## 3 Results and Discussions
### Modeling of Layer Growth Kinetics  
Figure 8 shows the modeling of layer growth kinetics and the relative unit cells during the B atoms' diffusion into titanium. When B atoms diffuse into titanium, a TiB\({}_{2}\) layer is formed on the surface first. TiB\({}_{2}\) is a hexagonal crystal system, C32 structure, space group is P6/mmm, the number of molecules contained in the Bravais lattice unit cell is M = 1. The origin is at the center of symmetry, and the lattice constant at room temperature is  
Figure 7: SEM images and EDX line analysis of cross-sections of samples with boriding temperatures of (**a**) 950 \({}^{\circ}\)C, (**b**) 1050 \({}^{\circ}\)C, and (**c**) 1150 \({}^{\circ}\)C.  
a = 0.304 nm, b = 0.304 nm, and c =0.322 nm. The relative unit cell structure model of TiB\({}_{2}\) is shown in Figure 8. As bording time increases, B atoms diffuse to the inside to form a TiB layer. TiB is an orthorhombic crystal system, B27 structure, space group Pnma, the lattice constant at room temperature is a = 0.305 nm, b = 0.456 nm, and c = 0.612 nm. The relative unit cell structure model of TiB is shown in Figure 6. The unit cell structure model of Ti has two types. When the bording temperature is below phase transition temperature, Ti is \(\alpha\)-Ti, space group is P63/mmc, and the lattice constant at room temperature is a = 0.293 nm, b = 0.293 nm, and c = 0.466 nm. When the bording temperature is above phase transition temperature, Ti is \(\beta\)-Ti, space group is Im3-m, and the lattice constant is a = 0.282 nm, b = 0.282 nm, c = 0.282 nm. Based on the results of the experiment, a uniform continuous TiB\({}_{2}\) layer was formed on the surface, and active B atoms in the molten salt bath further diffused into the substrate through the TiB\({}_{2}\) layer to form a needle-like TiB phase, which formed a two-phase composite sublayer structure with the remaining Ti substrate. The structure formation of the composite bordic layer was determined by the thermodynamic and kinetic processes of the reaction of Ti and B. The outermost layer was uniform and continuous, and the two sub-layers (TiB whisker layer + Ti substrate) maintained the bordiced layer structure in the crystallographic orientation relationship. Diffusivities of B in TiB\({}_{2}\) and TiB phases were determined from the research of B. [PERSON] et al. [34]. In that study, the diffusivities of B in TiB\({}_{2}\) and TiB were expressed with the following formula:  
\[D_{B}=D_{0}\exp\left(-\frac{Q}{RT}\right) \tag{8}\]  
R = 8.314 J\(\cdot\)mol\({}^{-1}\cdot\)K\({}^{-1}\), where \(Q\) and \(D_{0}\) values for B diffusion in TiB\({}_{2}\) are 187.1 kJ mol\({}^{-1}\) and 6.8 \(\times\) 10\({}^{-8}\) m\({}^{2}\) s\({}^{-1}\), respectively. The corresponding values in the TiB phase are 190.4 kJ mol\({}^{-1}\) and 437.6 \(\times\) 10\({}^{-8}\) m\({}^{2}\) s\({}^{-1}\), respectively. These values were determined from the research of [PERSON] [PERSON] et al. [34]. Table 4 presents the B diffusivities in the bordic phases with different bordic temperatures used in the present calculations. As shown in Table 4, the diffusion rate of B became faster with the bordic temperature increasing. In addition, when the processing temperature was higher than 950 \({}^{\circ}\)C (such as 1050 \({}^{\circ}\)C and 1150 \({}^{\circ}\)C), the diffusion rate of B in TiB and TiB\({}_{2}\) was much higher than when the processing temperature was 950 \({}^{\circ}\)C. It is the reason why TiB had no obvious needle-like structure at this processing temperature. Comparing the diffusion rate of B in TiB and TiB\({}_{2}\), it was found that the diffusion rate in TiB was higher than that in TiB\({}_{2}\) at the same bordic phase. Figure 8: Schematic of growth of the hardened layer (the TiB\({}_{2}\) outermost layer and the TiB whisker sublayer) and the unit cells corresponding to TiB\({}_{2}\), TiB, \(\alpha\)-Ti, and \(\beta\)-Ti, respectively. temperature. [PERSON] et al. also found that the diffusion rate of B in TiB is higher than that in TiB\({}_{2}\)[35].