## 3 Results and Discussions
### Composition and Microstructure
Under this condition, the Gibbs free energy of the reaction shown in Equations (3) and (4) was more negative than that of 1/2 Ti + B \(\rightarrow\) 1/2 TiB\({}_{2}\) (see Table 3) with the same boron content, which meant that boron affinity potential with titanium of TiB was larger than that of TiB\({}_{2}\), indicating that TiB was more easily formed than TiB\({}_{2}\) in the region with lower boron content in the bulk of the samples. Figure 7 shows SEM micrographs and EDX line analysis results of cross-sections of the treated layer of the titanium substrates borided at different boriding temperatures. A light gray double-borided layer composed of monolithic TiB\({}_{2}\) and needle-like TiB whiskers was observed under the surface. No lack of discontinuity and adhesion between the breaker layer and the substrate was observed. This shows that the whisker-like TiB firmly fixed the boride layer on the substrate. This dual layer with higher boron content at the surface was consistent with the thermodynamic results. Previous studies [29; 30; 31; 32; 33] showed that TiB has a B27 structure, which makes the growth rate of TiB along the [010] direction faster than along the other crystal directions. In the B27 structure, the zigzag B chain and the Ti channel without B are parallel to the [010] direction. Therefore, based on the periodic bond chain theory, TiB grows faster in the [010] direction than the other directions, such as [101] and [100], making TiB morphologically needle-like or whisker-like. TiB\({}_{2}\) has a simple hexagonal structure with a graphite-like B layer perpendicular to the [001] direction, which indicates that the growth rate of TiB\({}_{2}\) along the [001] direction is slower than that along the [100] or [010] direction. Therefore, the morphology of TiB\({}_{2}\) is layered perpendicular to the [001] direction. From Figure 7, the thickness of the total borided layer (TiB + TiB\({}_{2}\)) produced at 1150 \({}^{\circ}\)C in this study was about 30 \(\upmu\)m, which consisted of a 7.5 \(\upmu\)m-thick continuous and smooth monolithic TiB\({}_{2}\) layer, with the remainder consisting of TiB whiskers. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Boriding** & **TiB (Equation (3))** & **TiB (Equation (4))** & **TiB\({}_{2}\)** & **1/2 TiB\({}_{2}\)** \\
**Temperature/\({}^{\circ}\)C** & & & & \\ \hline
950 & \(-\)157.952 & \(-\)38.151 & \(-\)265.922 & \(-\)132.961 \\
1050 & \(-\)157.685 & \(-\)37.241 & \(-\)264.478 & \(-\)132.239 \\
1150 & \(-\)157.418 & \(-\)36.331 & \(-\)263.034 & \(-\)131.517 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Standard Gibbs free energy of the boronation reaction with different boriding temperatures (Under 1 mol boron content condition, the Gibbs free energy of the reaction can be defined as the boron affinity potential with titanium). As the boriding temperature increased, the apparent improvement in the boriding of Ti was attributed to the composition and the content of the boriding mixture. The reactions producing B atoms from sodium tetraborate and aluminum in the crucible are shown below. \[\text{Na}_{2}\text{B}_{4}\text{O}_{7}\to 2\text{B}_{2}\text{O}_{3}+\text{Na}_{2} \text{O} \tag{5}\]  
\[2\text{B}_{2}\text{O}_{3}+4\text{Al}\to 4\text{B}+2\text{Al}_{2}\text{O}_{3} \tag{6}\]  
\[\text{Na}_{2}\text{B}_{4}\text{O}_{7}+4\text{Al}\to 4\text{B}+2\text{Al}_{2}\text{O}_{3}+ \text{Na}_{2}\text{O} \tag{7}\]  
The TiB layer contained high-aspect-ratio whiskers inclined with respect to the substrate surface, some with a length of a few micrometers. Beneath this layer, we observed some discontinuous TiB particles, suggesting that some whiskers grew almost perpendicular to the surface (Figure 7). Additionally, comparing the SEM images of samples produced at 1050 \({}^{\circ}\)C and 1150 \({}^{\circ}\)C (Figure 7b,c, respectively), it was found that the thickness of the TiB\({}_{2}\) layers was similar.