6. HREM image map

The simulation of High Resolution Electron microscope image maps is possible by either the multislice or the Blochwave methods. 


 

6.1 Multislice method

After loading or creating a crystal file, activate the "Multislicer" window (menu Image, item Multisclice or Alt+I, Ctrl+M), this will open the multislicer window as shown on figure 6.1:

Figure 6.1 (Multislicer)

The multislicer consists in 6 different programs that perform the following calculation for a specific crystal and a specific zone axis direction.

Fresnel propagator

generates and shows  the complex Fresnel propagator

Phase object function

generates and  shows the complex phase object function

Projected potential

generates and shows the complex projected potential 

Atom position

generates and shows the projected position of the atoms

HREM map

calculates High Resolution Electron Microscope image maps

Super-cell image

calculates High Resolution Electron Microscope images

Direct access to the microscope selection dialog , the specimen settings dialog and the transfer function window . Further more the generated images can   be saved using the save dialog . The real part of the Fresnel propagator for ZnO in the [0,0,1] direction is calculated by clicking on the start button. It is shown on figure 6.2:

Figure 6.2 (ZnO [0,0,1] Fresnel propagator)

Clicking on the imaginary "tab" would display its imaginary part.

The complex phase object image is obtained by selecting the "Phase object function" tab and clicking the start button as for the Fresnel propagator. Its imaginary part (the weak phase object) is shown on figure 6.3 where Ce atoms are located at the largest and brightest spots position (Ce and O have very different atomic form factors that result in a much larger projected potential for Ce than for O). A mouse click on the bright dots identifies the atom column.

Figure 6.3 (Phase object function)

The positions of the cerium atoms are given on figure 6.4:

Figure 6.4 (Ce positions)

The positions of the oxygen atoms or of both the Cerium and oxygen  would be obtained by selecting the "O" or "All" tab.

These images can be saved as .gif images by activating the icon. The image of the O atoms is:

Figure 6.5 (O position image)

Finally, in order to calculate  HREM map it is necessary to define several parameters for the multislice iteration, the imaging parameters and the illumination. The HREM map dialog is shown on figure 6.6. At its top left corner one finds icons that allows to save the HREM map or beam plot, , to print the HREM map or beam plot, , to adjust the microscope settings,  , to change the specimen orientation, , and to work out the transfer conditions, .

Figure 6.6 (HREM dialogue)

The illumination conditions, imaging parameters and iteration parameters are organized in three panels. 

The illumination panel contains two sliders that controls the coherence of the illumination:

The imaging panel contains six controls:

Defocus min / nm is set to 94 : the first image is calculated for a defocus of 94 nm (in jems as the "z" axis is pointing up, i.e. towards the electron source, positive defocus is under focus).
Defocus step / nm is set to 2 : the defocus between to images of a map's row will be 4 nm.
Defocus number is set to 8 : each map row will contains 16 images.
Image dup-x is set to 2 : individual images are repeated 2 times in the horizontal direction.
Image dup-y is set to 2 : individual images are repeated 2 times in the vertical direction.
Noise % is set to 20 % : random noise of value 0.20 is added to the calculated images

The iteration panel contains three controls:

Start after is set to 2 : the first HREM image is calculated for a crystal 2 unit cells thick in the selected direction.
Number is set to 8 : the image map will contain 16 rows of images each row for a different thickness.
Increment is set to 2 : between two rows the thickness increases by 2 unit cells.

and an option box that at present allows to make image maps with the projected potential, wave function and HREM images placed side-by-side.

The beam plot box controls the type (if any) of the beam plot: conventional amplitude versus thickness, Argand or diffraction.

Furthermore, Transmission Cross-Coefficients are used to produce the images, a Plot of the beams' amplitude and phase is required. Clicking on the start button fires the calculation. After about 7 seconds (5 reflections transmitted by the objective aperture,  Pentium III at 450 MHz), the image map is put into the map window and into a dedicated window. The calculation time is very much dependent on the number of beams that participate to the image formation. This number is selected using the microscope dialog .

The HREM map dialog is now shown on figure 6.7. Using the scroll bars located below and on the right of the map, all the map can be inspected.

Figure 6.7 HREM dialogue after calculation (Au [0,0,1] 300 kV, the wave function at 2.4 nm is highlighted)

Selecting the Plot "tab" would show either a  amplitude/phase versus thickness plot, an Argand plot (complex plot) or the dynamical diffraction patterns for 2, 4, 6, .. unit cells thick Al crystals. Figure 6.8 shows the thickness plot, 6.9 the Argand plot and 6.10 the diffraction pattern. The slider on the left of the plots changes the beam that is shown (thickness/Argand plot) or the thickness of the diffraction pattern. The slider on the right changes the gamma correction used for the gray lookup table.

Figure 6.8 Intensity versus thickness plot (Au [0,0,1] 300kV)

Figure 6.9 Argand plot (Au [0,0,1] 300 kV)

Figure 6.10  Dynamical diffraction plot (Au [0,0,1] 300 kV, only the beams passing through the "objective aperture" are shown)

 

The image of the dedicated HREM montage map window is shown on figure 6.11:

Figure 6.11 HREM map image with identified atomic columns

The icons at its top left are used  to print , save or to overlay thickness/defocus information on a HREM map as show below on figure 6.12:

   Figure 6.12 (Annotated HREM map image)

Moving the mouse on the window will also show the defocus/thickness values of the individual images. A click of the mouse on the atomic column position identifies the column,

Figure 6.13 shows a very large map of Si at 200 kV, [1,1,0] direction that contains image features (extra "lattice" planes) due to interference effects between the reflections (non-linear imaging effects).

Figure 6.13 (HREM map image Si 200 kV, [1,1,0]

The effect of the objective lens aberrations like astigmatism (2- and 3-fold), coma, image shift and specimen vibration and drift can be imaged interactively (see paragraph 6.4).

Images of crystalline defects are calculated when the super-cell image panel is selected (see paragraph 6.5). 


 6.2 Blochwave method

The Blochwave method proceeds in the same spirit, but could be much faster for high [u,v,w] zone axis. Furthermore High Order Laue Zone reflections are included in the calculation of the exit wave function. The HRTEM dialogue is part of the larger Blochwaver dialogue. Figure 6.14 shows the panel as it appears after selection:

Figure 6.14 (HRTEM map - Blochwaver dialogue)

It is organized in two sub-panels, the left sub-panel controls the calculation, the right sub-panel shows the calculation results. The "Beam plot" box controls the plot of the amplitude/phase of the diffracted beam (either amplitude/phase versus thickness, complex or diffraction). On the sides of the diffraction sub-sub-panel, the left slider controls the camera length, the right slider the deviation parameter (i.e. the number of reflections considered). The green cross is positioned at the Laue Circle Center. Selecting it, and moving it under mouse control allows to change the tilt of the illumination. The orientation of the specimen, as well as the number of Laue zones considered or the foil normal are controlled by the specimen dialogue, . The microscope dialogue, , allows to change the accelerating voltage, the size of the objective aperture and the position of the optical axis.

On the left of the HREM map panel, the "Illumination" panel allows to control the image formation under coherent, partially coherent (envelope functions) or partially coherent using Transmission Cross Coefficients. Two sliders allow to modify the incident beam convergence (spatial coherence) and the defocus spread (temporal coherence). The [001] reflections (up to 0.1 nm) are shown on the transfer function plot. They are indexed using the mouse.

The imaging panel is shown on figure 6.15. The 6 sliders are used to calculate series of defocused images, the first image is calculated at "Defocus min", the subsequent at a defocus increased by "Defocus step". The series size is "Defocus number", each image is duplicated horizontally by "Image dup-x" and vertically by "Image dup-y". Some random noise can be added to the image. On figure 6.15, the center of the Laue circle (crystal tilt) has been moved to (1,1,0). Reflections (2,0,0), (0,2,0) and (2,2,0) are at Bragg condition. Clicking on a disk will display the reflection indices distance to (0,0,0) and deviation.

Figure 6.15 (Imaging panel of the HRTEM map panel)

Having adjusted the imaging conditions, the dynamical calculation parameters are selected using the "Iteration" sub-panel shown on figure 6.16. The iteration conditions selected are: a crystal of  initial thickness 1 nm, 20 wave functions will be calculated at thickness increasing by 8 increments of 0.25 nm (i.e. 2 nm), and the number of reflections that will be considered strong is 25. The check boxes labeled "Bethe", "All" and "Save" tells the program to use Bethe potential to include weak reflections, to include all reflections (selected with the deviation slider on the right of the Diffraction panel) and to save the beams amplitude/phase as a function of crystal thickness. In this figure, the convergence of the incident beam is quite large.

Figure 6.16 (Iteration sub-panel)

Figures 6.17 a and b show the microscope dialogue that allows to set the aperture diameter and the optical axis position.

Figure 6.17a and b (Objective aperture size and position, optical axis position)

With these settings pushing the start button makes the program calculates the following HREM map (Figure 6.18), where the incident beam convergence has been decreased (better spatial coherence) from 4.8 (a) to 0.8 nm-1(b), and the defocus spread from 20 (b) to 6 (c) nm. The effect of the crystal  tilt (Laue circle center), beam tilt (optical axis position) and objective aperture centering are obvious.

Figure 6.18a,b,c (HREM map, Al [0,0,1] 300 kV, CLC at (1,1,0), CM-300 UT)

Adjusting the crystal tilt, i.e. setting the Center of the Laue Circle (CLC) at (0,0,0) produces image a) of 6.19, centering  the objective aperture image b) and adjusting the optical axis image c).

Figure 6.19 a, b, c (Improving imaging parameters)

The specimen orientation and other related parameters are set using the "Specimen dialogue".

The Bloch wave approach is easy to apply to zone axis directions of high [u,v,w]. Figure 6.20 shows a montage of Al in the [0, 1, 2] direction.

Figure 6.20 (HREM montage Al in [0,1,2])

The dynamical diffraction pattern corresponding to the wave function at 7.5 nm is shown on figure 6.21.

Figure 6.21 (Dynamical diffraction pattern)


 

6.3 Exporting .ems images

      6.3.1 Saving or loading images from or into jems

jems HREM and CBED images can be saved in the *.ems format described below and loaded back without loosing the image map information or CBED information. HREM image in .ems format are automatically generated when the HREM image maps are saved as *.gif files.

Figure 6.22 (How to load .ems images)

    6.3.2 Loading .ems images into Mathematica

    The following lines show the Mathematica code used to read into Mathematica .ems images,


SetDirectory ["g:\jemsExamples"

Needs["Utilities`BinaryFiles`"]

         Off [General::spell]

         FileNames["*Si114*"]


    in = OpenReadBinary["Si114CBED6.ems"]
    col = ReadBinary[in, Int32];
    row = ReadBinary[in, Int32];
    data = ReadBinary[in, Table[Table[Single, {col}], {row}]];
    Close[in]
    Show[Graphics[Raster[data], AspectRatio -> Automatic]];


              ListPlot [data [[200]], PlotJoined -> True, PlotRange -> All];
              ListPlot [Take [data [[200]], {150, 250}], PlotJoined -> True, PlotRange -> All];

    The .ems image format is quite simple to read as it starts with two 32 bit integers that gives the number of rows and columns of the image. It is followed by the image data.

    The data points are Real 4 Bytes ( single precision floating point).

     Figures 6.23 and 6.24 a, b show a HREM montage map as loaded into Mathematica and line scans across it.

Figure 6.23 ( HREM montage as displayed by Mathematica bitmap).

Figure 6.24 a, b (line scans across Mathematica image)

Several simple Mathematica notebooks are given in jemsData/MathematicaCode.

6.3.3 Loading ems images into DigitalMicrograph

It is equally easy to read these images into DigitalMicrograph. The following procedure loads the .ems images into DM3.4:

Figures 6.25 a, b show some image filtering on noisy HREM montage.

Figure 6.25 a, b (DigitalMicrograph processing of HREM montage map)

 


 

6.4 Objective lens aberrations and specimen vibration and drift

When one selects the "Plot" panel and the "Image" radio button of the "Beam plot" box, the HREM image at a given thickness and defocus is displayed. The thickness of the crystal is selected using the slider positioned on the left, the right slider changes the gamma correction.  Figure 6.26 shows the panel controlling 2-fold, 3-fold astigmatism and axial coma. The sliders change the amplitude of these aberrations  and the compasses the angle. The image contrast depends on the illumination condition (coherent, envelope or TCC). The transmission cross-coefficients take fully into account 2-fold, 3-fold, axial coma and image shift.

 

Figure 6.26 2-fold, 3-fold and axial coma controls

The controls of the illumination, imaging, objective lens, shift and vibrations panel will modify interactively the high resolution image allowing to see their various effects in real time. A click on the image will draw the normal to two basis planes (figure 6.27).

Figure 6.27  Normal to the planes (reciprocal basis, Au [1,13])


 

6.5 Super-cell images

A panel similar to the HREM map panel controls the simulation of HREM images of crystal defects. When the defect has a 3-D structure one prepares several slices. The wavefunction propagates through the slices from top (first slice) to bottom (last slice). Figure 6.28 shows a Sigma 5 <310> interface in Au. It is distorded due to 3-fold astigmatism. A detail of the distortion is given on figure 6.29.

  

Figure 6.28 Image simulation of crystal defects

When 3-fold astigmatism is present it is easily demonstrated that , the orientation of the interface is of upper-most importance for obtaining an image without distortion.

Figure 6.29 Detail of right panel of figure 6.28


03/06/02 02:29:30