MASAP: A package for atomic scattering amplitude in solids

Abstract

We present the MsSpec Atomic Scattering Amplitude Package (MASAP), composed of a computation program and a graphical interface to generate atomic scattering amplitude (ASA) of an atom, either isolated or embedded in an environment, at any chosen energy of the impinging electron up to ≈15 KeV. The ASA is calculated using an effective, complex optical potential which provides damping effects in the scattering process in a fully relativistic framework. Optionally, scalar relativistic and non-relativistic approximations are also available to assess their applicability to a given problem. In order to describe electron propagation in solids we suggest to replace ASA's based on Plane Waves (PW) scattering with effective ASA's based on curved Spherical Waves (SW) using truncated-overlapped potentials of the Muffin-Tin (MT) type constructed according to the Mattheiss prescription. The graphical user interface generates not only ASA data files providing atomic Differential Cross Sections (DCS) but also files of related quantities such as total Cross Section (CS), both elastic and inelastic, atomic tl-matrices and phase shifts. We found in general that the imaginary part of the optical potential enhances the calculated elastic DCSs in the forward direction compared to the same potential without the imaginary part, a feature related to the optical theorem, but gives rise to a lower intensity at all other directions as expected due to the damping effect of the complex part of the potential. We show calculated differential and transport Cross Sections for aluminum and gold atoms both in isolation and in crystals with the Face-Centered-Cubic (FCC) structure. Program summaryProgram Title: MASAPCPC Library link to program files:https://doi.org/10.17632/gtxp3mn5hs.1Licensing provisions: Apache 2.0Programming language: FORTRAN 77, Python3External routines:•SciPy (https://www.scipy.org)•Atomic Simulation Environment (https://wiki.fysik.dtu.dk/ase/)•h5py (https://www.h5py.org)•wxPython (https://www.wxpython.org)Nature of problem: Calculation of atomic scattering amplitudes of scattered electrons by an embedded atom in a solid including damping and relativistic effects. Comparison between ASA's in an isolated atomic system and a solid. Introduction of an effective ASA for electrons propagating in a solid derived from Multiple Scattering Theory.Solution method: Potential scattering theory. Muffin-tin approximation. Superposition of atomic electron densities obtained by self-consistent Dirac-Fock atomic calculations. Hedin-Lundqvist potential as an optical potential. Fully relativistic theory, with scalar-relativistic and non-relativistic approximations for comparison.Additional comments including restrictions and unusual features: Even though the program can perform calculations at impinging electron energies up to ≈15 Kev, DCS calculations are recommended in the range 50 : ≈1500 eV both in the case of isolated atoms and atoms embedded in solids, since this interval is more suitable for studying the details of the atomic potentials in their environment.In the case of solids, at energies lower than ≈50 eV, the details of the electronic structure might be important, whereas in the case of isolated atoms this range might suffer from the neglect of the polarization potential and coupling to available inelastic channels. In this respect an option to add an empirical form of a polarization potential to investigate its effects is available to the interested user.