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MSA
The program MSA calculates the diffraction of fast electrons in an atomic structure with the multislice algorithm [1]. The results can be complex-valued wave functions, STEM images, CBED patterns, or probe intensity distributions. The latter two can be calculated as function of probe position to simulate 4D-STEM type of imaging.
The program is controlled via a parameter list provided in a text file and by command-line options. Detailed descriptions of options are given in the file howto msa.txt.
msa -prm msa.prm -out STEMimage.dat
msa -prm msa.prm -in STEMimage.dat -out STEMimage_convoluted.dat -sr 0.06
4D-STEM simulation controlled via parameter file storing a thickness series of CBED patterns for each scan pixel:
msa -prm msa.prm -out 4D-STEM.dat /3dout /pdif
msa -prm msa-tem.prm -out wavefunc.dat /ctem
msa -prm msa-tem.prm -out wavefunc_tilted.dat -otx 5.4 -oty 1.5 /ctem
The multislice algorithm is used for calculating the electron diffraction by the electrostatic potential of an atomic structure [1]. In this approach the scattering by a thicker sample is described as a sequence of scattering events on thin sample slices taken along the main direction of the incident electrons. Between the scattering events, the electron wave function is propagated in free space towards the next slice.
The approach of sequential scattering and propagation can be implemented in an efficient numerical form. The the scattering of electrons from projected slice potentials is a multiplication of the electron wave function with an object transmission function (phase grating). The subsequent free-space propagation to the next slice plane is calculated by a multiplication of the scattering result with a propagator function in Fourier-space. The calculation for a thick sample comprises thus two multiplications, one forward and one inverse Fourier transform for each structure slice.
MSA supports the calculation of thermal diffuse scattering as well as calculations within the elastic channel using absorptive potentials. Phonon configurations of the scattering potentials are expected to be pre-calculated e.g. by the program CELSLC or the Dr. Probe GUI and are stored in input slice files. During the calculation of the electron propagation through a specimen, MSA selects and applies a random phonon configuration of each slice. By this way, each single multislice calculation, e.g. for each STEM image pixel, is effectively calculated with an individual phonon configuration of the whole sample. Repeated calculations can be used to achieve convergence of this Monte-Carlo scheme.
Calculations for STEM and TEM differ by the shape of the incident wave function and by the way how the electron wave function obtained at the exit-plane of the sample is transferred into an image intensity distribution.
For STEM image calculations, the incident electron wave function is converging into a focused probe and scanned over the sample. For each probe position, the wave function below the sample is analyzed in diffraction space, where the absolute square is integrated for given detector areas, generating STEM images. This means that MSA can be used in its default STEM mode to calculate STEM images, CBED and even scanned CBED (aka. 4D-STEM) data sets.
For TEM image calculations (option /ctem), the incident electron wave is approximated by a plane wave and the electron wave below the sample is passed further through imaging optics towards a detector where the absolute square is taken in real space. In the TEM case, MSA can be used to calculate the electron wave function below the sample (exit-plane wave function). The calculation of TEM images including the application of wave aberrations, partial coherence and incoherent contrast dampening effects is performed by the program WAVIMG.
[1] J.M. Cowley and A.F. Moodie, Acta Cryst. 10 (1957) p. 609-618, https://doi.org/10.1107/S0365110X57002194