TWIN-BASED TOUGHENING MECHANISMS IN PINNA NOBILIS SHELL

The shell structure of the Pinna nobilis species constitutes a model for others formed by bivalves of the Ostreida order. The outer part is built of monocrystalline columns whose axes remain parallel to the calcite c -axis. The present work reveals a new microstructure induced by mantle damage in the early stage of growth. The calcite c -axes, oriented perpendicularly to the strongly rough outer surface, deviate significantly from the shell thickness direction. The inclination angle is maintained up to the nacre layer. The transfer is made by the monocrystalline prisms which initially run along the c -axis and then deflect taking the thickness direction. They form coherent systems with low-energy twin boundaries. The uncovered twin relationships significantly improve the mechanical properties, as demonstrated using the nano-indentation and impact tests. Moreover, compression tests were performed, which confirms that the untypical structure exhibits a unique combination of high fracture toughness and strength.


Introduction
Bivalve shells are hierarchically complex biocomposites consisting of calcium carbonate with different polymorphs (calcite or aragonite) and an organic matrix [1]. The outer skeleton has been improved over millions of years of evolution to provide effective protection against predators. As a result, the structures formed are lightweight and exhibit outstanding mechanical properties compared to materials from which they are built. Thus, the protective armors are an excellent source of inspiration for the formation of biomimetic engineering materials with an equally unique combination of high strength and fracture toughness [2 -5]. Reproducing the shell's microstructure requires in-depth knowledge of it as well as identification of the mechanical properties of the components [6,7]. The present work is part of the search for engineering materials inspired by nature. The subject of the study is a shell of the Pinna nobilis species with an unusual morphology due to the repair of an extensive injury occurred in an initial growth stage. Widespread observations indicate that the self-healing process generates a secondary structure with higher strength and fracture toughness than the primary one.
The Mediterranean pen shell Pinna nobilis Linnaeus, 1758 (superfamily Pinnoidea, Order Ostreida) is a large bivalve species that lives with its anterior end buried within the sediment (semiinfaunal), and attached by the byssus to clasts or shells within the sediment. It inhabits seagrass meadows and is presently an endangered and protected species. The shell is made of two layers with different microstructures. The outer layer has a columnar calcite prismatic (CCP) microstructure: large polygonal prisms elongated perpendicular to the outer shell surface, surrounded by organic sheaths. The inner shell layer is made of nacre and extends for less than half the anteroposterior diameter (e.g. [1]). This microstructural distribution is typical of the order Ostreida, except for the superfamily Ostreoidea. The two layers perform different functions. The thick periprismatic organic membranes make the outer prismatic layer particularly flexible [8]. When the two valves abut, shell closing is achieved by flexible deformation of the wide prismatic margins, providing a tight sealing ( [9][10]). The inner nacreous layer is relatively thin and constitutes the tough and relatively rigid part of the shell. The prisms of Pinna nobilis may reach lengths of up to several mm, particularly in large specimens. From the crystallographic viewpoint, each prismatic unit is a single crystal (e.g. [1,[10][11][12][13]), with very low misorientation values ( [14][15][16][17]), i.e., very similar to inorganic calcite crystals. The c axes of prisms remain parallel to their long axes [14,18]. This is unlike other related bivalves, such as the pterioid Pinctada margaritifera, in which prisms display high orientation instabilities, which makes them break progressively into new crystalline domains [14].
The aim of this study is to accurately identify the CCP microstructure of P. nobilis and link it with the mechanical properties of the constituent elements as well as with the response to the load of a representative shell volume. Investigations using the electron backscatter diffraction (EBSD) method have revealed new prism orientations, which play a key role in transferring the external load. This was demonstrated through theoretical analysis and then confirmed by the identification of mechanical properties at the local and global levels in the nano-indentation, nano-impact and compression tests.

Microstructure identification
The studied shell has a morphology unusual for the P. nobilis species. A clear division line running longitudinally on both valves is visible (Fig. 1a). The probable reason is the damage of the mantle at the initial stage of growth. As a result, two separate parts develop, and the shell acquired a bilobate appearance. Besides the division, the outer shell surface exhibits a significant roughness ( Fig. 1b-e), which is related to the formation of thin calcitic ribs, produced by the pleated border of the mantle.
The disturbed geometry entails untypical microstructure. In order to identify it, the in-depth EBSD investigations were carried out.
The prisms, growing perpendicularly to the repaired outer surface, deviate from the normal direction (ND) determined by the shell thickness. As a result, in the outer layer, the directions of fast growth i.e. c axes of calcite crystals are mostly oblique (Fig. 2). With the shell development, growth lines become flatter and the orientation of the growth axes of prisms becomes more and more parallel to ND. This process leads to the deflection of prisms as well as to the elimination of those that exhibit a significant initial deviation from the normal direction (Fig. 2a). The ordered orientation of prisms does not mean that it is preserved by calcite grains. It turns out that during the growth of crystallites, the c  axes maintain their initial direction. As a result, incorrectly, obliquely initiated orientation becomes obligatory on the entire thickness of the shell. Thus, the island-shaped surface determines the structure of the entire protective armor. Analysis of the EBSD results reveals a clear division into three areas. The middle one is initiated by an island (a local shell elevation) with a small curvature, while the lateral ones begin with a greater slope. As a result, in the central region, the c axes of prisms are the most frequently tilted by a small angle of 12° relative to ND, and their initial orientation is maintained up to the nacre layer (Fig. 2b). The central area is flanked by fragments of islands with a larger curvature, particularly on the left. They initiate regions in which the c axes of grains most often orientate at an angle of 32° and 14° relative to ND, respectively (see Fig. 2c). The organization of both zones is similar. Initially formed grains with an oblique inclination tend to disappear, whereas their neighbors expand at their expense. In this way, crystallites with c axes significantly deviated from ND are eliminated while those which form a group with a similar orientation of c axes reach the nacre layer (G1, G2). Each prism constitutes a single calcite crystal. Even its sudden deflection causes only a slight change in the orientation of calcite -the difference remains within 2° (G2).
The orientation of grains is presented in the convention of axis/angle rotation with the use of a color code. The color determines the position of the axis according to the pole figures (Fig. 2a). The other variable -the angle of rotation is expressed by the color saturation. Thus, 0° and 90° correspond to gray and full saturation, respectively. Grains, typical for Pinna nobilis, with axis c || ND, are generated by means of an axis with red (e.g. G3) or blue pole (e.g. G4). Then the rotation by 90° moves the c axis to the ND position. A strong prism slope in the lateral areas prevents contact with the central region.
The resulting gaps are filled by additional prisms. They enable a smooth transition between distinct regions by introducing a gradual rotation of the c axis towards ND (G5).
The question arises whether there is a preference in the mutual orientation of adjacent grains.
The calculated Misorientation Distribution Function (MDF) shows that the crystallites rotate with respect to each other around the c axis, taking three preferential positions. They are determined by the following values of the rotation angle : 18° (A), 38° (B) and 60° (C) (Fig. 3a). High preference is usually due to the system's striving to the formation of low-energy boundaries. Hence, calculations were carried out which reveal how interfacial energy changes when adjacent calcite crystallites are rotated around the c axis. Accurate determination of the quantity for the continuous rotation is virtually impossible due to the too high computational cost. Therefore, an approximated method developed by Gautam and Howe [34] is used. According to it, interfacial energy decreases with the increase of the total intensity I contained in the areas of overlapping the diffraction reflections from neighbouring crystallites. Thus, using the last quantity we can find disorientations, to which local energy minima correspond (see Sec. 6).
The results clearly show that strictly defined low-energy boundaries, i.e. rotation angles, are preferred ( Fig. 3b). Particularly important is the disorientation based on rotation around the c axis by 60°. Two symmetrically equivalent orientation relationships correspond to it. They constitute two twin boundaries formed by the reflection planes (0 1 1 ̅ 0) and (0 0 0 1), respectively. The prismatic structure, whose elements mostly run through the entire thickness of the shells, causes that the first of them mainly occurs. The twin boundary (0 1 1 ̅ 0) positioning perpendicular to the growth line, allows it to be curved (comp. Fig. 3c, d and Fig. 4a, b). As a result, grains separated by a morphological plane of symmetry form a coherent connection. Another example is the boundary running along the symmetry axis of the central region (indicated by the arrow in Fig. 2a). The other preferred disorientations are also generated by twin relationships but this time the mirror planes have higher indices (1 5 ̅ 4 0) and (4 7 11 ̅̅̅̅ 0) for 38° and 18°, respectively. These two uncovered twins are formed only in biogenic calcite. They define new, hitherto unknown orientation relations.
Something one could wonder is how twin relationships can exist when monocrystalline prisms are separated by thick organic membranes. Checa et al. [24] showed how new membranes are introduced very early during the growth of prisms in the CCP layers of several pterioids, thus dividing otherwise continuous crystalline domains. We can hypothesize that twins were formed in initial growth stages in Pinna and twinned crystals were later separated by membranes. Given the low misorientations recorded in Pinna prisms, crystals remained in twin relationship long after they were separated by membranes.
The EBSD investigations performed for the representative fragment of the shell surface confirm that the slopes associated with island-like morphology lead to calcite prism inclination (Fig. 4). The c axes oriented perpendicular to the curved surface assume four preferential positions. It is revealed by the pole distribution function (PDF) whose four maxima show that c axes deviate from ND by 26°, 16°, 38°, and 36°, respectively (Fig. 4c). The identified orientations of c axes reflect the microstructure division into regions in which grains start to grow from differently sloping surfaces. The four zones formed are clearly depicted by means of axis/angle colour coding (Fig. 4b). Both calcite crystals situated along the ND, as well as those inclined rotate around their c axes, showing a tendency to locate the planes {0 1 -1 0} perpendicular to the longitudinal direction (Fig. 4d). Actually, the rotation is continuous, so there are not clear angular preferences (Fig. 4e). We can say, that in the initial growth stage the misorientation of prisms is largely random. With shell development, low-energy boundaries are continued and others tend to disappear. It is shown by the results obtained for the cross-section (Fig. 3a, b). The surface image captures the area of elongated grains, whose longer boundaries are determined by the directions of growth. At the place of strong curvature in the growth line, they deviate from each other. It is enabled by the twin boundary that runs along the longitudinal direction (LD) (comp. Fig. 3d and Fig. 4a, b). In this way, the mirror symmetry between adjacent grains is combined with the symmetry of the entire area morphology.
The question arises how the unique microstructure affects the mechanical properties of the material.
In order to solve the problem posed, research was carried out at different levels of the scale. In the first stage, static and dynamic nano-indentation of prisms with various orientations was performed. Then, we conducted static compression tests of cubic elements representing shell areas with strongly inclined c axes. respectively. The Schmid factor depends on orientation of a grain and the slip system which is activated inside it. If we assume an initial reference system with the z axis parallel to the loading direction (see Fig. 5a) and a final one determined by the system of a rotated crystal ̂∥ ሾ2 1 ̅ 1 ̅ 0ሿ,̂∥ ሾ0 1 1 ̅ 0ሿ,̂∥ ሾ0 0 0 1ሿ (Fig. 5), then the considered coefficient can be expressed by Euler angles and coordinates of unit vectors of the analyzed slip system ̂ and ̂. As a result, we obtain the following formula: = ( sin 2 sin Φ + cos 2 sin Φ + cos Φ)( sin 2 sin Φ + cos 2 sin Φ + cos Φ) (1) The relation is depicted for those slip systems, that give the highest values of the Schmid factor in the case of indented grains (Fig. 6a-c). A positive sign of the quantity means agreement between the signs of the applied normal stress and the resulting slip in the considered system. Interpretation becomes easier if we take into account positive slip systems. Then, a positive S factor means that during unloading a positive slip arises, while at the loading stage a negative slip is generated. to the plane and Euler angles that orientate an intended grain. This is expressed by the following formula: = ( sin 2 sin Φ + cos 2 sin Φ + cos Φ) 2 (2) The relation is illustrated for three planes representing the mentioned families. The chosen planes generate the highest values of the factor in the case of intended grains (Fig. 6d-f). Prisms typical of the Pinna nobilis species with the c axes running along the shell's thickness (ND) (Fig. 5a) are not the best mechanical solution. Then, regardless of the rotation of the grain around the c axis, a maximal resolved shear stress equal to half the compressive stress applied to the outer surface is generated in the (0 1 ̅ 1 4)ሾ0 2 2 ̅ 1ሿ − system (Fig. 6a). Thus, in a given orientation of the prism slips can be activated in three planes {0 1 ̅ 1 4} simultaneously. Similarly, basic twin systems   {1 ̅ 0 1 8}〈4 0 4 ̅ 1〉 + . achieve a high Schmid factor exceeding 0.4 (Fig. 6b). They are activated during unloading. As a result, grains typical of Pinna nobilis undergo intensive plastic deformations. Moreover, there is a possibility of fracture along the {0 0 0 1} plane because during unloading tensile stresses are perpendicular to it (Fig. 6f).
Geometric analysis of plastic processes shows that the inclination of grains significantly improves their mechanical properties. Due to deviation of c axis from the outer surface normal, the systems of easy slips are so-oriented that the formation of shear stresses necessary to induce permanent deformations is difficult. As the angle Φ increases, the factor S of the slip family {0 1 ̅ 1 4}〈0 2 2 ̅ 1〉 decreases (Fig. 6a). Thus, during loading the key glide mechanism r 〈0 2 2 ̅ 1〉 − is confined. At the appropriately high stress a single system (0 1 1 ̅ 2)ሾ2 2 ̅ 0 1ሿ − is activated. Initially, it is constrained to a small group of grains with orientations near the (49°, 35°) point which constitutes a maximum of Schmid factor (Fig. 6c). It is worth noting that, at the same time, in other systems of this family, the S coefficient does not exceed 0.13. At the unloading stage, the glide mechanism r 〈0 2 2 ̅ 1〉 − is not activated at all. Thus, with a relatively low external load, the glide processes inside typical grains are activated.
When the prisms deviate from ND above 30°, the initiation of slips requires the application of higher normal stresses to the outer surface. Then confined plastic deformations will occur in the systems r 〈0 2 2 ̅ 1〉 − , and in grains with a specific orientation will continue in a single system (0 1 1 ̅ 2)ሾ2 2 ̅ 0 1ሿ − . Thus, the degree of permanent deformation is lower. In the case of engineering materials, an increase in strength is associated with a decrease in fracture toughness. This relationship also affects the Pinna nobilis protective armor, but is limited to a small group of grains with specific orientations determined by Euler's angles from the vicinity of the (60°, 45°) point (Fig 6d). Then the plane of easy cleavage (1 0 1 ̅ 4) is located perpendicular to the normal force acting on the outer surface (see Fig. 5b). Hence, during unloading, an extensive crack will form. Other grains tend to split along planes {1 ̅ 1 0 8 ̅ }, {0 0 0 1}. Then separation requires higher energy. Hence, the fracture process is initiated at a higher load and is often combined with plastic deformation, which limits the crack growth. To sum up, the anisotropy of calcite crystal makes the inclined prisms show higher strength and fracture toughness in comparison to those with c axes parallel to ND. An exception is a small group in which planes {1 0 1 ̅ 4} orient perpendicular to ND. Nevertheless, the twin boundary (0 1 1 ̅ 0) transforms the grains into the adjacent ones which show significantly higher strength and toughness (Fig. 5c).

Experimental results
The regularities revealed in the theoretical analysis are mapped by the relation that combines the values of the mechanical property measured for representative grains in the nano-indentation test. Two groups were studied, each of which consists of three grains. The first prism preserves the c axis parallel to ND, the second one shows a strong inclination, while the other due to the specific tilting has a plane {1 0 1 ̅ 4} oriented perpendicular to ND with an accuracy of 10°. Schmid and cleavage factors for individual grains are presented in previously prepared distributions (Fig. 6). The first prism exhibits the lowest hardness, the second one, the highest, and the third one is characterized by an intermediate value (Tab. 1). The obtained maps show that the response of the second grain is largely uniform, while that of the first one is varied. A large part of prism 1 exhibits a hardness at a low level of 3.0 GPa (Fig. 7c, d).
The higher average value results from locally occurring harder areas. Research conducted on biogenic calcite shows that one of the sources of improving mechanical properties are structural defects [32].

Er [GPa]
10 m 10 m packing makes the elastic modulus the lowest. Orientations of prisms 3 and 2 are similar to those shown in Fig. 5. The first of these crystals exhibits the maximal cleavage factor for the key plane (1 0 1 ̅ 4).
The other one, due to the twin relationship, reduces this coefficient to 0.
Additional information on how the orientation of the grains controls the mechanical properties is provided by the second group of grains subjected to the impact test. Most cracks are formed in prism 4, typical for Pinna nobilis shells (Fig. 8a). They develop in a radial direction from the corners of the impression or along the traces of planes {1 0 -1 4}. The reason is significant plastic deformation caused at the loading stage. As in the case of the indentation of synthetic ceramics [37], the zone of plastic deformation located below the impression becomes a source of cracks which propagate to the external surface. According to theoretical analysis, a grain with axis c || ND undergoes the strongest plastic deformation. This gives rise to a dense crack system. They combine to form surfaces along which portions of material adjacent to the indents' edges undergo separation. The inclined grain represented by prism 5 behaves completely differently. Individual cracks are consistently running along the traces of the (0 1 ̅ 1 4) plane deviated by an angle of 38° from the surface (Fig. 8c). Thus, decohesion occurs at a lower depth, and in many cases is only partial. The atomic force microscopy (AFM) measurements show that the depths and areas of the impressions as well as the heights of the material pileups are smaller compared to grain 4 (comp. Fig. 8d and Fig. 8b). The visible reduction of plastic deformation as well as limitation of fracture processes is induced by the prism inclination. Higher strength and fracture toughness means that absorption of the impact energy is much lower than in the case of grain 4. This is indicated by greater distance to which the indenter is bounced from the sample back. It amounts 4000 nm, whereas for grain 4 it is 3800 nm. A small group of oblique grains shows reduced fracture toughness. It is represented by prism 6, which is illustrated in Fig. 6d. Then, during unloading, tensile stresses generate lateral cracks along the easy cleavage plane (1 0 1 ̅ 4) almost perpendicular to ND. As a result, the material is chipped, which partly occurs along the plane (1 1 ̅ 0 4 ̅ ) deviated by the large angle of 71° from the surface (Fig. 8e, f). Both the depths of impressions and the volumes of material detached from the bulk are the largest among the grains tested. Extensive damage entails significant absorption of impact energy, resulting in a shorter distance of the indenter bounce -3600 nm.

Compression tests
Besides the identification of mechanical properties at the nano-and microscopic levels, the response at the macroscopic level was also examined. The compression test was carried out for 6 samples cut from the rib areas at the places of outgrowths (see Fig. 4b) where the prisms strongly deviate from ND.
The results in the form of the stress-strain diagram together with the compressive strengths (c) determined for the individual shell specimens are presented in Fig. 9.
The values obtained are remarkably high considering the mechanical properties of the materials the shell is made of. Compressive strength up to 700 MPa results from the unique structure which is a weave of strong and weak units. This gives a great ability to dissipate energy, as well as enables blocking and delocalization of the fracture process. As a result, the loss of load capacity occurs at high stresses, when a significant part of the structure, or even the entire one is destroyed. Examples of such mechanical responses are samples 5 and 6, respectively.

Conclusions
The   (15 kV). The obtained EBSD data were analysed using the MTEX software [38].
Estimation of interfacial energy. According to the Gautam -Howe method, overlapping intensity I is a measure of the bonding strength at the phase boundary i.e. of matching the potential fields. Thus the higher the quantity I, the lower the energy of the interface treated as a disturbance [39].
In order to determine the distribution of total overlapping intensity I, in the Cartesian system ̂∥ ሾ2 1 ̅ 1 ̅ 0ሿ, ̂∥ ሾ0 1 1 ̅ 0ሿ, ̂∥ (0 0 0 1), two calcite crystals are considered. One of them is fixed, while the other rotates around the axis by an angle . The antisymmetric domain is investigated with an accuracy of 0.1°, thus ∈ 〈0°, 60°〉. Diffraction intensity Ii was assigned to each node in the reciprocal space using a structure factor = • * [40,41]. It is assumed that the intensity is distributed according to the Lorentzian function ( ) = Γ 2 2 2 ( 2 +Γ 2 ) , where Γ is the half of width at the half of the maximum. . It is assumed that Γ = 12 , then nearly 95% of the intensity is taken into account. The distribution of diffraction intensities in the reciprocal space maps the potential field of a crystal. The introduction of a phase boundary significantly disturbs the continuity of the field along a given family of planes if there is a considerable misfit between the systems of the planes in the neighbouring crystallites. Thus, it is assumed that the bonding along the most densely packed planes of calcite (1 0 1 ̅ 4) is broken when the mismatch amounts to 20%. As a result, using formulas derived in [42], radii of the individual spheres are obtained = 0.1 1 1 , 1 , 1 are interplanar distance and intensity for the considered system of planes, respectively.
Identification of mechanical properties. Nano-indentation and nano-impact tests were carried out by means of NanoTest Vantage system with a diamond Berkovich three-sided pyramid indenter.
Indentations were made parallel to the normal direction with a maximal load of 1.