## 4 Discussion
### Kinetics of Phase Transformation
It can be concluded that with the increase in the size of nanocrystallites, their unit cell volume and the diffusion coefficient value decrease and the Gibbs free energy of nitrogen dissolution in iron volume increases. In particular, in the first area \(\gamma^{\prime}\)r (solution, small nanocrystallites), slight changes in both the diffusion coefficient and the unit cell volume are observed. In the second area \(\gamma^{\prime}\)k (large nanocrystallites) there are significant changes in both the diffusion coefficient and the unit cell volume. Figure 5: Dependence of the Gibbs free energies of nitrogen dissolution in iron on nitriding degree of the catalyst. In the study [96], the mean size of nanocrystallites and the interplanar distances were measured, so it is possible to correlate the current results with the results from the previous work (Figure 7). The dependence of the nitrogen diffusion coefficient in nanocrystalline iron on the mean size of the nanocrystallites, \(\mathrm{d_{m}}\), can be described by the following equations:  
* for small nanocrystallites and low concentrations (nitrogen solution in the \(\gamma^{\prime}\) lattice) \[\mathrm{D^{S}}=0.03\;\mathrm{d_{m}}+4\]
* for large nanocrystallites and high concentrations: \[\mathrm{D^{S}}=-0.47\;\mathrm{d_{m}}+24\]  
It can be seen that in the area \(\gamma^{\prime}\mathrm{{}_{k}}\) of high nitrogen concentrations, the Gibbs free energy of nitrogen dissolution in iron depends exponentially on the nitrogen concentration in iron. Taking into account the results presented in Figures 5-7, it should be stated that the changes in the nitrogen diffusion coefficient in nanocrystalline iron are related to the Gibbs free energy of nitrogen chemisorbed on the surface dissolution in iron volume. It is this parameter that limits the diffusion rate in the tested system. Moreover, it can be observed that there are areas \(\gamma^{\prime}\mathrm{{}_{r}}\) of nitrogen solution for small nanocrystallites where this enthalpy slightly depends on their size. There are also areas where changes in the structure  
Figure 6: Dependence of the calculated diffusion coefficients \(\mathrm{D^{s}}\) and Gibbs free energies of nitrogen dissolution \(\mathrm{\Delta G_{N_{J}}}^{\mathrm{diss}}\) on the unit cell volume of iron in the sample. Figure 7: Dependence of the diffusion coefficient \(\mathrm{D^{s}}\) on the mean size of nanocrystallites. of nanocrystallites are pronounced, and thus this enthalpy changes. Thus, the Gibbs free energy of nitrogen dissolution is related to the structure of the nanocrystal. Figure 8 shows the dependencies of the diffusion coefficient, the Gibbs free energy of nitrogen dissolution and iron unit cell volume on RMP for two regions of \(\gamma^{\prime}{}_{r}\) and \(\gamma^{\prime}{}_{k}\). From the above figures, it can be concluded that the values of parameters such as unit cell volume, diffusion coefficient, and activation energy of the diffusion process can be determined by measuring the magnetic permeability of the sample during an in situ chemical reaction. It was found [96] that in the nitriding process, carried out using the CPPR method, the unit cell volumes depend on the average size of nanocrystallites. It can therefore be concluded that discontinuity in the values of both the diffusion coefficient, the Gibbs free energy of nitrogen dissolution in iron volume, and magnetic permeability are the result of changes in the structure of iron nanocrystallites as a result of increasing nitrogen concentration in nitrogen solution in nanocrystalline \(\alpha\)-iron and iron nitrides. Among the parameters influencing the speed of the process, the surface structure and active specific surface are also decisive. As a model, we assume two values of the active specific surface A, but this is a simplification, and we should remember that each nanocrystallite may have an individual value of A.