## 1 Introduction  
Boronization is a widely used thermochemical surface treatment technology to improve the friction and wear properties of metal materials. It can increase the hardness, up to 1400-2000 HV, of metal surfaces and enhance the corrosion resistance of metal surfaces, so it is more advantageous than carburizing and nitriding [1; 2; 3]. H13 steel is an air-cooling hardening hot working die steel with good strength and toughness. It is one of the most widely used in the manufacture of hot extrusion die, mandrel, hot forging die, and aluminum, copper, and its alloy die casting die. Its composition is shown in Table 1. In order to improve the surface properties of H13, quenching, tempering, ion nitriding, and other methods are generally used, but the effect of these conventional treatments often cannot meet higher and higher application requirements. Boronizing the parts of this material can improve its surface hardness and wear resistance so as to improve the service life of the die [4; 5; 6]. During the boronizing process, the structure and properties of the boronizing layer can be significantly improved by adding different elements such as rare earth, Cr, and Al for composite boronizing treatment. It has been found that the addition of rare earth can improve the microstructure and properties of boronizing layer and increase the boronizing rate [7; 8; 9].  
To understand the boronizing kinetics is of scientific and industrial importance (for example, [9; 10]). It is found that the addition of rare earth in the boronizing process can reduce the diffusion activation energy required by boron atoms during boronizing, so as to improve the effect of boronizing layer and improve boronizing efficiency. Since the radius of a rare earth atom is larger than that of an iron atom, the \(\gamma\)-Fe lattice is deformed and crystal defects are increased, which provides a channel for the diffusion of active boron atoms into the material and accelerates the diffusion speed of active boron atoms into the material, so as to reduce the diffusion activation energy of active boron atoms. For example, in [11; 12], the addition of rare earth Nd\({}_{2}\)O\({}_{3}\) (5%) reduced the diffusion activation energy from 184 kJ/mol to 122 kJ/mol in 45 steel and from 261 kJ/mol to 155 kJ/mol in T12 steel, which reduced the diffusion activation energy by 34% and 41% respectively, and significantly improved the boronizing efficiency. Therefore, boronizing kinetic analysis for different steel materials is a very valuable method to reveal the boronizing process.  
Rare earth additives used for boronizing mainly include CeO\({}_{2}\), La\({}_{2}\)O\({}_{3}\), Nd\({}_{2}\)O\({}_{3}\), etc. Among them, CeO\({}_{2}\) has higher oxidation and strong adsorption performance and is easy to prepare. Therefore, CeO\({}_{2}\) is a valuable boronizing additive, which can effectively improve the microstructure of boronizing layer. Its application in boronizing with 5% rare earth(CeO\({}_{2}\)) of high entropy alloy AlCoCuFeMnNi can make the alloy hardness change in gradient between 260-420 HV\({}_{0.2}\) and stabilize at about 400 HV\({}_{0.2}\)[13; 14; 15]. For titanium alloy TC21, after boronizing with rare earth CeO\({}_{2}\), the wear rate of boronizing sample is 50-60 times lower than that of non boronizing sample [14; 16]. In addition, adding metal elements such as aluminum (Al) and chromium (Cr\({}_{2}\)O\({}_{3}\)) during boronizing is conducive to further improve the microstructure of boronizing layer and reduce the brittleness of boronizing layer [17].  
In this paper, compound boronizing with rare earth CeO\({}_{2}\) and chromium(Cr\({}_{2}\)O\({}_{3}\)) for H13 steel is studied, and the effects of different proportions of rare earth CeO\({}_{2}\) in boronizing agent on the diffusion activation energy of H13 steel and the properties of boronizing layer are analyzed in order to provide a basis for further improving the properties of H13 steel.