## 3 Results  
The exemplary results of the performed experiments, including changes of nitriding degree, gas-phase hydrogen concentration and relative magnetic permeability (RMP) during the nitriding at 350 \({}^{\circ}\)C as functions of time, are presented in Figure 1. RMP is defined as follows:  
\[RMP=\frac{\mu_{N}}{\mu_{P}} \tag{1}\]  
where \(\mu_{P}\) (marked in Figure 2b) is the counterpart, whereas \(\mu_{N}\) means the value of bridge voltage recorded for the iron sample during its nitriding. The measured nitriding reaction rate can be described as follows [77]:  
\[ \begin{split}\frac{dx^{y}(t)}{dt}=\sum_{i=min}^{i=max}n_{i}^{b}N _{i}\Big{[}\frac{dx^{y}(t)}{dt}\Big{]}_{i}=\sum_{i=min}^{i=max}n_{i}^{b}N_{i} \Big{[}\frac{dt^{y}(t)}{n_{i}^{b_{i}}dt}\Big{]}_{i}=\\ =\sum_{i=min}^{i=max}f(CVD)\Big{[}\frac{dt^{y}(t)}{dt}\Big{]}_{i}=\frac{d(n_{N}/n _{F_{i}})}{dt}=\frac{da}{dt}\end{split}  \tag{2}\]  
where n\({}_{i}\)b--number of moles of nitrogen in i-th nanocrystalline volume, N\({}_{i}\)--number of i-th nanocrystallites, CVD--nanocrystallite volume distribution (determined using the chemical method described in [79]), n\({}_{N}\)/n\({}_{Fe}\) (in short \(\alpha\))--nitriding degree of nanocrystalline iron (ratio of moles of nitrogen, n\({}_{N}\), to moles of iron). Based on the measurements of the catalyst weight changes, the nitriding reaction rate, d(n\({}_{N}\)/n\({}_{Fe}\))/dt, and relative magnetic permeability changes, dRMP/d\(\alpha\), viz. the change in relative magnetic permeability with the change in nitriding degree, \(\alpha\) (which is a property of the tested substance), were determined and presented as a dependence on the catalyst nitrogenization degree, \(n_{N}\)/n\({}_{Fe}\) [mol of nitrogen/mol of iron], in two areas, \(\gamma\)'r and \(\gamma\)'k, in Figure 2. Enlargement of a fragment of the above Figure--increasing the relative magnetic permeability in the field of phase change \(\alpha\rightarrow\gamma\)' depending on the degree of nitriding of the catalyst is presented in Figure 2b. Figure 1: Nitriding degree, relative magnetic permeability (RMP), and concentration of hydrogen in the gas phase as functions of time during nitriding reaction. The blue color shows the bimodal size distribution of iron nanocrystallites according to their volume in the range of sample reaction \(n_{\rm N}/n_{\rm Fe}\) = 0.00-0.25 mol/mol, consisting of two sets of nanocrystallites, marked as \(\gamma^{\prime}{}_{\rm r}\) and \(\gamma^{\prime}{}_{\rm k}\), differing in the active specific surface, A, 0.10 nm\({}^{-1}\) (in the range of 0.07-0.15 nm\({}^{-1}\)) and 0.05 nm\({}^{-1}\) (in the range of 0.04-0.08 nm\({}^{-1}\)), respectively [69]. The phase change occurs in direct proportion to the S/V of the nanocrystallites in order from the largest to the smallest [58]. The specific active surface is the ratio of the active area, \(S_{\rm a}\), to the iron nanocrystallite volume, V, in the sample, A = \(S_{\rm a}\)/V, and is equal to the sum of the areas for the i-th iron nanocrystallites \(A_{\rm i}\) = \(S_{\rm a,i}\)/V\({}_{\rm i}\) [nm\({}^{-1}\)] (can be also expressed in [mol/mol] units when: \(S_{\rm a,i}\) represents number of moles of active sites on the catalyst surface [mol] equal to the total number of moles of surface iron atoms minus the number of these atoms occupied by promoters; V\({}_{\rm i}\) represents moles of iron in the volume of a nanocrystallite [mol]). The iron surface is mainly wetted by a two-dimensional layer of groups of surface potassium oxide Fe-O-K, and an active surface is formed [91]. We have two sets of nanocrystallites with different active specific surfaces due to the processes during the reducing of the iron catalyst precursor [92]. The distribution is bimodal and proportional to the rate of the chemical reaction, and the active specific surface area is the proportionality factor [93]. In terms of the formation of the \(\gamma^{\prime}\) phase, there are two areas of \(\gamma^{\prime}{}_{\rm r}\) and \(\gamma^{\prime}{}_{\rm k}\) (points 0-1 and 1-2).