Diffraction calculator of 3D-cubic lattices.

Enter the number of shells in the 3D-square unit cell, the shape of the shells (spherical or cubical), their radii r and their electron densities c, the type (P/F/I) and lattice spacing d of the cubic space group (P221/F225/I229). The radius r in case of a cube is the radius of the inscribed sphere. The radii should be increasing from 1 to 10 and intersecting of cubes and spheres should be avoided. The first up to 12 diffraction peaks of the cubic lattice will be calculated. The values are listed h^2+k^2+l^2, q(hkl), 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 hkl^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. 12 for F-225 and I-229, max. 24 for P-221) and plotted for Nr points (2D) from the center of the symmetric unit cell up to rmax (for one unit cell rmax = d/2) at the lattice plane rz (0 < rz < d). F(0) will also be calculated and used in the electron density calculations (for proper scaling and offset of the electron density).

Input h*h+k*k+l*l, q, y-data(q) Output/Plot
 shells 10 9 8 7 6 5 4 3 2 1 shape: sphere cube P/F/I: 221(P) 225(F) 229(I) a=b=c: 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) rz F(0): phi: theta:

 Nr (points, 2D): unit cells (n x n ): colorscale: Jet Hot Rainbow Earth Electric Viridis Cividis Portland Blackbody Picnic RdBu YlGnBu YlOrRd Bluered Greys Blues Reds Greens colorscale/background: normal/white reverse/white normal/black reverse/black 2D-plot: heatmap heatmap-smooth contour contour+heatmap contourlines 3D-plot: surface surface+contour colorscale-zmin: colorscale-zmax: Nr (peaks, 1D) Nr (points, 1D) FWHM y-data-correction F(q) / LC+MC I(q) / LC+MC I(q) / LC I(q) / none scaling factor offset overlay (1D) no overlay

Author: M.Kriechbaum, TU-Graz (2018), e-mail: manfred.kriechbaum@tugraz.at