Small-Angle Scattering (Neutrons, X-Rays, Light) from Complex Systems by Eugen Mircea Anitas

Author:Eugen Mircea Anitas
Language: eng
Format: epub
ISBN: 9783030266127
Publisher: Springer International Publishing

Object

I(q) / I(0)

Refs.

Notes

Sphere of radius R

[1]

Eq. (3.78)

Parallelepiped of edges a, b, c

[1]

–

Disk of radius R

[14]

–

Square of edge a

[1]

–

Triangle of height h

[21]

Figure 3.2 shows the behaviour of scattering intensity for nm on a double logarithmic scale. The main feature is the presence of a Guinier region, followed by a Porod one. The end of the Guinier region is marked by a vertical line, and from its position an estimation of the overall size of the sphere can be obtained. The Porod region is characterized by a nearly periodic behaviour where the minima are given by the condition , that is , with . Note, that the presence of minima in the scattering curve is characteristic to object with higher symmetry, that is the minima are sensibly smoothed in the case of cubes, due to lower symmetry. Also, a change in the radius leads to a horizontal shift of the whole scattering curve either to left (for nm) or to the right (for nm).

Fig. 3.2SAS from: a Monodisperse and polydisperse systems of spheres (Eq. (3.78)) at various relative variances of the log-normal distribution given by Eq. (3.69). Lower (black) curve: ; Middle (blue) curve: ; Upper (green) curve: b Sphere (lower-black curve) and cube (upper-red) of the same radius of gyration. The normalized scattering amplitude of the cube is given in Table 3.2. The average over orientations for the cube has been performed according to Eq. (3.66). Vertical (magenta) dotted-lines delimitates the Guinier and Porod regions

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