## 3 Results and Analysis
### Thickness and Microhardness of Boronizing Layer with Rare Earth Addition  
In order to investigate the process of rare earth boronizing and analyze the boronizing kinetics, Table 5 lists the thickness of boronizing layer under different rare earth content and temperature when rare earth CeO\({}_{2}\) is added to boronizing agent and boronizing time is 4 h. Figure 1 is the variation curve of different rare earth content, boronizing temperature and boronizing layer thickness with a boronizing time of 4 h.  
From the comparison between Tables 3 and 5, it is easy to find that the boronizing layer thickness increases greatly with the addition of rare earth CeO\({}_{2}\). For example, when the boronizing temperature is 950 \({}^{\circ}\)C and the boronizing time is 4 h, the thickness of the boronizing layer increases from 42 \(\upmu\)m when rare earth is not added to 71 \(\upmu\)m when rare earth is 4%. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Time** & **850 \({}^{\circ}\)C** & **900 \({}^{\circ}\)C** & **950 \({}^{\circ}\)C** & **1000 \({}^{\circ}\)C** \\ \hline
2 h & 623.46 HV & 635.12 HV & 646.06 HV & 665.32 HV \\
3 h & 612.45 HV & 626.09 HV & 723.47 HV & 684.16 HV \\
4 h & 604.78 HV & 678.32 HV & 1246.90 HV & 1133.42 HV \\
5 h & 632.60 HV & 667.06 HV & 1136.05 HV & 1068.30 HV \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Hardness of penetration layer at different temperature and time (40 \(\upmu\)m from the surface of the infiltration layer). Figure 1: The increase of thickness of boronizing layer with solution and temperature (4 h). \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Content** & **Temperature** & **CeO\({}_{2}\) (2\%)** & **CeO\({}_{2}\) (4\%)** & **CeO\({}_{2}\) (6\%)** \\ \hline
1123 K (850 \({}^{\circ}\)C) & 22 \(\upmu\)m & 31 \(\upmu\)m & 33 \(\upmu\)m \\
1173 K (900 \({}^{\circ}\)C) & 42 \(\upmu\)m & 57 \(\upmu\)m & 58 \(\upmu\)m \\
1223 K (950 \({}^{\circ}\)C) & 54 \(\upmu\)m & 71 \(\upmu\)m & 74 \(\upmu\)m \\
1273 K (1000 \({}^{\circ}\)C) & 59 \(\upmu\)m & 75 \(\upmu\)m & 79 \(\upmu\)m \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Thickness of infiltration layer at different temperatures (Boronizing time 4 h). It can be seen from Table 5 and Figure 1 that the boronizing layer thickness increases gradually with the increase of temperature, and at the same temperature, and at the same temperature, with the increase of the content of rare earth CeO\({}_{2}\), the thickness of the boronizing layer also shows an increasing trend. This shows that the increase of rare earth content can promote the infiltration of boron atoms into the bulk material and increase the thickness of boronizing layer [18]. For example, when the boronizing temperature is 950 \({}^{\circ}\)C (1223 K), when the rare earth content increases from 2% to 4%, the boronizing layer thickness increases significantly from 54 \(\upmu\)m to 71 \(\upmu\)m (up to 31.5%). However, when the rare earth content increases from 4% to 6%, the increase of infiltration layer thickness is not obvious (From 71 \(\upmu\)m to 74 \(\upmu\)m, the increase is only 4.2%). This phenomenon will be explained by the boronizing kinetic analysis below. Table 6 shows the microhardness of the boronizing layer with different rare earth CeO\({}_{2}\) content (2%, 4% and 6%) at the boronizing temperature of 950 \({}^{\circ}\)C and boronizing time of 4 h. Figure 2 shows the microhardness curve of the boronizing layer. It can be seen from Table 6 and Figure 2 that the microhardness of each group when the content of rare earth CeO\({}_{2}\) is 4% is greater than that when the content is 2% and 6%. When the content of rare earth is 4%, the hardness at 70 \(\upmu\)m from the surface layer reaches 1546.32 HV, which is significantly higher than that at the same depth when the content is 2% and 6% (662.47 HV and 1125.45 HV, respectively). At the same time, when the rare earth content is 4%, there is little difference in hardness from the surface to 70 \(\upmu\)m