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.


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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.

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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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