You can try to do it with methods like used for describing the texture, for example, using the distribution function of the identified crystallographic orientations. Perhaps, a good idea would be to use the order parameter which is linearly transformed with the matter symmetry transformations in the transition layer from the disordered phase to the nanocrystalline phase, as in the Landau’s theory of phase transitions of 2nd kind.

I meant more of a description. Thank you for your interest in my questions.

I guess people may find your question a bit confusing. Try to be more precise and put more "meat" in this question. Start form describing what is the transition phase in your case and what sort of impact you expect to have or should have? Is this a transition phase between ordered crystal and amorphous phase or a distorted boundary layer at the crystal interface (this would not be a phase then). 

If you have π-conjugated organic molecules in the amorphous matrix, it could be explained as aggregation of monomers to dimers, trimers or tetramers (it depends on the rate of crystallinity).

To Darina: Not organics. In accordance with many other questions by this author, in his case, it refers to amorphous alloys based on ferromagnetic metals, the formation of transition regions with short-range order and, possibly, the formation of nanocrystalline structures in amorphous matrix.

I worked with solid lubricant coatings, varying the amorphousness by modifying deposition parameters or by introducing dopants. These processes prevented large  grains to form; so either there were randomly spread, randomly ordered small crystalline grains, or no crystal grains at all.

Increasing amorphousness was an improvement, in general. To put it simply: no crystals prevented surface defects (cracks, spallation) from spreading and prevented oxidation below the topmost surface; consequently, adhesion to the substrate, wear resistance and hardness were improved. (Of course, this is an oversimplification.)

I know that is a relatively restricted case, I don't know if it is the answer you were looking for.

I'm sorry but I am interested in metallic materials.

Andrew thank you for your attention. The transition phase between a grain crystal and amorphous matrix is called interface. Reveals a change in the arrangement of atoms and smooth transition between long range order interactions between the atoms into short range order.

Now I have a clearer picture. Depending at which point of the transition the interface is studied you will see changing mechanical/electronic/thermal conductivity properties. João provided very nice examples what will happen if you play with dopants and deposition rates. Properties of this transition boundary nearly always represent a trade off between those of liquid and solid and will depend on the chemical composition, thickness and transition kinetics (I'm far from being a purist but thermodynamically speaking this transition layer is not a phase). I usually imagine this process as tiding up a messy oriented and distributed molecules back to their places shown by the global free energy minimum at given thermodynamic conditions. As with any tiding scheme there are many ways to do it, at different rate and through various stages.

To understand such transition the first choice would be checking out published work to see what one may expect (I know it is trivial but still better than reinventing a wheel). Then move to spectroscopic methods Raman/IR/UV/EXAFS/XANES that show you a shift of vibration modes or change in coordination from your amorphous starting material to a fully crystalline product. Here you can have already first gimps on what is going on in the interface. A skilled chemist may be already able to derive a general picture of the interface. Yet, without additional information from MD/MC modeling it may be still very difficult. 

From the crystallographic point of view an amorphous-to-crystalline transition nearly always go through a multiple nucleation events leading to the initial very high number of fine crystals. Depending on the nucleation rate and uniformity you may have well defined or broad crystal size distribution. At the same time formed crystals will undergo so called "coarsening" on the rate specific to p-T conditions that is again a fight to lower the free energy of the system. SAXS may be a nice tool to study the kinetics of the crystal size change as a function of time/p-T/reagent/dopant. I think the upper limit was a several hundreds of nm. For bigger crystals you will have to go for some other methods like X-ray diffraction (Scherrer broadening or more advanced crystal size determination) or visual like TEM.

Vladimir is a very good point.

Generally, it interests me influence on the magnetic properties but am open to reading other explanations regarding other materials.

We are interested in the change of properties of amorphous ferromagnetic microwires at different heat treatments. It was noticed a strong change in K, Hc due to the formation of nanocrystalline structures in amorphous phase. However, a detailed study has not yielded reliable results. Our research continues