Discrete spectroscopic electron tomography: using prior knowledge of reference spectra during the reconstruction
Authors: Goris Bart , Meledina Maria , Turner Stuart , Zhong Zhichao , Batenburg Joost , Tendeloo Gustaaf Van , Bals Sara 
Published: December 2016

A three‐dimensional (3D) characterization of the morphology of nanostructures can nowadays routinely be obtained using electron tomography. [1] Nevertheless, resolving the chemical composition of complex nanostructures in 3D remains challenging and the number of studies in which electron energy loss spectroscopy (EELS) is combined with tomography is limited. [2‐5] In most of these studies, two dimensional (2D) elemental maps of the object are first extracted at each tilt angle and used as an input for tomographic reconstruction. [2,3] An alternative approach is to reconstruct each energy loss separately yielding a 4D data cube where an EELS spectrum can be extracted from each 3D voxel. [4,5] During the last decade, dedicated reconstruction algorithms have been developed for HAADF‐STEM tomography which use prior knowledge about the investigated sample. For example, the discrete algebraic reconstruction technique (DART) is based on the idea that a 3D HAADF‐STEM reconstruction of a (nano)material only contains a limited number of grey values. [6] In this manner, several artefacts, typical to electron tomography, are mininized leading to reconstructions with a higher reliability. An additional advantage of discrete tomography is that the quantification of the final reconstruction is straightforward since the segmentation is part of the reconstruction algorithm. Here, we will extend discrete tomography to its application for spectroscopic datasets where it is assumed that the experimental spectrum of each reconstructed voxel is a linear combination of a well‐known set of references spectra.

To investigate the performance of discrete spectroscopic electron tomography, a phantom object is made resembling a Ce
4+
nanoparticle with a reduced Ce
3+
edge as presented in Figure 1a. A tilt series of projected spectrum images are simulated and different amounts of Poisson noise are applied to the projection data. These datasets are used as input for two conventional reconstruction approaches and the discrete spectroscopic reconstruction technique. In the first method, elemental maps are first extracted which are used to reconstruct the individual chemical elements. The second method first reconstructs all energy losses yielding a complete 4D dataset. The reconstructions of the different elements are then obtained using a spectrum fitting procedure. The average reconstruction error as a function of the signal to noise ratio (SNR) is displayed in Figure 1b. This graph indicates that discrete spectroscopic electron tomography, displayed in red, provides superior results especially for datasets with a relatively low SNR. Therefore, it is well suited for the 3D reconstruction of small dopants in nanoparticles typically having a low SNR in the projected spectrum images.

Next, we investigated the spatial distribution of Fe dopants in Fe:Ceria nanoparticles. During the tomographic reconstruction, reference spectra for Fe
2+
, Ce
3+
and Ce
4+
are used as prior knowledge. Visualizations of the final reconstructions are presented in Figure 2. As indicated by the white arrows, we can observe that the presence of the Fe
2+
dopants is correlated with a reduction of the Ce atoms from Ce
4+
towards Ce
3+
. This indicates that both the Ceria nanoparticle and the Fe dopants are reduced by the generation of oxygen vacancies. In addition, from the comparison of the slices through the HAADF‐STEM reconstruction and the Fe
2+
reconstruction (Figure 2f), it can be observed that most of the Fe dopants are located near the voids of the nanoparticle.