Films comprised of randomly oriented crystals

As we showed in Chapter 1, when a bitUgr sample, comprised of an infinite number of grains with perfectly random orientations, is irradiated with a 

Once an estimate of the film thickness width is known, it is possible to choose the incidence angle that will lead to the highest possible irradiated volume. This angle is determined from the mass absorption coefficient and the density. We have seen in Chapter 2 that the adequate incidence angles for films which are a few tens of nanometers thick are in the range of a few tenths of a degree. 

However, we have to point out three limitations to this approach. First of all, it is easy to determine the absolnte density of the material in qnestion if the film s chemical nature is known but, most of the time, the films produced have a significant residual porosity and, there is a chance that the path of the X-ray beams inside the material will be longer than estimated. Additionally, when a sample is irradiated at a very low angle, the beam is completely reflected and do not penetrates the film at all. Therefore, we have to work beyond the critical angle characteristic of this effect. The value of this angle, which depends on the density of the phase, is usually between 0.2 and 0.5°. Finally, it is important to choose an 

The pattern, produced in these conditiorrs with an incidence angle eqttal to 0.35° and an acqrrisition time of 12 horns, is shown in Figirre 7.4b [GUI 98, GUI 99]. The diffraction peaks characteristic of tetragonal zirconia are clearly visible and the measrrred intensities are corrsistent with the JCPDS entry for that ph.  

The design of functional systems often leads to the production of multi-layered objects in which each layer has a specific function which is different from the function of the layer that supports it. It is common to come across samples comprised of three or four different layers. These systems are sometimes the result of superficial changes in the substrate (an oxidation, for example) or they are produced by creating consecutive deposits. In both cases, the nature and the relative rate of each phase is a key question. X-ray diffraction is one of the only non-destractive techniques that can be used to determine these parameters. 

---

Throughout this section, we will be dealing with a polycrystalline film comprised of randomly oriented crystals. 

---