Rg-Calculator for concentric core/shell shapes (SAS)

Core/shell shapes can be composed of up to 5 different or same shapes with the shell's centroids in the common center of gravity. Select the geometrical shape, lengths of the axes (a,b,c), or radii (rx,ry,rz) and/or height (h) or torroidal radius (R) in the x-, y- and z-directions and the electron density (e) of each shell, with e(1) being the innermost shell and e(n) the outermost shell, respectively. The values of the radius of gyration Rg and of the zero-angle intensity I(0) will be calculated. Units are arbitrary.

ellipsoid (rx,ry,rz), hexahedron/tetrahedron/octahedron (rx=ry=rz=a), cylinder (rx,ry,rz=h)
semi-ellipsoid/paraboloid (rx,ry,rz=h), semi-cylinder (rx,ry,rz=h, cut along ry), cone (rx,ry,rz=h), semi-cone (rx,ry,rz=h, cut along ry)
pyramid (3): (rx=a,a,ry=b,a>b/2,rz=h), prism (3): (rx=a,a,ry=b,rz=h) *(isosceles) triangular base*
pyramid (4): (rx=a,ry=b,rz=h), prism (4): (rx=a,ry=b,rz=h) *rectangular base*
pyramid (5,6): (rx=a,ry=a,rz=h), prism (5,6): (rx=a,ry=a,rz=h) *equilateral base*
pyramid (rhombic): (rx,ry,rz=h), prism (rhombic): (rx,ry,rz=h)
torus o (elliptic): (rx,ry,rz=R), torus # (rectangular): (rx=a/2,ry=b/2,rz=R)
torus (o and #): rx: parallel to the torus plane, ry: parallel to the central torus axis

e(1): rx (a): ry (b): rz (c/h):
e(2): rx (a): ry (b): rz (c/h):
e(3): rx (a): ry (b): rz (c/h):
e(4): rx (a): ry (b): rz (c/h):
e(5): rx (a): ry (b): rz (c/h):

Rg-Calculator for concentric core/shell - curved or plane - shapes (SAS)

Core/shell shapes can be composed of up to 5 different or same shapes with the shell's centroids in the common center of gravity. Select the geometrical shape, lengths of the axes (a,b,c), or radii (rx,ry,rz) and/or height (h) or torroidal radius (R) in the x-, y- and z-directions and the electron density (e) of each shell, with e(1) being the innermost shell and e(n) the outermost shell, respectively. The values of the radius of gyration Rg and of the zero-angle intensity I(0) will be calculated. Units are arbitrary.

ellipsoid (rx=ry,rz), semi-ellipsoid (rx=ry, rz=h)
cylinder (rx=ry,rz=h), semi-cylinder (rx=ry,rz=h), cone (rx=ry,rz=h), semi-cone (rx=ry,rz=h)
triangle (3): (rx=ry=a,rz=b,a>b/2), rectangle (4): (rx=a,rz=b) *(non)equilateral*
pentagon (5): (rx=a,rz=a), hexagon (6): (rx=a,rz=a) *equilateral*
rhombus: (rx,rz), ellipse: (rx,rz), semi-ellipse (rx,rz, cut along rz)
torus o (elliptic): (rx=ry,rz=R), torus # (rectangular): (rx=ry=a/2=b/2,rz=R)

e(1): rx (a): rz (b/h):
e(2): rx (a): rz (b/h):
e(3): rx (a): rz (b/h):
e(4): rx (a): rz (b/h):
e(5): rx (a): rz (b/h):

Rg-Calculator for concentric core/shell - skeletal or wireframe - shapes (SAS)

Core/shell shapes can be composed of up to 5 different or same shapes with the shell's centroids in the common center of gravity. Select the geometrical shape, lengths of the line (a), of the polygon (a) or radius (rx) of the (semi)ring and the electron density (e) of each shell, with e(1) being the innermost shell and e(n) the outermost shell, respectively. The values of the radius of gyration Rg and of the zero-angle intensity I(0) will be calculated. Units are arbitrary.

line (rx=a), circular ring (rx), semi-circular ring (rx)
triangle (rx=a), square (rx=a), pentagon (rx=a), hexagon (rx=a)
(polygons are equilateral)

e(1): rx (a):
e(2): rx (a):
e(3): rx (a):
e(4): rx (a):
e(5): rx (a):