppm). Among the trace elements measured by LA-ICP-MS, only Mn emerges with a concentration of 115(15) wt ppm; all the others are lower than 2.5 wt ppm. Overall, the EPMA-WDS and LA-ICP-MS data show that the chemical composition of inderite from the Kramer deposit is virtually identical to the ideal one. This finding is consistent with our previous results obtained on a series of hydrous borates: colemanite (ideally CaB3O4(OH)3·H2O; Lotti et al. 2017a,b), kurnakovite (ideally MgB3O3(OH)5·5H2O, Gatta et al. 2019), kernite (ideally Na2B4O6(OH)2∙3H2O, Gatta et al. 2020), probertite (ideally CaNa[B5O7(OH)4]·3H2O, Gatta et al. 2022a), meyerhofferite (ideally CaB3O3(OH)5·H2O, Gatta et al. 2022b) and inderborite (ideally CaMg[B3O3(OH)5]2(H2O)4·2H2O, Gatta et al. 2023). For all of those, no significant content of isomorphic substituents was measured. It is worth nothing that the aforementioned hydrous borates share a similar crystallization environment, represented by lacustrine basins fed by thermal springs, but they come from different deposits dislocated even in different continents. This led to discussion whether the unusual purity of the hydrous borates is the effect of the absence of potential substituents, in the growing environment, or if it is governed by crystallochemical reasons. Even in the case of the inderite from the Kramer deposit, with its complex mineral assemblages described in one of the previous sections, it is unlikely a scenario with the absence of potential substituents, especially for Mg. However, this common feature of all the borates formed in lacustrine deposits under hydrothermal activity led Gatta et al. (2019, 2020, 2022a,b) to consider that, in this peculiar geological environment, crystal nucleation and growth could promote purification by iterated dissolution and recrystallization. Furthermore, even crystallochemical reasons can be invoked to explain the compositional purity: the bonding configuration of the slightly distorted Mg-octahedron hinders a substitution of the other environmentally available fluid-mobile cations (both during formation and later diagenesis), e.g., Na, K, Ca, Sr; any potential substitution would require a significant local distortion of the structure, with a consequent chemical strain. The same consideration can be extended also to B, likely with higher barriers: despite Al, Si or S could replace B at least in tetrahedral coordination, though with a strong chemical strain into the structure, only C could be considered for the planar-triangular configuration. In this light, the high purity of inderite can be reasonably ascribed even to crystallochemical reasons, in the form of a high elemental selectivity required by the crystal structure.

The LA-MC-ICP-MS data shows that the B isotopic composition of the Kramer inderite is relatively homogeneous. Single spot analyses along a rim-core-rim profile, parallel to the b-axis of the investigated crystal, report fairly similar B isotope composition within error (from − 6.97 ± 1.83 to − 9.52 ± 1.23 ‰), with a weighted mean δ11B of − 7.70 ± 1.85‰ (2σ, N = 4) (Table 1). This average δ11B value lies within the range of values in which the source of boron is ascribable to terrestrial reservoirs (e.g., hydrothermal brines), rather than to marine ones (e.g., Swihart and Moore 1986; Hussain et al. 2021, and references therein). This negative B isotopic signature is consistent with what we recently reported on the hydrous borate probertite from the Kramer deposit (Gatta et al. 2022a) and with previous isotopic data from other borates from the same deposit reported by Swihart et al. (1996), ranging from − 9 to + 2‰. These findings corroborate what was previously inferred on the basis of geological evidence about the genesis of the deposit (Gale 1946; Christ and Garrels 1959; Barnard and Kistler 1961).

The neutron structure model here obtained is consistent, in first approximation, with that previously reported by Corazza (1976) based on single-crystal X-ray intensity data. The building units of the structure of inderite consist of: two BO2(OH)2 tetrahedra (B-ion in sp3 electronic configuration) and one BO2(OH) triangle (B-ion in sp2 electronic configuration), linked by corner-sharing to form a (soroborate) B3O3(OH)5 ring, and a Mg-octahedron Mg(OH)2(OH2)4 (Fig. 1, Tables 3 and 5). The B3O3(OH)5 ring and the Mg-octahedron are connected, by corner-sharing, to form an isolated Mg(H2O)4B3O3(OH)5 (molecular) cluster (Fig. 1). The tri-dimensional edifice of inderite is therefore built by heteropolyhedral Mg(H2O)4B3O3(OH)5 clusters mutually connected by H-bonds, even mediated by the zeolitic (“interstitial”) H3-O13w-H9 molecules lying between the clusters (Figs. 1 and 2, Table 5). The corner-sharing B3O3(OH)5 ring is a combined building unit that occurs in the crystal structure of a series of hydrous borates, among those: kurnakovite, meyerhofferite, inderborite, or inyoite (Hawthorne et al. 1996). The weak interconnections between Mg(H2O)4B3O3(OH)5 molecular clusters govern the perfect cleavage {010}, observed in the crystals of inderite, along with its low hardness (Mohs 3).

Fig. 2
figure 2

The complex and pervasive H-bonding network in inderite structure, based on the neutron structure refinement of this study (at 280 K). Displacement ellipsoid probability factor: 80%

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The neutron structure refinements of this study prove that:

  1. 1.

    The planar-triangular BO2(OH) unit shows a fairly regular geometrical configuration, with Δ(B3-O)max ~ 0.03 Å (i.e., here defined as the difference between the longest and the shortest bond length; structural model at 280 K without the O9w split), average O-B3-O ~ 120° (with O-B3-O angles ranging between ~ 115° and ~ 124°), and aplanarity < 1.4° (here defined as the average angle described by the plane on which the 3-oxygen sites lie and each of the three independent B3-On vectors) (Table 5). The two independent tetrahedral BO2(OH)2 units show a modest distortion, in response to the common feature with one bond length systematically longer than the other three, with Δ(B1-O)max ~ 0.06 Å and Δ(B2-O)max ~ 0.05 Å, and an average O-B-O angle for both the tetrahedra of ~ 109.5° (Table 5). The Mg(OH)2(OH2)4 octahedron is more distorted, with Δ(Mg-O)max ~ 0.13 Å (Table 5) and maximum deviation from the ideal O-Mg-O angle of ~ 6°; however, there is no significant difference among the Mg-O bond lengths in response to the different nature of the ligand (i.e., Mg-OH or Mg-OH2).

  2. 2.

    The neutron structure refinement at 280 K shows evidence of a static disorder pertaining to the O9w site, which is better modelled with two mutually exclusive subsites (O9w and O9w’, Table 3) only ~ 0.4 Å apart. This local disorder disappears at low temperature: the refinement based on the intensity data collected at 10 K does not show any robust evidence of the two split subsites. Static disorder pertaining to the hydroxyl groups or H2O molecules is not unusual in this class of material, as previously observed in colemanite (Lotti et al. 2017a,b) or in kernite (Gatta et al. 2020). However, the reason of the structural disorder in inderite remains unclear. The only significant difference between the H5-O9w-H14 molecule and the other three independent H2O molecules pertains to their H-bond geometry: whereas the O6…O9w…O1 angle is ~ 105.5°, the other configurations show acute angles (i.e., O5…O10w…O1 ~ 81.1°, O3…O12w…O10w ~ 76.2° and O4…O11w…O13w ~ 88.3°). However, the split configuration does not change significantly the scenario: the O6…O9w…O1 angle is ~ 104.7° and O1…O9w’…O6 is ~ 105.8°. In addition, at low temperature, the unique O6…O9w…O1 angle is only slightly lower if compared to the one at 280 K (unsplit model): ~ 104.8°. Furthermore, the libration regime of some O and H sites is significantly anisotropic, as shown by the Uij tensors at 280 and even at 10 K (Fig. 2, Table 4). This could partially be the effect of an ineffective absorption correction due to high B content of inderite (B2O3 ~ 37.3 wt%).

  3. 3.

    All the thirteen independent oxygen sites of the structure are involved in H-bonding, as donors (O1, O2, O5, O7, O8, O9w, O10w, O11w, O12w, O13w) or as acceptors (O1, O3, O4, O5, O6, O7, O8, O9w, O10w, O12w, O13w) (Table 5). This confirms the pervasive nature and the important role played by the H-bonding network on the structural stability.

  4. 4.

    The four independent H2O molecule bonded to Mg (i.e., H5-O9w-H14, H7-O10w-H13, H6-O11w-H12, H10-O12w-H15; Table 5) shows an almost regular geometry, with the H–Ow–H angles ranging between 104.5° and 107.7° at 280 K, and between 103.8° and 106.0° at 10 K (Table 5). Differently, the zeolitic H3-O13w-H9 molecule shows a stretched configuration with the H3-O13w-H9 angle of 110.0° at 280 K and 108.6° at 10 K. This configuration likely reflects the H-bonding scheme in which the molecule is involved: the O3…H9-O13w-H3…O4 angle is 111.5° at 280 K and 112.0° at 10 K, so that the opening of the H-Ow-H angle is an adaptive effect driven by the bonding geometry. All the O–H distances of the H2O molecules, corrected for “riding motion effect” (following Busing and Levy 1964), range between 0.962 and 1.001 Å at 280 K and between 0.983 and 1.004 at 10 K (Table 5). Excluding the H10-O12w-H15 molecule, all the others belonging to the coordination environment of Mg show a H-bonding scheme with one donor (OD) and one acceptor (OA) site, with OD-H…OA angle ranging between 152.3° and 172.9° (at 280 K, but without any significant variation at 10 K), OD…OA distance between 2.69 and 2.91 Å and H…OA between 1.72 and 1.94 Å at 280 K (1.68–1.97 Å at 10 K) (Table 5), with an energetically favourable configuration (i.e., Steiner 1998; Gatta et al. 2021). The H10-O12w-H15 molecule shows a more complex configuration: H10 is H-bonded to O3 (with H10…O3 ~ 1.94 Å, O12w-H10w…O3 ~ 169.0° at 280 K, Table 5) and H15 shows a bifurcate bonding scheme with O10w and O9w as acceptors (H15…O10w ~ 2.59 Å and O12w-H15…O10w ~ 129.4°, H15…O9w ~ 2.43 Å and O12w-H15…O9w ~ 161.0° at 280 K).

All the O–H distances of the hydroxyl groups (i.e., O1-H11, O2-H4, O5-H8, O7-H1, O8-H2, Table 5), corrected for “riding motion effect”, range between 0.967 and 0.995 Å at 280 K (and between 0.970 and 1.009 at 10 K) (Table 5). All the OH groups, excluding O5-H8, are involved in H-bonds with one acceptor site, with OD…OA distances between 2.67 and 2.89 Å, H…OA between 1.75-1.93 Å and OD-H…OA between 157.4 and 176.1° at 280 K (Table 5). The O5-H8 group shows a bifurcated H-bonding scheme, with O12w and O13w as acceptors (with O5…OA between 3.30 and 3.37 Å, H8…OA 2.58-2.79 Å, O5-H8…OA 120.4-133.5°, at 280 K, Table 5). There is no significant variation of the bonding scenario of the OH-group at 10 K (Table 5), if compared to that at 280 K.

On the whole, all the H-bonds, in which OH2 molecules or OH-groups are involved, are relatively strong, excluding the H10-O12w-H15 molecule and the O5-H8 group that show relatively weak H-bonds. Interestingly, there is no evidence of intra Mg(H2O)4B3O3(OH)5 cluster H-bonding: all the H-bonds here observed are inter Mg(H2O)4B3O3(OH)5 clusters.

A careful analysis of the structural data obtained in this study reveals a substantial consistency with the previous structural model obtained by DFT calculations by Zhou et al. (2012). More specifically, the ab initio DFT calculations were performed using Full Potential Linear Augmented Plane Wave (FP LAPW) with the WIEN2k software package, in combination with high-resolution solid-state 11B and 25 Mg MAS NMR spectroscopy, permitting the location even of the hydrogen positions at their 15 crystallographically-independent sites. The atomic coordinates of all the independent crystallographic sites have been provided by Zhou et al. (2012), but not all the O–H bond distances. However, a general comparative analysis can be done, and the most important results are given in Table 6, in which the average bond distances of coordination polyhedra and O–H distances are listed, based on the DFT modelling and on the experimental data obtained in this study. It is worth nothing that the difference between DFT and experimental data (e.g., ND at 280 K, Table 6), pertaining to the average bond distances of the Mg-octahedron, B1- and B2-tetrahedra and B3-planar unit, are all ≤ 0.01 Å. The scenario is only slightly worse if we consider that O–H distances: the maximum difference between the theoretical vs. experimental O–H distances pertaining to the hydroxyl groups is ≤ 0.08 Å, to the H2O molecules (including even the zeolitic H3-O13w-H9 molecule) is ≤ 0.07 Å (Table 6). Overall, the theoretical structural model appears to be highly consistent with the experimental one.

Table 6 Comparison of the bond distances (Å) obtained by DFT calculations (Zhou et al. 2012) and in this study (ND: neutron diffraction, Table 5) (*distances corrected for riding motion effect; <  > indicates the average bond distances of a given polyhedron; n.p.: not provided)
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The crystal structure of inderite and its dimorph kurnakovite are significantly different. In kurnakovite, the same building units observed in inderite structure (i.e., B3O3(OH)5 ring + Mg-octahedron Mg(OH)2(OH2)4) form Mg(H2O)4B3O3(OH)5 clusters, but with a different bonding topology: clusters are connected to give (neutral) ···[Mg(H2O)4B3O3(OH)5]··· chains parallel to [001]. Such chains are mutually bonded to give the tri-dimensional structure only via H-bonds, even mediated by the extra-chains zeolitic H2O molecules (as also observed in inderite). In response to the different bonding topology, in kurnakovite structure there are even intra ···[Mg(H2O)4B3O3(OH)5]··· chain H-bonds; in contrast, as already reported above, in inderite only inter Mg(H2O)4B3O3(OH)5 clusters H-bonds occur.

The H-bonding scheme obtained in this study can be considered as consistent with the IR and Raman spectra of inderite reported by Li et al. (1995), Kloprogge and Frost (1999), Frost et al. (2013), and Chukanov (2014), in particular referred to the O–H stretching region. Frost et al. (2013) reported a series of distinct Raman bands at 3052, 3233, 3330, and 3392 cm−1, attributed to H-Ow-H stretching vibrations, and at 3459, 3530 and 3562 cm−1, assigned to hydroxyl O–H stretching vibrations. However, some broader bands likely reflect the convolution of more independent active modes. Even the IR spectra show a series of signals ascribable to the O–H stretching region of H-Ow-H and O–H groups (at least at 3625, 3580, 3470, 3435, 3360, 3260, 3060, 2940 cm−1), with systematic convolutions. Such complex Raman and IR spectra reflects the occurrence of a series of independent O–H stretching bonds, ascribable to hydroxyl groups or H2O molecules, consistently with the complex and pervasive H-bonding network observed on the basis on the neutron structure refinements of this study. The almost superimposed Raman or IR signals are the effect of similar geometric configurations of a series of independent H-bonds, as observed in this study in terms of OD…OA and H…OA distances (Table 5).

We have recently investigated the high-pressure behavior of inderite by in-situ single-crystal synchrotron X-ray diffraction up to 17 GPa (Comboni et al. 2023), to explore its stability field at high-pressure, the anisotropy of its compressional pattern and the deformation mechanisms at the atomic scale. We observed that inderite experiences a first-order phase transition (from P21/c to P21/n, with a = 13.4308(7), b = 11.9970(5), c = 10.4466(8) Å, and β = 100.030(6)°), between 6.45(5) and 6.94(5) GPa. Such a pressure-mediated transition is reconstructive in character, and perfectly elastic. The structure of the high-pressure polymorph (called “inderite-II”) was successfully solved and refined. In response to the phase transition, the B-site with a triangular coordination changes its coordination configuration from planar-triangular to tetrahedral, bonding the zeolitic H2O. As a consequence, if the crystal structure of inderite can be described as a repetition of isolated Mg(H2O)4B3O3(OH)5 clusters, in inderite-II the newly formed B-tetrahedra connect two of these clusters, thus forming complex cluster units made by 2 Mg-octahedra and 6 B-tetrahedra, with Mg2(H2O)8B6O6(OH)10(H2O) stoichiometry. The Mg2(H2O)8B6O6(OH)10(H2O) units are mutually connected by a complex net of H-bonds to form the crystalline edifice of the high-pressure polymorph. The effects of low temperature observed in this study, in terms of structural deformation at the atomic scale, are almost incomparable with those observed at high pressure, as the unit-cell volume at 10 K corresponds to that estimated at 0.1–0.2 GPa, and the first structural refinement at high pressure was performed on the basis of the data collected at 0.46(5) GPa.