Calculation of the potential for interaction of particles with complex atomic structures

We present a method for calculation of the potential and related physical quantities experienced by a particle traversing an aligned periodic complex atomic structure. Classical physics equations and the expansion of periodic functions as a Fourier series have been used for the calculation. Based on this method, we have developed the ECHARM program, which calculates one- and two-dimensional averaged physical quantities of interest along the main axes of any orthorhombic and tetragonal structure. For the case of cubic symmetry, the calculation holds for any orientation. Complex structures such as zeolites have been worked out to show the capability of the program.

Figure 1

(Color online) Calculation of potential between (111) planes and (110) planes in Si with Moliere atomic form factor and the form factor achieved by x-ray experiments. The potential calculated with the latter method is lower than for the former method, especially in proximity of the atomic planes.

Figure 2

(Color online) Contour plot of physical quantities of interest along the [001] axis of Mordenite at $T=300\text{K}$, as a function of coordinate $x$ and $y$. (a) Potential: a wide channel with uniform potential is visible on the center of the figure. The ion breaking the symmetry of the potential are $C{a}^{++}$ cations bound to the well of the channel. (b) Electric field ($x$ component). (c) Electron density. (d) Atomic density: this figure gives a picture of the extent of the atomic oscillations in the crystal.

Figure 3

(Color online) Contour plot of physical quantities of interest along the [100] axis of Boggsite at $T=300\text{K}$, as a function of coordinate $y$ and $z$. (a) Potential. (b) Electric field ($x$ component). (c) Electron density. (d) Atomic density.

Figure 4

(Color online) Potential (a) and electric field (b) in the axial case along the [112] axis for a SiC at $T=297\text{K}$.