Diffraction calculator of a 2D-square lattice.
Enter the number of shells in the 2D-square unit cell, the shape of each shell (circular or square), their radii r and their electron densities c and lattice spacing d (a=b). The radius r in case of a square is the radius of the inscribed circle. The radii should be increasing from 1 to 10 and intersecting of squares and circles should be avoided. The diffraction peaks up to hk-max ((h*h+k*k) < 400) of the square lattice will be calculated. The values are listed as h, k, h*h+k*k, multiplicity and y-data (scattering amplitudes Fhk). These diffraction peaks are plotted either as amplitudes F(q) or as intensities I(q) with a chosen FWHM-value. 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 calculated diffraction peaks and plotted for Nr points (2D) from the center of the symmetric unit cell for n x n cell units. F(0) will also be calculated and used in the electron density calculations (for proper scaling and offset of the electron density).
Input
h, k, h*h+k*k, multiplicity, y-data(q)
Output/Plot
shells
10
9
8
7
6
5
4
3
2
1
hk-max
a=b:
F(0):
r(1)
c(1)
circ
squ
r(2)
c(2)
circ
squ
r(3)
c(3)
circ
squ
r(4)
c(4)
circ
squ
r(5)
c(5)
circ
squ
r(6)
c(6)
circ
squ
r(7)
c(7)
circ
squ
r(8)
c(8)
circ
squ
r(9)
c(9)
circ
squ
r(10)
c(10)
circ
squ
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 (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 (2023), e-mail:
manfred.kriechbaum@tugraz.at