Single and Twinned Li2CO3 Crystals (Zabuyelite) Epitaxially Grown on {0001} and {101j4} Forms of CaCO3 (Calcite) Crystals Francesco Roberto Massaro,† Linda Pastero,† Emanuele Costa,† Giulio Sgualdino,‡ and Dino Aquilano*,†
CRYSTAL GROWTH & DESIGN 2008 VOL. 8, NO. 6 2041–2046
Dipartimento di Scienze Mineralogiche e Petrologiche, UniVersita` degli Studi, Via V. Caluso, 35, I-10125 Torino, Italy, and Dipartimento di Chimica, UniVersita`, Via L. Borsari, 46, I-44100 Ferrara, Italy ReceiVed February 8, 2008; ReVised Manuscript ReceiVed February 22, 2008
ABSTRACT: Single microcrystals of Li2CO3 (zabuyelite) were observed on {0001} calcite surfaces, epitaxially grown and oriented along the directions of calcite, the {001} form of zabuyelite being by far the best candidate to form the epitaxial interface. In addition, 3-fold pseudotwins of zabuyelite were observed in epitaxy on the cleavage {101j4} rhombohedron surface of calcite. The new twinning law is described along with the most probable zabuyelite/calcite interface. Further, a general rule is proposed, concerning the conservation of the orientation of the carbonate groups across the epitaxial interfaces and twin boundaries in carbonates.
1. Introduction It has been shown, since the finding by Rajam and Mann,1 that in lithium bearing aqueous solutions supersaturated with respect to calcite, the {0001} pinacoid enters the crystal morphology.2,3 Recently, we observed that the {0001} calcite form can appear growing layer by layer, on both nucleated and seeded crystals, even if the mother solution was unsaturated with respect to the bulky Li2CO3 crystal phase. Thus, we put forward the hypothesis that 2D epitaxial (001) layers of Li2CO3 form and spread over the {0001} calcite surfaces, owing to the very low geometrical misfit between the 2D meshes of the {0001} calcite form (host) and the {001} Li2CO3 crystal form (guest). Indeed, a simple structural model has been proposed for the (001)-Li2CO3/(0001) calcite interface, having taken into account the striking analogy between the reconstructed outermost layers of the (0001) face of calcite and those of the NaCl like structures considered built by electrically neutral octopoles.4 The influence of lithium on the growth morphology of calcite has been further investigated, and experimental findings showed that also the stepped character of the {011j8} form of calcite changes to the flat one when cleavage calcite rhombohedra, nucleated from pure solution, continue growing in a mother solution supersaturated with respect to calcite and unsaturated with respect to lithium carbonate. Also in this case it was demonstrated that Li2CO3 layers can be epitaxially adsorbed either on {011j8} or {101j4} calcite forms, the former only being relevant for a growth mechanism transition.5 From all these findings one can conclude that the influence of lithium on different forms of the growth morphology of calcite cannot be due to the interaction between single lithium ions and the surface structures of calcite. On the contrary, one can reasonably suppose that lithium ions, even in unsaturated solutions with respect to bulky Li2CO3 crystal phase, cooperate with the calcite surfaces to temporarily generate on them different 2D structures corresponding to well-defined surface profiles of the Li2CO3 crystal. To open new prospects on this problem, precise knowledge is needed on the relationships between the growth morphology of both Li2CO3 (zabuyelite) * Corresponding author. Tel: +39 011 6705125. Fax: +39 011 6705128. E-mail address:
[email protected]. † Universita` degli Studi, Torino. ‡ Universita`, Ferrara.
Figure 1. Epitaxy on the {0001} calcite form of single zabuyelite individuals elongated along the symmetry planes of calcite.
and CaCO3 (calcite) crystals. The first step of this objective has been very recently reached studying the experimental and theoretical morphology of single and twinned crystals of zabuyelite.6,7 A second step is developed in the present paper in which we aim at investigating the complex phenomenology shown by the cocrystallization of zabuyelite and calcite. As we outlined in a preceding paper, the interest of this work is related neither to applied sciences nor to geological research, since few findings of zabuyelite are known in nature; nevertheless we think that it is not trivial to search for the genetic aspects relating different carbonates among them and, at the same time, to understand how the increasing departure from the chemical equilibrium allows one to obtain more and more complex structures (twins, epitaxies) showing increasing symmetry degrees.
2. Experimental Section 3D epitaxies of Li2CO3 crystals on calcite single crystal have been obtained in two ways. In the first one, small natural crystals (∼5 mm in size) exhibiting the {0001} form were immersed, at room temperature, for half a day in a gently stirred and slightly unsaturated solution (with respect to calcite) to clean up the outermost layers of crystal surfaces. In this solution the (Ca2+/Li+) ionic ratio was maintained around 0.5 to keep stable the surface profile of the {0001} form and to avoid, at the same time, the 3D precipitation of Li2CO3 crystals.3 Then, the cleaned crystals were transferred to another solution, slightly
10.1021/cg8001515 CCC: $40.75 2008 American Chemical Society Published on Web 05/20/2008
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Table 1. The Most Probable Coincidence Lattices between the {0001} Calcite Form (Host) and the Epitaxially Grown Li2CO3 Crystals (Guests) calcite (host) form
2D lattice vectors (nm)
Li2CO3 (guest) form
2D lattice vectors (nm)
misfit (%)
{0001}
|| ) 0.8642 || ) 0.4989 || ) 0.8642 || ) 0.4989 || ) 0.4989 2 × || ) 1.7284 3 × || ) 1.4846 || ) 0.8642
{001}
|100| ) 0.8359 |010| ) 0.4972 |101| ) 0.8048 |010| ) 0.4972 |010| ) 0.4972 |201| ) 1.51944 |201| ) 1.51944 2 × |010| ) 0.9944
+3.37 +0.35 +7.38 +0.35 +0.35 +13.75 -1.50 -15.06
{1j01} {1j02} {1j02}
supersaturated with respect to calcite; successively, LiCl was continuously added until the solution became slightly supersaturated also with respect to Li2CO3. After three days the crystals were extracted from the solution, rapidly washed in progressively unsaturated solutions (with respect to both calcite and Li2CO3) and wiped off with a blotting-paper. In the second way the mother solution was prepared following a more complex path, as described in detail in a preceding work.12 Two aqueous solutions were initially mixed in a crystallizer, at room temperature and pressure: the first one was saturated with CaCO3 in excess with respect to the solubility product by means of CO2 bubbling, while a LiOH solution was slowly added to the first one by stirring and forcing the resulting environment to reach high pH values (up to 14) and to become strongly supersaturated with respect to calcite. Carbon dioxide was continuously bubbled during and after the alkali addition, in order to avoid the sudden fall of the supersaturation level, due to the massive precipitation of bulky calcite crystals, and to supply
2D common mesh multiplicity 2 2 4 6
a continuous gas support for the nucleation of the calcite bubbles.12 Indeed, bulky calcite crystals and calcite bubbles could deposit and adhere to both sides of glass sheets hanging in the solution. Finally, the glass sheets extracted from the crystallizer were put to dry in an oven at 50 °C, in such a way that the residual mother solution could rapidly evaporate so reaching high supersaturation level with respect to the lithium carbonate. The obtained crystalline phases where preliminarily observed in situ by optical microscopy and then by means of a Cambridge S360 scanning electron microscope equipped with a Oxford Inca energy 200 EDS system. Since the lithium cannot be detected by the microprobe and because only two crystal phases can crystallize (calcite and zabuyelite), Li2CO3 crystals were correctly singled out not only by their shape but by the absence of calcium signal as well.
3. The 3D Epitaxy between Li2CO3 Crystals and the {0001} Calcite form Starting from these considerations, we investigated the behavior of a naturally grown {0001} form of calcite immersed in an aqueous solution slightly supersaturated with respect to both calcite and Li2CO3 bulky crystal phases. Figure 1 shows that a wide population of single Li2CO3 nanocrystals nucleated and grew oriented along the three equivalent and prevailing directions on the {0001} calcite form. In Table 1 are illustrated the most probable coincidence lattices which can set up at this epitaxial interface. Since any deeper observation (through AFM) cannot be made on the morphology of the epitaxially grown Li2CO3 nanocrystals, due to the large size of the host crystal, it is worth finding the best coincidence lattice among those illustrated in Table 1. From our previous morphological analysis on Li2CO3 crystals, carried
Figure 2. The outermost layer of the {0001} calcite form (a) compared with those of zabuyelite in the zone of the common [010] axis: {001} (b); {1j01} (c); {1j02}.
Figure 3. If the 3-fold twin axis is perpendicular to the 001 zabuyelite plane, the dihedral angle between the planes parallel to the carbonate groups of two adjacent twinned individual reaches 28°. This structural misfit makes the twin boundaries unstable.
Figure 4. SEM pictures of 3D microtwins of zabuyelite: grown on a rhombohedral calcite bubble12–14 formed encompassing a CO2 cavity in solution (a); grown on a bulky rhombohedron of calcite: one of the lamellae building the twins is always parallel to the short diagonal of the rhombohedron faces (b,c); grown on a glass substrate (d).
Epitaxy between Crystals of Li2CO3 and Calcite
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Figure 5. The comparison between the outermost layer of the cleavage rhombohedron of calcite and the surface profiles of the main forms of the epitaxially grown Li2CO3 3-fold twins: {001} (a); {1j01} (b); {1j02} (c); {101} (d). The horizontal direction represents the [010] axis for all the 2D structures. Table 2. The Most Probable Coincidence Lattices between the {101j4} Calcite Form (Host) and the Main Forms of the Epitaxially Grown Li2CO3 3-fold Twins (Guests) calcite (host) form {101j4}
2D lattice vectors (nm) (1/3)|| ) 0.8103 || ) 0.4989 (1/3)|| ) 0.8103 || ) 0.4989 2 × (1/3)|| ) 1.6206 || ) 0.4989 6 × (1/3)|| ) 4.8618 || ) 0.4989
Li2CO3 (guest) form and character {1j01}-F {001}-F {1j02}-S {101}-S
out by means of Hartman-Perdok method,8 both {001} forms turned out to show F character, while {1j02} is an S form. Moreover, there is a common feature opposing the slices of thickness d2j02 and d2j04 to the d002 slice. In fact, within the former, one-half of the carbonate ions point toward the [010] direction and the other half are [01j0] oriented, while in the latter all the CO32- groups point along the common [01j0] direction (Figure 2). This difference has major consequences on the structure of the epitaxial interface. As a matter of fact, the deposition of a d002 slice of zabuyelite on the {0001} calcite form does not interrupt the alternate sequence of CO32- groups along the [001] axis of the calcite crystal, in such a way that the zabuyelite could ideally continue the calcite structure. On the contrary, the deposition of either d2j02 or d2j04 layer turns to be inconsistent with the outermost 0001 calcite layers, since strong repulsions should generate between carbonate ions having the same orientation on the opposite sides of the interface. This is the main reason why, beyond the larger parametric misfits and the multiplicity of the common 2D meshes, the {001} pinacoid of zabuyelite is by far the best candidate to epitaxially adhere to the {0001} calcite form when Li2CO3 bulky crystals nucleate and grow on it. Drawing the atomic structure and thickness of the interface that rules the transition between the rhombohedral calcite and
2D lattice vectors (nm)
misfit (%)
|101| ) 0.8048 |010| ) 0.4972 |100| ) 0.8359 |010| ) 0.4972 |201| ) 1.5194 |010| ) 0.4972 4 × |101j| ) 4.9275 |010| ) 0.4972
+0.68 +0.34 -3.16 +0.34 +6.66 +0.34 -1.35 +0.34
2D common mesh multiplicity 2 2 4 12
the monoclinic zabuyelite is beyond the aims of the present paper; nevertheless, some preliminary features and constraints can be fixed now: (1) As a first step, we already suggested that “... the outermost Li+ ions which should face the outermost 0001 layer of calcite form a perfect 2D hexagonal lattice”.3 This lattice coincides, within a misfit of 0.2%, with the lattice built by the vacant sites resulting from the second restructured 0001 layer of calcite, according to the octopole model. This means that in the cationic layer shared by the two structures, 75% of the available sites will be occupied by Ca2+ ions while the Li+ ions could fill the remaining ones; moreover, the shared anionic layer will be occupied by iso-oriented CO32- ions. (2) Further, ab initio calculations carried out in our research group6 allowed us to evaluate the relaxation of the outermost zabuyelite layers. Having taken into account that the coordination of Li+ ions varies from four to three when going from the bulk to the (001) surface configuration, it comes out that these ions move toward the surface while the CO32- groups undergo both a distortion and a tilting around the [010] direction in such a way that in the top 001 surface layer the angle formed by the plane containing the carbonate groups and the 001 ideal plane reduces to 13.2° (instead of that of 19.2° found in the bulk structure).
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Figure 6. The epitaxial relationship between a triple lamellar twin of zabuyelite and a calcite rhombohedron: reconstructed shape of a triple twin of zabuyelite (see Figure 4), with the dominating {010} form (a); reconstruction of Figure 4b showing that one out of the three twinned lamellae is always parallel to the short diagonal of the calcite rhombohedral faces (b); the triple twin and the rhombohedron seen along the common axis: the {101} form of one lamella develops parallel to one rhombohedron face and the twin axis is nearly parallel to the triad axis of the calcite crystal (c); the resulting arrangement of the carbonate groups does not suffer discontinuity across the epitaxial interface and the strongest PBC of calcite continues in an important PBC of zabuyelite (d).
(3) Finally, from atomistic simulation9 and molecular dynamics modeling10 it ensues that the carbonate groups in the reconstructed outermost 0001 calcite layers slightly deviate from the rigorous parallelism with respect to the ideal 0001 plane (as it occurs in the bulk crystal structure). This means that it is reasonable to imagine that the transition from the rhombohedral (calcite) to the monoclinic (zabuyelite) structure should occur by complying with the following conditions: (a) The successive carbonate layers maintain their alternating antiparallelism, so avoiding any repulsive interaction when going from the calcite {0001}to the zabuyelite {001}, while the tilting of the carbonate groups progressively increases from 0° (calcitebulk) to nearly 13.2° (first layer of pure zabuyelite). (b) The neutral dipolar d0006 CaCO3 bulk layers11 “transform” in the neutral nonpolar d002 Li2CO3 bulk layers through the reconstructed layers in which the lacking of the negative electrostatic density (due to the missing carbonate groups) is compensated by the lacking of the positive electrostatic density (due to the Li+ ions replacing the missing Ca2+ charges). (c) Finally, it is worth remembering that the character of the {0001} form of calcite transforms from K to F during growth in the presence of Li+ ions3 and then its surfaces advance layer by layer. This is also the growth mechanism of the {001} form of zabuyelite crystal, that shows F character, as it comes out from the structure of its d002 layers.7 Consequently, it is reasonable assuming that the growth units coming from the mother phase and originating the transition zone in the calcite {0001} zabuyelite {001} 3D epitaxy, should comply with the same mechanism of lateral growth. Hence, having considered that each elementary layer of both calcite {0001} and zabuyelite {001} forms shows a striking pseudohexagonal symmetry, the transition zone should be characterized by the same symmetry as well. These considerations have to be carefully taken into account when facing the modeling of the reconstructed interfaces that must necessarily obey the locally observed symmetry.
Always concerning the mechanisms of the 3D epitaxially grown zabuyelite crystals on the {0001} pinacoid of calcite, one can ask why zabuyelite nucleates and grows as individual crystals, instead of forming 3-fold twins, as one should expect from symmetry of the host face. As a matter of fact, 3-fold twins of zabuyelite are frequently observed crystallizing either on amorphous glass substrates or on as grown {101j4} flat calcite surfaces, as we anticipated in the Introduction. Figure 3 represents a reasonable answer to this question. In fact, a 3-fold twin could be generated in two ways: (a) either through a 3-fold twin axis perpendicular to the 001 zabuyelite plane (the misalignment with respect to [103] direction being only 1.9°); or (b) through the symmetry related 3j31 and 331j twin planes, which are perpendicular to the 001 plane of zabuyelite and parallel to the [110] and [11j0] directions, respectively. In this case the misalignment with respect to the ideal rotation angle of the 3-fold interpenetrating twin (60°) is even more negligible, the intertwin angle being 61.48°. Both the operations described in (a) and (b) lead to the same situation, illustrated in Figure 3 where a portion of the parent zabuyelite crystal is projected along the [010] direction, while on its right and left sides are represented the structures of the two twinned individuals, rotated by +120° and -120° respectively, around the twin axis =[103]. It can be easily seen that the carbonate groups facing the twin boundaries are strongly disoriented, since the dihedral angle between the planes parallel to the CO32- groups of two adjacent twinned individual reaches 28°. Thus,suchaboundaryconfigurationisenergeticallyunsustainable.
4. The 3D 3-fold Twins of Li2CO3 Crystals Epitaxially Grown on the {101j4} Calcite Form
If the mother solution in which calcite rhombohedra nucleated and grew maintains a slight supersaturation value with respect
Epitaxy between Crystals of Li2CO3 and Calcite
to calcite, while its supersaturation as regards the zabuyelite bulky crystal phase is increased, 3D microtwins of zabuyelite systematically appear on the faces of rhombohedra (Figure 4). These twins exhibit a pseudo-3-fold symmetry, and their longest branches are regularly oriented along the shortest diagonal of the rhombohedron (i.e., the [421j] direction). The two other branches are parallel to the symmetry equivalent [47j1j] and [4.11.1j] directions, respectively, forming an angle of 61.58° with respect to the [421j] direction. In Figure 5 and Table 2 are illustrated the most probable coincidence lattices which can set up at this epitaxial interface. From the coincidence lattices one should suppose that both {101j4}calcite/{1j01}zabuyelite and {101j4}calcite/{001}zabuyelite could be the most favored epitaxial interfaces, because of the lowest multiplicity and the smallest misfit of their 2D common meshes. But, remembering that epitaxy is ruled not only by geometrical relationships, we have to notice that the structural ordering of the {1j01} form of zabuyelite has a large advantage with respect to that of the {001} form, since the alternating [010] rows of carbonate groups maintain only at the {101j4}calcite/{1j01} zabuyelite interface (Figure 5b). Further, considering that both {1j01} and {001} zabuyelite forms show F character,10 their successive growth layers have to be laterally correlated and then neither 2D islands nor spirals having the {001} zabuyelite structure can deposit on the host {101j4} calcite faces, owing to the periodic repulsions generated by the iso-oriented carbonate groups (Figure 5a). This excludes the {101j4}/{001}zabuyelite interface and hence the competition reduces to the remaining ones: {101j4}calcite/{1j01}zabuyelite, {101j4}calcite/{1j02}zabuyelite and {101j4}calcite/{101}zabuyelite. At first sight, the first one out of these three interfaces should be favored, due to both its lower misfit and 2D common mesh multiplicity. Moreover, its alternating [010] rows of carbonate groups represent the ideal continuation of the calcite structure. On the contrary, in the second interface, the alternation of rows built by the carbonate groups of zabuyelite is out of phase with respect to that of calcite (Figure 5c) and the character of the {1j02} form is S, which “a priori” should lower the adhesion energy at the epitaxial interface. Surprisingly, the last interface, the {101j4}calcite/{101}zabuyelite, even if its multiplicity is high when compared to the other ones, has a very low misfit and fulfills at the same time to the structural continuity representing the master condition which has to be respected when two crystalline individuals grow within the twinning or epitaxial relationships. This structural continuity is well illustrated in Figure 6 where a comparison is drawn between the observed triple twins of zabuyelite epitaxially grown on a rhombohedron calcite crystal and its schematic representation projected along the calcite axis. In this drawing one may easily see that, when the 101 planes of zabuyelite are parallel to the 101j4 planes of calcite, (a) the parallelism of the carbonate groups is very well conserved when crossing the calcite/zabuyelite interface, the misalignment between the perpendiculars to the 0001 planes of calcite and to the 1j02 planes of zabuyelite being only 3.07°; (b) the PBC, which is the most important periodic bond chain of calcite, ideally continues in the [101] PBC of the zabuyelite crystal, the angular misfit between the two directions being lower than 5°. Then, once the 101 planes of zabuyelite have been ascertained to be the most suitable for making epitaxy with the {101j4} calcite form, the problem reduces to finding the crystallographic elements describing the 3-fold zabuyelite twins mentioned above. The answer is also contained in Figure 6. In fact, the only twin operation allowing the three twinned individuals to
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maintain their carbonate groups always parallel to the same 1j02 plane is the [001] zabuyelite axis. Hence, this means that this axis not only behaves like the 2-fold twin axis for the very common 100 twin law of zabuyelite we described in a recent paper,7 but it may also act as a 3-fold twin axis which runs nearly parallel to the 3j symmetry axis of the calcite crystal epitaxially related to it. Concerning the stepped (S) character of the {101}zabuyelite form, this is not a dramatic drawback hindering the {101j4}calcite/ {101}zabuyelite epitaxy to start. In fact the {101} S character implies that any correlation exists during growth among its [010] PBCs. Consequently, to epitaxially nucleate on calcite, a zabuyelite crystal starting from its {101} form, it should be sufficient that one out of phase of the [010] zabuyelite PBCs is missing at the interface level, even if some elastic energy could be needed to rearrange the dislocated epitaxial interface. Finally, an interesting problem arises when considering the shape of the individual zabuyelite crystals building the multiple twins formed both on calcite rhombohedra (Figure 4a,b,c) and on glass substrates (Figure 4d). As described in section 2, the mother solution which generates zabuyelite twins and calcite rhombohedra is, obviously, supersaturated to both zabuyelite and calcite. This means that an excess of lithium and calcium ions remains in solution after the depletion due the nucleation of the two crystal species. This excess can surely induce sensible modifications in the habits of the growing crystals. As a matter of fact, the calcite rhombohedra show the apex truncation due to the presence of the {0001} form3 and, at the same time, the shape of the zabuyelite crystals is by far strongly modified with respect to that obtained from pure lithium bearing solution.7 As it comes out from the last quoted paper, when crystallizing single and twinned zabuyelite crystals, we avoided any interference between zabuyelite crystals and calcium ions which are always present in solutions containing impure lithium chloride, by putting in solution a suitable amount of EDTA. But, in the present case, the calcium contained in the mother solution which does not contribute to the growth of calcite crystals is preferentially adsorbed between the adjacent [001] PBCs of the {010} zabuyelite stepped form7 which becomes stable and flat so entering both the equilibrium and growth shape of the crystal. Hence, zabuyelite crystals grown in the presence of calcium exhibit a lamellar habit, dominated by the {010} form; moreover, also the stepped {101} form can belong to the growth shape, as we shall show in a forthcoming paper.
5. Conclusions The crystallization in the CaCO3-Li2CO3 system proved to be rich in morphological phenomenology: (1) The morphology of the growing calcite crystals is strongly influenced by the presence of lithium in the mother solution (unsaturated with respect to Li2CO3) which adsorbs and generates 2D epitaxies on several important calcite forms, inducing the transition of character of the {0001} form (from kinked to flat) and of the {011j8} form (from stepped to flat).3,4 (2) When the mother solution is slightly supersaturated with respect to Li2CO3, single and 100 twinned crystals of zabuyelite appear;7 but, if the supersaturation increases and the growth solution is enriched in calcium to such a point that also calcite crystals become stable, thus zabuyelite crystals coprecipitate with calcite giving rise to (a) a 3D epitaxy of single zabuyelite individuals on the {0001} form of calcite; and (b) a 3D epitaxy of triple zabuyelite twins on the {101j4} faces of the cleavage rhombohedron of calcite. At the same time, the growth morphology of zabuyelite is deeply modified by the presence
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of calcium in solution which, in turn, changes the character, from S to F, of the {010} and, probably, of the {101} zabuyelite form as well. The triple zabuyelite twins can form not only with the aid of the epitaxial zabuyelite/calcite interface, but also in the solution bulk, through the heterogeneous nucleation on amorphous glass substrates. The [001]zabuyelite direction is the 3-fold twin axis of this new twin law, while the 110 planes can be considered as the most probable original composition planes of the twin. It is not trivial recollecting that whether in zabuyelite/calcite epitaxies or in both 100 and triple twins the carbonate groups tend to maintain always the parallelism when crossing the common interfaces and boundaries: indeed, this is the general rule we applied to obtain a reasonable interpretation of our observations, even if we could not use any diffraction technique to characterize the so small objects we had to do with. By the way, it is also worth remembering that the boundaries in both calcite and aragonite growth twins are characterized by a common rule: the carbonate groups facing on the opposite sides of the twin boundary relax and tend to arrange as much as possible parallel to each other in order to minimize the potential energy of the boundary. This can be easily verified for both the 0001 and 110 twin laws of calcite and aragonite, respectively, where the twin law maintains the parallelism of the carbonate groups, whereas the tendency to the parallelism is confirmed when viewing the relaxed composition boundaries of 101j4, 011j2 and 011j8 twins of calcite along the common [010] axis. All these considerations, along with the relationships among twinning, epitaxy, symmetry variation of these composed and complex structures and the supersaturation of the mother phase generating them, represent the main topic we are working with.
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Acknowledgment. We thank Prof. Marco Rubbo, Dr. Marco Bruno and Dr. Mauro Prencipe (Universita` degli Studi di Torino) for useful discussions. This work was supported by Ministero dell’Istruzione, Universita` e ricerca (MIUR), with funds related to PRIN 2005.
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