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Make orthogonal

Multislice simulations of HRTEM or HRSTEM bright, dark or sector field images is usually performed with orthogonal cells since they require often to slice the unit cell. Often slicing unit cells in low symmetry [uvw] directions is impossible without redefining the cell and making it orthogonal (or nearly orthogonal).

Make orthogonal generates a unit cell that is orthogonal or close to orthogonal with a given zone axis [u,v,w] as Oz direction (Fig. 1). Tools are provided to:

Figure1

Figure 1 Make orthogonal cell window. The left table shows the atoms position of the ZnTe unit cell, the right table will show the atoms position of the new orthogonal cell after selecting a [uvw] zone axis direction.

Zone axis [121] is selected with the specimen settings (Fig. 2a).

Figure2a

Figure2b

Figure 2a Zone axis [121].

Figure 2b Orthogonal cell [121].

After the setting of the [uvw] indices of the Oz (or c) the right table is filled with with the atoms of the new cell. The new cell has (abc) parallel to [1, -1, 1], [1, 0, -1], [1, 2, 1] respectively and a volume of 6 original unit cells (48 atoms).

Figure3

Figure 3 Orthogonal cell.

Note

It happens very often that the new unit cell is only nearly orthogonal and very large. In such cases, some atoms of the new cell may not be generated due to rounding errors and/or memory limitation.

The orthogonal [172] ZnTe cell contains 3400 atoms and has of volume 425 larger than the original ZnTe unit cell (Fig. 4, 5). It is nearly orthogonal (α, β, γ) = (90.0, 89.69855, 90.0) and have large unit cell parameters (a, b, c) = (16.010456, 1.3841261, 4.5487027). It can be used to simulate HRTEM images with the multislice method, though the Bloch-wave method will be much more convenient and faster for ZnTe [uvw]=[172].

Figure4

Figure 4 Atoms of orthogonal cell [172].

Figure5

Figure 5 Orthogonal cell [172].

The Montage map (Fig. 6), calculated with the Bloch-wave method, displays the projected potential, the intensity of the wave-functions and HRTEM images at 3 different defocuses (0.1 nm defocus step). The dots of cursor marks the projected position of atoms.

Figure6

Figure 6 HRTEM montage map, ZnTe [172], 300kV.