S. Weiner and L. Addadi, Design strategies in mineralized biological materials, Journal of Materials Chemistry, vol.7, issue.5
DOI : 10.1039/a604512j

O. M. Boggild, The shell structure of molluscs

C. Grégoire, Structure of molluscan shell, 431 T.) VII, pp.45-145, 1972.

J. D. Taylor and W. J. Kennedy, The shell structure and mineralogy of the Bivalvia : 433 introduction, nuculacea-trigonacea, Bull. Br. Mus. Nat. Hist, vol.3, pp.1-125, 1969.

B. Farre, Shell layers of the black-lip pearl oyster Pinctada margaritifera, p.438
URL : https://hal.archives-ouvertes.fr/hal-00605861

Y. Dauphin, Structure and composition of the nacre???prisms transition in the shell of Pinctada margaritifera (Mollusca, Bivalvia), Analytical and Bioanalytical Chemistry, vol.278, issue.6, pp.1659-1669, 2008.
DOI : 10.1007/s00216-008-1860-z
URL : https://hal.archives-ouvertes.fr/insu-00378692

Y. Dauphin, The nanostructural unity of Mollusc shells, Mineralogical Magazine, vol.72, issue.1, pp.243-246, 2008.
DOI : 10.1180/minmag.2008.072.1.243
URL : https://hal.archives-ouvertes.fr/hal-00357202

I. Sethmann, R. Hinrichs, G. Wörheide, and A. Putnis, Nano-cluster composite 445 structure of calcitic sponge spicules?A case study of basic characteristics of biominerals, J

D. E. Jacob, Nanostructure, composition and mechanisms of bivalve shell growth, Geochimica et Cosmochimica Acta, vol.72, issue.22, pp.5401-5415, 2008.
DOI : 10.1016/j.gca.2008.08.019

A. Berman, Biological Control of Crystal Texture: A Widespread Strategy for Adapting Crystal Properties to Function, Science, vol.259, issue.5096, pp.776-779, 1993.
DOI : 10.1126/science.259.5096.776

B. Pokroy, Anisotropic lattice distortions in biogenic calcite induced by intra-crystalline organic molecules, Journal of Structural Biology, vol.155, issue.1, pp.96-103, 2006.
DOI : 10.1016/j.jsb.2006.03.008
URL : https://hal.archives-ouvertes.fr/hal-00198280

B. Pokroy, A. Fitch, and E. Zolotoyabko, The Microstructure of Biogenic Calcite: A 467

P. U. Gilbert, A. Young, and S. N. Coppersmith, Measurement of c-axis angular 475 orientation in calcite (CaCO3) nanocrystals using X-ray absorption spectroscopy, Proc. Natl

I. C. Olson, Crystal lattice tilting in prismatic calcite, Journal of Structural Biology, vol.183, issue.2, pp.180-478, 2013.
DOI : 10.1016/j.jsb.2013.06.006

A. Berman, Intercalation of Sea Urchin Proteins in Calcite: Study of a 480

D. Sayre, Some implications of a theorem due to Shannon, Acta Crystallographica, vol.5, issue.6, pp.843-482, 1952.
DOI : 10.1107/S0365110X52002276

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, Extending the methodology of X-ray 484 crystallography to allow imaging of micrometre-sized non-crystalline specimens, Nature, vol.400, issue.6742, pp.342-344, 1999.
DOI : 10.1038/22498

K. Ayyer, Macromolecular diffractive imaging using imperfect crystals, Nature, vol.70, issue.7589, pp.530-202, 2016.
DOI : 10.1107/S0021889807021206
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4839592

F. Büttner, Dynamics and inertia of skyrmionic spin??structures, Nature Physics, vol.21, issue.3, pp.225-228, 2015.
DOI : 10.1364/OE.21.030563

A. Ulvestad, Topological defect dynamics in operando battery nanoparticles, Science, vol.154, issue.10, pp.1344-1347, 2015.
DOI : 10.1149/1.2759840

V. Chamard, Three-Dimensional X-Ray Fourier Transform Holography: The 495
DOI : 10.1103/physrevlett.104.165501
URL : https://hal.archives-ouvertes.fr/hal-00945045/document

J. M. Rodenburg and R. H. Bates, The Theory of Super-Resolution Electron 497

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, Three-dimensional mapping of a deformation field inside a nanocrystal, Nature, vol.5, issue.7098, pp.63-66, 2006.
DOI : 10.1038/nature04867

M. Dierolf, Ptychographic X-ray computed tomography at the nanoscale, Nature, vol.109, issue.7314, pp.436-439, 2010.
DOI : 10.1038/nature09419

J. M. Rodenburg, Hard-X-Ray Lensless Imaging of Extended Objects, Physical Review Letters, vol.339, issue.3
DOI : 10.1103/PhysRevLett.94.164801

P. Godard, Three-dimensional high-resolution quantitative microscopy of extended crystals, Nature Communications, vol.576, p.568, 2011.
DOI : 10.1016/j.nima.2007.01.131
URL : https://hal.archives-ouvertes.fr/hal-01254536

A. I. Pateras, Nondestructive three-dimensional imaging of crystal strain and 510 rotations in an extended bonded semiconductor heterostructure, Phys. Rev. B, vol.92, p.511, 2015.

M. E. Birkbak, M. Guizar-sicairos, M. Holler, and H. Birkedal, Internal structure of sponge glass fiber revealed by ptychographic nanotomography, Journal of Structural Biology, vol.194, issue.1, pp.124-128, 2016.
DOI : 10.1016/j.jsb.2016.02.006

M. V. Holt, Strain Imaging of Nanoscale Semiconductor Heterostructures with X-Ray Bragg Projection Ptychography, Physical Review Letters, vol.25, issue.16, p.165502, 2014.
DOI : 10.1038/nature09419

A. G. Checa, Crystallographic orientation inhomogeneity and crystal splitting in biogenic calcite, Journal of The Royal Society Interface, vol.153, issue.2, p.20130425, 2013.
DOI : 10.1016/j.jsb.2005.10.009
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3730695

P. Godard, M. Allain, V. Chamard, and J. Rodenburg, Noise models for low counting rate coherent diffraction imaging, Optics Express, vol.20, issue.23, p.25914, 2012.
DOI : 10.1364/OE.20.025914
URL : https://hal.archives-ouvertes.fr/hal-00870322

S. Takagi, A Dynamical Theory of Diffraction for a Distorted Crystal, Journal of the Physical Society of Japan, vol.26, issue.5
DOI : 10.1143/JPSJ.26.1239

S. O. Hruszkewycz, High-resolution three-dimensional structural microscopy by single-angle Bragg ptychography, Nature Materials, vol.80, issue.2, pp.244-251, 2017.
DOI : 10.1103/PhysRevA.80.063823
URL : https://hal.archives-ouvertes.fr/hal-01252892

J. Nouet, A. Baronnet, and L. Howard, Crystallization in organo-mineral micro- 526 domains in the crossed-lamellar layer of Nerita undata (Gastropoda, Neritopsina) Micron 43, pp.456-462, 2012.

J. P. Cuif and Y. Dauphin, The Environment Recording Unit in coral skeletons – a synthesis of structural and chemical evidences for a biochemically driven, stepping-growth process in fibres, Biogeosciences, vol.2, issue.1, pp.61-73, 2005.
DOI : 10.5194/bg-2-61-2005

B. Bayerlein, Self-similar mesostructure evolution of the growing mollusc shell reminiscent of thermodynamically driven grain growth, Nature Materials, vol.9, issue.12, pp.1102-1107, 2014.
DOI : 10.1038/nmeth.2089

L. B. Gower, Biomimetic Model Systems for Investigating the Amorphous Precursor Pathway and Its Role in Biomineralization, Chemical Reviews, vol.108, issue.11, pp.4551-4627, 2008.
DOI : 10.1021/cr800443h

A. Xu, Y. Ma, and H. Cölfen, Biomimetic mineralization, J. Mater. Chem., vol.45, issue.286, pp.415-536, 2007.
DOI : 10.1002/anie.200600029

H. Li, H. L. Xin, D. A. Muller, and L. A. Estroff, Visualizing the 3D Internal Structure of Calcite Single Crystals Grown in Agarose Hydrogels, Science, vol.310, issue.5747, pp.1244-1247, 2009.
DOI : 10.1126/science.1117908

F. C. Meldrum and H. Coelfen, Crystallization and formation mechanisms of 542 nanostructures, Nanoscale, vol.2, pp.2326-2327, 2010.

L. Addadi, J. Moradian, E. Shay, N. G. Maroudas, and S. Weiner, A chemical model 546 for the cooperation of sulfates and carboxylates in calcite crystal nucleation: Relevance to 547 biomineralization, Proc. Natl. Acad. Sci, pp.2732-2736, 1987.

L. B. Gower and D. J. Odon, Deposition of calcium carbonate films by a polymer-induced liquid-precursor (PILP) process, Journal of Crystal Growth, vol.210, issue.4, pp.719-734, 2000.
DOI : 10.1016/S0022-0248(99)00749-6

M. A. Bewernitz, D. Gebauer, J. Long, H. Cölfen, and L. B. Gower, A metastable 551 liquid precursor phase of calcium carbonate and its interactions with polyaspartate. Faraday 552 Discuss, pp.291-312, 2012.

:. Y. Acknowledgments and J. Dauphin, Cuif are warmly acknowledged for their invaluable 560 inputs to the research program. G. Le Moullac (IFREMER) is acknowledged for giving access 561 to the shell samples. J. Savatier is warmly acknowledged for his help during the optical 562 microscopy imaging session. We acknowledge the ESRF for providing access to the source, This work was funded by the French ANR under project number ANR-11-BS20-0005 and it 564 has received funding from the European Research Council (ERC) under the European 565

*. Midex, ANR-11-IDEX- 567 0001-02) ANR grants France Bio Imaging (ANR-10-INSB-04-01) and France Life Imaging

. Fig, Structure of Pinctada margaritifera shell at different length scales. (A-C) Optical 603 micrographs of a juvenile Pinctada margaritifera. (A) The whole shell. (B) Zoom-in view 604 showing the prism assembly in the vicinity of the growth border. (C) The shell growth border, p.605

. Fig, 3D Bragg diffraction ptychography set-up. (A) The sample is placed in the focus of 611 a coherent x-ray nano-beam and oriented in Bragg diffraction condition in Laue geometry

. Fig, 3D Bragg ptychography reconstruction. (A) Schematic view of the reconstructed 629 volume within the prism (in yellow-gray), embedded into the probed region

. Fig, Crystalline coherence in the iso-oriented domain. 2D cuts of the retrieved phase 644 map ? extracted for the iso-oriented domain of Fig. 3E. This quantity is related to the 645 crystalline coherence: abrupt changes in the phase value correspond to breakdown of the 646 crystalline continuity. In average, the phase shift is about 4.2 radians, corresponding to a 647 displacement of about 0