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Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography


The mechanical properties of many materials are based on the macroscopic arrangement and orientation of their nanostructure. This nanostructure can be ordered over a range of length scales. In biology, the principle of hierarchical ordering is often used to maximize functionality, such as strength and robustness of the material, while minimizing weight and energy cost. Methods for nanoscale imaging provide direct visual access to the ultrastructure (nanoscale structure that is too small to be imaged using light microscopy), but the field of view is limited and does not easily allow a full correlative study of changes in the ultrastructure over a macroscopic sample. Other methods of probing ultrastructure ordering, such as small-angle scattering of X-rays or neutrons, can be applied to macroscopic samples; however, these scattering methods remain constrained to two-dimensional specimens1,2,3,4 or to isotropically oriented ultrastructures5,6,7. These constraints limit the use of these methods for studying nanostructures with more complex orientation patterns, which are abundant in nature and materials science. Here, we introduce an imaging method that combines small-angle scattering with tensor tomography to probe nanoscale structures in three-dimensional macroscopic samples in a non-destructive way. We demonstrate the method by measuring the main orientation and the degree of orientation of nanoscale mineralized collagen fibrils in a human trabecula bone sample with a spatial resolution of 25 micrometres. Symmetries within the sample, such as the cylindrical symmetry commonly observed for mineralized collagen fibrils in bone8,9,10, allow for tractable sampling requirements and numerical efficiency. Small-angle scattering tensor tomography is applicable to both biological and materials science specimens, and may be useful for understanding and characterizing smart or bio-inspired materials. Moreover, because the method is non-destructive, it is appropriate for in situ measurements and allows, for example, the role of ultrastructure in the mechanical response of a biological tissue or manufactured material to be studied.

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Figure 1: Schematic of the experimental set-up for SAS tensor tomography.
Figure 2: Data processing.
Figure 3: Orientation of collagen fibrils within a human trabecular bone sample.


  1. 1

    Fratzl, P., Jakob, H. F., Rinnerthaler, S., Roschger, P. & Klaushofer, K. Position-resolved small-angle X-ray scattering of complex biological materials. J. Appl. Cryst. 30, 765–769 (1997)

    CAS  Article  Google Scholar 

  2. 2

    Rinnerthaler, S. et al. Scanning small angle X-ray scattering analysis of human bone sections. Calcif. Tissue Int. 64, 422–429 (1999)

    CAS  Article  Google Scholar 

  3. 3

    Bunk, O. et al. Multimodal x-ray scatter imaging. New J. Phys. 11, 123086 (2009)

    Article  Google Scholar 

  4. 4

    Georgiadis, M. et al. 3D scanning SAXS: a novel method for the assessment of bone ultrastructure orientation. Bone 71, 42–52 (2015)

    CAS  Article  Google Scholar 

  5. 5

    Jensen, T. H. et al. Molecular X-ray computed tomography of myelin in a rat brain. Neuroimage 57, 124–129 (2011)

    CAS  Article  Google Scholar 

  6. 6

    Schroer, C. G. et al. Mapping the local nanostructure inside a specimen by tomographic small-angle x-ray scattering. Appl. Phys. Lett. 88, 164102 (2006)

    ADS  Article  Google Scholar 

  7. 7

    Álvarez-Murga, M., Bleuet, P. & Hodeau, J.-L. Diffraction/scattering computed tomography for three-dimensional characterization of multi-phase crystalline and amorphous materials. J. Appl. Cryst. 45, 1109–1124 (2012)

    Article  Google Scholar 

  8. 8

    Seidel, R. et al. Synchrotron 3D SAXS analysis of bone nanostructure. Bioinspir. Biomim. Nanobiomater . 1, 123–131 (2012)

    Article  Google Scholar 

  9. 9

    Giannini, C. et al. Scanning SAXS–WAXS microscopy on osteoarthritis-affected bone – an age-related study. J. Appl. Cryst. 47, 110–117 (2014)

    CAS  Article  Google Scholar 

  10. 10

    Pabisch, S., Wagermaier, W., Zander, T., Li, C. H. & Fratzl, P. in Methods in Enzymology Vol. 532 (ed. De Yoreo, J. J. ) 391–413 (Elsevier, 2013)

  11. 11

    Currey, J. D. Bones: Structure and Mechanics (Princeton Univ. Press, 2002)

  12. 12

    Fratzl, P. & Weinkamer, R. Nature’s hierarchical materials. Prog. Mater. Sci. 52, 1263–1334 (2007)

    CAS  Article  Google Scholar 

  13. 13

    Schneider, P., Meier, M., Wepf, R. & Muller, R. Towards quantitative 3D imaging of the osteocyte lacuno-canalicular network. Bone 47, 848–858 (2010)

    Article  Google Scholar 

  14. 14

    Holler, M. et al. X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution. Sci. Rep. 4, 3857 (2014)

    CAS  Article  Google Scholar 

  15. 15

    Martin, R. B. & Ishida, J. The relative effects of collagen fiber orientation, porosity, density, and mineralization on bone strength. J. Biomech. 22, 419–426 (1989)

    CAS  Article  Google Scholar 

  16. 16

    Riggs, C. M., Vaughan, L. C., Evans, G. P., Lanyon, L. E. & Boyde, A. Mechanical implications of collagen fibre orientation in cortical bone of the equine radius. Anat. Embryol. 187, 239–248 (1993)

    CAS  PubMed  Google Scholar 

  17. 17

    Granke, M. et al. Microfibril orientation dominates the microelastic properties of human bone tissue at the lamellar length scale. PLoS ONE 8, e58043 (2013)

    CAS  ADS  Article  Google Scholar 

  18. 18

    Giannini, C. et al. Correlative light and scanning X-ray scattering microscopy of healthy and pathologic human bone sections. Sci. Rep. 2, 435 (2012)

    CAS  Article  Google Scholar 

  19. 19

    Zhao, Q. & Wagner, H. D. Raman spectroscopy of carbon-nanotube-based composites. Phil. Trans. R. Soc. London Ser. A 362, 2407–2424 (2004)

    CAS  ADS  Article  Google Scholar 

  20. 20

    Bi, X., Li, G., Doty, S. B. & Camacho, N. P. A novel method for determination of collagen orientation in cartilage by Fourier transform infrared imaging spectroscopy (FT-IRIS). Osteoarthr. Cartilage 13, 1050–1058 (2005)

    CAS  Article  Google Scholar 

  21. 21

    Rauch, E. F. et al. Automated nanocrystal orientation and phase mapping in the transmission electron microscope on the basis of precession electron diffraction. Z. Krist . 225, 103–109 (2010)

    CAS  Article  Google Scholar 

  22. 22

    Heidelbach, F., Riekel, C. & Wenk, H.-R. Quantitative texture analysis of small domains with synchrotron radiation X-rays. J. Appl. Cryst. 32, 841–849 (1999)

    CAS  Article  Google Scholar 

  23. 23

    Feldkamp, J. M. et al. Recent developments in tomographic small-angle X-ray scattering. Phys. Status Solidi A 206, 1723–1726 (2009)

    CAS  ADS  Article  Google Scholar 

  24. 24

    Ludwig, W., Schmidt, S., Lauridsen, E. M. & Poulsen, H. F. X-ray diffraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. I. Direct beam case. J. Appl. Cryst. 41, 302–309 (2008)

    CAS  Article  Google Scholar 

  25. 25

    Basser, P. J., Mattiello, J. & Lebihan, D. Estimation of the effective self-diffusion tensor from the NMR spin echo. J. Magn. Reson. B . 103, 247–254 (1994)

    CAS  Article  Google Scholar 

  26. 26

    Malecki, A. et al. X-ray tensor tomography. EPL (Europhys. Lett.) 105, 38002 (2014)

    ADS  Article  Google Scholar 

  27. 27

    Gourrier, A. et al. Scanning small-angle X-ray scattering analysis of the size and organization of the mineral nanoparticles in fluorotic bone using a stack of cards model. J. Appl. Cryst. 43, 1385–1392 (2010)

    CAS  Article  Google Scholar 

  28. 28

    Roe, R. J. Description of crystallite orientation in polycrystalline materials. III. General solution to pole figure inversion. J. Appl. Phys. 36, 2024–2031 (1965)

    CAS  ADS  Article  Google Scholar 

  29. 29

    Bunge, H. J. & Roberts, W. T. Orientation distribution, elastic and plastic anisotropy in stabilized steel sheet. J. Appl. Cryst. 2, 116–128 (1969)

    CAS  Article  Google Scholar 

  30. 30

    Jensen, T. H. et al. Brain tumor imaging using small-angle x-ray scattering tomography. Phys. Med. Biol. 56, 1717–1726 (2011)

    Article  Google Scholar 

  31. 31

    Kraft, P. et al. Performance of single-photon-counting PILATUS detector modules. J. Synchrotron Radiat. 16, 368–375 (2009)

    CAS  Article  Google Scholar 

  32. 32

    Howells, M. R. et al. An assessment of the resolution limitation due to radiation-damage in X-ray diffraction microscopy. J. Electron Spectrosc . 170, 4–12 (2009)

    CAS  Article  Google Scholar 

  33. 33

    Hubbell, J. & Seltzer, M. Tables of X-ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients Version 1.4. Report No. NISTIR--5632 (National Institute of Standards and Technology, 1995);

  34. 34

    Tinti, G., et al. Performance of the EIGER single photon counting detector. J. Instrum. 10, C03011 (2015)

    Article  Google Scholar 

  35. 35

    Guizar-Sicairos, M., Thurman, S. T. & Fienup, J. R. Efficient subpixel image registration algorithms. Opt. Lett. 33, 156–158 (2008)

    ADS  Article  Google Scholar 

  36. 36

    Thibault, P. & Guizar-Sicairos, M. Maximum-likelihood refinement for coherent diffractive imaging. New J. Phys. 14, 063004 (2012)

    ADS  Article  Google Scholar 

  37. 37

    Grenander, U. Abstract Inference Ch. 9 (Wiley, 1981)

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We thank M. Holler and J. Raabe for their help in sample preparation and A. Diaz, F. Schaff and M. Bech for discussions. M.G. was supported by the ETH Research Grant ETH-39 11-1. The vertebral specimen was provided by W. Schmölz, Department for Trauma Surgery, Innsbruck Medical University, Innsbruck, Austria.

Author information




M.L., M.G., A.M., P.S., O.B., and M.G.-S. conceived the research project. M.G. prepared the sample. M.L., M.G., and M.G.-S. carried out the X-ray experiments. M.L. developed the data analysis framework with support from O.B. and M.G.-S. Results were interpreted by M.L., M.G., P.S., and J.K. M.L. wrote the manuscript with contributions from all authors.

Corresponding authors

Correspondence to Marianne Liebi or Manuel Guizar-Sicairos.

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The authors declare no competing financial interests.

Supplementary information

3D reconstruction of the small-angle scattering tensor tomography

Orientation of bone ultrastructure as retrieved from small-angle scattering (SAS) tensor tomography. The cylinder orientation represents the main orientation of collagen fibrils in the corresponding voxel. The degree of orientation is represented by both colour and length of the cylinders, where a low degree of orientation (blue) means low ordering of the collagen fibrils, while in regions with a high degree of orientation (red) the collagen fibrils are well aligned with respect to each other. (MOV 4386 kb)

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Liebi, M., Georgiadis, M., Menzel, A. et al. Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography. Nature 527, 349–352 (2015).

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