The ADF Imager uses of the multslice approach to calculate Bright Field (BF), Annular Dark Field (ADF), Sector Dark Field (SDF) and High Angle Annular Dark Field (HAADF) STEM images (Fig. 1).
ADF imager Manual.
The ADF Imager uses of the multslice approach to calculate Bright Field (BF), Annular Dark Field (ADF), Sector Dark Field (SDF) and High Angle Annular Dark Field (HAADF) STEM images (Fig. 1).
ADF imager Manual.
Figures 1a to 1d show the images of the 4 sectors. Figures 1e and 1d show a HAADF image and the graphene model with a nitrogen atom replacing a carbon atom. Note that the nitrogen atom has a larger contrast in the HAADF image than in the sector images.
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Figure 1a Sector 1 (graphene). |
Figure 1b Sector 2 (graphene). |
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Figure 1c Sector 3 (graphene). |
Figure 1d Sector 4 (graphene). |
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Figure 1e HAADF (graphene). |
Figure 1f Graphene model. |
The tool buttons (from left to right) allows to:
The following buttons:
The controls are placed in 6 panes:
The Iteration pane (Fig. 2a) provides a table of the slices (from top to bottom) making up the model. The table can be duplicated (using the popup menu). The tool buttons at attached to the table allow to:
The iteration number allows to repeat the multislice iteration with the slice.
The thickness of the slices should not be much larger than 0.2 nm (in this example they are 0.204 nm thick). Note that in this example the total specimen thickness is 30 x 0.204nm = 6.12 nm.
The Multislice pane (Fig. 2b) controls the generation of the projected potential, the lattice vibration (Einstein model), and the number of frozen lattice configurations (1). Bicubic interpolation will be employed to generate the projected potential and the final images.
The Option pane (Fig. 2c) contains controls to select the atomic form factors for the generation of the projected potential and the calculation methods (Frozen lattice, and K. Ishizuka), options to:
Select the source of the Atomic Form Factors.
Select the detector Channels to display and to save them.
Show the images after each slice (Image stack)
Display the BF/DF images during the calculation (Show progress)
The Sampling pane (Fig. 2d) displays the detectors inner and outer radii. Their inner and outer radii are set using the ADF detector window. Their optimum radii depend on the metrics of the super-cells and the sampling of the projected potential.
The BF/ADF/SD detectors (hkl) center is (0, 0, 0).
The detectors radii are:
BF1 outer detector radius: 3.80 [mrad] (1.93 [nm-1]).
ADF1 inner detector radius: 39.10 [mrad] (19.86 [nm-1]).
ADF1 outer detector radius: 173.00 [mrad] (87.76 [nm-1]).
SD inner detector radius: 13.00 [mrad] (6.60 [nm-1]).
SD outer detector radius: 39.00 [mrad] (19.81 [nm-1]).
Multislice maximum scattering angle: 246.77 [mrad]
Potential maximum scattering angle: 247.26 [mrad]
Note that when the parent crystal and its zone axis are defined (in general a small unit cell crystal) the ADFDetector window opens much faster.
The scanning defines the dimension of the multislice calculation, of the scanned area and the scan step size. For example, a scan step size of 2 will perform the multislice calculation one column over 2 and 1 line over 2. With the settings of Figure 2e, The multislice iterations dimension is (512 × 512) and BF and ADF images are calculated on a 256x256 grid (displayed in panels Bright field, Dark field, Sector image) and HAADF image. The final images of (dimension 256 × 256) are interpolated to dimension (512 × 512) using a bicubic interpolation scheme.
The larger interpolated images are displayed using the tool button (Fig. 4).
Since the electron probe is not spread over large distances it is not necessary to perform a multislice calculation that will take into account the whole object. One can restrict it to substantially smaller area. In order to avoid the formation of high spatial frequencies (detected by the ADF detector) that occur when the potential is not periodic, i.e. when the multislice dimension is smaller than the phase object dimension, it is necessary to introduce a mask in the calculations. The Phase object and Probe multislice masks will attenuate these frequencies. The mask introduces a gaussian damping of spatial frequencies larger than 2/3 of the Nyquist frequency. These masks also act as anti-aliasing high spatial frequencies cut-off.
This tab displays the intensity integrated over either the BF, ADF or SD detectors (Fig. 2f). The intensity is the ratio of the detected signal and the incident beam intensity (normalized to 1). The Brightness, Contrast and Gamma check boxes opens sliders for controlling brightness, contrast and gamma of the BF or ADF images. When the Histogram radio button is selected the histogram of the image is displayed.
The gain of the BF signal is fixed (1).
The gain of the ADF signal can be selected in the range 106 to 1015.
The gain of the SD signals can be selected in the range 1 to 109.
The gain of the HAADF signal can be amplified by a factor 103 to 1012.
Figure 3 shows the Probe shape window that sets the probe characteristics. Aberrations up to order 8 can be introduced in the probe generation. The square indicates the scan area. When the scanned area dimension is smaller than the potential dimension the probe position can be set dragging it on the potential image.
Figures 4a, 4b show a probe aberrated by defocus (30 nm) and 3-fold astigmatism (400 nm). Aberrations of order 0, W00 (chromatic aberration) to order 8, W88 (8-Fold astigmatism) can be introduced in the probe shape and therefore in the BF, ADF, SD and HAADF images.
When the calculation is completed the BF, DF, SD can be tabulated and interpolated to 512 x 512 (512 is the product of the scan area size, 256 and the scan step size, 2) (Fig. 5). The elapse time is made of the time necessary to generate the projected potential of n slices and the time necessary to peform n multislice iterations of dimension 256 x 256, multiplied by the number of frozen lattice configurations (here only 1).
Figures 6a, 6b shows one image of the BF and of the ADF image stacks. These images were calculated on a 256x256 grid and interpolated to 512x512 using a bicubic interpolation algorithm.
Calculations of the signal captured by the ADF and SD with a 256 × 256 mesh of GaN [210] (Fig. 7a) show that very often it is not necessary to use very large super-cell to get rid of aliasing effects (Figures 7b, 7c, 7c) and have images simulated in a few minutes.
The many tabs of the ADF Imager dialog display also the wavefunction, the power spectrum, the BF and ADF detectors (Figures 11a, 11b, 11c, 11d).
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Figure 11a Power spectrum. |
Figure 11b BF detector. |
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Figure 11c ADF detector. |
Figure 11d Sectors detector. |
The HRTEM images have been calculated for the whole graphene cell.
The STEM images are sized according to the scan area size which is one half of graphene cell. The BF images show the atomic column contrast of the HRTEM images. With negative Cs white atomic columns on a dark background, with positive Cs black atomic columns on a white background.