In this paper, the first principle method based on density functional theory is adopted to establish the interface model of WC/WC-Co through the software Materials Studio (MS). On the basis of this interface structure, rare earth element Y is doped, and then the energy of WC/WC-Co before and after doping is calculated respectively. The electronic structure is analyzed, and the calculation results of the two structures are compared. Finally, the grain growth is simulated by cellular automata of matlab to verify our calculation and analysis results. The results show that the interfacial adhesion work increases and the interface structure is more stable after doping Y element. The interface energy decreases and plays a role in grain refinement.
Cemented carbide is widely used to make cutting tool materials, because it is characterized by strong wear, high bending, compression load, high temperature, and serious fatigue . Cemented carbide WC-Co has been widely used in military, aviation, automobile, marine, petrochemical, mining, and electronics. With the continuous improvement of requirements of machining technology, the requirements for tool material properties are also gradually improving. Therefore, we need to adopt some methods to continuously improve the performance of cemented carbide tool materials .
Cemented carbide is prepared by powder sintering. The uncontrolled growth of a few crystals is harmful to the mechanical properties . It is well known that the mechanical properties of WC-Co cemented carbide, such as hardness, bending strength, and toughness, mainly depend on the grain size. As the grain size of WC decreases to submicron or nanoscale, its hardness increases. Therefore, the size of WC crystal has a great influence on the mechanical properties of WC-Co . Adding grain growth inhibitors, such as Cr3C2, VC, and rare earth oxides, is a common method to prepare ultrafine grain cemented carbide . Adding tiny amounts of rare earth elements to cemented carbide can improve the mechanical properties, which cannot only produce the effect of oxide dispersion strengthening, but also inhibit the growth of WC grains in the sintering process, to prolong the service life of the product . Wang, Lin, and other researchers [7,8] hold the idea that adding an appropriate amount of Ce, Y, and other rare earth elements could refine the grains and improve the comprehensive properties of cemented carbide, which was confirmed by the experimental results.
There are two main methods to study the interface in WC-Co alloy . One is microscopic analysis based on scanning electron microscope (SEM) and other images [10–14]. The other is the theoretical calculation based on the first principle. Due to the complexity of the interface, there are few reports about the doped WC-Co system in the study of cemented carbide interface based on the first principle in the world. At the beginning of the 21st century, Jaffrey et al. [15,16] used WC/WC interface to replace all Co/WC interfaces for first principle research and concluded that the grain boundary segregation of Co improved the grain boundary adhesion of WC/WC, and the mixing of C and Co would stabilize the surface of tungsten carbide. In recent years, there are less research on the interface calculation of adding rare earth elements to cemented carbide. Rare earth element doping in metal matrix composites can potentially improve the wettability between metal matrix and reinforcement and achieve the effect of grain refinement. This will improve the adhesion between surfaces and the overall mechanical properties of the composites.
Therefore, WC (0 0 0 1) and WC (1 −2 1 0) cross sections of cemented carbide were made by first principle software in this paper. The interface model of WC/WC-Co was established. Based on this interface, rare earth element Y was doped to study the effect of Y on WC/WC-Co interface. Density functional theory (DFT) and first principle calculation (FPC) methods were used to calculate and compare the parameters such as interfacial adhesion work, interfacial energy, and electronic structure before and after doping, to study the grain refinement mechanism of WC-Co. Cellular automata (CA) was used for simulation to verify our calculation and analysis results.
2 Calculation Model and Method
2.1 Analysis and Establishment of Model.
The research shows that WC (0 0 0 1)/WC (1 −2 1 0) is the most stable state in WC interface bonding. Two surface models of WC (0 0 0 1) and WC (1 −2 1 0) were established, respectively, as shown in Figs. 2(a) and 2(b). Bramfitt mismatch theory points out that in the heterogeneous nucleation process, the nuclear with mismatch degree δ < 6% is the most effective, 6% < δ < 12% is moderately effective, and mismatch degree δ > 12% is invalid . According to the optimized surface model of Cambridge sequential total energy package (CASTEP), it was found that the mismatch degree of lattice constant between WC (0 0 0 1) and WC (1 −2 1 0) is too large, so we carried out lattice vector rotation transformation on the box of WC (0 0 0 1) surface.
According to Fig. 1, a and b are the lattice constants of WC (0 0 0 1), respectively. The black line can be regarded as the top view of the structure of the original surface. First, the angle of the box needs to be transformed from 120 deg to 90 deg. We can easily find that the angle of 2a + b and b is exactly 90 deg. In other words, after the transformation of matrix , the angle of WC (0 0 0 1) structure can be adapted to WC (1 −2 1 0). We can express it more clearly by calculating in the matrix. The structure after transformation is shown in Fig. 2(c). After transformation, we find that the lattice constant mismatch of the two surfaces is less than 3%, which can be combined very effectively.
In order to reduce the error caused by the number of surface layers during calculation, we used CASTEP to calculate the energy of the two surface structures, and used the surface energy obtained from this energy to test the convergence of the number of slab layers. The test results are shown in Fig. 3. We can find that when the number of surface layers is seven, their energy does not increase and oscillates. According to the convergence test, it is most suitable to make seven-layer surface structure on WC (0 0 0 1) and WC (1 −2 1 0) surfaces, respectively, which is also consistent with the results calculated by Christensen .
The interfacial energy of WC (0 0 0 1) with tungsten surface as bonding surface of 2.1–2.6 J/m2, and that with carbon surface is 3.7–4.4 J/m2 . Generally, the lower the interface energy is, the more stable the interface is . Therefore, we chose the former as the bonding surface to establish the model. Because the position on the interface gap is usually too small to accommodate the cobalt monolayer, the Co atoms enter the interface through replacement. The results showed that Co replaces C atoms on WC (1 −2 1 0) surface to form a monolayer with W and Co on the same surface , i.e., a sub-monolayer of Co. Therefore, the interface model of WC-Co was easy to obtain. It has been concluded that the rare earth element does not been found in WC phase in the microstructure of cemented carbide, while found at the interface between hard phases and Co phase . Therefore, the Co atoms were replaced by the doped rare earth elements. In order to study the effect of rare earth elements at the interface structure of WC-Co, we carried out 2 × 2 × 1 cell expansion and doped with Y element. Therefore, the WC/WC-Co interface model before and after doping Y element was established, as shown in Figs. 4 and 5. A 15 Å vacuum layer was added to the free surface of the above surface and interface models to eliminate the influence of surface atomic interaction.
2.2 Calculation Method.
FPC is a kind of calculation method. It can predict various properties of micro-system and is independent of empirical parameters. Compared with empirical or semi-empirical calculation (theoretically), the FPC only needs the type and arrangement of atoms in elements in the micro-system. The FPC also can use the basic principles of quantum mechanics to calculate the electronic structure and other properties of the micro-system. The CASTEP uses the atomic number and type to predict, including lattice constant, structural properties, energy band structure, solid-state density, charge density, and so on .
The CASTEP based on DFT was used to calculate the surface structure of WC-Co and WC-Co doped Y element in the first principle. The Perdew–Burke–Emzerh of (PBE) approximation in the generalized gradient approximation (GGA) was used to deal with the exchange correlation energy between electrons in the model . The convergence of total energy was calculated by self-consistent iterative method (SCF), and the energy before and after doping rare earth elements was calculated respectively. In the calculation, the plane wave cutoff energy Ecut was set to 400 eV, and the value of the k-point was 4 × 7 × 1. The value of k-point of the supercell was 2 × 3 × 1. To ensure the complete convergence of system energy and cell configuration at the plane wave basis level. We set the SCF self-consistent convergence accuracy to 10−6 eV/atom, the interatomic force convergence standard to 0.1 eV/nm, and the lattice internal stress convergence standard to 0.02 GPa.
3 Results and Analysis
3.1 Interfacial Adhesion Work and Interfacial Energy.
Among them, σ1,2 are the surface energy of slab1, 2 .
After the calculation, the interfacial adhesion work and interfacial energy of WC/WC-Co before and after doping Y element are shown in Table 1.
|System||Before doping||After doping|
|E(0 0 0 1) (eV)||−1.16971066 × 105||−1.16971066 × 105|
|E(1−2 1 0)−Co (eV)||−6.20269827 × 104||−6.11781872 × 104|
|EWCWC−Co (eV)||−1.79015744 × 105||−1.78169429 × 105|
|System||Before doping||After doping|
|E(0 0 0 1) (eV)||−1.16971066 × 105||−1.16971066 × 105|
|E(1−2 1 0)−Co (eV)||−6.20269827 × 104||−6.11781872 × 104|
|EWCWC−Co (eV)||−1.79015744 × 105||−1.78169429 × 105|
The interface bonding strength can be judged by adhesion work and interface energy. Greater adhesion work accompanied by smaller interface energy have stronger interface bonding characteristics. The greater the interfacial adhesion work, the stronger the interfacial bonding. According to Table 1, the interface adhesion work after doping is greater than that before doping, i.e., the interface bonding ability after doping is stronger and the interface bonding is closer. Interface energy is the key to the study of interface stability. The smaller the interface energy is, the more stable the interface bonding is, so the stability of WC/WC-Co/Y is stronger than that of WC/WC-Co.
In Eq. (4), γ is the interface energy, R1, R2 are two radii of curvature of the surface, respectively.
It can be seen from Eq. (4) that the driving force of interface migration changes with the change of interface energy, so the interface energy has an important impact on grain refinement. On the one hand, the larger the interface energy is, the greater the resistance to nucleation is, and the nucleation rate decreases , i.e., the number of crystal nuclei forming a new phase per unit volume per unit time decreases, resulting in accelerated grain growth. On the other hand, the increase of interfacial energy improves the free energy of the system and promotes the growth of grains. After WC/WC-Co material is doped with Y element, the interface energy decreases, the nucleation rate increases, and the free energy decreases, which can achieve the effect of grain growth inhibition and grain refinement.
3.2 Electronic Structure.
The density of electronic states (DOS) is helpful to understand the binding properties of the studied compounds. We analyzed the structural density of states before and after doping to further study the mechanism of grain refinement. DOS diagram and partial density of states (PDOS) diagram can be used to study the dependence of electron energy on K vector along the high symmetry direction in the Brillouin region, and can help to qualitative analyze the material electronic structure. They can also give fast qualitative images describing the electronic structure of materials and sometimes are suitable for the experimental structure directly .
Under the condition of equilibrium geometry, the total DOS before and after doping the Y element and the PDOS of Co atom, Y atom, and its nearby atoms are calculated by PBE functional at the GGA level. The results are shown in Figs. 6 and 7. According to Figs. 6 and 7, both structures show metal characteristics and there are certain metal bonds. According to the PDOS curves of WC/WC-Co and WC/WC-Co/Y, after doping Y element, the W-d orbital density of states tends to widen. The larger the peak span of the DOS, the stronger the delocalization, indicating that the interaction and bonding between the W atom and its nearby atoms in WC/WC-Co/Y are enhanced. The obvious resonance phenomenon of W-d orbit and Y-p orbit shows that there exists interaction between W and Y atoms, which is mainly formed by the hybridization of electrons between the two orbits. Covalent bonds are formed between W and Y atoms, and the dissolution-precipitation of W and C is limited, so the crystal cannot be fully grown. In addition, the W-d orbitals and Co-d orbitals coincide better after doping. The doped structure has more covalent bonds, which is conducive to improving the bond strength and durability. Therefore, after doping, the structure is more stable, the interface adhesion work of the structure is greater, and the interface energy is smaller.
The following analysis will be performed to further study its electronic structure. In this part of the analysis, we can regard WC (1 −2 1 0)-CO and WC (1 −2 1 0)-Co/Y surfaces as adsorption surfaces and WC (0 0 0 1) surfaces as adsorbed surfaces. The d-orbital density of states of WC (1 −2 1 0)-Co before and after doping Y element is shown in Fig. 8(a). The energy of d-orbital increases after doping, so the d-band center of WC/WC-Co/Y becomes higher. As the position of the d-band center increases, the energy of the anti-bonding orbital generated after adsorption will also increase , the electrons will return to the system, and the energy becomes stable. After the d-state of the adsorption surface interacts with the p-state of the adsorbed surface, the p-orbital energy of the adsorbed surface increases (electrons are also occupied on the formed anti-bonding orbital), i.e., the generated anti-bonding orbital is pushed higher. Compared with that before doping, the position of d-band center after doping is higher, so the energy level of anti-bonding p-orbital will also be higher than that before doping, and the surface adsorption after doping is stronger.
The density of states of atomic Co2 in W/Co monolayer before and after doping was analyzed to study the role of Y atom. In Fig. 9(a), it can be found that after adding Y element, each peak in DOS diagram tends to be flat, indicating that its delocalization is enhanced. When electrons are delocalized, the bonding ability must be enhanced, and the bonding is stronger. Therefore, the role of Y atom should be to strengthen the bonding between its nearby atoms.
In order to verify this effect of Y atom, we calculate some interface structures and populations, as shown in Fig. 10 and Table 2. Mulliken’s population can convert the wave function obtained by molecular orbital theory to intuitive chemical information and thus research the electron transfer in molecules, the type and strength of polar chemical bonds, etc. According to Fig. 10 and Table 2, after doping Y element, Co2 and Co3 in the same layer have more covalent bonds, and form new covalent bonds with W22 and W64. At the same time, Co2 and the W atom above it also form more covalent bonds. Based on the analysis of Figs. 9 and 10, it can be inferred that one of the functions of adding Y atoms is to enhance the adsorption performance of the two surfaces and improve the stability of the adsorption interface.
In conclusion, the analysis of electronic density of states and population shows that after doping rare earth elements, the interface adsorption is stronger and the interface is more stable. This is in good agreement with the analysis results of interface adhesion work and interface energy calculated earlier.
4 Grain Refinement Analysis
According to the earlier analysis, the doping of Y element into WC/WC-Co can achieve the effect of grain growth inhibition and grain refinement. The effect of doping element Y on grain refinement of cemented carbide is further analyzed by simulation using CA. Cellular automata, a mathematical model of time discretization, space discretization, and state discretization. It can describe various complex system states through deterministic or probabilistic transition rules between cells . Cellular automata have become a method to study the microstructure evolution of materials. It can easily introduce the evolution rules of physical problems to realize the physical process of grain growth in the experimental process.
After doping element Y, the interface energy decreases and the activation energy increases. According to the aforementioned three formulas, the grain boundary mobility and growth rate also change with the change of interface energy and activation energy. In order to study this change, we use cellular automata for simulation. Figure 11 shows the change in average grain size with activation energy at the same temperature (1273 K). Figure 11(a) is the microstructure morphology before doping rare earth elements, and Fig. 11(b) is the microstructure morphology after doping. Parts other than white in the figure represents the generated grains, and different colors represent different grain orientations. Comparing the two figures, the average grain size after doping is significantly smaller than that before doping.
In order to avoid the contingency of the simulation results in Fig. 11, we changed the temperature for simulation. Figure 12 is a microstructure simulation diagram of WC-Co and WC-Co-Y at temperatures of 1173 K and 1373 K, respectively. Combined with the four diagrams in Fig. 12, it can be concluded that under the premise of the same temperature, the larger the activation energy is, the finer the grain is, i.e., the grain of WC-Co-Y is finer. This also confirms that the previous simulation results are not accidental. Moreover, we also found that as the temperature rises, the grain size decreases at high temperature.
As the interface energy descends and the activation energy rises, the grain boundary migration velocity, interface mobility, and grain growth rate decrease, so the grain size of WC-Co-Y is smaller. The simulation results of cellular automata are in good agreement with the interface adhesion work, interface energy, and their analysis results. This also proves the accuracy of our calculation and analysis of energy, electronic structure, and population.
In the process of our experimental research, it can be found that doping Y element can refine the grains of cemented carbide. The SEM images of cemented carbide materials before and after doping Y element under metallographic microscope are shown Figs. 13(b)–13(e). According to the quantitative microscope technology, the grain size before doping is concentrated in 5–15 µm. The average grain size is about 0.84 µm. The grain size after doping is concentrated in 3–10 µm. The average grain size is about 0.625 µm. According to Fig. 13, the WC particles doped with rare earth element Y are obviously smaller than those before doping. This is because the covalent bond between W atoms and Y atoms limits the dissolution-precipitation of W and C, and it only depends on the self-diffusion of WC grains for crystal growth. In the sintering process of cemented carbide without rare earth elements, the dissolution-precipitation is not limited, and the WC crystal is well developed and fully grown. Therefore, the size of WC particles after doping is smaller.
In this study, the interface structure WC/WC-Co of tungsten cobalt alloy was modeled before and after doping rare earth element Y. The interface adhesion work, interface energy, and electronic structure were calculated and deeply studied by using the first principle. The analysis results were verified by cellular automata simulation. The following conclusions are drawn:
Both interface structures are stable. However, the structure doped with rare earth element Y has greater interfacial adhesion work, closer adsorption, smaller interfacial energy, and more stable structure. WC/WC-Co system has greater free energy, which can promote the grain growth, accelerate the grain growth, and hinders the grain refinement.
Through the analysis of DOS and PDOS of electronic characteristics, both structures have metallicity, and both of them have metal bonds. The addition of Y atom makes the interface structure form more covalent bonds and stronger interaction. Therefore, the interface adsorption is more stable after doping. This can also be used as the grain refinement mechanism.
The grain refinement of WC/WC-Co and WC/WC-Co/Y was simulated by cellular automata. The simulation results of cellular automata are in good agreement with the interface adhesion work, interface energy, and their analysis results. We also found that the grain growth rate was slower and the grain size was smaller after doping Y.
Experiments show that adding Y element to WC made the grain size smaller, which coincides with the results of theoretical research and analysis well. Therefore, doping rare earth elements into tungsten cobalt alloy can refine grain.
This work is supported by National Natural Science Foundation of China (52275404), Key industrial technology research project of Jilin Province (20210201043GX), Project of Science and Technology Bureau of Changchun City, Jilin Province (21ZY40).
Compliance with Ethical Standards
This article does not contain any studies with human participants or animals performed by any of the authors.
Conflict of Interest
There are no conflicts of interest.
Data Availability Statement
The authors attest that all data for this study are included in the paper.