I(q) function calculator
Enter the shape of the model, its radius or semi-axes R1(x), R2(y), R3(z), range of the scattering vector q from qmin to qmax, number of intervals, scaling-factor (f) and an optional constant y-offset for the I(q)-scattering curve. If f >= 0, the scaling factor is V*V*f, if f < 0, then I(0) is scaled to abs(f). N1 and N2 (odd, 11-1001) are the numbers of intervals for the numerical (single- or double-) integration of the spatial averaging (not relevant for sphere/circle/line, but should be increased for highly anisotropic shapes and/or large q-values). The values of the radius of gyration (Rg) and of the volume (V) are also given. Optionally, the scattering curves I(q) of the cross-section and of the thickness from 2-D or 1-D shapes (circles, lines), respectively, can be multiplied by q^n (-2 < integer(n) < 2) to account for the infinite size of the shape in the perpendicular direction(s) (e.g., infinitely long rods or large dics, respectively). The values of the scattering curve are listed and plotted in I(q) or log(I(q)) vs q or log(q), respectively, in arbitrary units and can be copied and pasted from the text-window into any text-file for further processing and graphical displaying. The plot itself can be saved as a png-image file or edited/modified (see options by placing cursor on plot).
Input
Scattering Curve
Shape
R1 (x-axis)
R2 (y-axis)
R3 (z-axis)
q
_{min}
q
_{max}
intervals
N1
N2
scale-f
y-offset
I*q^n
0
1
2
-1
-2
lin (q)
log (q)
lin I(q)
log I(q)
overlay
no overlay
sphere (3SP)
rot.ellipsoid (3RE)
ellipsoid (3EL)
circ.cylinder (3CC)
ellipt.cylinder (3EC)
cuboid (3CB)
circle (2CC)
ellipse (2EL)
rectangle (2RA)
line (1LN)
Rg =
V =
Author:
M.Kriechbaum
, TU-Graz (2018), e-mail:
manfred.kriechbaum@tugraz.at