Diffraction calculator of 2D-hexagonal lattices.

Enter the number of shells in the 2D-hexagonal unit cell, the hexagonal lattice spacing d, their radii r, their electron densities c and their shapes (circular or hexagonal). The radius r in case of a hexagon is the radius of the inscribed circle. The radii should be increasing from 1 to 10 and overlapping of hexagons and circles should be avoided. The first 20 diffraction peaks of the hexagonal lattice will be calculated (note: the 20th peak is shared by two reflections: 5/3 and 7/0). The values are listed h^2+k^2+hk, q(hk), and y-data. These (y) can be either the amplitudes F(q) or the intensities I(q). Optionally the intensities I(q) can be multiplied by the multiplicities of the respective peaks (*M) and further also be divided by hk^2 (Lorentzfactor, /x**2). Units are arbitrary (A or nm) and can be copied and pasted from the window into any text-file for further processing and graphical displaying. The electron density will then be recalculated from the selected number of diffraction peaks (Nr peaks, max. 20) and plotted for Nr points (2D) from the center of the unit cell up to rmax (for one unitcell rmax = d/2). F(0) will also be calculated and used in the electron density calculations (for proper scaling and offset of the electron density). The respective diffraction pattern will be also plotted for Nr points (1D) for the number of peaks selected (except F(0)) where there the values of the FWHM of the peaks and an optional offset (if you overlay several curves) can be entered.

Calculation Input h*h+k*k+hk, q, y-data(q) Plot Input
 shells 10 9 8 7 6 5 4 3 2 1 d r(1) c(1) circ hex r(2) c(2) circ hex r(3) c(3) circ hex r(4) c(4) circ hex r(5) c(5) circ hex r(6) c(6) circ hex r(7) c(7) circ hex r(8) c(8) circ hex r(9) c(9) circ hex r(10) c(10) circ hex F(0):

 Nr (points, 2D) rmax y-data: F(q) I(q) I(q)*M I(q)*M/x**2 Nr (peaks) colorscale: Jet Hot Rainbow Earth Electric Viridis Cividis Portland Blackbody Picnic RdBu YlGnBu YlOrRd Bluered Greys Blues Reds Greens 2D-plot: heatmap heatmap-smooth contour contour+heatmap contourlines 3D-plot: surface surface+contour Nr (points, 1D) FWHM offset 1D-plot: overlay no overlay

Author: M.Kriechbaum, TU-Graz (2022), e-mail: manfred.kriechbaum@tugraz.at