By electron tomographic reconstruction based on conventional BF TEM, the general morphology of gold and silica NM was visualized in 3D. In orthoslices of the examined NM in the xy-plane, as presented in Figure 2B, the surface can readily be distinguished from the background and from missing wedge artifacts, like streaks. In such orthoslices, the surface features of a NM can be seen and measured without interference of higher or lower lying structures inherent to conventional TEM.
Segmentation by isosurface rendering allows accessing the 3D information of an ET reconstruction in greater detail than digital slicing. Such 3D visualization and measurement of the surface features of NM can contribute to bring the second condition of the definition of a nanomaterial proposed by the European Commission  in practice: structures in one or more dimensions in the size range of 1-100 nm can be shown.
From the 3D reconstructions, the surface area and the volume of the examined NM could be estimated directly and the VSSA was calculated. The mean VSSA of all examined NM was significantly larger than the threshold of 60 m2/cm3 such that these materials can be classified as NP according to the third condition of this definition. As opposed to the BET-method , ET is not limited to powders and/or dry solid materials: it can be applied to a large variety of NM samples, including suspensions of complex particles, provided that the material can be suitably coated on an EM-grid.
To optimally characterize the morphology of a NM by ET reconstruction, it is required that (i) the projection requirement is met ; (ii) missing wedge artifacts are minimal and (iii) isosurface rendering optimally fits the NM surface.
Our results indicate that, in principle, the characterization and definition of NM can benefit from application of conventional BF ET. In the scope of putting this technique in practice for the characterization and definition of gold and silica NM, following approach is suggested to reconcile the limitations of conventional BF ET with the above-described conditions.
(i) The projection requirement states that for an image intensity to be usable for ET reconstruction, it has to be a monotonic function of a projected physical quantity . The examined silica NM were shown to be amorphous and weak scattering such that their mass thickness is the dominant contrast mechanism. The BF images of the tilt series are thus essentially projections on which tomographic reconstructions can be based . In the branched gold particles, and to a small extent in the spherical gold particles, diffraction contributed to image formation and the projection requirement is not fulfilled for the entire tilt series. Certainly, a combination of scanning transmission electron microscopy (STEM) and high angle annular dark field imaging (HAADF) which is insensitive to Bragg diffraction will be preferable over bright field imaging to visualize these NM at high resolution [11–13]. Because diffraction increases the background of the reconstruction and reduces its resolution, BF ET has been suggested to be of only limited value to analyze crystalline nanostructures [11, 12]. However, Ahrenkiel et al.  argumented that conventional BF ET still can provide useful information on the structure of particles with relatively small crystallite size if suitable acquisition conditions are chosen. Hence, the examined material was not embedded to assure positive contrast originating from the specimen at all orientations, while diffraction contrast was minimized while preserving some mass-thickness contrast by using a large objective aperture.
(ii) An important physical limitation of electron tomography arises from the fact that finite specimen thickness and tilt geometry within an electron microscope column prevent the collection of projection images spanning a complete angular range (± 90° tilt series). This results in a "missing wedge" of information in reciprocal space and results in anisotropic resolution in the resulting reconstruction . Only for specific samples that were properly shaped using a focused ion beam and mounted in a special holder, these subsampling effects could be avoided . The missing wedge can be reduced by collecting a so-called dual-axis tilt series in two mutually orthogonal directions [7, 16–18] such that a missing pyramid is obtained. Because above-described approaches require high technicity and are unpractical for routine analyses, the missing wedge artifacts of the reconstructions of the silica and gold NM were only reduced using a small tilt increment and maximizing the tilt range of the electron tomogram. Because gold and silica NM are hardly sensitive to radiation damage, extensive data collection using a high frequency of imaging can be applied. Because our software and hardware limit the amount of data that can be aligned and reconstructed in a timely manner, 4*4 K micrographs were taken with one degree intervals and datasets were reduced to contain only few particles. New developments of soft- and hardware and GPU-based ET implementation  promise faster data processing allowing a combination of smaller intervals and the simultaneous analysis of several hundreds of particles under similar imaging conditions. Moreover, improvement of the quality of reconstructions seems possible by using newly developed reconstruction algorithms like the discrete algebraic reconstruction technique (DART) which suffers less from missing wedge artifacts than SIRT . In our hands, the correction of the tilt axis during alignment appeared very important to reduce reconstruction artifacts like streaks. When the axes were not corrected accurately, the streaks were included in the particle volume resulting in an elongation of the particles which was at least as strong as the missing wedge dependent elongation described in .
(iii) In the examined NM, the value of the threshold was selected such that the obtained surface optimally matches the boundaries of the reconstructed orthogonal digital slices (orthoslices) of the NM in the xy-plane, where resolution is highest. This threshold value was in general close to the minimal value between both peaks of the bimodal curve (Figure 1A) of the histogram representing the number of voxels in function of their grey value. In the future, computational techniques that determine the optimal grey value for thresholding can allow more efficient segmentation, eliminating the subjectivity associated with manual segmentation .
To evaluate the influence of missing wedge artifacts on the reconstruction and, in particular, on the validity of the quantitative results obtained from the reconstructions, the ET based analyses of colloidal gold nanoparticles with a known spherical morphology were evaluated as a control. The high correlation (r = 0.98) between the measured values of area and volume and the areas and volumes calculated from the ECD of projected NP indicates that the values measured from electron tomographic reconstructions are valid for these gold particles. On this basis, it is assumed that the surface and volume measures of the branched gold and silica NM, which lack symmetry, can be relied on also. However, it has to be stressed that the absolute numbers presented in Table 1 should be interpreted with caution since they are based on a very low number of observations. This table illustrates the possibilities of the method in principle but it remains unsure whether the selected particles are representative for the entire examined samples. The latter requires, at least, the ET analysis of larger numbers of randomly selected particles. The evaluation of the VSSA values measured using methods like ET, BET or small-angle X-ray scattering (SAXS), and their corresponding uncertainties and limitations requires a dedicated study. For NM-200, the VSSA estimated by ET (342 ± 36 m2/cm3) is higher than the value obtained by SAXS (270 ± 17 m2/cm3, personal communication Camille Guiot, French Atomic Energy and Alternative Energies Commission, France), but lower than the values obtained by BET (435 m2/cm3, personal communication Rosica Petrova, Institute of Mineralogy and Crystallography - Bulgarian Academy of Sciences, Bulgaria). For NM-203, the VSSA estimated by ET (219 ± 23 m2/cm3) is lower than both the VSSA obtained by SAXS (367 ± 30 m2/cm3, personal communication Camille Guiot) and BET (469 m2/cm3, personal communication Rosica Petrova).
The EU definition expects a resolution of at least 1 nm . It is doubtful whether this resolution can be obtained routinely by BF TEM . For an exact description of the physical characteristics of a NM, atomic resolution within a reconstruction can be important. It is however not an absolute prerequisite to apply the definition if it is taken into account that lack of resolution results in an underestimation of the VSSA because, relatively, nanometer-sized surface features contribute more to an increase of the particle surface than to an increase of its volume.