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I have come across many papers but still couldn't find the relationship between index of refraction or atomic scattering factors, and reflectivity.

My flow of thought goes as follows:

  1. Get the tabulated scattering factors with the respective energy($f'$ and $f"$)
  2. Calculate the absorption coefficients at their respective energy (or simply get it from the tabulated scattering factors too)
  3. Obtain the extinction coefficients, and perform Kramers-Kronig to get the refractive indices.
  4. From here onwards, could anyone advise me on how to calculate the reflectivity for p-polarized light, and plot it against angles of incidences to get a graph of Kiessig interference fringes?

Thank you so much! Any help is much appreciated! Please do correct any of the mistakes that I may have in my flow of thought =)

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One problem with Kramers-Kronig is it needs to integrate over all values of $\omega$, so you can do an estimation using it, but most materials don't have robust measurements over wide ranges of $\omega$ in order to accurately obtain the complete complex indices of refraction. – daaxix Dec 31 '12 at 8:10
up vote 1 down vote accepted

The Wikipedia article should provide some help,

The last section relates how the reflectivity of a thin film system can be calculated by considering the interface as a set of slabs of uniform scattering length density. For X-rays the scattering length density, $\rho$, of a material is related to the electron density: $$ \rho = r_e/V_m \times\Sigma_{i} f_i $$ where $f_i$ is the scattering factor of an element $i$ in the material (at a given energy), $r_e$ is the Compton radius ($A$), and $V_m$ is the molecular volume ($A^3$). $f$ and $\rho$ are complex.

Once you have the scattering length densities it is easy to calculate the reflectivity. There are several programs available to do so (e.g.

The refractive index can be linked to $\rho$ as follows: $$n\approx1-\frac{\rho\lambda^2}{2\pi}$$

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Welcome to Physics Stack Exchange! – Manishearth Jan 3 '13 at 5:53

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