nanoparticles and bulk alloys, where electron tomography has played an important role in identifying the 3D structures and spatial distribution of nanocrystals, dislocations, and precipitates. 2. Experimental Procedures We employed BF and high-angle annular dark-field (HAADF) imaging modes of STEM for the tilt-series acquisition using an FEI Titan 80-300 (S)TEM operating at 300 kV with a field emission gun. We set the beam convergence to be 10-14mrad in half-angle, taking into account the spherical aberration coefficient (1.2 mm) of the pre-field of objective lens. The Xplore3D software (FEI Co. Ltd) was used for data sets acquisition taking the dynamic focus into consideration. A single-tilt holder (Fischione model 2020) and a triple-axes holder (Mel-Build model HATA-8075) were used for the tilt series acquisition with the maximum tilt angle of 70º. Alignment of the tilt axis for the obtained data set by an iterative cross-correlation technique and subsequent 3D reconstruction were performed by using the Inspect3D software package (FEI Co. Ltd). As for the algorithm for 3D reconstruction, we employed weighted back-projection (WBP) [14], as well as simultaneous iterative reconstruction technique (SIRT) [15]. The reconstructed 3D density data were then visualized using the AMIRA 4.1 software (VISAGE IMAGING). 3. Results and Discussion 3.1 Shapes and distribution of FePd nanoparticles Figure 1a shows a series of STEM-HAADF images taken at different tilt angles with the detector inner half angle of 60mrad. The tilt-series was observed sequentially from 0 to -70º and then 0 to +70 º. The tilt angle increments were set 2º for angle ranges of 0 to |50|º, and 1º for |50| to |70|º. Out of this data set, we employed, by careful inspection of contrasts, images taken at tilt angles between -66 and +64º for later 3D reconstruction. As seen, the apparent particle length in the y-direction becomes shorter as the tilting angle increases. A nanoparticle enclosed by the circle in the figure is one of the examples to demonstrate the reduction of the particle image in the y-direction. To examine an accuracy of a reconstructed particle height in the z-direction, we therefore measured projected particle length in the y-direction as a function of tilt-angle, and deduced the particle height by extrapolating the projected length to the value expected at the tilt-angle of 90º. The results are plotted in Fig.1b. The projected length clearly decreases with tilting, which indicates that the particle height is actually shorter than the in-plane diameter. Here, the extrapolation was performed by fitting the data points at angles higher than 40º using cosine of the tilt angle (α), because of the fact that the projected y-length is proportional to cosα at high angles when the particle height is shorter than the diameter. Using the aforementioned procedure, here termed “tilt-series extrapolation (TSE) method”, we obtained a relation, which summarizes the relation between particle diameter and thickness estimated by using several different techniques (Fig.2a). Solid triangles and solid squares indicate the results obtained from the reconstructed images based on SIRT and WBP, respectively. In the present study, 20 iterations were carried out in SIRT to minimize the differences between the original projected series and the calculated ones. The large error bar for WBP indicates a possible elongation of dz = 4.1 nm [13]. Therefore, we divided the apparent particle thickness (tz), which was deduced from the 3D volumes based on WBP, by the elongation factor (eyz=1.42) [12] for the present experimental condition. The results, tz / eyz, are indicated by open squares. Solid circles denote the deduced particle thickness measured from the TSE method. A solid curve indicates the previous result based on the electron holography [16]. Note that the deduced thicknesses obtained by the TSE agree well 2
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