This document describes how to create a graphene layer (Fig. 3b) and how to modify it to change one or more carbon atoms and to have add-on atoms.
Graphite has a layered structure that consists of rings of six carbon atoms arranged in widely spaced horizontal sheets (Fig. 1b). In graphite each carbon has two single bonds to two other atoms and a double bond to another ring carbon. The carbon atoms in these ring arrays are sp2 hybridized and the layers are attached by weak pi bonds.
To create a graphene model one has to select a single layer of rings. This is done in 2 steps by Make orthogonal (Fig. 1c) and To slices (Fig. 2).
Duplicate the orthorhombic cell in x and y directions to obtain a tetragonal structure of large a and b cell parameters (Fig. 2).
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Figure 1a Graphite P 63mc. |
Figure 1b Graphene layers. |
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Figure 1c Make orthogonal defines an orthorhombic cell. |
Figure 1d Grahite, orthorhombic description. |
With the popup menu attached to the model (Fig. 3b) the projected potential, HAADF, WPOA and SAED images are readlily calculated with the current settings of the microscope, aberrations, coherence, etc. (Figures 4a, 4b, 4c, 4d).
ADF images of the graphene layer are obtained using the ADF imager. The simulations parameters are:
Each simulation run produces 4 Bright Field images with BF detector radius 10, 30, 50, 70 nm-1 (Figures 5a, 5b, 5c, 5d). With a negative W40 (C30) the first BF image is similar to the HRTEM image.
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Figure 5a BF outer radius 10 nm-1. |
Figure 5b BF outer radius 30 nm-1. |
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Figure 5c BF outer radius 50 nm-1. |
Figure 5d BF outer radius 70 nm-1. |
Each simulation run produces also 4 Dark Field images with detector inner and outer radii 60 to 150, 80 to 170, 100 to 190, 120 to 210 nm-1 (Figures 6a, 6b, 6c, 6d). With a negative W40 (C30) the first BF image is similar to the HRTEM image.
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Figure 6a DF 60 to 150 nm-1. |
Figure 6b DF 80 to 170 nm-1. |
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Figure 6c DF 100 to 190 nm-1. |
Figure 6d DF 120 to 210 nm-1. |
4 sector detectors (1 to 4) are placed between the BF and DF detectors. By default the inner and outer radii of the sector detectors are set to the outer radius of the BF detector and the inner radius of the DF detector (Figures 7a, 7b, 7c, 7d).
Differential Phase Contrast imaging is an interesting feature of sector detectors. DPC images calculated using the sector images (Figures 7a, 7b, 7c, 7d) are shown below. Indeed these DPC images result of simulations, experimentally provided ones will most likely be somehow different due to non-uniformity of the detectors, etc. In spite of that simulated DPC images could provide valuable insights on the graphene structure when it contains impurities like N or Si.
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Figure 8a S1 + S2 + S3 + S4. |
Figure 8b S1 + S2 - S3 - S4. |
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Figure 8c S1 - S2 + S3 - S4. |
Figure 8d -S1 + S2 - S3 + S4. |
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Figure 9a S1 + S2 + S3 + S4. |
Figure 9b -S1 - S2 + S3 + S4. |
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Figure 9c S1 - S2 - S3 + S4. |
Figure 9d -S1 + S2 + S3 - S4. |
As noted by K. Ishizuka, A practical approach for STEM image simulation based on the FFT multislice method, Ultramicroscopy 90 (2002) 71–83, it is not necessary for accurate calculations to scan the whole periodic model. Fig. 10a shows a HAADF image calculated with Ishizuka approach. The images shown in Figures 5, 6, 7, 8, 9 and 10a, were computed on a smaller part of the model of size 512 × 512 (Fig. 10a), with a probe shape shown in Fig. 10b. The projected potential was initialized on 1024 x 1024 grid with Weickenmeier-Kohl atomic form factors.
During the scanning one can observe the power spectrum, bright field, dark field and 4 sectors detectors (12a, 12b, 12c, 12d).
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Figure 12a Power spectrum. |
Figure 12b Bright field detector. |
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Figure 12c Dark field detector. |
Figure 12d 4 sectors detector. |
Finally the probe wave-function is shown in Fig. 13.
