# Thermal Behavior of Single-Crystal Diamonds Catalyzed by Titanium Alloy at Elevated Temperature
## 3 Results and Discussion of Thermal Analysis Experiments
### Thermodynamic Analysis of Diffusion Wear of Diamond Tools  
Diffusion flux is the flow of diffused material through a unit cross-sectional area perpendicular to the direction of diffusion per unit time. The first law of diffusion states that the diffusion flux is proportional to the concentration at the cross section, and the larger the concentration gradient, the larger the diffusion flux. Hence, as long as there is a concentration difference, diffusion between atoms will occur, and the higher the temperature, the greater the diffusion rate. In the cutting process, the diamond tool is always in close contact with the fresh surface of the workpiece. Under the action of cutting heat and concentration gradient, the carbon atoms in the diamond tool will diffuse into the titanium alloy workpiece. At the same time, during the cutting process, the continuous flow of the workpiece material in the cutting deformation zone keeps a large diffusion flux between the contact interfaces, and the strong plastic deformation of the workpiece material increases the dislocation density and the void. This further increases the diffusion of the tool material. At a certain temperature, if the concentration of the diffusion element in the workpiece material exceeds its solubility, the diffusion element from the tool material will react with the workpiece material, and the diffusion reaction will be converted into a chemical reaction. Among the factors influencing the interdiffusion of tool and workpiece during the cutting process, temperature is the main factor, and its influence level is greater than the influence of the metal lattice structure. Therefore, Gibbs free energy can be used to judge the law of diffusion of tool materials [11]. Through the calculation, the correct change law can be obtained, and the diffusion wear of the diamond tool can be qualitatively analyzed [12]. The free energy of diamond tool material can be calculated as follows [13]:  
\[\Delta G_{f}^{0}=\Delta G^{XS}+RTlnc \tag{1}\]  
where \(\Delta G^{XS}\) is the excess free energy of diamond tool materials in titanium alloy materials; \(\Delta G_{f}^{0}\) is the free energy generation of diamond tool material; T is the temperature; R is the universal gas constant; c is the solubility of diamond tool material in workpiece material. According to the reverse method [14], the excess free energy of carbon in the titanium alloy at 920 \({}^{\circ}\)C is 39.727 kJ/mol, which calculated by the Equation (2). The solubility of diamond tool materials in titanium alloy at different temperatures can be obtained by substituting this value into Equation (2) with the data in Table 1, as shown in Table 2.  
Figure 5: Micromorphology and EDS analysis of experimental surface of titanium alloy in air. (a) Micromorphology; (b) EDS analysis. According to Equation (1), c can be calculated as follows:  
\[c=e^{\frac{\Delta\Omega_{f}^{\Theta}-\Delta C^{\text{KS}}}{RT}} \tag{2}\]  
In the Ti-6 Al-4V, the mass of \(\alpha\)-titanium accounts for 80% of the total mass, so the solubility of the diamond tool material in \(\alpha\)-titanium is mainly considered. Carbon has a solubility of 1% in \(\alpha\)-titanium at 920 \({}^{\circ}\)C [15] Diamond is a metastable lattice structure of carbon, and graphite is a stable lattice structure of carbon. Under certain conditions, the crystal lattice of carbon atoms in diamonds is automatically converted into a graphite structure, that is, graphitization of diamond. At the same time, since the carbon atoms in the diamond are arranged in a denser arrangement than the carbon atoms in the graphite structure, the diffusion of carbon atoms is bound to occur after the graphitization of the diamond [6]. The Gibbs generation free energy of carbon in diamond tools at different temperatures is calculated by the first approximate equation of Gibbs-Helmholtz as Equation (3) [16], that is, the Gibbs generation free energy of diamond into graphite.