Ribs of Pinna nobilis shell induce unexpected microstructural changes that provide unique mechanical properties

The reinforcement function of shell ribs depends not only on their vaulted morphology but also on their microstructure. They are part of the outer layer which, in the case of the Pinna nobilis bivalve, is built from almost monocrystalline calcitic prisms, always oriented perpendicular to the growth surfaces. Originally, prisms and their c -axes follow the radii of rib curvature, becoming oblique to the shell thickness direction. Later, prisms bend to reach the nacre layer perpendicularly, but their c -axes retain the initial orientation. Calcite grains form nonrandom boundaries. Most often, three twin disorientations arise, with two of them observed for the first time. Nano-indentation and impact tests demonstrate that the oblique orientation of c -axes significantly improves the hardness and fracture toughness of prisms. Moreover, compression tests reveal that the rib area achieves a unique strength of 700 MPa. The detection of the specific microstructure formed to toughen the shell is novel. experimental results confirm typical


Introduction
Bivalve shells are hierarchically complex biocomposites consisting of calcium carbonate (calcite or aragonite) and an organic matrix [1][2][3] . They have been improved over millions of years of 2 evolution to provide effective protection against predators. Consequently, the shells are lightweight and exhibit outstanding mechanical properties compared to the materials from which they are built. Thus, 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 [4][5][6][7] . Reproducing the shell's microstructure requires in-depth knowledge of it as well as of the mechanical properties of the components 8,9 . The present work is part of the search for engineering materials inspired by nature.
The subject is a shell of the Pinna nobilis species with an unusual morphology due to the repair of an extensive injury that occurred at a submature stage. Thus, the examined specimen is distinguished by a large, strongly ribbed surface.
The Mediterranean pen shell Pinna nobilis Linnaeus, 1758 (superfamily Pinnoidea, Order Ostreida 10 ) is a large endobyssate bivalve species that lives with its anterior end buried within the sediment. The shell is ornamented with radial ribs that periodically produce scales directed towards the margin (see App. A). The shell wall is made of two layers. The outer one has a columnar calcite prismatic (CCP) microstructure: large polygonal prisms elongated perpendicular to the outer shell surface, surrounded by organic sheaths. The inner layer is made of nacre, which extends for less than half the anteroposterior diameter (e.g. 1 ). The two layers perform different functions. The thick (1-5 µm) periprismatic organic membranes make the outer prismatic layer particularly flexible 11 . When the two valves abut, tight sealing [12][13][14] is achieved by flexible deformation of the wide prismatic margins. With progressive thickening of the prismatic layer towards the apical end (up to several mm in large specimens), flexing becomes hindered and the prismatic layer exerts an armoring function. The radial ribs developed on the prismatic layer contribute to reinforcement. Given the ability of the animal to retract deeply inside the shell, damage to the margin is not lethal. The protection is provided by the tough and rigid nacre layer.
Each prismatic unit is characterized by low disorientation (the term is explained in Sec. 6) and therefore becomes a grain similar to a monocrystal (e.g. 12,13,[15][16][17]. Previous studies on flat shell areas report that the c-axes of prisms remain parallel to their long axes [18][19][20][21] .
The CCP layers of bivalves have been widely studied 17,[22][23][24][25][26][27] . However, their mechanical properties have received little attention compared to nacre [28][29][30][31] and crossed-lamellar microstructures 32,33 . Strąg et 3 al. 34 reported values of 460 MPa and 3.86 GPa for the compressive strength and nanohardness of the calcitic layer of Pinctada margaritifera, respectively. Kunitake et al. 35 showed that the hardness of the Atrina rigida CCP layer varies with the rotation of the indenter tip around the normal to the loaded c plane. Accordingly, the range of 3. 47-4.19 GPa was obtained at a penetration depth of 170 nm. A similar dependence was found in Pinna nobilis: 3.89-4.86 GPa at a variable indentation depth of 100-250 nm 36 .
The aim of this study is to accurately characterize the CCP microstructure of P. nobilis in the areas of ribs and link it with the mechanical properties of the constituent elements as well as with the response to load of a representative volume. A specimen with a large, densely ribbed surface was used, shaped by extensive damage in the early stage of growth. Investigations with application of the electron backscatter diffraction (EBSD) method have revealed unusual orientations of prismatic calcite grains, 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 with nano-indentation, nano-impact and compression tests.

Microstructure identification
The studied shell has a morphology unusual for the P. nobilis species (compare App. A). A clear division line running longitudinally on both valves is visible (Fig. 1a). The reason is breakage of the shell at a submature stage of growth. The trace of the former fracture begins with a clear notch separating the posterior of the primary shell from the restored area. The further course of the crack is determined, on the external surface, by the discontinuity of the ribs, which are distributed more densely in the repaired part. In the same area, there is a thick nacre coating on the inside. After breaking, the shell was rebuilt asymmetrically. The dorsal and ventral parts developed independently. The first of them underwent significant expansion. In spite of the bilobate appearance, the examined shell preserves the geometric structure of the surface characteristic for the P. nobilis species. Its key component is the waviness generated by ribs running in the radial direction ( Fig. 1b-e). They are formed by periodically distributed segments of mantle specialized for the production of ribs. Upon growth, segments move along radial trajectories, thus producing a series of radial ribs 37 . The waviness integrally inscribed in the 4 three-dimensional surface topography induces a specific microstructure of the shell's cross-section. In order to identify it, in-depth EBSD investigations were carried out.

Height
[mm] Prisms, growing perpendicularly to the undulated 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 grains, are mostly oblique (Fig. 2). With shell thickening, 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 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 grains, the c-axes maintain their initial direction. As a result, obliquely initiated orientation becomes obligatory throughout the entire thickness of the shell. Thus, the wavy surface determines the texture of the entire protective armor. Analysis of the EBSD results reveals a clear division into three areas. Both the outer surface profile and the growth lines indicate that these regions correspond to three adjacent ribs running perpendicular to the image in the longitudinal direction (LD) (see Fig. 2a). The middle area is initiated by 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 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, compare red and black plots). The central area is flanked by two half ribs with a higher curvature, particularly the left one. Hence, in their upper parts, the c-axes of grains most often orientate at an angle of 32° (left rib) and 14° (right rib) relative to ND (Fig. 2b, red plot). The organization of both zones is similar. Initially, grains with an oblique inclination tend to disappear, whereas their neighbors expand at their expense. In this way, grains 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. The grains G1 and G2 are perfect examples. The first one exhibits the deviation angle of 15°, preferred in the right rib area. The other one has a much larger angle of 23°. Finally, G1 reaches the nacre layer while G2 vanishes. Even its sudden deflection causes only a slight change in the orientation of calcite -the difference remains within 2°.  The question arises as to whether there is a preference in the mutual orientation of adjacent grains. The calculated Misorientation Distribution Function (MDF) shows that the grains 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, we conducted calculations to 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 excessively high computational cost. Therefore, an approximated method developed by Gautam and Howe 38 is used. According to it, interfacial energy decreases with the increase of the total intensity I contained in the areas of overlapping diffraction reflections from neighboring 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 described by the 60° rotation about the c-axis. 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, means 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, because the crystallographic plane terminating the growth stage is mirrored to the adjacent area (comp. Something that could be of interest is how twin relationships can exist when monocrystalline prisms are separated by thick organic membranes. Checa et al. 26 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 the low-energy disorientations were formed in initial growth stages in Pinna and twinned grains were later separated by membranes. Given the low disorientations recorded in Pinna prisms, grains remained in the twin relationship long after they were separated by membranes. The EBSD investigations performed for the representative fragment of the shell surface confirm that the waviness leads to calcite prism inclination (Fig. 4). The c-axes oriented perpendicular to the curved surface assume four preferential positions. This is revealed by the pole distribution function 9 (PDF) whose four maxima show that c-axes deviate from ND by 26°, 16°, 38°, and 36°, respectively 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 color coding (Fig. 4b). Both calcite grains situated along 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 disorientation of prisms is largely random. With shell development, low-energy boundaries are continued and others tend to disappear. This 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. This 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 as to how the microstructure induced by ribs 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 rib areas with strongly inclined c-axes. respectively. The Schmid factor depends on the orientation of a grain and the slip system that 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:

Nano-indentation tests
= ( 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. 12 indenter: = 0 2 = 0 . Thus, the amount of tensile stress on a given plane is determined by the cleavage factor C. Its value depends on coordinates of a unit vector normal 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 the deviation of the 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 an appropriately high stress, the 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 the maximum 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. Instead, in the single systems (1 ̅ 0 1 8)ሾ4 0 4 ̅ 1ሿ + and (1 ̅ 1 0 2 ̅ )ሾ0 2 2 ̅ 1ሿ − , twinning and slipping occur respectively. Starting the last process is identified by the Schmid factor, which at the point (71°, 35°) reaches the minimal value -0.5.

13
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 the 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 the 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 the planes {1 0 1 ̅ 4} orientate 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 (see App. B). 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 is structural defects 35 .     (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 (compare Fig. 8b and Fig. 8d). The visible reduction of plastic deformation, as well as limitation of fracture processes, is induced by the prism inclination. Higher strength and fracture toughness mean that absorption of the impact energy is much lower than in the case of grain 4. This is indicated by the greater distance to which the indenter is bounced from the sample back. It amounts to 4000 nm for grain 5, 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. A compression test was carried out for 6 samples cut from the rib areas of the CCP layer at the places of scales (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 and also 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 present work focuses on radial ribs in a shell of the Pinna nobilis species. A specimen with a large, densely ribbed surface, generated due to a breakage at an early stage of growth, was investigated.
P. nobilis shows a great capacity for shell reconstruction. Thus, the fracture area is distinguished only by a slightly denser arrangement of the ribs, and then they continue in a manner typical for the species under consideration. The external part of the shell is built of calcite prisms running perpendicular to the outer surface. The rib area is, naturally, strongly curved. Thus, prisms starting the growth orientate obliquely to the thickness direction. Angles between the c-axes of calcite grains and ND are considerable and often exceed 30°. With development, the structure is ordered and the prisms reach the nacre layer perpendicularly. Despite this, the grain crystallographic c-axes preserve their initial oblique orientation.
The EBSD investigations reveal that the disorientation of grains is not random. Most often they rotate relative to each other around the c-axis by 18°, 38° and 60°. In order to uncover the reason for the

Appendix A. Morphology of a typical Pinna nobilis shell
The appearance of the examined shell, which was broken at the early stage of growth, differs insignificantly from the shell representative for the P. nobilis species. In order to facilitate the comparison, additional images of the external and internal surfaces of a typical specimen were created ( Fig. A.1). The ribs run uninterruptedly from the narrow umbo to the broad posterior margin, are quite distinct and create a characteristic sculpture of the shell. The only difference is in the part of the posterior margin, which in this case is one whole. Nacre occupies most of the anterior half of the shell and is divided into two lobes by a narrow longitudinal sulcus. The middle part of the shell, in which the median ridge (ligament) is located, has a similar structure in both cases. The surface of the sample is characterized by large, widely spaced spines and rows of scales. Pinnoidea live partially buried to one third of their length in sediment 47 . Therefore, part of the spines on the surface can be abraded and absent in the anterior portion of the shell. This is particularly evident in adult specimens. Undamaged P. nobilis has scars that are formed during the degradation of the spines. The surface ribbing is similar to the damaged specimen studied in the present work.

Appendix B. Arrangement of prisms subjected to nano-indentation and impact tests
The examinations were carried out in the area of the rib belonging to the posterior of the primary shell, below the fracture trace (see Fig. B.1). Basic structural units prisms grow perpendicular to the outer surface. Thus, the calcite c-axes of the grains runs along the radii of the rib curvature.

25
The nano-indentation test was performed on three prisms with specific orientations (see Fig. B.2 a).
The c-axis of the first one (G1) remains parallel to ND with an accuracy of 2° and in the next two (G2, G3) it deviates by an angle of 50°. Between grains G2 and G3 there is disorientation close to the twin relationship with respect to the plane (1 0 -1 0). Thus, the normal to the easy cleavage and slip plane (1 0 -1 4), deviated by an angle of 39° from ND in G2, undergoes rotation and forms a small angle of 9° with ND. Consequently, the grain G2 shows a high fracture toughness and the grain G3 significantly lower. The first prism G1 was initiated in the ridge of the rib (see Fig. B.2 b). As a result, the c-axis