Example 2 - Electron probe propagation through SrTiO3 
This document exemplifies the simulation of the propagation of an
electron probe through a cubic perovskite SrTiO3 crystal in 
orientation using the Dr. Probe GUI.
The example is based on a preceeding example on STEM image simulations of SrTiO3 . The same general prerequisites apply here, it is therefore recommended that you at least read the preceeding example. The current example will use the same input data and also the same simulation parameters. It starts in the middle of the setup procedure where the first differences occur. Prerequisite setup data and input data is provided via download.
Starting considerations - simulation target
For the present example we aim for the calculation of the electron probe intensity distribution when propagating through a crystal of cubic perovskite SrTiO3 in  zone-axis orientation. The example considers a spherical-aberration corrected 300 kV scanning transmission electron microscope with 1.2 Angstrom resolution. Images of the electron probe intensity distribution will be simulated in real space and Fourier space as a thickness series. 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.
This example simulation starts with loading software setups and input data concerning the crystal object information. The parameters of the multislice calculation are modified slightly to take partial spatial and partial temporal coherence into account. After the calculation of the probe intensity distributions, the results will be saved to files.
Loading previously saved program parameters and object structure data
In order to make sure that the parameters and appearance of the user interface is similar to this documentation, please download the user interface setup and save it to your hard drive. Extract the files from the ZIP archive and load the setup with the Dr. Probe UI by pressing the [Load] button in the program parameters section of the main dialog. Select and open the parameter file Example01.UISetup.
Please download also the slice phase gratings, unzip the archive and store the *.sli files on your hard drive.
For your convenience, please download further the object slice sequence setup, unzip the archive and store the contained parameter files on your hard drive.
We continue now with the modification of the current program setup concerning the multislice calculation parameters.
[Slice data setup for the STEM simulation of SrTiO3 .]
Open the multislice setup dialog by pressing the respective button in the Dr. Probe main dialog. Choose the second tab for the [Slice Data Setup] and use the [Load] button below the list on the right side to load the downloaded slice phase gratings into the computer memory. Then load also the downloaded object slice sequence using the [Import] button below the list on the left side. The slice data setup should now contain 2 sets with phase grating data sampled by 480 x 480 pixels and a sequence of 128 object slices with alternating slice IDs (0, 1, 0, 1, ..., 0, 1) as shown in the figure above.
Switch to the third tab labeled [Calculation Setup], and reproduce the setup as shown in the figure below!
[Suggested calculation parameter setup for electron probe propagation simulations through a SrTiO3 crystal along the  projection direction.]
With this setup the STEM image simulation will be calculated using no additional object
tilt. The calculation will now consider the partial spatial and partial temporal coherence
of the microscope using an explicit averaging over 500 multislice calculations. Each
individual multislice calculation starts with a random source offset and applies a random
permutation of frozen lattice variants in the sequence of object slices. The source offset
in the x-y-plane follows the source distribution function specified
by the microscope parameter setup, which is a Lorentz distribution of 0.06 nm radius (HWHM).
A random defocus is applied according to a Gaussian distribution function with 3 nm 1/e-half-width
(check the microscope setup).
Probe intensity distributions are extracted in periods of 2 slices, which corresponds to one unit cell of SrTiO3.
The number of calculation threads is ignored. For the calculation of the wave propagation only one CPU core is used.
Select the fourth tab labeled [Scan Frame Setup] and enter the scan frame parameters as displayed in the figure below.
[Scan frame setup for the simulation the electron wave propagation through SrTiO3 . The frame offset parameters specify the central position of the incident electron proble. The other parameters are ignored in this calculation scheme.]
The chosen beam positition corresponds to a point just next to a pure oxygen column close to the center of the calculation frame.
At this point you have setup all the parameters required for the probe image simulation. Exit the multislice parameter setup by clicking the [OK] button.
In order to make sure that the appearance of the user interface is similar to this documentaion, 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.
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. Doing so, you select a maximum object thickness of 25 nm for the calculation. Further, select the item phase sum up to sel. slice from the object data list and wave propagation from the calculation type list. The object data display shows now the sum of all phase gratings and marks the selected beam position by a white cross.
Start the image calculation by clicking on the [Start Calculation ...] button. Two additinal 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 average electron probe intensity distribution builds up with multiple runs of the multislice algorithm, as shown in the image below. Already after approximately 100 repreated calculations you will hardly notice changes of the average intensity distribution.
[Screenshot of the Dr. Probe user interface with a running probe image calculation]
The progress dialog is closed automatically when the calculation is finished, which takes less than 15 minutes on my desktop computer.
Use the controls of the calculation results section to navigate through
the calculated images. Select either the representation of the probe intensity
in real space [Wave power (r)] or in Fourier space [Wave power (k)]
from the present results dropdown list.
Use the slider to browse through the images extracted at different object thicknesses. You will notice in the real space representation, that the highest probe intensity remains focussed at the oxygen column. However, also a significant fraction of the probe spreads out over the calculation frame with increasing object thickness interacting with many atoms far away from the incident probe position. In Fourier space you will see several line features in the intensity distribution following major crystallographic directions of the projected structure in the vicinity of the incident probe position. The Fourier space is filled with diffuse scattering signal up to the artificial blocking aperture at 2/3 Nyquist. Also a bright ring shows up at the expected position of the first order Laue zone.
[Simulated electron probe intensity distributions through a 25 nm thick SrTiO3 crystal in  orientation. (Left) thickness series in real-space representation. (Right) Fourier space representation at 25 nm thickness. The animation was created with the iMtools software.]
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.
[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 at once. Press the [Write Files] button to initiate the saving procedure. An MRC file should now be saved to the specified disk path with the specified file title. You may use the MRC import script for loading and visualizing the series of simulated STEM images with Gatan Digital MicrographTM.
Repeat the saving of results using the image format PNG. 65 PNG images will be saved to the selected disk path. 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.
Last update: August 1, 2017