## 4 Conclusions  
This paper shows that the compound boronizing of H13 steel with rare earth CeO\({}_{2}\) is conducive to the diffusion of boron atoms, and can significantly improve the thickness, microhardness, microstructure and wear resistance of boronizing layer. 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 to 71 \(\upmu\)m. The microhardness at the depth of 70 \(\upmu\)m from the surface layer can reach 1546.32 HV. This shows that not only the thickness of the boronizing layer is increased, but also the hardness consistency in the boronizing layer is good, which can effectively improve the surface properties and service life of the boronizing layer.  
The kinetic analysis of rare earth boronizing of H13 steel shows that when the content of rare earth CeO\({}_{2}\) increases from 2% to 4%, the diffusion activation energy decreases by 16.76 kJ/mol (relative decrease of 10.4%), and when the content increases from 4% to 6%, the diffusion activation energy changes very little, only 0.54%. Boronizing kinetic analysis can provide quantitative basis for determining the content of rare earth. The study shows that adding 2% Cr\({}_{2}\)O\({}_{3}\) can obtain better microstructure and wear resistance, since rare earth and Cr\({}_{2}\)O\({}_{3}\) can provide more diffusion channels and strengthen the B-B atomic bond. The research methods and results of this paper can provide reference for rare earth boron-chromium co-infiltration process of carbon steel. Therefore, in order to improve the utilization rate of rare earth and Cr\({}_{2}\)O\({}_{3}\) materials, the content of rare earth CeO\({}_{2}\) of 4% and Cr\({}_{2}\)O\({}_{3}\) of 2% is an ideal proportion. The theoretical analysis and experimental results show that the boronizing kinetic analysis can provide a quantitative basis for determining the  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Wear Time/min** & **Mass Loss of Single** & **Mass Loss of Boronizing** & **Mass Loss of Boronizing** \\  & **Boronizing Sample/mg** & **Sample with Rare Earth Content of 4\%/mg** & **Sample with Chromium Oxide Content of 2\% and Rare Earth of 4\%/mg** \\ \hline
10 & 4.8 & 1.2 & 0.8 \\
20 & 6.6 & 2.5 & 1.7 \\
30 & 9.2 & 3.8 & 2.7 \\
40 & 12.1 & 5.1 & 3.6 \\
50 & 16.7 & 6.9 & 4.8 \\
60 & 22.3 & 9.2 & 6.1 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Mass loss of boronizing samples for the three cases.  
content of rare earth. The research methods and results of this paper can provide reference for rare earth boron-chromium co-infiltration process of carbon steel.  
Conceptualization, S.M., Y.Z., B.L. and A.G.; methodology, S.M., Y.Z. and Q.Z.; software, Y.Z., Q.Z. and Y.F.; validation, S.M., Y.Z.; formal analysis, Y.Z., Q.Z. and Y.F.; investigation, Q.Z., Y.F.; resources, S.M.; data curation, Y.Z., Y.F.; writing--original draft preparation, Y.Z., S.M.; writing--review and editing, S.M., Y.Z.; visualization, S.M., Y.Z.; supervision, S.M.; project administration, S.M.; funding acquisition, S.M. All authors have read and agreed to the published version of the manuscript.  
This work was supported by The Science and Technology Program of Hubei Province (No.2019 AE011, 2018 AAA036) and The National Science Foundation of China of China (No.51175385).  
The study did not involve humans or animals.  
The study did not involve humans.  
Data Availability Statement: Data is contained within the article.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.