Example 1 - STEM image simulation of SrTiO3

 

 

This document gives an example of a full STEM image simulation using the Dr. Probe GUI version 1.7.

The example concerns the very easy case of the cubic perovskite SrTiO3 in [001] orientation. The main purpose of this example is to demonstrate the basic concepts and functions of STEM image simulations with Dr. Probe. The example documents the simulation procedure step by step, such that it may serve as a template for your own STEM image simulations. It is however required, that you have installed the Dr. Probe software package properly following the Installation instructions available on this website. The example involves the Dr. Probe graphical user interface application (Dr. Probe.exe) only. For reproducing the individual steps below, it is recommended that you create an empty folder on your hard drive where all intermediate data will be stored, e.g. C:\Simulations\Example01. This folder is used as the working directory for all the example steps.

 

Starting remarks - simulation target

Before starting with a simulation it is important to denote the aim of the simulation and to clarify the involved parameters concerning the material and the microscope.
For the present example we want to calculate STEM images of cubic perovskite SrTiO3 in [001] zone-axis orientation considering a spherical-aberration corrected 300 kV scanning transmission electron microscope with 0.8 angstrom resolution. Images will be simulated for three detectors placed in the diffraction plane, a bright-field detector (BF), an annular bright-field detector (ABF), and a high-angle annular dark-field detector (HAADF). For each detector we will calculate a thickness series, meaning a set of images with variable object thickness but otherwise constant simulation parameters. The images will be saved to files on the hard disk in form of raw series data using the MRC file format and in the standard image format PNG.

The example simulation procedure starts by setting up the parameters of the microscope and of the calculation engine of the software. In a second step, the input structure model, which is a unit cell of the cubic perovskite SrTiO3 (STO), is modified to a super-cell containing several of the input STO units. In a third step we create the intermediate data (phase gratings) for the actual image simulation, which is done by means of the multislice algorithm [1]. Finally, after setting up the parameters of the scan frame, small STEM images are calculated and saved to files.

 

Step 1: Setup the microscope and calculation parameters

The microscope parameters for the simulation are set up using the Dr. Probe graphical user interface. Run the application (Dr. Probe.exe) and proceed to the 'Microscope Setup' by clicking on the respective button in the main dialog.

The microscope parameter dialog, contains several sections concerning 'Saved Settings' of parameters, the attached probe 'Display', the setup of the 'Illumination' parameters, and the setup of 'STEM detectors'. For the present example we will set up specific illumination parameters and detectors. In order to do so, click on the button labeled [Basic Illumination Setup ...], which opens another dialog with input controls for microscope parameters such as Accelerating voltage and the probe convergence angle. Setup the microscope parameters as shown in the image below and click the [OK] button, which brings us back to the 'Microscope Parameters' dialog.

Example 1 - basic illumination setup.

[Basic illumination setup for the STEM simulation of SrTiO3 [001] with 300 kV electrons, a Sub-Angstrom effective source profile of Lorentz-shape, 25 mrad illumination aperture, and 3 nm focus spread. No de-center of the aperture and no illumination tilt is applied.]

We assume further a perfectly aligned aberration-corrected microscope. Set all aberrations to zero by clicking on the [Zero All] button in the microscope parameters dialog.

Finally, open the [Detector Setup] dialog by clicking on the respective button, and create a list of STEM detectors as shown in the image below, including (1) a bright-field detector (BF) collecting electrons in a disk around the optics axis up to 5 mrad, (2) an annular bright-field detector (ABF) in the angular range from 12 to 24 mrad, and (3) a high-angle annular dark-field detector (HAADF) from 80 to 250 mrad.

Example 1 - detector setup.

[Detector setup for the STEM simulation of SrTiO3 [001]. The setup contains three detectors covering different ranges of scattering angles: (1) a bright-field detector (BF) collecting electrons in a disk around the optics axis up to 5 mrad, (2) an annular bright-field detector (ABF) in the angular range from 12 to 24 mrad, and (3) a high-angle annular dark-field detector (HAADF) from 80 to 250 mrad.]

If you have problems setting up the detectors, you can download the detector setup, store it on your hard disk (preferably in the example working directory adding a sub-directory named prm), and load the parameter file with Dr. Probe by clicking the respective button in the detector setup dialog.

Acknowledge the detector setup by clicking the [OK] button, which brings you back to the microscope parameter dialog. You may add the current microscope parameter setting to the list of pre-saved settings by clicking the [Add] button in the upper dialog section.

Example 1 - microscope setup.

[Microscope setup for the STEM simulation of SrTiO3 [001].]

With this step, the microscope parameter setup is finished and the setup dialog should now display as shown in the image above. Acknowledge the settings with the [OK] button, which brings you back to the main dialog of Dr. Probe.

 

Step 2: Setting up the parameters for the multislice calculation

This section concerns the setup of parameters related to the object and to the computation of the elastic electron diffraction. Open the multislice setup dialog by clicking the respective button in the main dialog. The multislice setup dialog displays four tabs which will be used from left to right in the following.

 

2.1 Loading the input atomic structure data of SrTiO3 [001]

The structure model of SrTiO3 is taken form Abramov et al. [2]. The applying space group is P m -3 m (221) with a lattice constant of a = 0.3901 nm, Sr in the corners, Ti in the centre and three oxygen atoms at the face centres as illustrated by the figure below.

SrTiO3 cubic perovskite unit cell.

[SrTiO3 cubic perovskite unit cell, image created by VESTA.]

The initial structure file is loaded by pressing the [Select File] button in the 'Slice Creation' of the multislice setup dialog. A file explorer window will open and allow you to browse through your hard disk. Select CIF file format and open the file SrTiO3-input.cif, which is provided here by download.
The info box below the file name should now indicate that a structure has been loaded and report the dimension of the current super-cell and the number of atoms contained in this cell, as in the image below.

Slice Creation dialog - after loading the structure model.

[Slice creation dialog after loading the input structure model, which is a unit cell of cubic perovskite SrTiO3.]

 

2.2 Modification of the structure model to a larger super-cell of STO [001]

The structure model will now be extended in the Structure modification dialog, which opens by pressing the [View & Modify] button. The dialog should display a large projection image of the STO unit cell along the [001] zone axis with a Ti-O column in the center.

We will now increase the size of the super-cell by a factor of 3 along the x and the y directions. Do to so, click on the [Multiply] button and enter the multiplication factors for x = 3, y = 3, and z = 1 in the small setup dialog. Acknowledge the setting by pressing the [OK]. As a result, the structure projection should now show 9 projected unit cells of STO [001] in a super-cell of 1.1703 nm × 1.1703 nm × 0.3901 nm size as shown by the screenshot below.

Slice Creation dialog - after loading the structure model.

[Structure modification into a 3 x 3 extended super-cell of SrTiO3 [001].]

The increase of the structure model is necessary to better represent the diffuse scattering by the frozen lattice approximation, which introduces a random atomic displacements and should therefore not be described by a very small quasi-periodic super-cell. Increasing by a factor of 3 is a compromise between the representation of randomized frozen states and acceptable computation time for small sample thicknesses.

By selecting the other two projection options for the structure display (x-z and y-z) you will notice, that the structure consists of two atomic planes along the projection direction (z). We always want to represent the individual atomic planes by the slicing of the structure in the following step (2.3), where the super-cell is divided into equidistant slices along z. By representing the distance of atomic planes with the slicing, the diffraction calculations will reproduce higher-order Laue zone interferences correctly. In the present example we want to create 2 slices along z. It might be advantageous for numerical reasons to place the atomic planes in the centre of the future slices. In the present example this shift along z is accomplished by setting the shift vector for all atoms in the new super-cell to (0, 0, 0.25).

When you have made all these structure modifications, and the dialog displays as shown in the image above, you may save the modified structure model to disk in form of a CIF or CEL file. For your convenience a backup of the modified structure is available here by download. A display of the extended structure model generated by the program VESTA is shown in the image below. You should now finally [Accept] the changes and return to the 'Slice Creation' dialog.

SrTiO3 cubic perovskite super-cell of 3 x 3 x 1 unit cells.

[SrTiO3 cubic perovskite super cell of 3 x 3 x 1 unit cells. The image was created by VESTA.]

 

2.3 Creation of phase gratings

The Slice Creation tab should now reflect the modified cell size and number of atoms in the info box below the file name. We now set the numerical sampling of the phase gratings and the number of slices automatically by clicking on the [Suggest Sufficient Sampling] button. This function sets the sampling of the projected potentials, phase gratings, and of the wave function calculation to 480 x 480 pixels and the number of slices to 2. This sampling is sufficient to calculate the high angle scattering up to more than 250 mrad, thereby comprising the complete angular range of the previously defined detector setup. Further set the number of frozen lattice variants for the two slices to 50 and activate the generation of 'Frozen-lattice configurations' by marking the respective check box.
The 50 frozen-lattice variants per slice will be used to simulate the effect of thermal diffuse scattering. A frozen-lattice simulation excludes the application of Debye-Waller factors. We will also neglect absorption in this example and therefore leave the respective check boxes unmarked. The slice creation tab should now display information as shown in the image below.

Example 1 - slice creation setup.

[Slice creation setup for the STEM simulation of SrTiO3 [001].]

Start the slice creation by clicking the respectively labeled button and wait until the calculation has finished. The calculation should be a matter of less than a minute on a modern conventional PC.

 

2.4 Slice data setup

Switch to the [Slice Data Setup] tab, which should now list two slices in each of the two list boxes. The left list box shows the object slice sequence consisting currently of a Sr-O slice and a Ti-O2 slice, while the right list shows the available phase grating data. It is recommended to save the phase gratings to your hard disk. Do this by clicking the [Save] button below the list on the right side. Another dialog will open up asking for an existing directory and a file name for storing the phase gratings. You may leave the current names as are and click the [OK] button to start the file saving.

In case of problems with one of the previous steps, you can download the slice phase gratings from this website, save them to your hard drive and load them in Dr. Probe using the [Load] button below the list on the right side.

We will now increase the maximum object thickness of our calculation by adding more slices to the object slice sequence. We do this by repeating the super cell periodically along the projection direction using the duplicate function of the object slice list. Click 6 times on the [Duplicate All] button to increase the object slice sequence length from 2 to 128 slices, which corresponds to a maximum object thickness of 25 nm. When scrolling to the end of the object slice sequence, the dialog should display as shown in the figure below

Example 1 - Slice data setup.

[Slice data setup for the STEM simulation of SrTiO3 [001].]

In case of problems with the setup of the object slice sequence, you can download the object slice sequence setup from this website, save it to your hard disk, and load it in Dr. Probe by clicking the [Import] button below the list on the left side.

 

2.5 Calculation setup

Switch to the 'Calculation Setup' tab, for setting up some additional parameters managing the multislice calculation procedure. Reproduce the setup as shown in the figure below!

Example 1 - Calculation setup.

[Suggested calculation parameter setup for the STEM simulation of SrTiO3 [001].]

With this setup the STEM image simulation will be calculated using no additional object tilt. The calculation will not consider the partial spatial and partial temporal coherence of the microscope. We will apply the partial spatial coherence later, after the primary images are calculated.
For each pixel, one multislice algorithm is performed for the selected maximum object thickness. However, every pixel will be calculated with a different permutation of the pre-calculated frozen-lattice variants.
STEM images for all three detectors are extracted every 2 slices.
Six calculation threads will be started in parallel executing one multislice calculation each. Since this is a setup for my PC, which supports 8 CPU threads, it could be required to set a lower number on your PC or Laptop. You may also use more threads if your PC supports this. Please, set the number of calculation threads to a value which is by 1 or 2 smaller than the number of supported CPU threads, which should be the highest number you are able to select from the drop-down list. Working with less than the maximum number of CPUs will leave some breath for the GUI and manager thread, and maybe you are able to work on your publication while the calculation runs.

2.6 Scan frame setup

Select the tab 'Scan Frame Setup' and enter the scan frame parameters as displayed in the figure below. The scan will start from the origin of the phase gratings and span over 2 x 2 unit cells of the projected STO [001] structure. The sampling by 60 x 60 pixels corresponds to a scan step of 13 pm, which is a typical value for high-resolution STEM images.

Example 1 - Calculation setup.

[Suggested setup of scan frame parameters for the STEM simulation of SrTiO3 [001]. The scan frame starts at the coordinate of a Sr column, which is at the lower left corner of the calculation frame determined by the phase gratings. The scan frame spans over 2 x 2 projected unit cells and is sampled using 60 x 60 equidistantly distributed beam positions.]

The chosen scan frame spans over 2 x 2 unit cells. Feel free to reduce the frame size and the number of samples to reduce the total computation time. The present setup requires less than 20 minutes of calculations for the STEM images on my computer using 6 parallel calculation threads.

 

At this point you have setup all the parameters required for the STEM image simulation. Exit the Multislice parameter setup dialog by clicking the [OK] button.

In order to make sure that the appearance of the user interface is similar to this documentation, you can download the user interface setup, save it to your hard drive, and load it by using the [Load] button in the program parameters section of the Dr. Probe UI main dialog.

 

Step 3: Running the simulations

Before starting the actual image calculation you may check the current setup by taking a look at the present object data. Activate the object data view and move the object thickness slider to the right. With doing this you select a maximum object thickness of 25 nm for the calculation. Further, select the item Phase of object functions from the object data list and scan image from the calculation type list. The object data display shows now the sum of all phase gratings and marks the applying scan frame including each beam position.

Start the image calculation by clicking on the [Start Calculation ...] button. Two additional dialogs will appear. One dialog informs you about the total calculation progress including an estimate of the remaining calculation time. The other dialog gives a preview on the calculation result, where the scan image builds up from bottom to top during the calculation, as shown in the image below.

Example 1 - Running calculation.

[Screenshot of the Dr. Probe user interface with a running STEM image calculation]

The progress dialog is closed automatically when the full STEM image is calculated. Use the controls of the calculation results section to navigate through the calculated images. Use the slider to browse through the images extracted at different object thicknesses. Note that images for all detectors and for the specified periodic readouts for different object thicknesses have been calculated at the same time.
Just after the calculation is finshed, the STEM images show very sharp features at the atomic columns and a high contrast. This is because the resolution limiting effect of the partial spatial coherence has been omitted so far. By clicking on the [Apply Source Profile] button all images are convoluted by the effective source profile specified in the microscope setup above. The resulting images appear with a significantly smoothed and lower contrast as shown in the figure below.

Example 1 - Calculation results.

[Simulated STEM images of a 25 nm thick SrTiO3 crystal in [001] orientation for three detectors. The top row shows images before the convolution with the effective source profile, the second row shows the same images after the convolution with a 0.8 Angstrom wide Lorentzian source distribution.]

 

Step 4: Saving simulation results

There are different ways how to save the current results to files. The most convenient way is given by an additional dialog, which opens up when you press the [Save Results to File ...] button. The other way is using the [Save] button in the calculation results display window.

Example 1 - Calculation results.

[Dialog for saving multiple simulation results to files and images in various formats.]

The dialog for controlling the saving of results to files as shown in the image above denotes information regarding the currently selected result in the upper part and lets you setup file saving options in the lower part.

For the current example, choose an appropriate destination folder (disk path) on your hard drive and enter a file name prefix (file title). Choose the MRC data file format and mark the two check boxes for saving all images of the thickness series and images for all detectors at once, respectively. Once you have done this, press the [Write Files] button. Three MRC files should now be saved to the specified disk path with the specified file title. Each file name is extended by the respective name of the detector. You may use Gatan Digital MicrographTM for visualizing and inspecting the results of the STEM image simulation.

Repeat the saving of results using the image format PNG. Now 65 PNG files will be saved to the selected disk path for each detector. A number index is added to the file name distinguishing the images of the thickness series, where "001" is the image at zero object thickness and "065" is the image at 25 nm object thickness. The contrast and color settings of the calculation results display window are used for the image creation.

Download the results of this simulation example for comparison with your own calculation results.

The example documentation on the simulation of wave propagation is suggested for further reading. This second example is based on the present example and can be accomplished with only a few changes in the multislice parameter setup.

 

Literature:

  1. J.M. Cowley and A.F. Moodie, Acta. Cryst. 10 (1957) p. 609.
  2. Yu.A. Abramov, V.G. Tsirel'son, V.E. Zavodnik, S.A. Ivanov, and I.D. Brown, Acta Cryst. B 51 (1995) p. 942.

 


Last update: August 1, 2017

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