- 1. Introduction
- 2. A short summary on the {10.4} surfaces of calcite
- 3. Bassanite {010}: the sharp stacking difference of its elementary d020 layers with respect to those of the {001} and {100} forms. A comparison with the d10.4 layers of the cleavage calcite rhombohedron
- 4. Conclusions
- Supporting information
- References
- 1. Introduction
- 2. A short summary on the {10.4} surfaces of calcite
- 3. Bassanite {010}: the sharp stacking difference of its elementary d020 layers with respect to those of the {001} and {100} forms. A comparison with the d10.4 layers of the cleavage calcite rhombohedron
- 4. Conclusions
- Supporting information
- References
research papers
Epitaxies of Ca sulfates on calcite. II. The main {010}, {001} and {100} forms of bassanite epi-deposited on the {10.4} substrate form of calcite
aDipartimento di Scienze della Terra, Università degli Studi di Torino, Via Valperga Caluso 35, Torino 10125, Italy, bSpectraLab s.r.l., Spin-off Accademico dell'Università degli Studi di Torino, Via G. Quarello 15/a, Torino 10135, Italy, and cNIS, Centre for Nanostructured Interfaces and Surfaces, Università degli Studi di Torino, Via G. Quarello 15/a, Torino 10135, Italy
*Correspondence e-mail: dino.aquilano@unito.it
2D and 3D epitaxies of the main {010}, {001} and {100} forms of deposited bassanite (CaSO4·0.5H2O) on {10.4} calcite (CaCO3) as a substrate are described to provide a theoretical crystallographic background for the replacement of calcite by bassanite both in nature and in the laboratory and by weathering linked to cultural heritage. First, in the third dimension, perpendicular to the investigated interfaces, has been verified in order to establish whether adsorption/absorption can occur (as anomalous mixed crystals) at the bassanite/calcite epi-contacts. Secondly, and by applying the Hartman–Perdok method, 2D lattice coincidences have been obtained from the physical-geometric matches of bonds running in the common directions within the elementary slices facing the substrate/deposit interfaces. This research represents the second and more detailed part of a wider program extended to the epi-interactions between the following pairs: (i) {010}-gypsum/{10.4}-calcite (just published); (ii) bassanite/{10.4}-calcite (the present work); and (iii) anhydrite (CaSO4)/{10.4}-calcite (coming soon).
Keywords: bassanite; calcite; epitaxy; twins; anomalous mixed crystals.
1. Introduction
We recently investigated all compatible 3D and 2D lattice coincidences (herein 3D- and/or 2D-LCs) that can occur at the interface between the {10.4} form of cleaved calcite (substrate) and the {010} pinacoid of gypsum (deposit) (Aquilano et al., 2022). Working on calcium sulfates deposited on gypsum, we knew that when gypsum is heated above ∼150°C in the dry state (or at 75°C in methanol–water solutions), a part of the crystalline water is removed and CaSO4·0.5H2O is formed (Maslyk et al., 2022). This mineral, metastable at all temperatures, occurs in nature as bassanite (Bss) (Weiss & Bräu, 2009) and, as a biomineral, in some deep-sea medusae (Tiemann et al., 2002; Becker et al., 2005). In recent times, bassanite has been shown to play an important role in the complex system where gypsum, bassanite and anhydrite replace calcite (Cc) – in both natural and industrial processes. The authors who work in this sector have mainly focused on studies in the thermodynamic and kinetic fields, using the most advanced techniques of characterization. Thus, bassanite has been viewed as a precursor of gypsum (Van Driessche et al., 2012), or as a key product among the Ca sulfates replacing gypsum (Ruiz-Agudo et al., 2015, 2016). During recent years, we have arrived at the point of formulating a tentative general model for Ca sulfate precipitation from solutions and, through nucleation, to explain the occurrence of bassanite on the surface of Mars (Stawski et al., 2020).
Of all this work, the study we consider the most representative was conducted by Ruiz-Agudo et al. (2016), who determined the 3D crystallographic relationship between calcite (parent) and Ca sulfates (products) using X-ray texture analysis. They chemically obtained all the CaSO4 crystalline phases from the reaction of H2SO4 foreign solutions with the replaced calcite and characterized the CaCO3–CaSO4 transformations by means of their experimental 2D X-ray diffraction analyses. Through this method, they indicated a clear crystal of the three Ca sulfate phases (both hydrated and anhydrous) formed during the interaction of calcite with sulfate-bearing solutions; briefly, they found that an epitaxial {10.4}Cc/{010}Bss relationship was observed in such a way that `…the orientation of the parent calcite determines the disposition of the crystals of the final CaSO4 phase during transformation. The exact mechanism by which the crystallographic information is transferred in a dissolution–precipitation reaction is not well understood yet' (Ruiz-Agudo et al., 2016). Using our notations, the geometry of the (in Å) was described, at that time, as follows: only [001]Bss = 6.336 is parallel to the 1/3[441]Cc vector = 6.425, the linear misfit between them only reaching 1.45%. No other match was found at the calcite/bassanite epi-contact, and this suggests that only 1D- and not 2D-LCs can exist at this interface, in our opinion.
Here, we did not intend to repeat experiments already carried out by others, but only to integrate them and establish a useful tool for comparison and complementary purposes; moreover, we wanted to intervene only when the rules of
have been clearly violated, especially the crystallographic ones.Starting from this background and bearing in mind that searching for 2D Cc and the main {010}, {001}, {100} morphological forms of bassanite (Becker et al., 2005; Ruiz-Agudo et al., 2016). It is therefore a matter of starting from scratch, slowly moving in crystallographic morphology: to do this, we began with the surface profiles of all the involved forms, obtained through a strict application of the Hartman–Perdok method (Hartman, 1973). As we recently treated the {10.4}-calcite/{010}-gypsum (Aquilano et al., 2022) in the same way, we will complete our program in a subsequent study dealing with the {10.4}Cc/anhydrite (CaSO4) starting from crystallographic experience (Aquilano et al., 1992) acquired many years ago.
among low-symmetry structures is not always easy, we aim in the present work to investigate all compatible 2D-LCs among the {10.4}2. A short summary on the {10.4} surfaces of calcite
The usual R3/c) reads a0 = b0 = 4.9896; c0 = 17.06, α = β = 90°, γ = 120°. For the rectangular 2D cell of its {10.4} form, the vectors are [010] = 4.9896 and 1/3[421] = 8.103, this cleavage form being limited by a set of symmetry-equivalent vectors 1/3〈[441]〉 = 12.85, running parallel to the {10.4} edges. Each {10.4} face shows a sharp pseudohexagonal symmetry; in fact, a large occupying an area of 242.58 Å2 with multiplicity (6×) can be drawn (Fig. S1 of the supporting information), and these features are more pronounced when we consider the epi-relationship of calcite/bassanite.
(in Å) of rhombohedral calcite (space groupThe {10.4}Cc is a flat (F) form growing through the layer-by-layer mechanism (either 2D nucleation or spiral, or both). Actually, four periodic bond chains (PBCs) run within the slice d10.4 = 3.034 Å thick. The two main PBCs develop along the 〈441〉 and 〈481〉 directions, made equivalent through the glide plane `c' [Fig. 1(a)], so building all the edges limiting the six rhombohedron faces. The two other main vectors run along the 〈421〉 and 〈010〉 directions. It is fundamental here to recollect the related PBC strength (the end chain energy, erg ion−1 × 1010), i.e. the energy released when an ion enters, in a crystallographic position, at one end of each semi-infinite chain: 0.391, 0.359 and 0.333 for the PBCs 〈441〉, 〈421〉 and 〈010〉, respectively (Ruiz-Agudo et al., 2016; Stawski et al., 2020). It has also been demonstrated that there is only one way to choose the surface profile of {10.4}. Accordingly, the {10.4} profile does not need to be reconstructed, since no atoms can be found on the ideal planes separating two adjacent d10.4 slices. In other words, d10.4 are `self-consistent slices'. Thirty years ago, more or less, we quantified its compactness (Hartman, 1973), i.e. the interaction energy () between the atoms contained within the d10.4 slice, and found that = 0.222 erg × 10−10 ion−1, corresponding to no less than ∼94% of the calcite crystallization energy (Aquilano et al., 1992). The shape of growth (or dissolution) of {10.4} patterns (spirals and/or 2D nuclei) is theoretically defined (Hartman, 1973) by the 〈441〉 steps limiting the faces, followed by the 〈421〉 vertical and 〈010〉 horizontal directions, as anticipated and demonstrated in Fig. 1.
3. Bassanite {010}: the sharp stacking difference of its elementary d020 layers with respect to those of the {001} and {100} forms. A comparison with the d10.4 layers of the cleavage calcite rhombohedron
Table 1 and Fig. 2 show the profound differences between the behaviour of the main forms {010}, {001} and {100} of bassanite with respect to the same {10.4}Cc substrate. In other words, there is no compatibility between the thickness of the elementary slices d10.4 = 3.043 Å (calcite) and d020 = 3.4635 Å (bassanite). To find an acceptable correspondence in the thickness (10.4)Cc/(010)Bss, one has to rise up to the thickness of (6–9) × d020 layers of bassanite; after this, the misfit starts to rise again (from +2.43%) and adsorption/absorption of 2D-{010}Bss layers into the bulk of the {10.4} form of calcite becomes improbable in comparison with the cases for other basic bassanite forms. This means that bassanite adsorption can only occur at the (10.4)Cc/(010)Bss interface. Fig. 2 provides evidence showing that, for the other two interfaces (10.4)Cc/(001)Bss and (10.4)Cc/(100)Bss, the thickness correspondences are everywhere very close to each other, in such a way that the misfit reaches a maximum of −1.16 and +4.1% for d200 and d002, respectively. Underlining this difference is useful, as it highlights the pseudo-quadratic 2D symmetry of (010)Bss with respect to the pseudo-hexagonality of both the (100) and the (001) planes.
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3.1. The pseudo-quadratic hexagonal symmetry of bassanite viewed along [010] and the pseudo-hexagonal symmetry along both [100] and [001] directions
As described in the Introduction, we adopted the bassanite structure proposed by Ballirano et al. (2001) and Hildyard et al. (2011), who determined the monoclinic I2 and the cell parameters (in Å) a0 = 12.032, b0 = 6.927, c0 = 12.671 and β = 90.27°. Fig. 3 roughly describes the sub-symmetry of bassanite:
The right side shows that the {010} form looks `pseudo-quadratic'; in fact, the vector [200]Bss = 24.064 and its perpendicular [002]Bss = 25.342 differ by a misfit of 5.31%. The comparison between the made by these two vectors and that made by calcite [421] = 24.309 and 5[010] = 24.948, building the {10.4}Cc points out the striking 2D-LCs (see cases 4a and 4b in Table 2) occurring between {010}Bss and {10.4}Cc.
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The left side outlines that the {001} and {100} forms are `pseudohexagonal'. In fact, (i) the vertical side is common and has a length of 13.854; (ii) the diagonal ones have lengths of 13.883 and 14.441 in the forms {001} and {100}, respectively; and (iii) the six internal angles range from 119.93 to 120.14° in the {001} form, and from 118.67 to 122.64° in the {100} form. The areas (in Å2) of these 2D-LCs [multiplicity (6×)] vary from 500.074 to 526.63, going from the {001} to {100} forms. The resulting Δ% reaches 5.31.
To summarize, through the exposed surfaces, we can obtain further proof that it is reasonable to treat {010}Bss separately from {001} and {100}, when the epi-contact with {10.4}Cc is made.
3.2. 2D coincidence lattices between bassanite {010} and calcite {10.4}
According to the preceding sections, the best fit between a vector in the (010) plane of bassanite and a chain in the (10.4) plane of calcite is that between the most important edge 1/3〈441〉calcite = 12.85 Å and the most important axis of bassanite [001]Bss = 12.671 Å, the linear misfit being 1.45%. Accordingly, the statement (Ruiz-Agudo et al., 2016) that no 2D-LC can be found at this interface (see the Introduction) is rather pessimistic. In fact, from Table 2 and Fig. 4, one can find the following:
(i) The [441]Cc chain is fundamental to build up an on (010)Bss, and the corresponding side of the shared 2D-LC is [100]Bss. The linear misfit between the two vectors is −6.84%, which is compensated by the opposite misfit (+7.82%) occurring between the two other sides of the 2D-LC. The linear compensation is reflected in the low value (∼6%) of the maximum area misfit which, together with the minimum multiplicity (1×) of the 2D-LC of bassanite and its tolerable (4.44°) obliquity value, allows us to say that the constraints in case 1 are well satisfied.
(ii) Another reasonable condition that could be found for a 2D ). The constraints are also fulfilled in this case, but the linear misfits are coherent and hence the error propagates towards the long-range interactions, and the multiplicity of the 2D common area is twice the preceding value. Accordingly, the probability of exists, but is lowered.
occurs with case 2 (Table 2(iii) In cases 3a and 3b, the 2D common areas or angular misfits (or both) exceed the geometrical constraints in order for an
to occur.(iv) In cases 4a and 4b, one obtains the largest 2D common areas but the best of the angular misfits. Furthermore, the linear misfits are in opposition everywhere.
To summarize, {010}Bss has two opportunities to form good epitaxies with {10.4}Cc. Case (1) illustrates the `short-range' 2D-LC, owing to the lowest multiplicity (1×) of the {010}Bss lattice. Cases 4a and 4b describe the `long-range' 2D-LC, as it ensues from the multiplicity (4×). By now, only the values of the adhesion energy between {010}Bss and {10.4}Cc could indicate which one of the epitaxies will be the preferred one. Anyway, it is worth remembering that the small 2D epi-nuclei of bassanite could form at medium–high whereas the larger ones are stable even at low (with respect to bassanite). In the first case, short-range 2D-LCs are coupled with small nuclei, whereas the long-range ones will be coupled with the larger nuclei. Accordingly, this is the best evidence that {010}Bss/{10.4}Cc has good probability to occur.
From the occurrence frequency expressed in Table 2, one obtains these observed rules:
(i) [100]Bss is parallel to [441]Cc, [421]Cc, [010]Cc and, less frequently, to [4.19.1]Cc,
(ii) [001]Bss is parallel to [421]Cc, [010]Cc and, less frequently, to [4.17.1]Cc,
(iii) [101]Bss is parallel to [421]Cc and, less frequently, to [451]Cc and [4.11.1]Cc,
(iv) [201]Bss is parallel to [441]Cc,
(v) [101]Bss is parallel to [4.11.1]Cc.
In other words, one has to search for these alignments, having remembered that only adsorption of bassanite on calcite can occur, according to the last row of Table 1. In these cases, (for adsorption alone) the action of screw dislocation cannot be foreseen at the outcropping calcite/bassanite interface: this means that periodic polysynthetic twins cannot be obtained on the growing surfaces (Boistelle & Aquilano, 1977; Aquilano, 1977), although they could easily occur when adsorption/absorption mixes one or more complex interfaces.
The situation shown by 2D-LCs (cases 4a, 4b) is quite interesting. In fact, in both cases, the linear and 2D-area misfit are very low or negligible; the obliquity is nil; the linear misfits are opposite. Finally, and this is amazing, both 2D-LCs are practically quadratic, the directions of their sides being parallel to the cell axes a0 and c0 of bassanite. It is not by chance that we suppose [in Fig. 4(b)] the reasonable existence of 〈101〉 ledges in bassanite, to avoid the superposition of the original parent embryos.
3.3. The surface structures of the {001} form of bassanite
In cases 1, 2a and 2b described in Table 3, the sides [010]Bss and [110]Bss exactly coincide with the sides of the pseudohexagonal 2D described in Fig. 3 (left). In Figs. 5(a) and 5(b) the 2D is the same: [120] is the twin axis, even if in Fig. 5(a) [010]Bss is parallel to [441]Cc, whereas in Fig. 5(b), [110]Bss//[441]Cc. In Fig. 5(c) the 2D changes too: [140] is the new twin axis. Note that the angle of 78.15° is the same in the `swallow tail' of different laws (upper side left and lower side), because in both cases the twin axis runs parallel to the main [010] calcite PBC.
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3.4. The surface structures of the {100} form of bassanite
In both cases of Table 4, the {100} bassanite nucleus has its sides parallel to the most important 〈441〉 PBC of the substrate. In the first case [Fig. 6(a)], a new 2D twin axis [021]Bss is obtained. The penetration twin has a swallow angle of 84.91° determined by the 〈010〉 directions of the bassanite parent (P) and `c' twinned (T) individuals. The lateral sides of the penetration twin are both parallel to the other sides of the nucleus and coincide with the 2D twin axis [021] of bassanite. Concerning case 2 [Fig. 6(b)], another 2D twin axis [032]Bss works: the angle formed by the `c' equivalent 〈010〉 bassanite directions is 101.85°.
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4. Conclusions
Starting from the premise cited in the Introduction, it could be assumed that bassanite is a valuable replacement for CaSO4 to make 2D and/or 3D with the {1.04} cleaved form of calcite. By closely observing the interface between bassanite and {10.4}Cc with deeper crystallographic insight, we instead realized in the present work that all the main bassanite forms can produce new 2D twin laws, when in epi-contact with the basic {10.4}Cc rhombohedron. By taking into account the point established in Section 3 on the properties of the interfaces, we can summarize the following interactions between the calcite substrate and the new twin laws determined by bassanite deposition:
(i) {010}Bss: three twin laws were determined, [101]Bss, [100]Bss and [001]Bss. In the first 2D-[101]Bss the swallow-tail angle (92.68°) is formed by the 〈100〉Bss steps and can be attributed to the `c' glide plane that is invariably present in the {10.4} cleaved calcite. In the other two laws ([100]Bss and [001]Bss), the swallow angle that originated between the 〈101〉 directions varies between 84.07° (2D-[100]Bss twin law) and 86.78° (2D-[001]Bss twin law). Readers will notice that the maximal variation in these three swallow angles is minimal (<9°) and that visually the triplets look alike, so that they can be easily confused; actually, they differ from each other both in physics and in geometry.
(ii) {001}Bss: first, it is remarkable that in all three main twin laws the bassanite {001} nuclei are always perfectly aligned along the 〈441〉Cc sides. When the alignment is parallel to [010]Bss or [110]Bss, a new arises, with [120]Bss as a new 2D twin axis (cases 1, 2a); instead, in case 2b, where [110]Bss is again aligned along the 〈441〉Cc side, [140]Bss becomes the new 2D twin axis. Three other cases are given in Table S1 of the supporting information, either because some coincidence has been found with the 〈441〉 sides of calcite or because the 2D-Cl area misfit is too high. In two of them, the new 2D twin axes are [210]Bss and [010]Bss. Finally, also for this bassanite form, cases 1 and 2b show the same bassanite swallow angle (81.89°), which differs only by a total obliquity of 3.74° with respect to the theoretical one (calcite), as drawn in Fig. 5 of the text.
(iii) {100}Bss: despite the hexagonal of bassanite, the {0kl} forms have fewer 2D-CL lattices than the previous ones, the weak difference between a0 and c0 of bassanite being the cause. New twins have been calculated, the new 2D twin axes being [021]Bss and [032]Bss. In case 1, the swallow angle formed on this occasion by the two 〈010〉 equivalent directions of the two bassanite individuals reaches 84.91°. Once again, this highlights how deceptive first appearances can be when observing `swallow-tail twins'.
Accurate research, based on the lattice epi-correspondence between the main bassanite and (10.4)Cc PBCs, allowed us to identify nine unexpected 2D twin laws, generated by the intrinsic (10.4)Cc symmetry coupled with the surface symmetry of bassanite, which increasingly works like a transition compound. Further, swallow-tail twins do theoretically occur in all three cases of the epitaxies of bassanite on (10.4)Cc. In brief, these new 2D twin laws have been found for bassanite, promoted by the calcite substrate; together with the (10.4)Cc/(010)Gypsum coupling examined earlier (Aquilano et al., 2022), a new way of thinking is being developed in detail about the between different species. This can be particularly useful when a new mineralogical species tends to replace another, as in the case of Ca sulfates (gypsum, bassanite, anhydrite) replacing calcite, in nature and/or the laboratory (Ruiz-Agudo et al., 2016). According to our planning, the next step will be the CaSO4 anhydrite/(10.4)Cc epitaxy.
Supporting information
Supporting figure and table. DOI: https://doi.org/10.1107/S1600576722008196/gj5284sup1.pdf
Acknowledgements
Open Access Funding provided by Universita degli Studi di Torino within the CRUI-CARE Agreement.
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