The intrinsic twinning and enigmatic twisting of aragonite crystals

Significance

Based on our single crystal X-ray diffraction (SCXRD) and transmission electron microscopy (TEM) study of aragonite crystals from various localities, we show that in some zones of geological aragonites, the twin densities are comparable to those of crystals from molluscs shells. This is consistent with performed calculations according to which at ambient conditions, the Gibbs free energy of twin-free aragonite crystal is close to that of periodically twinned aragonite structure. In some cases, high twin densities result in the appearance of diffuse scattering in SCXRD patterns. The obtained TEM and optical micrographs show that besides the twin boundaries of growth origin, there are also twin boundaries and especially stacking faults that formed as the result of local strain compensation.

Abstract

It is generally accepted that aragonite crystals of biogenic origin are characterized by significantly higher twin densities compared to samples formed during geological processes. Based on our single crystal X-ray diffraction (SCXRD) and transmission electron microscopy (TEM) study of aragonite crystals from various localities, we show that in geological aragonites, the twin densities are comparable to those of the samples from crossed lamellar zones of molluscs shells. The high twin density is consistent with performed calculations, according to which the Gibbs free energy of twin-free aragonite is close to that of periodically twinned aragonite structure. In some cases, high twin densities result in the appearance of diffuse scattering in SCXRD patterns. The obtained TEM and optical micrographs show that besides the twin boundaries (TBs) of growth origin, there are also TBs and especially stacking faults that were likely formed as the result of local strain compensation. SCXRD patterns of the samples from Tazouta, in addition to diffuse scattering lines, show Debye arcs in the $a^{\ast }{b}^{\ast }$ plane. These Debye arcs are present only on one side of the Bragg reflections and have an azimuthal extent of nearly 30°, making the whole symmetry of the diffraction pattern distinctly chiral, which has not yet been reported for aragonite. By analogy with biogenic calcite crystals, we associate these arcs with the presence of misoriented subgrains formed as a result of crystal twisting during growth.

The twinning of geological aragonite crystals can be deduced already from its pseudohexagonal form, which is due to the intergrowth of three crystals in the twin orientation (1). Active research of aragonite twinning began soon after it was confirmed by the transmission electron microscopy (TEM) technique in biogenic crystals from molluscs shells (2). The outstanding mechanical properties of these biogenic constructions, in particular of the nacre, significantly exceed those of individual aragonite crystals (3, 4). This, in addition to other factors, is connected with the microstructure of individual aragonite grains (5).

Nanoscale polysynthetic twinning of growth nature has further been confirmed on aragonites of biogenic, geological, and synthetic origin (2, 6–10). Due to the small size of the samples, studies of biogenic aragonites microstructure typically rely on the TEM, which is inherently local in nature. The estimation of twin density based on comparison of full width at half maximum (FWHM) of X-ray powder diffraction peaks was proposed by Mukai et al. (6–8). An obvious disadvantage of this approach is the presence of additional factors affecting the FWHM, among which are crystal defects, local strain, and coherent scattering length (6). According to the obtained estimations, the twin density of biogenic aragonites is maximum in the crossed lamellar zone of the mollusc shell, which is much higher than that of geological samples (6–8). It is generally accepted that abiotic aragonites are characterized by only sporadic twinning planes and twin densities much lower than for biotic samples (11).

In this study, we propose that for obtaining the final conclusion about twin densities, a more detailed investigation of geological aragonites is necessary. By means of high-resolution TEM and single crystal X-ray diffraction (SCXRD) analyses, in combination with classical optical microscopy of thin sections under polarizing light, we demonstrate that aragonites of geological origin are no less twinned than biotic ones.

1. Methods

A. Specimen and Thin Section Preparation.

For this study, we chose geological crystals of aragonite of infiltration–sedimentary and hydrothermal genesis from Tazouta (Morocco), Enguidanos (Spain), Molina de Aragon (Spain), and Koge-Dava (Tuva region, Russia). Specimens collected from Morocco (Tazouta) and Spain (Enguidanos and Molina de Aragon) appear in Mg-rich clays. The formation of Spain crystals is suggested as the result of hydrothermal activity within a sedimentary succession (12). The investigation of Morocco crystal genesis has not been performed yet. Based on the low temperature of the formation of Morocco crystals (13), which will be discussed below, we suggest the infiltration–sedimentary genesis for them. Both Morocco and Spain specimens are widely represented in geological museums and on mineral markets and are widely used as type-material in studies of geological aragonites (8, 14, 15). Another type of the specimens used in the study was needle-like aragonite crystals from low-temperature hydrothermal veins in shallow-level dolerite bodies found on Koge-Dava pass in the Tuva region (Russia) (16).

Pseudohexagonal crystals from Tazouta and Molina de Aragon were cut into slabs parallel to the (001) plane using a Well 3400 diamond wire saw. The slabs were used to prepare the through-depth thin sections for optical microscopy and for the preparation of SCXRD and TEM samples.

Unfortunately, the small size of aragonite needles from Koge-Dava hindered the preparation of the oriented thin sections, so the SCXRD specimens were picked up from the pieces of the crushed crystals.

B. Chemical Composition and X-ray Diffraction.

B.1. Chemical composition.

The chemical composition of the samples was determined by the energy-dispersive scanning electron microscopy (SEM-EDS) technique and by wavelength-dispersive X-ray spectroscopy (WDS) electron microprobe analysis. In total, the composition was determined for the samples of all three localities in more than 270 points.

SEM–EDS studies of the samples were performed using an Oxford Instruments INCA Energy 350 microanalysis system with a liquid nitrogen-free Large area EDS X-Max-80 Silicon Drift Detector installed on a JEOL JSM-6510LV SEM. EDS spectra were collected with an acquisition time of 30 s at an accelerating voltage of 20 kV and a beam current of 1 nA. The beam diameter was approximately 2 to 3 µm. EDS spectra were optimized for quantification using the standard XPP procedure included in INCA Energy 350 software. The technique is similar to that described in our work (17).

The WDS analysis was performed using a CAMECA Camebax Micro. The measurements were performed at an accelerating voltage of 20 kV, beam current of 30 to 50 nA, and an electron beam size of 2 µm. Counting times for each element were generally 30 s (15 s for peaks and 15 s for background from both sides), except for Ca (10 s on peak with $\pm$5 s for background). Raw analytical microprobe data were processed using a standard ZAF matrix correction routine. The detection limits (3$\sigma$ criterion) are within typical analytical conditions, 0.01 to 0.03 at %. The technique is similar to that described in our work (18).

Further details of the used SEM-EDS and WDS techniques can be found in ref. 19.

B.2. X-ray diffraction.

The crystals of aragonite for the SCXRD experiments were selected from the slabs as follows. First, several large blocks with different twin densities were cut out along the existing fracture lines. Then, the blocks were carefully divided into several parts, which, in turn, were crushed, and SCXRD samples were taken from the resulting fragments. This procedure allows us to connect the obtained diffraction patterns with the specific microstructures, observed in thin sections under polarized light.

The single-crystal X-ray diffraction study was performed using a Rigaku XtaLAB Synergy-S four-circle diffractometer, MoK$\alpha$ radiation.

C. Transmission Electron Microscopy.

The frequency of twinning in aragonite crystals was studied in crystal foils, cut parallel to (001) plane, and powdered samples. The orientations were fixed based on crystal morphology, then thin $2\times 2$-mm oriented sections of crystals were cut by a wire saw and mounted into 3-mm brass rings and fixed in position with an epoxy resin. The discs were cut and polished to $\sim$ 100-µm thickness and dimpled down to 20 µm at the disc center. The samples were subsequently ion–milled using 4-kV Ar⁺ ions (Pips Model 691, Gatan Inc., Pleasanton, CA) until perforation. To prevent charging during observations, the samples were sputtered by a thin layer of carbon. TEM studies were performed using a 200 kV field–emission transmission electron microscope (JEM 2010F, Jeol Ltd., Tokyo, Japan) with an ultrahigh–resolution objective pole piece having a resolution limit of 1.1 Å that allows to resolve lattice images. High-resolution TEM (HRTEM) images were recorded close to the first reverse passband, where atomic columns are resolved as white dots under the weak phase object imaging regime. EDS (Link ISIS 300, Oxford Instruments, Oxfordshire, UK) was employed to verify the local chemical composition of the samples. Slow decomposition was observed under high electron doses.

D. Calculations.

All calculations were performed within the density functional theory (DFT) implemented in the VASP 5.4.4 package (20, 21). The exchange-correlation interaction was taken into account within the generalized gradient approximation in the scheme of Perdew–Burke–Ernzerhof (22). In the case of 2O-polytype, the total energies are converged to ${10}^{-7}$ eV/cell with the energy cutoff of 800 eV. Since the unit cell of 6O-polytype is three times larger than that of 2O-polytype, we set the energy convergence criterion to ${10}^{-5}$ eV/cell with the energy cutoff of 600 eV. The Brillouin zone was sampled according to the Monkhorst–Pack scheme (23) with the $k$-point mesh of $4\times 4\times 5$ and $1\times 2\times 2$ for 2O- and 6O-polytypes, respectively. Gaussian smearing with a parameter $\sigma$ = 0.05 eV was used. Calculations of the phonon spectra and temperature effect on Gibbs free energy were performed using the PHONOPY program (24). The real space force constants were calculated using supercell and finite displacement approaches, with $3\times 1\times 1$ and $2\times 1\times 1$ supercells for 2O- and 6O-polytypes, respectively.

2. Results

A. Thin Sections.

Aragonite crystals from Tazouta, Molina de Aragon, and Enguidanos are characterized by their pseudohexagonal habit due to a mimetic twinning by the {110} planes (Fig. 1). In crossed-polarized light, the polysynthetic twinning can be also observed for the crystals of each locality (Fig. 2).

Fig. 1.

Mineralogical specimens of aragonite used in this study. (A) Tazouta (Sefrou, Morocco), (B) Molina de Aragon (Guadalajara, Spain), (C) Enguidanos (Cuenca, Spain), and (D) Koge–Dava (Tuva, Russia). The illustration of pseudohexagonal interpenetration twin of aragonite, characteristic for the mineralogical samples, above panel (B) (Courtesy of Dr. Mirjan Žorž).

Fig. 2.

Thin sections prepared from Tazouta (A), Molina de Aragon (B) and Enguidanos (C) crystals under polarized light; the inset A on panel C shows the morphology of the twin boundaries at higher magnification; numbers I, II, and III show different twin domains.

The studies of successive series of thin sections parallel to the (001) plane of Tazouta crystals have shown that the real location of the domains is more complex than the idealized picture of Fig. 1 and can differ significantly throughout the crystal (SI Appendix, Figs. S1 and S2). Tazouta crystals are further complicated by fine polysynthetic twinning within individual domains (Fig. 2A). The density of this polysynthetic twinning in Morocco crystals varies significantly both within individual crystal and among different crystals (SI Appendix, Fig. S2).

Enguidanos and Molina de Aragon crystals differ from the Tazouta crystals in size, color (Fig. 1), and twin pattern (Fig. 2). In Molina de Aragon crystals, a high density of polysynthetic twinning is observed near the contacts of large domains of the cyclic twin. Polysynthetic lamellae, present at these boundaries, are quickly discontinued without going deeper into the crystal, as a result of which the boundary between the domains acquires a characteristic jagged form (Fig. 2B). Similarly, in the Enguidanos crystal, the twinning boundaries are characterized by the jagged shape due to fine polysynthetic twinning (Fig. 2C).

Areas of strain-associated polysynthetic twinning were found in the peripheral areas of the crystals from Tazouta and Molina de Aragon (Fig. 3).

Fig. 3.

Strain-associated TBs are marked as white arrows in the thin sections of Tazouta (A) and Molina de Aragon (B) crystals.

B. Chemical Composition.

The results of the chemical analyses are summarized in SI Appendix, Tables S1–S7. The average compositions of the samples are the following:

Tazouta: Sr_0.003Na_0.005Ca_0.992(CaO₃),

Enguidanos: Sr_0.009Na_0.001Ca_0.99(CaO₃),

Molina de Aragon: Sr_0.005Ca_0.995(CaO₃),

Koge-Dava: Sr_0.001Na_0.001Ca_0.998(CaO₃).

In addition, inclusions of quartz grains and some alkaline aluminosilicates were detected in the crystals from Tazouta and Molina de Aragon. In crystals from Tazouta, the grains of dolomite were found as well. The unambiguous connection between the mineral composition, inclusion content, and/or density of twinning observed in thin sections was not found.

C. X-ray Diffraction.

Aragonite twinning is characterized by the well-known splitting of reflections, as shown in Fig. 4. In addition, two more diffraction features, which were not previously described, were observed. These are diffuse scattering in the form of straight lines passing along the [110]* and Debye arcs presented in the $a\ast b\ast$ planes. Both diffuse scattering and Debye arcs were found only in the Tazouta crystals and were not observed in the samples from Molina de Aragon, Enguidanos, and Koge-Dava. The thin sections of Tazouta crystals with marked sampling areas are shown in Fig. 5. The positions of sampled areas are approximate, and the actual positions may be slightly shifted.

Fig. 4.

Scheme of the diffraction pattern of aragonite single crystal (A) and twin (B); the allowed reflections are marked with filled circles, the forbidden reflections—with empty circles; the twinning plane (110) is shown with a dashed blue line.

Fig. 5.

Optical micrographs in polarized light of two different Tazouta crystals (A, B); the circles show the sampling areas, the results of X-ray diffraction experiments are summarized in three sectors of the circle, the five blocks on which the initial slab was split up are outlined with a dashed line.

Diffuse scattering lines are clearly seen in the $hk2$ section of the XRD pattern (Figs. 6 and 7), but they are absent in the sections $hk0$ and $hk1$ (Fig. 6). Usually, only the $hk0$ section is used for the preliminary visual analysis of the diffraction patterns before the structure solution. This may explain why earlier findings of diffuse scattering were absent. In some cases, diffuse scattering lines form a characteristic six-beam star around the central reflection (Fig. 8A). The estimation of the intensity of diffuse scattering has shown that it is about 2 to 4 times more intense than the background and in the case of the diffraction pattern shown in Fig. 8B it is nearly five times less intense than the (130) reflection.

Fig. 6.

$\mathit{hkn}$ sections of SCXRD patterns with blue arrows marking the diffuse scattering lines. The sample is from area J in Fig. 5.

Fig. 7.

$hk2$ section of the SCXRD pattern with intense diffuse scattering lines. The sample is from area B’ in Fig. 5.

Fig. 8.

$hk2$ section of the SCXRD pattern (A) and corresponding A-B and C-D sections through the diffuse scattering lines (B). The sample is from area K in Fig. 5.

The diffuse scattering lines were found in 8 out of 16 studied samples (Fig. 5). They are usually present in specimens with diffraction patterns typical for the twin. Some of these diffraction patterns are shown in Figs. 6 and 7. However, we have found two samples where diffuse scattering lines were observed in the diffraction pattern of a single crystal (SI Appendix, Fig. S3).

The second feature of the obtained diffractograms is the presence of Debye arcs at one side of Bragg reflections. These arcs have an azimuthal extent of nearly 30° and are located in the sectors between two neighboring reflections (Fig. 9A). As a rule, Debye arcs have a discontinuous character, and individual reflections are clearly distinguished within them (Fig. 6). The chiral arrangement of the Debye arcs is noteworthy—in Fig. 6 and in Fig. 9, they run in a clockwise direction. Like diffuse scattering, the Debye arcs are present only locally and were observed in 4 out of the 16 studied samples (Fig. 5).

Fig. 9.

$hk0$ section of the SCXRD patterns of aragonite crystals from Tazouta (A) and from Koge-Dava (B).

As already noted, the diffuse scattering and the Debye arcs were not detected in crystals from Molina de Aragon, Enguidanos, and Koge-Dava. In the case of Koge-Dava, all four specimens prepared from different crystals gave the standard twinned diffraction pattern (Fig. 9B) and we failed to find a specimen with a diffraction pattern of a single crystal. In the case of Molina de Aragon and Enguidanos crystals, on the contrary, most of the samples were single crystals.

D. Transmission Electron Microscopy.

In all samples, {110} twinning is traced down to the optical microscope resolution limit and goes further to a much finer scale, approaching that of a single (110) layer. Under bright-field imaging conditions, twin domains are seen as bands of alternating contrast when the crystal is tilted close to the [001] projection in TEM. In this way, it is rather straightforward to observe the relative density of twin domains in different parts of the crystal. Fig. 10 shows the TEM image of polysynthetic (110) twins in outer sections of an aragonite crystal from Tazouta, with the corresponding selected area electron diffraction in [001] projection (Fig. 10A). Wider crystal domains within the twin lamellae are crosshatched by a network of planar defects running along two sets of {110} planes (Fig. 10B). These defects are typically pinned to primary TBs and correspond to (110) stacking faults (SFs) of a secondary origin.

Fig. 10.

Polysynthetic twinning in aragonite. (A) Lamellar twinning in the sample from Tazouta with characteristic twin reflections in the electron diffraction pattern recorded in [001] projection (Inset) over the twinned region. The red outline denotes a transposed aragonite cell in the reciprocal lattice; black arrows indicate twin boundaries. (B) Crystal domains intersected by a network of stacking faults running in both sets of {110} planes.

While in the outer regions of pseudohexagonal crystals TBs are predominantly parallel, occupying one set of the {110} planes, in their core, TBs occupy both sets of {110} planes (Fig. 11A). In some parts of the crystal, the density of twins approaches the level of disordered polytypes (Fig. 11B). Along with the high density of TBs, SFs in (110) and $(1\overline{1}0)$ planes are quite frequent (Fig. 11C). Close to the first reverse passband of the contrast transfer function, Ca-atomic columns contribute the most of the intensity in phase contrast imaging. As a result, the aragonite structure appears as a pattern of white dots forming a honeycomb pattern when viewed along [001], whereas weaker dots within these pseudohexagonal channels correspond to the centers of the [CO₃] triangles.

Fig. 11.

(A) Core section of cyclic aragonite twin from the Tazouta locality with high density of TBs and SFs and electron diffraction pattern with split reflections (Inset). (B) Sequence of parallel TBs with varying numbers of (110) layers ($n=2,3,8,9$) in the sample from Koge-Dava. (C) Intersecting SFs in two sets of {110} planes.

If we follow the array of white dots along the $(1\overline{3}0)$ plane in the HRTEM image of Fig. 12A, we see that it deflects upward when crossing the TB. This is due to the so-called desymmetrization of the aragonite structure (25, 26), resulting in a +3.78° tilt of $(1\overline{3}0)$ planes from the (110) plane normal. Kinks of $(1\overline{3}0)$ planes can be used for simple identification of the TBs in HRTEM images. In the HRTEM image of a SF (Fig. 12B), we observe a double kink that brings the second domain back into original orientation with a slight upward shift of $(1\overline{3}0)$ planes for $\mathrm{\Delta }SF=+0.2758$ Å. Thus, effectively, SF is a repeated twin in two successive (110) planes of [CO₃] triangles, where one (110) layer ($n=1$) is in twin orientation. Longer periods of double (110) twins ($n=2,3,$ etc.) can be found, and an example of that is shown in the HRTEM image in Fig. 12A.

Fig. 12.

HRTEM analysis of twinning viewed in [001] direction. (A) An experimental HRTEM image of (110) twin lamella deflecting $(1\overline{3}0)$ planes for a fraction of [110]. (B) Experimental (above) and simulated (below) HRTEM images of (110) twin in aragonite; a feeble kink of $[1\overline{3}0]$ direction (red line) when crossing the (110) twin plane (green vertical line, located on the plane of [CO₃] triangles). (C) Experimental (above) and simulated (below) HRTEM images of (110) SF in aragonite; twinning in two consecutive (110) planes producing a SF with one (110) layer in twinned orientation. Small deviations from experimental and simulated images are due to minor misorientation of crystals under experimental conditions. The strong white dots represent Ca atomic columns.

During TEM investigations of geological aragonite samples, we observed that the density of twins decreases from core to rim zones. The highest density of TBs and SFs is observed near the nucleation point of aragonite crystals. This zone is rich in defects and clay mineral inclusions as can be seen in SI Appendix, Fig. S1. Very high density of TBs along all {110} planes is observed in the Koge-Dava sample.

E. DFT Calculations.

To estimate the energy ratio of a single-crystal aragonite and disordered polytype of aragonite similar to that observed in HRTEM images (Fig. 11B), we have calculated the Gibbs free energies for the structures with the aforementioned parameter $n$ equal to 1 and 3. The sequence $...|+-|+-|...$ corresponds to the structure with $n=1$, where $+$ and $-$ represent the initial and twinned orientations of the (110) slab. A graphical illustration of this structure can be found in ref. 17. The structure with $n=3$ is described by the sequence $...|+++---|+++---|...$ Due to the orthorhombic symmetry of both structures, they can be designated as 2O- and 6O-aragonite, respectively, according to the Ramsdell notation (27). The atomic coordinates of these structures are given in SI Appendix, Table S8. Here, it should be noted that the idea to consider such structures as aragonite polytypes was proposed by Makovicky (25), who suggested the possibility of the formation of $n=1$ structure.

The performed calculations have shown the dynamic stability of both 2O- and 6O-polytypes (SI Appendix, Fig. S4). In static atom approximation, the enthalpy of the 6O-polytype is even lower than that of aragonite. Normalized on the enthalpy of aragonite, the enthalpies of 2O- and 6O-polytypes are equal to $0.004$ and $-0.013$ eV/f.u., respectively. However, with increasing temperature, the Gibbs free energies of polytypes increase, and at temperatures above 130 K aragonite becomes more energetically favorable (Fig. 13). At room temperature, the energies of the 2O- and 6O-polytypes are approximately equal to each other and by 0.015 eV/f.u. above the energy of aragonite. This energy difference can be characterized as insignificant and close to the error of the method.

Fig. 13.

The dependence of Gibbs free energy on temperature for 2O- and 6O-polytypes of aragonite.

We also calculated the dependence of the Gibbs free energy for aragonite and 2O-polytype on pressure at temperatures of 0 K, 500 K, and 1,000 K (SI Appendix, Fig. S5). According to the obtained results, the energy difference between aragonite and the 2O-polytype increases by 0.02 eV/f.u. when the pressure increases from 0 to 10 GPa. Finally, it can be concluded that at low temperatures and pressures, the energies of aragonite and twinned polytypes are close to each other, while at high pressures and/or temperatures, aragonite is more energetically favorable. Hence, aragonite crystals forming in the Earth’s mantle should be less twinned than the specimens formed at subsurface conditions.

3. Discussion

A. Diffuse Scattering and Twinning.

Diffuse scattering in the [110]* direction detected by XRD analysis can be unambiguously associated with the disordered series of TBs observed at TEM. It is noteworthy that diffuse scattering was detected on Tazouta crystals and was not observed on crystals from Koge-Dava, for which locally we observed even higher twin densities (Fig. 11B). This can be explained by the fact that in the case of crystals from Tazouta, disordered series of TBs are reproduced in the areas whose size is comparable or even exceeds the size of the XRD sample (about 0.1 mm), while on crystals from Koge-Dava the size of these areas is significantly smaller. The obtained HRTEM images (Fig. 11) give an idea of the twin densities realized in geological aragonites. The comparison of them with similar pictures of biogenic samples from crossed lamellar zones (7, 8) shows that the twin densities of biogenic and inorganic samples are comparable and there is no reason to claim that the biogenic specimens are more densely twinned. In this context, it can be also mentioned that Kogure and co-authors observed rather regulated polysynthetic twins with parallel twin planes and unregulated polycyclic ones with two or three directions for the twin planes in crossed-lamellar structures (8). Similarly, we observed diffraction patterns with diffuse scattering lines going in one (Fig. 6), two (Fig. 7), and three (Fig. 8) directions. Thus, not only the density but also the pattern of twins are similar in organic and inorganic aragonites.

The conclusion about the similar twin densities of geological and biogenic aragonites is consistent with the results of thermodynamic calculations. The results show that the energies of the 2O- and 6O-polytype are equal to each other at room temperature and slightly higher than the energy of a single crystal aragonite. The similar energies result in the appearance of disordered series of TBs during crystal growth. The presence of extensive single crystal regions in the samples from Enguidanos and Molina de Aragon is due to the rapid termination of TBs after their generation, which is clearly visible in the thin sections presented in Fig. 2. Thus, there is a legitimate question of whether we should search for the causes of twinning or for the causes of twinning inhibition. The obtained results imply the validity of the second option, which was not considered earlier.

The obtained HRTEM images (Fig. 11A) and photographs of thin sections (Fig. 3) indicate that, in addition to TBs of a growth nature, there are also SFs, and possibly individual TBs, which likely results from stress compensation. The TBs of deformational origin were earlier described around calcite crystals appeared inside aragonite at aragonite$\to$calcite transformation (10).

B. Debye Arcs and Twisting.

The detected Debye arcs on XRD patterns can be explained by the presence in the samples of subgrains with slight misorientation. To the best of our knowledge, twisted aragonites have not been described earlier, and the only example we have found is the helical intergrowth of multiple aragonite crystals from Bisbee Arizona (28). Based on the small width of Debye arcs, which is comparable with the width of the main reflections, we suggest the submicron size of these subgrains. The relatively big size of the subgrains and their local character suggest that there is a low chance of finding them using TEM techniques, and we have not observed them in our TEM experiments. The chiral character of the Debye arcs and their presence only in $a^{\ast }{b}^{\ast }$ sections indicates the mutual orientation of the subgrains. To obtain such a diffraction pattern, the subgrains should be successively rotated around [001] direction all clockwise or all counterclockwise, i.e., the initial crystal should be twisted around the [001] direction.

A similar situation with the formation of rotated around the $c$-axis subdomains at crystal twisting was observed on calcitic micro-structures of the columnar prismatic layer of bivalves (29, 30). Misorientation of calcite domains in this case varies from several to more than 10° and is associated with the presence of internal domains separated by low-angle tilt boundaries. Nanometer-scale subgrains rotated around the $c$-axis were found in biogenic aragonites as well (11). It is characteristic that in both cases, layers of organic matter were not found at the boundaries of the subgrains. Thus, similar processes can be suggested to account for the formation of Tazouta crystals. At the same time, the forces that ensure the chiral orientation of submicron crystals with their successive rotation through an angle of 30° remain enigmatic, and the formation of such a structure as the result of relaxation of the strained structure cannot be excluded.

C. Density of Twinning and Temperature of Crystallization.

As we have shown, the studied crystals significantly differ from each other by twin density, and we attempted to assess the influence of crystallization conditions on this parameter. Carrying out such an assessment is complicated by the difference in crystallization conditions for a number of parameters and the possibility of a joint influence of several parameters on the actual twin density. Another difficulty is the lack of information on the crystallization conditions of geological aragonites. However, regardless of their origin, all geological aragonites seem to have a high density of twins even if they apparently look like single crystals like specimens from Koge-Dava. Only samples from the Iberian Basin, to which Molina de Aragon and Enguidanos (12) belong, were studied in sufficient detail regarding their geochemical origin (12). Information about other aragonites is scarce or absent.

Due to these reasons, we limit ourselves to analyzing the influence of only one, the simplest and most obvious parameter—the crystallization temperature. As we have shown above, it should be inversely proportional to twin density. Analysis of fluid inclusions in crystals from Molina de Aragon indicates that their formation temperature is 210 to 225 °C (12), and crystals from Enguidanos are likely characterized by similar values. Performed clumped-isotope analysis of Tazouta crystals indicated a temperature of 20 to 22 °C (13), and we assume this temperature as the temperature of crystals formation. For crystals from Koge-Dava, the formation temperature has not been estimated, but from the observed mineralization, we assumed that it did not exceed 100 °C (16). Samples of biogenic origin are comparable in crystallization temperature to samples from Tazouta. Thus, according to the available data, the temperature of formation decreases in the row:

Enguidanos, Molina de Aragon $\to$ Koge-Dava $\to$ Tazouta, Molluscs shell.

The same row characterizes the decrease of the twin density. Low-temperature samples from Tazouta are characterized by maximum twin densities, resulting in the appearance of diffuse scattering. In samples from Enguidanos and Molina de Aragon, the polysynthetic twinning is poorly developed and these are the only crystals for which the preparation of single-crystal specimens was not a problem. We suggest the intermediate value of twin density for the crystals from Koge-Dava; the diffuse scattering was not observed for them, while the difficulties encountered in picking up a single crystal specimen indicate the widespread development of polysynthetic twinning. Samples from molluscs shells are similar in twin density to samples from Tazouta according to estimates of Kogure et al. (8). Thus, the available data on natural aragonite crystals at least do not contradict the relation of twin density and crystallization temperature obtained based on the thermodynamic consideration.

D. Twinned Precursor of Aragonite.

Due to the pseudohexagonal character of aragonite structure, the Ca-sublattice crosses the twinning plane only with minor perturbations, while the orientation of [CO₃] triangles became anti-parallel (1, 17) as the result of which, polysynthetically twinned aragonite is characterized by the disorder of [CO₃] triangles through two orientations and the degree of disorder is proportional to the twin density (1, 17, 25, 26). For convenience, we denote this disordered aragonite as tAra (twinned Aragonite). Due to the presence of partial disorder in tAra structure, its atomic arrangement is intermediate between aragonite and amorphous aragonite-structured phase pAra (31, 32). As it was shown above, the energy of tAra is slightly higher than the energy of aragonite, but it is apparently lower than the energy of amorphous phase. Thus, in both energy and atomic arrangement, tAra occupies the intermediate place between aragonite and amorphous phase, and hence, according to Ostwald’s rule of stages, it should/can appear at transition from pAra to aragonite single crystal (33, 34). Formation of tAra at the initial stages of aragonite crystallization was actually observed by Nemeth et al. (35). In this work, a precursor phase with monoclinic symmetry, referred as mAra, was found, which over time was transformed into the twinned aragonite. Based on this, the authors (35) suggested that the presence of {110} twins in the core section of the crystal is indicative of the appearance of the precursor phase mAra. The argumentation presented above indicates that the crystallization of pAra will also result in the formation of tAra, at least in some cases; it can not be also excluded that tAra could act as independent precursor phase, i.e., appear first at aragonite crystallization.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

All study data are included in the article and/or SI Appendix.