Scattering from rough surfaces

Classical description

In the classical mechanics framework, a rough surface, such as a machined metal surface, randomizes the probability distribution function governing the incoming particles, leading to net momentum loss of the particle flux.

Quantum description

In the quantum mechanical framework, this scattering is most noticeable in confined systems, in which the energies for charge carriers are determined by the locations of interfaces. An example of such a system is a quantum well, which may be constructed from a sandwich of different layers of semiconductor. Variations in the thickness of these layers therefore causes the energy of particles to be dependent on their in-plane location in the layer. |doi-access=free This assumption may be formulated in terms of the ensemble average for some given characteristic height, \Delta, and correlation length, \Lambda, such that :\langle\Delta_z(\mathbf{r})\Delta_z(\mathbf{r'})\rangle = \Delta^2\exp\left(-\frac{|\mathbf{r}-\mathbf{r'}|^2}{\Lambda^2}\right)

Types of Scattering

Selective Scattering : In selective Scattering scattering depends upon the wavelength of light.

Mie scattering** :** Mie theory can describe how electromagnetic waves interact with homogeneously spherical particles. However, a theory for homogeneous spheres will completely fail to predict polarization effects. When the size of the molecules is greater than the wavelength of light, the result is a non-uniform scattering of light.

Lambertian Scattering: This type of scattering occurs when a surface has microscopic irregularities that scatter light perfectly uniformly in all directions, causing it to appear equally bright from all viewing angles.

Subsurface Scattering: This type of scattering occurs when light scatters within a material before exiting the surface at a different point.

Isotropic crystal scattering (aka powder diffraction): This type of scattering occurs when every crystalline orientation is represented equally in a powdered sample. Powder X-ray diffraction (PXRD) operates under the assumption that the sample is randomly arranged such that each plane will be represented in the signal.

Notes

References

1. Sommerfeld, M., Huber, N. (1999) "Experimental analysis and modelling of particle-wall collisions." International Journal of Multiphase Flow 25(6), 1457–1489
2. Konan, N.A., Kannengieser, O., Simonin, O. (2009) "Stochastic modeling of the multiple rebound effects for particle-rough wall collisions" International Journal of Multiphase Flow 35(10), 933–945
3. Jonasz, M., & Fournier, G. R. (2007). ''Refractive indices and morphologies of aquatic particles. Light Scattering by Particles in Water, 447–558.'' doi:10.1016/b978-012388751-1/50006-5
4. Twardowski. (July 15, 2001). "A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters". Journal of Geophysical Research.