Example - Creation of a structure data file of SrTiO3 [110]

 

This document describes how to create atomic structure data for TEM and STEM image simulations in a different crystallographic orientation than the original structure model. The material in this example is the cubic perovskite SrTiO3, and we want to prepare structure data for imaging along the [110] zone-axis of the crystal using the two command-line tools BuildCell and CellMuncher.

Prerequisites for a successful reproduction of the calculation protocol:

Command protocol to create a SrTiO3 [110] super-cell

  1. Create the crystal unit cell using BuildCell by filling a primitive cubic cell with atoms. Thermal vibration parameters are specified in terms of Debye-Waller parameters Biso in units of square Angstroms.

    BuildCell --spacegroup=221 --lattice=3.905,3.905,3.905,90.0,90.0,90.0 --atom=Sr,0.0,0.0,0.0,1.0,0.66 --atom=Ti,0.5,0.5,0.5,1.0,0.51 --atom=O,0.0,0.5,0.5,1.0,1.08 --output=cel\STO_001.cel

    SrTiO3 cubic perovskite unit cell.

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

    You may download the resulting super-cell file from here [ ZIP of STO_001.cel]

  2. Orient the unit cell along the [110] zone axis using CellMuncher. Here you have to take care to extend the periodic unit, such that the tilted structure is again periodic in an orthorhombic cell along the new crystal axes. The present case is rather simple as the initial structure is cubic. The new cell dimensions along x and z will be by a factor of square root of 2 larger than the cubic cell: a' = c' = a * Sqrt(2). Use at least 6 digits precision for the new cell dimensions in order to prevent round-off problems.

    CellMuncher -f cel\STO_001.cel -o cel\tmp.cel --create-block=1,1,0,0,0,1,0.5522504,0.3905,0.5522504

    SrTiO3 [110] unit cell.

    [Super-cell of SrTiO3 in [110] projection, image created by VESTA.]

    The unit cell is now of size sx=0.5522504nm, sy=0.3905nm, sz=0.5522504nm and contains 2 of the original SrTiO3 units, i.e. 2 Sr atoms, 2 Ti atoms and 6 O atoms.

    The create-block function of CellMuncher orients the structure with the zone-axis as specified by the first three parameters [1,1,0] along the z-axis, which is the projection direction of the simulation. The following three parameters [0,0,1] specify, which direction will be used as the new y-axis. The final three parameters [0.5522504,0.3905,0.5522504] determine the total block size in nanometers. Rounding on the 6th digit is sufficient to obtain a good periodicity and to prevent round-off errors. By this way it is ensured that every atom of the periodic unit is present in the new super-cell. In the present case, the projected size of the cubic unit cell is Sqrt(2)*0.3905 = 0.55225039610... < 0.5522504.

    However, using the slightly larger block may lead to the unwanted situation that two identical atoms are placed close to the fractional 0 and 1 coordinates, which is almost the same position, when taking into account periodic boundary conditions. Possible artifacts from using the slightly larger block size than necessary is cured with the next two steps.

  3. Wrap all atomic sites periodically into the fractional coordinate range [0,1[. CellMuncher (version 2.7.1+) will also remove duplicate atoms from the structure with this operation.

    CellMuncher -f cel\tmp.cel -o cel\tmp1.cel --periodic=x --periodic=y --periodic=z

    The current super-cell (file cel\tmp1.cel) will look as in the image above but should contain now only 10 atoms (= 2 original unit SrTiO3 cells).

  4. Next, all atoms are translated by half an atomic plane along each cell dimension. This step prevents later possible numerical round-off errors, e.g. during the subsequent distribution of the super-cell atoms into 4 equidistant slices along z. The translation by half atomic planes should be done always, when atoms are placed at the termination planes of object slices.
    For the current example of SrTiO3 [110] the fractional shifts by half planes along each axis are (0.125, 0.25, 0.125). Note that other structures will require different fractional shifts. The fractional shift should be 1/(2Np), where Np is the number of atomic planes along a cell axis.

    CellMuncher -f cel\tmp1.cel -o cel\tmp2.cel -T x,0.125 -T y,0.25 -T z,0.125

    Again, we want to wrap the atomic sites back to the interval [0,1[. This operation is not always required, we do it here again just to be sure that all atomic sites reside in this interval.

    CellMuncher -f cel\tmp2.cel -o cel\tmp3.cel --periodic=x --periodic=y --periodic=z --cif

    Some structures might require to remove close atoms, because actually identical atomic sited atoms may not be wrapped back to a periodic position due to round-off errors or deviations from the orthorhombic system. A threshold for removing close atoms must be given in Angström units, usually 0.2 A are sufficient.

    CellMuncher -f cel\tmp3.cel -o cel\STO_110.cel --remove-close-atoms=0.2 --cif

    The result of the above procedure up to this point is shown in the figure below.

    SrTiO3 [110] super cell.

    [SrTiO3 [110] super cell., image created by VESTA.]

    This super-cell can be the input for a coherent TEM image calculation using Debye-Waller factors to describe thermal diffuse scattering (TDS).
    [Download SrTiO3 [110] super-cell for TEM simulations]

    For STEM image simulations or TEM image simulations using a frozen lattice (frozen phonon) approach to describe TDS, please proceed to the next step!

  5. In a further step the SrTiO3 [110] super-cell is repeated 3 times along x and 4 times along y.

    CellMuncher -f cel\STO_110.cel -o cel\STO_110_3x4.cel --repeat=x,3 --repeat=y,4 --cif

    The new super-cell dimensions are now Lx = 1.6569 nm, Ly = 1.562 nm, and Lz = 0.5523 nm containing now 24 of the original SrTiO3 unit cell in periodic repitition and projected along the [110] zone-axis.

    An increased x- and y-dimension of the super-cell allows us to introduce aperiodic atomic displacements to apply the frozen-lattice approach for the simulation of TDS. It should be done if severe artifacts can be expected due to the real-space wrap-around of the spreading wave function with increasing object thickness. You should adopt the number of repeats to your simulation. As a general rule of thumb: calculations for thicker objects require also a larger super-cell along the x- and y-dimension.

    An image of the 3x4 extended SrTiO3 [110] super-cell is shown in the figure below.

    Extended SrTiO3 structure projected along [110] unit cell.

    [Extended SrTiO3 structure in [110] zone-axis orientation, image created by VESTA.]

    The extended super-cell can be used for a small-scale STEM image simulation with frozen-lattice calculations of thermal diffuse scattering. It should give reasonable results for a specimen thickness below 40 nm.
    [Download the extended SrTiO3 [110] super-cell for STEM simulations]

 

Summary of commands:

Following is the complete sequence of all commands used above. You may copy this sequence and execute it by one call from a batch file or shell script.

BuildCell --spacegroup=221 --lattice=3.905,3.905,3.905,90.0,90.0,90.0 --atom=Sr,0.0,0.0,0.0,1.0,0.66 --atom=Ti,0.5,0.5,0.5,1.0,0.51 --atom=O,0.0,0.5,0.5,1.0,1.08 --output=cel\STO_001.cel

CellMuncher -f cel\STO_001.cel -o cel\tmp.cel --create-block=1,1,0,0,0,1,0.5522504,0.3905,0.5522504
CellMuncher -f cel\tmp.cel -o cel\tmp1.cel --periodic=x --periodic=y --periodic=z
CellMuncher -f cel\tmp1.cel -o cel\tmp2.cel -T x,0.125 -T y,0.25 -T z,0.125 --cif
CellMuncher -f cel\tmp2.cel -o cel\tmp3.cel --periodic=x --periodic=y --periodic=z --cif
CellMuncher -f cel\tmp3.cel -o cel\STO_110.cel --remove-close-atoms=0.2 --cif
CellMuncher -f cel\STO_110.cel -o cel\STO_110_3x4.cel --repeat=x,3 --repeat=y,4 --cif

 

Tip:

Use the command

CellMuncher -f dummy-file-name.cel -o dummy-file-name.cif -w CIF

to translate an EMS cel file into a CIF file. You can open the resulting CIF file directly with the program VESTA to visualize the structure. Please modify the file name in the generic command above to your needs.

 


Last update: August 1, 2017

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