Crystallisation in biomineral mollusc shell studied by 3D Bragg ptychography

Abstract

Biomineralisation integrates complex biologically assisted physico-chemical processes leading to an extraordinary diversity of calcareous biomineral crystalline architectures, in intriguing contrast with the consistent presence of a submicrometric granular structure. While the repeated observation of amorphous calcium carbonate is interpreted as a precursor to the crystalline phase, the crystalline transition mechanisms are poorly understood. Access to the crystalline architecture at the mesoscale, i.e., over a few granules, is key to building realistic crystallisation models. Here we exploit three-dimensional X-ray Bragg ptychography microscopy to provide a series of nanoscale maps of the crystalline structure within the “single-crystalline” prism of the prismatic layer of a Pinctada margaritifera shell. The mesocrystalline organisation exhibits several micrometre-sized iso-oriented/iso-strained crystalline domains, the detailed studies of which reveal the presence of crystalline coherence domains ranging from 130 to 550 nm in size. The further increase in the lattice parameter with the size of the coherence domain likely results from the crystallisation mechanism, pointing towards a maturation process occurring after the initial amorphous-to-crystalline transition.

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1 Introduction

Biocrystallisation gathers complex and regular physico-chemical processes whereby living organisms control the crystalline form and texture of their organo–mineral components by biological mediation.^1,2 Only considering calcium carbonate polymorphs (in molluscs, corals, sponges, etc.), a variety of sub-millimetric structures and shapes are observed.³ These controlled biocrystallisation pathways result not only in the synthesis of otherwise unstable crystalline forms¹ but also in hierarchical composite structures with a variety of microstructures.^3,4 This latter feature is remarkably illustrated by the famous pearl oyster Pinctada margaritifera, possessing an internal nacreous aragonite layer and an outer prismatic calcite layer,^3,5 composed of 10–50 μm large tablet and prism units, respectively.

This architectural diversity at the micro-scale strongly contrasts with the systematic occurrence in calcareous biominerals of crystalline spheroid units^6–10 of apparent diameter in the 50–500 nm range, coated by a visco-elastic organic cortex,^7,11 and referred to as granules. Despite the irregularity of the rounded nanometric granules, a crystalline organisation is observed at the micrometric length scale, showing the existence of a high degree of ordering, propagating from the crystal lattice cell to the mineralizing unit scale,^12,13 justifying the need of studying the mechanisms by which biocrystallisation occurs.

While in many marine species crystallisation does not follow the classical nucleation theory and crystallisation scheme of ion-by-ion addition,^14–16 the full description of the biological, physical and chemical mechanisms of biomineralisation still escapes our knowledge.¹⁷ A commonly described feature is the presence of one or several amorphous calcium carbonate (ACC) metastable precursor phases,^8,15,18–23 which subsequently transform into the final high-quality crystal.^24,25 In P. margaritifera, spectroscopy microscopy investigations have evidenced the simultaneous presence of amorphous calcium carbonate and organics matter, pointing towards a stabilisation of the amorphous precursor by organic molecules.²⁵ Other stabilizing factors such as finite-sized granules^26,27 and/or trace elements (e.g., Mg)^28,29 are also proposed. The mechanism by which the amorphous to crystalline transition occurs remains also an open question.¹⁷ Whether the crystallisation includes a solid-state transformation, a dissolution–reprecipitation mechanism or a combination of the two are different possible scenarios with strong implications e.g., in the field of geochemistry: a pure solid-state transformation would record the initial chemical signature of the local environments associated with ACC into the final shell, whereas a dissolution–reprecipitation would be able to erase or alter these signatures, leading to a final crystal with little resemblance to the initial conditions.³⁰

This work aims at shedding light on the amorphous-to-crystalline transition mechanisms exploiting a recently proposed experimental approach, X-ray Bragg ptychography, on a model biomineral, the P. margaritifera mollusc shell. X-ray Bragg ptychography^31–34 belongs to the so-called coherent diffraction imaging microscopies,³⁵ which retrieve the 3D sample scattering function from a set of coherent intensity measurements, using numerical approaches. This synchrotron-based method is specifically designed for imaging crystalline sample with nanometric spatial resolution, taking advantage of the weak interaction of X-rays with matter and corresponding large penetration depth, allowing for structural investigations of a sample without invasive preparation.³³ Once in Bragg diffraction condition, the internal periodicity of the sample crystalline lattice produces highly intense Bragg peaks that contain information on the crystal properties of a given crystal plane family.^36,37 Bragg ptychography measurement consists of recording a set of 3D Bragg diffraction intensity patterns (i.e., in the vicinity of a chosen Bragg peak), resulting from the interaction between a finite-sized coherent beam and the investigated object under Bragg conditions.^31–33 From the data set, phase retrieval algorithms reconstruct numerically the 3D sample map, which provides detailed information on the sample crystalline properties, such as crystalline coherence, relative lattice mismatch fields and relative crystalline plane rotations.^32–34 The high sensitivity of this crystalline microscopy allows one to distinguish crystalline domains with lattice mismatch of a few 10⁻⁴ and/or presenting misorientations of a few 10⁻² degrees.³³

The chosen P. margaritifera mollusc shell sample is ideally suited for this study. At the shell edge, early calcareous mineralizing units are visible,^25,38 which allows us to probe the early stages of mineralisation. Each valve of the shell is organized in two main mineralized layers: an external layer composed of elongated calcite prisms and an inner layer made of aragonitic nacreous tablets.³⁹ The outside of the shell is lined with a thin organic membrane, the periostracum, and both prisms and nacre tablets are enveloped in thin organic sheaths.^40,41 While all these organic layers are composed of proteins, sugars, and lipids,^40,42,43 the prismatic layer is produced by cells located at the very edge of the animal mantle and the nacre layer by other, more internal cells.⁴⁴ Therefore, only the prismatic layer is present at the shell edge. The shell thickens progressively in a layer-by-layer growth fashion as observed in many biominerals^3,25,39 and is therefore rather thin at its border, a geometrical constraint that needs to be fulfilled for Bragg coherent diffraction-based methods.³³ This constraint results from the finite longitudinal coherence length of the synchrotron beam, which restricts the investigation to samples thinner than about 1–2 μm.

In a previous work, Bragg ptychography was successfully used to investigate the crystalline properties of a P. margaritifera calcite prism.³³ It allowed evidencing the presence of iso-oriented domains, which compose the prism crystal at the mesoscale (i.e., at the 100 nm length scale). In the present work, this approach is extended by producing a large series of Bragg ptychography reconstructions, which target different regions of a P. margaritifera prism. The detailed analysis of the obtained crystalline information provides a new description of the mesoscale crystalline organisation, likely arising from the amorphous-to-crystalline transition mechanisms.

2 Experimental

2.1 Pinctada margaritifera mollusc shell

The juvenile P. margaritifera (Fig. 1) were farmed at the IFREMER hatchery at the biological station of Vairao (Tahiti). They were cultivated in an optimal and bio-secured environment (sea water temperature at 29 °C and pH at 8.2) to avoid any contamination during growth. Once selected, they were preserved in a 70% ethanol/water solution and transferred to the Institut Fresnel in Marseille in 2017 (France). Before the X-ray experiment, the shells were cut into small pieces of about 1 mm² and glued on the top of a metallic tip. This process ensures that the integrity of the investigated part of the shell is preserved.

Fig. 1 Description of the Pinctada margaritifera sample. Scanning electron microscopy images produced in the vicinity of the growth edge. (A–C) The growth edge. Note the difference between mature juxtaposed prismatic units and disc-like rather isolated early-mineralized units at the border. In B, the spotty feature at the centre of the units is referred to as the centre of calcification (also visible in E). The ring-like patterns are visible at the surface of discs and prisms. (C) Lateral growth asymmetry of the successive layers along the prism thickness, visible through the periostracum organic layer (in the vicinity of the white *). (D) Prism thickness close to the shell edge. (E) Organics accumulation at the periphery of the prisms. (F) Internal side of the shell exhibiting a homogeneously rough surface. (A–E: external side of the shell).

2.2 Sample characterization methods

2.2.1 Optical birefringence microscopy. Optical birefringence images were recorded on an LV100N Nikon polarized light microscope in a diascopic illumination scheme between crossed polarizers. To observe small birefringent effects resulting from the limited thickness of the samples, a red tint plate was added. It allows enhancing the colour contrast and emphasizing the birefringence homogeneity (Fig. 2).

Fig. 2 Calcite prisms at the shell edge. (A and B) Optical birefringence microscopy picture at the edge of a P. margaritifera sample shell. (C) Shell edge as seen by the optical microscope of diffraction set-up at the synchrotron. The prism selected for the Bragg ptychography experiment is highlighted (black rectangle). (D) Nanodiffraction map of the 012 reflection integrated intensity acquired for the selected prism. The regions further investigated by Bragg ptychography are labelled from A to G. The x and y length scales represent 5 μm. (E) Schematic representation of these positions with respect to the prism crystallisation history. The prism cross-section is shown along two axes: the direction perpendicular to the shell edge and the thickness. This latter one also encodes the time axis, as the prism thickens gradually, by addition of successive calcite layers (in gray), on the surface of the initial disc which is therefore located on the outer shell side. Laterally, the growth layers extend until they abut on another prism. As the mineralizing units are sparser towards the shell edge, the growth layers expand further in this direction. At the periphery of the growth layers, expelled organics matter accumulates (in green), resulting from the lateral amorphous-to-crystal transition process. On the diffractometer, the shell is mounted so that the X-ray beam (in orange) impinges first on the inner shell side.

2.2.2 Scanning electron microscopy (SEM). The SEM micrographs were acquired with a Phenom X Pro. The samples were mounted with carbon tape and the instrument was operated in low-vacuum mode to reduce sample charging. The acceleration voltage was set to 15 kV and the backscattered electrons were used as the imaging contrast.

2.2.3 X-ray nanodiffraction. The X-ray nanoprobe Bragg diffraction experiments were performed at the nanobranch of the ID13 beamline at the European Synchrotron Radiation Facility. A 14.8 keV monochromatic beam was selected with a channel-cut Si(111) monochromator and was prefocused onto the final focusing optics with a set of white-beam beryllium compound refractive lenses. The final focusing was obtained with a set of crossed silicon refractive lenses of 25 μm effective aperture and 0.01 m focal length, producing a beam size of about 300 nm full width at half maximum (FWHM) at the focal plane with a flux of 1 × 10¹⁰ ph per s. The sample, fixed on a metallic tip was mounted onto a three-axis piezo-electric stage, itself placed on the top of a hexapod and an air-bearing rotation stage used for the sample angular scanning acquisition. It was further translated into the focal plane, using an optical microscope with a 1 μm depth of focus. For collecting diffraction patterns, a 2D Dectris Eiger X 4M (2070 × 2167 pixels, 75 μm width) pixel array detector was placed at about 100 mm from the sample allowing the recording of multiple Bragg peaks simultaneously, in transmission geometry. The peaks appeared as soon as Bragg diffraction conditions are met, either during the spatial scanning of the sample across the beam or during the rocking curve acquisition (angular exploration of the sample with respect to the incident beam direction). Prior to the nanodiffraction measurement the set-up was calibrated using an α-Al₂O₃ reference compound (NIST SRM 674a), allowing us to access absolute angular values from the detector pixel positions. The Pm shell was first investigated with nanodiffraction to identify a series of prisms close to the shell border and presenting a crystalline orientation compatible with the Bragg ptychography set-up, i.e., prisms with intense Bragg reflections close to the horizontal plane. Once selected the chosen prism was scanned in detail over a 24 μm large region with step size of 200 nm and exposure time of 0.05 s, at a fixed angular position.

2.2.4 3D X-ray Bragg ptychography.
2.2.4.1 Data acquisition. Collection of the X-ray Bragg ptychography data sets was performed with the same set-up as described above. However, to increase the transverse coherence length of the beam, the white beam prefocussing lenses were removed, leading to a beam size of about 150 nm (FWHM) with a flux of 5 × 10⁸ ph per s. To further ensure the detailed measurement of the coherently diffracted intensity pattern, the Eiger detector was placed at about 3 m from the sample. The preliminary nanodiffraction investigation of the shell border allowed identifying a well-suited prism (thickness below 2 μm) with an accessible 012 Bragg reflection. A large series of Bragg ptychography acquisitions was performed over this prism, using various scanning parameters to adapt to the local crystalline orientational disorder observed across the prism. Typically, about 10 sample translation points were recorded along both x and y (resp., horizontal and vertical directions) with step sizes of 45 nm along each scanning direction. The angular step was set to 0.005°, covering an angular extent ranging from 0.7° to 3.9° corresponding to 140 up to 780 acquisitions. The acquisition time was set to 0.5 s per point.
2.2.4.2 Data inversion. The inversion of the five-dimensional data set was performed with our 3D Bragg ptychography algorithm, as described in detail in previous articles.^33,34,45 The inversion was performed with an optimized procedure, extensively tested on noisy numerical data,³³ mimicking as much as possible the experimental conditions (probe, sampling, scanning, intensity dynamical range, etc.). All along, the error-metric derived from a Gaussian likelihood was used to account for the photonic shot noise in the intensity measurements.⁴⁵ A regularisation term was introduced in the criterion to favour thickness-limited solution.³³ The local thickness of the shell sample was first refined directly from the inversion process, using the method described previously³³ and referred to as the L-curve approach. Once the regularisation thickness was optimized, 1500 to 2000 cycles of ptychography iterative engine were run on both object and probe,³⁴ resulting in the presented reconstructions.
2.2.4.3 Data analysis. The result of the 3D Bragg ptychography reconstruction is a 3D complex-valued solution (Fig. 3) corresponding to the sample scattering function, which for a crystal can be expressed by³⁶

ρ(x,y,z) = |ρ(x,y,z)| exp[iφ(x,y,z)] (1)

where the phase φ is related to the crystalline properties through

φ = G₀₁₂·u (2)

with u the crystalline displacement field and G₀₁₂ the Bragg vector of the investigated reflection (G₀₁₂ = 16.277 nm⁻¹). Note that, in eqn (2), the x, y, z spatial coordinates within the sample have been omitted for conciseness. The knowledge of φ gives access to the u₀₁₂ projection of the displacement field onto the Bragg vector and its variations provide information on the local crystalline properties. For instance, a linear variation of the phase along the direction parallel to the Bragg vector corresponds to a shift of the associated Bragg peak along this direction, i.e., a change in the lattice parameter. In the absence of crystalline shear, a linear variation of φ perpendicularly to the Bragg vector corresponds to an angular rotation of the associated crystalline planes.³² More generally, the derivative of u₀₁₂ with regards to the coordinate collinear to G₀₁₂ gives access to a relative lattice mismatch while the relative crystalline plane rotations around the two directions perpendicular to G₀₁₂ are extracted directly from the derivative of u₀₁₂ with regards to these two axes (derivations of the complete expressions can be found elsewhere³²). The relative lattice mismatch and the relative rotations are calculated with respect to a reference crystal whose Bragg peak would be observed at the centre of the detector frame (Fig. 4 and 5). Finally, a homogeneous phase region (i.e., a phase region presenting linear variations only) corresponds to a crystalline coherence domain (Fig. 6). In this work, the coherence domain sizes are estimated directly from the retrieved phase maps, after the subtraction of the 3D homogeneous phase component (linear phase gradients and phase offset). This produces locally constant phase maps, from which the coherence length is measured, in 3D, as the distance for which the phase shift amplitude is smaller than 1 radian. This phase shift cut-off was arbitrarily chosen, as it allows description of all observed phase domains. Note that the coherence length extracted from the Scherrer width approach referred to a phase shift definition of 2π. Hence, except that our definition provides coherence length estimation smaller by a factor of 0.16 (i.e., 1/2π) than the one extracted by the Scherrer width, these two definitions of the coherence length refer to the same physical parameter, if the phase shift scales with the distance from the centre of the domain. It is also important to underline that Bragg ptychography allows disentangling the coherence length along each spatial direction within the sample.

Fig. 3 3D Bragg ptychography results. (A and B) Cross section of the retrieved phase maps along the (x, y) and (z, x) planes respectively (colour scale in radians), obtained in the vicinity of the region A (Fig. 2D). From the phase map, several crystalline properties can be calculated, shown in C–H. (C and D) Relative lattice mismatch (unitless colour scale). (E and F) and (G and H) Relative crystalline rotations about two axes perpendicular to the Bragg vector, respectively (colour scales in degrees). Through the investigated volume, each map is composed of domains, characterized by a homogeneous value of lattice mismatch and tilts. The same domain shapes are observed for the three extracted crystalline properties, meaning that each domain is characterized by a unique set of lattice mismatch and rotations forming an iso-domain. The black lines indicate the position of the cross-sections.

Fig. 4 3D representations of the iso-domains across the prism. (A–G) 3D representation of the iso-domains extracted from the data obtained in regions A to G (Fig. 2D). The colour scale encodes the second crystalline rotation parameters (as shown in Fig. 3G and H for region A). The same crystalline rotation reference is used across the plots, allowing following the iso-domains from one region to another. The length scale shown in A is common to all 3D plots (250 nm horizontally and 500 nm vertically).

Fig. 5 3D crystalline coherence domains. (A–F) Cross sections of the phase maps after subtraction of the homogeneous phase components, to highlight the crystalline coherence domains observed in each iso-domain (here in regions A, C and E), respectively. Along x, y and z, the coherence length is measured as the distance between two points exhibiting a phase shift amplitude of 1 radian. (G) Plot of the crystalline coherence size measured along z as a function of the lateral size (mean value along x and y). The solid line is a guide to the eye. It corresponds to a linear fit of the data with slope of 0.81 nm nm⁻¹.

Fig. 6 3D relative lattice mismatch. (A–F) Cross sections of the 3D relative lattice mismatch map in the iso-domain shown in Fig. 5 (regions A, C and E, respectively). (G) Plot of the relative lattice mismatch as a function of the mean crystalline size (average along x, y and z) extracted for each coherent domain. The solid line is a guide to the eye. It corresponds to a linear fit of the data with a slope of 9.5 × 10⁻⁶ nm⁻¹ and a vertical offset of −3 × 10⁻³. In A–F the colour scale is unitless.

3 Results and discussion

Samples were first selected from a batch of juvenile specimens of P. margaritifera for the quality of their growth edge. The structure of this specific region is illustrated in Fig. 1. The shell presents a continuous growth history (Fig. 1A and B) with the bulk of the shell being composed of well-developed and tightly packed mineralizing units, referred to as prisms (typical size of about 20 μm), while the growth edge exhibits isolated, smaller and rather disc-like units. Those are the early stages of the prismatic units. Additional structural features are identified, related to the growth mode of the units. The ring-like features observed on the external side of the shell, as observed previously,²⁵ correspond to the edges of the successive mineralizing layers which have been produced onto the initial disc, in a layer-by-layer growth fashion. They develop asymmetrically with respect to a centre (the so-called centre of calcification) extending laterally until they abut on a neighbour prism (Fig. 1B and C), which are sparsely present at the forefront of the shell, i.e., close to the shell edge. At the shell border, the individual growth layers are rather thin (about 500 nm)²⁵ leading to mineralizing units with thickness ranging typically between 500 nm to 5 μm (Fig. 1D). On the external side of the shell, the periostracum organic layer is well visible (Fig. 1A–C), and organics matter is observed at the periphery of the prisms (Fig. 1E), resulting from the accumulation of expelled organics during the radially propagating amorphous-to-crystal transformation.²⁵ The inner side of the shell is rather different. The prism surfaces exhibit nano-granules, like those often observed in biomineralizing systems.⁷

The prismatic layer of the P. margaritifera shell is composed of calcite units whose single crystallinity is evidenced by optical birefringence microscopy (Fig. 2A and B). Each prism presents a homogeneous colour, resulting from the homogeneity of its crystalline properties (such as its optical birefringence). The change in colour from one prism to another results from the different crystalline orientations with respect to the optical axis. A closer look at the shell border highlights a smooth change of colour within individual prisms, corresponding to a change in calcite thickness, resulting from the lateral growth asymmetry at the very early stages (Fig. 1B and C). The single-crystalline behaviour of the prisms is further evidenced with the X-ray nanodiffraction experiment performed at the synchrotron. The investigated shell sample is shown in Fig. 2C, while the integrated intensity of the 012 Bragg reflection peak of the selected prism (black rectangle in Fig. 2C) is plotted as a function of the sample scanning positions in Fig. 2D. For this prism, the calcite 012 Bragg reflection was observed at a Bragg vector value of 16.465 nm⁻¹, corresponding to a d-spacing value of 3.816 Å (to compare to the synthetic calcite (012) d-spacing of 3.86 Å). While the prism could be clearly identified, from its position and shape, among the different prisms present in the investigated region, some parts of the prisms are missing. They likely correspond to crystalline regions slightly misoriented with respect to the main part of the prism, and which could not be caught during the acquisition because the presented nanodiffraction map was performed at a fixed angular orientation with an angularly limited bandwidth set-up (in the order of 0.3°). For Bragg ptychography investigation, seven regions were further selected within the prisms and labelled from A to G. They were chosen to probe regions with different crystallisation histories. More specifically, A and G are in the vicinity of the centre of calcification. D, E and F are close to the prism edges, F being closer to the shell edge while D and E were on the opposite side of the prism. Finally, B and C were chosen far from centre and edges, away from any specific features. A schematic representation of these locations with respect to the structural growth features of the prism is further shown in Fig. 2E, as an illustration.

Result from 3D Bragg ptychography reconstructions are shown in Fig. 3 for the data acquired in region A (Fig. 2D). In the following, perceptually uniform colour scales were systematically used, to produce fair representations of the observed spatial distributions. In Fig. 3A and B, two cross sections of the retrieved phase are shown, parallel to the prism surface and across the prism thickness, respectively. The finite extent of the retrieved region results from the size of the probed area, along x and y, and from the finite prism thickness, along z.

Strong phase gradients are observed, characterized by different rates from one region to another. From the phase, the relative lattice mismatch is calculated (Fig. 3C and D). It corresponds to (d₀₁₂ − d_ref)/d_ref with d₀₁₂ being the d-spacing within the sample and d_ref corresponding to a reference d-spacing (i.e., the one that would produce a Bragg peak at the centre of the detector). From nanodiffraction preliminary investigations, we could estimate that d_ref = 3.816 Å. A positive (resp. negative) value of the relative lattice mismatch means that d₀₁₂ is larger (resp. smaller) than d_ref. To provide a comparison, the relative lattice mismatch of calcite would correspond to +1.1 × 10⁻². In Fig. 3C and D, while the relative lattice mismatches take either positive or negative values, all values are smaller than the pure calcite relative lattice mismatch, indicating that d₀₁₂ is smaller than the (012) d-spacing of pure calcite. From the phase, the crystalline plane rotations are further calculated. They correspond to angular tilts about two axes perpendicular to the Bragg vector and are presented in Fig. 3E–H. Their values are spanning an angular range of about 2°. Interestingly, domains of homogeneous values are observed in Fig. 3C–H, evidencing a spatial organisation of the crystalline properties at this length scale. Moreover, each domain is characterized by a unique set of lattice mismatch and tilt values. Therefore, we further refer to them as iso-oriented/iso-strained domains or (more concisely) iso-domains.

Fig. 4 presents the full 3D representation of the iso-domains across the seven investigated regions (A to G in Fig. 2D). The colour scale encodes the second lattice rotation parameter (as shown in Fig. 3G and H for region A), as a means to track the domains from one investigated region to another. The use of the same crystalline orientation reference for all investigated regions allows following the evolution of the iso-domains across the prism. Some domains are rather large, expanding over regions separated by more than 10 μm (see Fig. 4D and E). Along the thickness, which is about 1.9 μm in the thickest part of the prism, 3 to 4 domains are observed, while 2 domains are observed in the thinnest parts (Fig. 4E and F), which correspond to regions close to the prism periphery. Iso-domains with larger misorientation than those of regions D–E are observed in regions A, F and G, i.e., in the vicinity of the centre of calcification and at the forefront of the prism periphery. While in F the misorientation could result from a global curvature of the prism in this region, this is unlikely the case in A and F, as domains with the same orientations as observed in D–E are also identified. In A, the large iso-domain at 1.6° is observed at z < 0 i.e., close to the outside of the shell.

Each identified iso-domain was further analysed. They were first extracted by selecting the ensemble of pixels belonging to a given set of lattice mismatch and tilt values, allowing for some limited angular fluctuations for the tilt values, in agreement with the observed angular distribution within the individual iso-domains. Each iso-domain was further investigated to identify sub-domains presenting a smooth variation of the phase. They are referred to as crystalline coherence domains. In all investigated iso-domains, the largest crystalline coherent domain was systematically extracted and an estimate of their size was performed, along x, y and z, respectively, using the method described in the data analysis paragraph of Section 2.2.4. Three examples are shown in Fig. 5A–F, arising from iso-domains observed in regions A, C and E respectively, chosen to illustrate the variability of the coherence domain sizes, which range from 130 nm up to 1.1 μm. The results are summarized in Fig. 5G, which presents the average lateral coherence size (i.e., the mean of the sizes along x and y) plotted as a function of the longitudinal size along z, obtained for 15 crystalline coherent domains extracted from all the identified iso-domains. Despite the variability of these extracted values, a general trend emerges, indicating that the lateral and longitudinal sizes are correlated, the larger the lateral size of the coherent domains, the larger its thickness along z. The increase rate of the size along z shows that the coherent domains are rather anisotropic (larger than thicker). A linear fit of the data produces a fair agreement, with a fitted slope of 0.81 nm nm⁻¹.

The crystalline properties of the iso-domains are further explored by analysing the relationship between the relative lattice mismatch and the size of the coherent domains. As an illustration, the lattice mismatch maps of the domains shown in Fig. 5A–F are plotted in Fig. 6A–F. They present homogeneous values, changing significantly from one coherent domain to another. The whole data set is plotted in Fig. 6G, which gathers, for all identified coherent domains, their mean relative lattice mismatch value as a function of the size of the coherent domain (average in 3D). A linear dependence is observed between these two parameters, supported by a linear fit of the data which produces a good agreement for a slope of 9.5 × 10⁻⁶ nm⁻¹ and a vertical offset of −3 × 10⁻³. The smaller the coherent domains the smaller the d₀₁₂ lattice parameter of the crystal.

In summary, presence of several iso-domains could be evidenced and followed across the P. margaritifera prism. These domains are characterized by their homogeneous lattice parameter and rotation values, in agreement with previous work.³³ They present various shapes and sizes, the larger ones expanding over the whole prism thickness and propagating laterally over more than 10 μm. The iso-domains are composed of crystalline coherent domains, whose size could be directly measured in 3D and further analysed. Over the explored coherent domain series, the lateral size of the domain scales with its longitudinal size, which is however smaller by 20% than the lateral one. The lattice parameter of the coherent domain presents a clear dependence on the size of the domain, the smaller the domain the smaller the lattice parameter. These observations, which require to spatially link the three extracted crystalline properties over micrometric length scales and with a high sensitivity, illustrate the performance of Bragg ptychography with respect to other crystalline microscopy approaches (e.g., high resolution X-ray diffraction,^12,46 transmission electron microscopy⁴⁷ or optical birefringence).^25,48

The present characterisation of the iso-domains in P. margaritifera agrees well with previous works, where the presence of a mesoscale ultrastructure has been (indirectly) reported. Low mosaicity, in the order of 1° or less between adjacent domains, was noted or inferred in some biogenic crystals,^12,13,47 while largely misoriented crystalline domains (by a few tens of degrees) were observed along the growth direction of mature crystalline units.^38,49,50 Micro-strain fluctuations, in the order of a few 10⁻³ with respect to the mean lattice spacing, were reported as well.^12,46,47 These structural fluctuations (orientations and strains) within the crystal are attributed to the presence of occluded organic molecules.^12,13,47,51 Sub-micrometer sized coherent crystalline domains were also evidenced. These were reported from high-resolution X-ray diffraction analysis in several bivalve mollusc shells, containing many micrometre-sized units. The broadening of the Bragg peaks was interpreted as result of sub-micrometric crystalline domains of coherence lengths in the 250–700 nm range.^12,46 Domains of comparable sizes were also imaged with 2D transmission electron microscopy.⁴⁷ In the present study, coherent domain sizes between 130 and 800 nm were observed, in full agreement with these previous observations. The extent of the larger ones, larger than the granule size, indicates that granules might be fused by particle attachment and coherent bounding. Another scenario, able to lead to the formation of large coherent domains, would involve atomic diffusion through a ripening process.

The strong relationship between size and lattice mismatch, as evidenced in Fig. 6G indicates that the size of the coherent domain is linked to the lattice parameter of the crystal. In this size range, the strain/size relationship cannot result from a size effect (i. e., a change in the crystal lattice induced by the strain state of the coherent domain surface) as it occurs for particle sizes in the nanometre range. It rather points towards a change in chemical composition of the domains. As the coherent domain corresponds to a perfect crystal, the change in lattice parameter cannot result from the presence of large defects like organic molecule-induced dislocations. While different organic molecules may present different kinds of interactions with the calcite crystal, the inclusion of large molecules like amino-acid lysine proteins, induced during calcite synthesis, is expected to produce dislocation lines or loops.⁵² In those cases, the strain concentrates only along the lines, without modifying the crystal away from these.⁵² Other studies regarding the crystalline properties of calcite synthesised in presence of polymer⁵³ or acidic monosaccharides⁵⁴ in ambient conditions show an increase in the lattice spacing with respect to the lattice of pure calcite. These results are in contradiction with the above observation of 3D domains with homogeneous strain states and lattice spacing smaller than reference calcite. On the contrary, point defects (e.g., vacancy, interstitial or substitutions) could explain the homogeneous modification of the strain on a long length scale. However, with d₀₁₂ being significantly smaller than the one of synthetic calcite, interstitial defects are unlikely, as they would increase the lattice parameter. Identifying the nature of these defects and their composition is challenging and several candidates are legitimate to consider. A series of observations points towards the same direction. Previous analyses of the P. margaritifera shell²³ have evidenced the presence of a Raman contribution at about 1089–1091 cm⁻¹, occurring at a slightly larger wavenumber value than the pure calcite ν₁ wavenumber (1085 cm⁻¹), using coherent Raman microscopy. This shift is compatible with Mg inclusion in the calcite crystal (note that CaCO₃–H₂O and CaCO₃–6H₂O are expected at 1066 and 1071 cm⁻¹, respectively). The presence of Mg was indeed also evidenced by surface sensitive energy dispersive X-ray spectroscopy with electron microscopy.²³ The observations of ring-like Mg distribution at the surface of the prism agrees well with the structural and chemical (ACC and organics) ring-like features observed by SEM (Fig. 1) and coherent Raman microscopy.^23,25 Finally, a close look at the diffraction curve (between 10 and 35 nm⁻¹) produced during the nanodiffraction investigation of the prism analysed in this work did not allow evidencing the presence of another crystalline phase than (strained-like) calcite. Therefore, we hypothesise that the change in lattice parameter observed in the different coherent domains is induced by the presence of Mg in the calcite crystal. The synthesis of Mg–calcite crystal at a fixed (rather small) Mg content shows that single-crystalline micro-particles present a rather homogeneous strain state, with coherence domain size in the micrometre range, in fair agreement with our observations.⁵² Using Vegard’s law applied to our observed relative lattice mismatch values, the Mg concentration is estimated to range between 8% and 16%, the largest concentration being associated to the smallest coherent domains. The strain offset observed at the origin of the size/strain fit corresponds to a Mg concentration of 17%. In the literature, controlled Mg distribution was found in other species, identified as high-Mg calcite biominerals (as seen in e.g., sea urchin tooth,⁵⁵ red coral⁵⁶ and red algae⁵⁷). Seknazi et al.⁵⁸ report on the observation of Mg-rich calcite coherent domains within a calcite matrix in the Mg-rich brittle-star lens biomineral. The size of the domains, of a few nanometres, and the bimodal distribution of the Mg composition (either rich or poor) support a formation model involving the spinodal decomposition of a gel-like Mg–ACC precursor leading to the formation of Mg-rich ACC particles embedded into a Mg-poor ACC matrix that further transforms into Mg-rich/Mg-calcite. However, calcite produced by molluscs is usually considered as low-Mg calcite⁵⁹ and the Mg concentration in P. margaritifera calcite is below the critical concentration value for spinodal decomposition.^57,60 Under the hypothesis that the observed lattice parameter results from the compositional level of Mg in calcite, a continuous distribution of Mg-rich to Mg-poor calcite domains would be present in the investigated P. margaritifera prism, with the smallest Mg–calcite particles presenting a Mg concentration of about 16% or slightly more. This continuum could result from a slow ripening process occurring after the transformation of the initial Mg-rich crystalline nanoparticles. In this scenario, atomic diffusion between an initial Mg-rich crystalline nanoparticle and its environment would lead to the formation of a larger crystalline domain and release of Mg. This idea is also supported by the spatial distribution of the different coherent domains within the prism. Domains with the smaller lattice parameter are systematically observed at z > 0 (i.e., closer to the youngest part of the prism), while the largest domain, observed in region A, is in the vicinity of the outer surface, (i.e., the oldest part of the prism). This asymmetry observed along the shell thickness is confirmed by a recent 3D coherent Raman microscopy investigation of a P. margaritifera shell edge, where the 3D distribution of the 1091 cm⁻¹ contribution (attributed to Mg–calcite as evidenced previously)²³ is significantly larger in the vicinity of the inner side (i.e., the youngest part) of the shell.⁶¹ Our observations may indicate that a phase separation also occurs in low-Mg calcite biominerals. Several remarks may help to reconcile the low-Mg and high-Mg calcite models. With high-resolution electron transmission microscopy methods,^57,58,60 the detection of the Mg-rich particles although highly spatially resolved, is likely less efficient than with Bragg ptychography, this latter one being able to detect orientational or lattice mismatch with a sensitivity in the order of a few 10⁻⁴. In addition, the estimated Mg content of the biomineral tissue is estimated from the final material and may be significantly different, if a Mg release mechanism is at play during the final crystal ripening, from the Mg content in the initial ACC precursor (which is the relevant parameter to compare to the spinodal critical concentration). Finally, the detection of possibly Mg-rich domains with Bragg ptychography relied on the possibility to image a full prism thickness, investigating the prism as a function of its aging and specifically, in the vicinity of its growing edge.

4 Conclusions

The shown results are based on the detailed investigation of a mollusc prism, using spatially resolved, highly sensitive X-ray Bragg ptychography microscopy. The presence of coherent domains, and other experimental chemical-sensitive evidence, point towards a non-homogeneous Mg distribution within the crystal, likely arising from the property of the initial amorphous precursor. This further opens the question regarding the role of Mg in the mechanisms of biomineral formation, even for low-Mg calcite biominerals.

Data availability

3D reconstructions data and associated Matlab codes are available at https://doi.org/10.5281/zenodo.14731235.

Author contributions

VC conceived the experiment with contributions from MB. PL and VC developed the inversion code. TAG and VC performed the experiments at ID13, ESRF with support from MB and OB. The 3D ptychography reconstructions were performed by VC, PL and TAG. JN performed the SEM experiments. JVD and DS supervised the sample shell production. VC wrote the manuscript with JD and contributions from all co-authors.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We acknowledge the ESRF, Grenoble, France for supplying beam time for the experiments and the Partnership for Soft Condensed Matter for support during the preparation of the experiment. Mohammed Al-Mosawi and Maisoon Al-Jawad are warmly acknowledged for their support during the synchrotron beamtime. We acknowledge the help of Gilles le Moullac and other colleagues at Centre Ifremer du Pacifique (Vairao) for giving access to the shell samples. This work received funding from the European Research Council (European Union’s Horizon H2020 research and innovation program grant agreement no. 724881).

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