W. Van den Broek

Exploring different inelastic projection mechanisms for electron tomography

Several different projection mechanisms that all make use of inelastically scattered electrons are used for electron tomography. The advantages and the disadvantages of these methods are compared to HAADF-STEM tomography, which is considered as the standard electron tomography technique in materials science. The different inelastic setups used are energy filtered transmission electron microscopy (EFTEM), thickness mapping based on the log-ratio method and bulk plasmon mapping. We present a comparison that can be used to select the best inelastic signal for tomography, depending on different parameters such as the beam stability and nature of the sample. The appropriate signal will obviously also depend on the exact information which is requested.

Optimization of a FIB/SEM slice-and-view study of the 3D distribution of Ni4Ti3 precipitates in Ni–Ti

The 3D morphology and distribution of lenticular Ni4Ti3 precipitates in the austenitic B2 matrix of a binary Ni51Ti49 alloy has been investigated by a slice‐and‐view procedure in a dual‐beam focused ion beam/scanning electron microscope system. Due to the weak contrast of the precipitates, proper imaging conditions need to be selected first to allow for semi‐automated image treatment. Knowledgeable imaging is further needed to ensure that all variants of the precipitates are observed with equal probability, regardless of sample orientation. Finally, a volume ratio of 10.2% for the Ni4Ti3 precipitates could be calculated, summed over all variants, which yields a net composition of Ni50.27Ti49.73 for the matrix, leading to an increase of 125 degrees for the martensitic start temperature. Also, the expected relative orientation of the different variants of the precipitates could be confirmed.

A model based atomic resolution tomographic algorithm.

Tomography with high angular annular dark field scanning transmission electron microscopy at atomic resolution can be greatly improved if one is able to take advantage of prior knowledge. In this paper we present a reconstruction technique that explicitly takes into account the microscope parameters and the atomic nature of the projected object. This results in a more accurate estimate of the atomic positions and in a good resistance to noise. The reconstruction is a maximum likelihood estimator of the object. Moreover, the limits to the precision have been explored, allowing for a prediction of the amount of expected noise in the reconstruction for a certain experimental setup. We believe that the proposed reconstruction technique can be generalized to other tomographic experiments.

Defocus and twofold astigmatism correction in HAADF-STEM

A new simultaneous autofocus and twofold astigmatism correction method is proposed for High Angle Annular Dark Field Scanning Transmission Electron Microscopy (HAADF-STEM). The method makes use of a modification of image variance, which has already been used before as an image quality measure for different types of microscopy, but its use is often justified on heuristic grounds. In this paper we show numerically that the variance reaches its maximum at Scherzer defocus and zero astigmatism. In order to find this maximum a simultaneous optimization of three parameters (focus, x- and y-stigmators) is necessary. This is implemented and tested on a FEI Tecnai F20. It successfully finds the optimal defocus and astigmatism with time and accuracy, compared to a human operator.

Throughput maximization of particle radius measurements through balancing size versus current of the electron probe

In this paper we investigate which probe size maximizes the throughput when measuring the radius of nanoparticles in high angle annular dark field scanning transmission electron microscopy (HAADF STEM). The size and the corresponding current of the electron probe determine the precision of the estimate of a particles radius. Maximizing throughput means that a maximum number of particles should be imaged within a given time frame, so that a prespecified precision is attained. We show that Bayesian statistical experimental design is a very useful approach to determine the optimal probe size using a certain amount of prior knowledge about the sample. The dependence of the optimal probe size on the detector geometry and the diameter, variability and atomic number of the particles is investigated. An expression for the optimal probe size in the absence of any kind of prior knowledge about the specimen is derived as well.

Tomographic spectroscopic imaging; an experimental proof of concept

Recording the electron energy loss spectroscopy data cube with a series of energy filtered images is a dose inefficient process because the energy slit blocks most of the electrons. When recording the data cube by scanning an electron probe over the sample, perfect dose efficiency is attained; but due to the low current in nanoprobes, this often is slower, with a smaller field of view. In W. Van den Broek et al. [Ultramicroscopy, 106 (2006) 269], we proposed a new method to record the data cube, which is more dose efficient than an energy filtered series. It produces a set of projections of the data cube and then tomographically reconstructs it. In this article, we demonstrate these projections in practice, we present a simple geometrical model that allows for quantification of the projection angles and we present the first successful experimental reconstruction, all on a standard post-column instrument.

Acquisition of the EELS data cube by tomographic spectroscopic imaging

The EELS data cube combines spatial and spectral information because it has an EELS spectrum in each pixel of a spatial image. The two major methods of acquiring it are image-spectroscopy (or an Energy Filtered Series or EFS) and spectrum-imaging. In [1] we proposed a new method: Tomographic Spectroscopic Imaging (TSI). A proper defocus of the energy filter induces a mixing of spatial and spectral information that is equivalent to a projection of the data cube onto the CCD camera. The projection angles are directly related to the defocus value and all angles between 0° and 180° are reached. The projections are used to reconstruct the data cube by tomographic techniques. In [1] we concluded that TSI needs a lower electron dose than EFS to acquire a data cube with the same resolution and mean signal-to-noise ratio.

3D Reconstruction of Ni4Ti3 Precipitates in Ni-Ti by FIB/SEM Slice-and-View

Ni4Ti3 precipitates with lenticular shape and rhombohedral atomic structure growing in the austenitic B2 matrix of binary Ni-rich Ni-Ti alloys upon proper annealing treatment have an important influence on the shape memory effect which originates from the martensitic transformation of B2 — B19’ [1]. Figure 1 shows a typical 2D distribution of such precipitates as obtained by TEM under conventional imaging conditions.