## 5 Conclusions  
The phase transformation process \(\alpha\rightarrow\gamma^{\prime}\) is an isothermal-isobaric process and takes place when the nanocrystallites reach the critical concentration of nitrogen in iron and the sum of Gibbs free energy of chemisorbed nitrogen on the surface and dissolved in the volume of an iron nanocrystallite compensates the Gibbs free energy of deformation of the unit cell volume of the \(\alpha\)-iron phase. In the kinetic region, the nitrogen potential on the surface is constant and greater than the molar critical potential, the rate limiting step of the process is diffusion through the phase boundary of a single crystal, and the achievement of the critical concentration depends on the crystal volume. The diffusion activation energy is defined by the process enthalpy, which is the difference between the chemical potential of a chemisorbed nitrogen atom on the surface and chemical potential of this atom in the volume of iron. The diffusion coefficient is directly proportional to the degree of nitriding at exponentially changing activation energy. In the nitriding process, nanocrystallites react in their entire volume in the order from the smallest to the largest, which is proportional to the volume of the crystals and inversely proportional to the specific active surface. The tested catalyst has a bimodal structure consisting of two sets, both from the point of view of the active surface area of the crystal and changes in magnetic permeability. The difference in sets may be due to a change in the concentration of promoters on the  
Figure 8: Dependence of the diffusion coefficient and the Gibbs free energy of nitrogen dissolution in iron volume (**a**) and dependence of \(\alpha\)-iron unit cell volume (**b**) on RMP (blue points—stationary conditions, red points—kinetic measurements). cataly surface. This dependence is related to the change in the diffusion rate related to the changes taking place in the crystal volume. These sets are related to the different diffusion mechanisms in \(\alpha\rightarrow\gamma^{\prime}\)r and in \(\gamma^{\prime}\)k \(\rightarrow\varepsilon_{\tau}\) solutions and with step changes in the parameters of the crystal lattice, depending on the crystal size and the degree of nitriding \(\alpha\rightarrow\gamma^{\prime}\)k:  
* \(\alpha\)\(\rightarrow\)\(\gamma^{\prime}\)r (smaller nanocrystallites, relative magnetic permeability of 1.02); the dependencies typical for solutions are observed; the relationships of diffusion coefficient and unit cell volume are linear, with negligible variation in the diffusion coefficient, the volume of unit cells, and relative magnetic permeability,
* \(\alpha\)\(\rightarrow\)\(\gamma^{\prime}\)k (bigger nanocrystallites, relative magnetic permeability of 1.00); the relationships are also described by a linear function with a significant variation in the diffusion coefficient, the volume of unit cells, mean size of nanocrystallites, and relative magnetic permeability. In the \(\gamma^{\prime}\)k area, changes are observed that indicate step changes in the crystal lattice. * \(\gamma^{\prime}\)k\(\rightarrow\)\(\varepsilon_{\tau}\): in the range of nitriding degree of 0.25-0.45 mol/mol there is a phase transformation of iron nitride \(\gamma^{\prime}\)-Fe\({}_{4}\)N to the \(\varepsilon_{\tau}\)-Fe\({}_{3}\)N solution with concentration x = 0.45 mol/mol in the order of the crystal size from the smallest to the largest, with an approximately constant value of the relative magnetic permeability of 0.42. With the further nitriding process, only the nitrogen concentration in the solution phase \(\varepsilon_{\tau}\) increases. Based on the obtained results, we anticipate that the performed experiments and possibilities offered by the apparatus used will open new perspectives of investigations in such fields of knowledge as heterogeneous catalysis, materials engineering, sensorics, etc.