Diffraction calculator of 2D-square lattices.

Enter the number of shells in the 2D-square unit cell (p4m), the lattice spacing d, their radii r, their electron densities c (circular). The radii should be increasing from 1 to 10. The first (max.) 30 diffraction peaks of the square lattice will be calculated (note: the hk-peaks 5/0, 4/3 and 7/1, 5/5 and 8/1, 7/4, respectively are shared peaks, i.e. have the same q-value, therefore max. 33 peaks in total). The values are listed h^2+k^2, 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. 10) and plotted for Nr points (2D) from the center of the symmetric unit cell up to rmax (for one unit cell 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 the values of the FWHM of the peaks and an optional offset (for overlaying several curves) can be entered.

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