Nice challenge. No solution from my side, unfortunately.

Questions I would raise though:

• in one case the crystallites are much smaller than the wavelengths in the measurement. In the second, they're of the same order, at least in the upper frequency range. This might somehow contribute?
• Are there voids or is the material non-porous? If the latter is the case then there is grain boundary matter and possibly strain etc. This stuff will not show up in XRD but still contribute to the optical properties.
• In making the comparison with the single crystal, what geometry is the one to consider in case of reflecton measurements?! I would tend to say that, at least approximately, I would expect the optical polarizability to be described by the superposition you mention. But that need not translate in the same superposition of reflectance spectra (especially with the geometrical conditions given here).
• In order to know what questions make sense, I would have to know more about the samples. Question might go along the line whether it actually makes sense to speak of s and p polarization in the same manner as for a single crystal surface. (If there are no preferential orientations, then there might be crystallite surface facets being exposed to the radiation at various angles). Finally, it might be necessary even to treat the material as an effective medium (such as inhomogeneous media, when the inhomogeneities are sub-wavelength scale).

Just a couple ideas.

Just a wild guess: the size of crystallites is comparable with wavelength (1000 cm-1 corresponds to 10 microns). Maybe that's the reason for 'deformed' spectra? Similar effects are quite often encountered when investigating perfect, but otherwise very thin crystals, in IR range.

Kai Fauth :

1. Definitely! The larger crystallites can be resolved by IR light and the light waves split in two as in the usual birefringent crystal; therefore even when randomly oriented, the optical properties cannot be described by a scalar dielectric function in contrast to the sample consisting of small crystallites

2. One is a stochiometric glass ceramics, the other prepared by Spark Plasma Sintering and the densities cannot be discerned from that of the corresponding single crystal. As can be shown by forward calculation from the dielectric tensor of the crystal by the proper theory, there is no (visible) other contribution from surfaces or voids.

3. The 2/3 a + 1/3 c approximation cannot work. Instead every single orientation contributes to the average. The reason for this is, that it is not only the orientation relative to the polarization direction that counts, but also the orientation relative to the surface due to the continuity relations of the electric field at interfaces.

4. If you are interested in the "proper" solution, all references are mentioned above.

Marek Wojciech Gutowski :

The different shapes of the bands result from the usual damped harmonic oscillator when the proper orientational averaging is performed. The choice of the method depends on the crystallite size relative to the resolution limit of light.