## 3 Results and Analysis
### Boronization Kinetics Analysis  
According to the Arrhenius equation, the relationship between the penetration time, the thickness of the penetration layer, and the growth coefficient can be written as the following Equation (1) [16].  
\[X^{2}=Gt \tag{1}\]  
where \(X\) is the thickness of the boronizing layer (um), \(G\) is the growth coefficient (m\({}^{2}\cdot\)s), and \(t\) is the boronization time (s).  
From the Arrhenius equation can get Equation (2) [16], where \(T\) is the absolute temperature (K), \(Q\) is the diffusion activation energy (J mol), \(R\) is the gas constant (J\(\cdot\)(mol\(\cdot\)k)\({}^{-1}\)), and \(G_{0}\) is the diffusion constant (m\({}^{2}\cdot\)s),  
\[\ln G=\ln G_{0}-\frac{Q}{R}\frac{1}{T} \tag{2}\]  
From Equations (1) and (2), the growth coefficient and diffusion activation energy at different rare earth can be obtained as shown in Table 7, The growth coefficients under different rare earth CeO2 contents can be obtained from Equations (1) and (2), as shown in Table 7. The relation curve of diffusion activation energy \(LnG\) and \(1/T\) is shown in Figure 3, where K represents the absolute temperature (K1123 = 850 \({}^{\circ}\)C, K1173 = 900 \({}^{\circ}\)C, K1223 = 950 \({}^{\circ}\)C, K1273 = 1000 \({}^{\circ}\)C).  
It can be seen from Figure 3 that the linear slope at 2% of rare earth content is greater than 4%, and the slope at 4% is almost parallel to that at 6%, indicating that the diffusion activation energy of boron atom changes when the rare earth content increases from 2% to 4%, while there is basically no change from 4% to 6%. Table 8 shows the activation energy of different contents of rare earth CeO2, 160.70 kJ/mol at 2%, 143.94 kJ/mol at 4% and 143.16 kJ/mol at 6%. It can be found from Table 7 that when the content of rare earth CeO2 increases from 2% to 4%, the diffusion activation energy decreases by 16.76 kJ/mol (relative decrease of 10.4%), and when the content of rare earth CeO2 increases from 4% to 6%, the diffusion activation energy only decreases by 0.78 kJ/mol (relative decrease of 0.54%), which is not obvious [18].  
It shows that when rare earth CeO2 increases from 4% to 6%, the effect of further promoting boron atom diffusion is very small, so the increase of infiltration layer thickness is also very small. This also shows that the utilization rate of rare earth decreases significantly when the content of rare earth is further increased.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Condition** & & **Growth Factor (m\({}^{2}\cdot\)s)** \\ \hline
2\% CeO2 & K1123 = 3.36 \(\times\) 10\({}^{-14}\) & K1173 = 1.23 \(\times\) 10\({}^{-13}\) & K1223 = 2.03 \(\times\) 10\({}^{-13}\) & K1223 = 2.42 \(\times\) 10\({}^{-13}\) \\
4\% CeO2 & K1123 = 6.67 \(\times\) 10\({}^{-14}\) & K1173 = 2.26 \(\times\) 10\({}^{-13}\) & K1223 = 3.5 \(\times\) 10\({}^{-13}\) & K1223 = 3.91 \(\times\) 10\({}^{-13}\) \\
6\% CeO2 & K1123 = 7.56 \(\times\) 10\({}^{-14}\) & K1173 = 2.34 \(\times\) 10\({}^{-13}\) & K1223 = 3.8 \(\times\) 10\({}^{-13}\) & K1223 = 4.33 \(\times\) 10\({}^{-13}\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Growth factors at different rare earth (CeO2) contents.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline  & **CeO2 2\%** & **CeO2 4\%** & **CeO2 6\%** \\ \hline Diffusion activation energy (J/mol) & 160.70 & 143.94 & 143.16 \\ Relatively reduced diffusion activation energy (J/mol) & Contrast value & 16.76 & 0.78 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Reduction of activation energy with different contents of rare earth CeO2.  
Therefore, this theoretically shows that the content of rare earth CeO\({}_{2}\) of 4% is an ideal proportion.