## Abstract

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.

## 1 Introduction

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 [1]. 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 [2].

Cemented carbide is prepared by powder sintering. The uncontrolled growth of a few crystals is harmful to the mechanical properties [3]. 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 [4]. Adding grain growth inhibitors, such as Cr3C2, VC, and rare earth oxides, is a common method to prepare ultrafine grain cemented carbide [5]. 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 [6]. 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 [9]. One is microscopic analysis based on scanning electron microscope (SEM) and other images [1014]. 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 [17]. 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 $(2101)$, 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 $(2101)(ab)=(2a+bb)$ 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.

Fig. 1
Fig. 1
Close modal
Fig. 2
Fig. 2
Close modal

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 [8].

Fig. 3
Fig. 3
Close modal

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 [8]. Generally, the lower the interface energy is, the more stable the interface is [17]. 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 [8], 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 [18]. 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.

Fig. 4
Fig. 4
Close modal
Fig. 5
Fig. 5
Close modal

### 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 [19].

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 [20]. 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.

The surface energy refers to the extra energy of the surface particles compared with the internal particles. The calculation of cemented carbide surface energy Esurf can be expressed as
$Esurf=Eslab−Ebulk2A$
(1)
where Eslab is the energy of slab, Ebulk is the energy of bulk, and A is the area of structural interface [4,21].
The strength of atomic interaction at the interface can be described by the adhesion work Wad, which is numerically equal to the reversible work done by separating an interface into two independent free surfaces. It is crucial to predict the bonding at the interface [22]. The calculation formula of interfacial adhesion work Wad is
$Wad=Eslab1+Eslab2−E1/22A$
(2)
where Eslab1 is the energy of the surface structure WC (0 0 0 1), Eslab2 is the energy of WC (1 −2 1 0)-Co or WC (1 −2 1 0)-Co/Y, E1/2 is the total energy of the adsorbed structure, and A is the area of the structure interface [23].
Because the arrangement of atoms on the grain boundary is distorted, the free energy increases. This additional free energy is called interface energy. Interface energy plays an important role in the nucleation process. The interface energy γ can be calculated by the following formula:
$γ=σ1+σ2−Wad$
(3)

Among them, σ1,2 are the surface energy of slab1, 2 [24].

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.

Table 1

Surface energy, interfacial adhesion work, and interfacial energy before and after doping

SystemBefore dopingAfter 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
γ (J/m2)5.10864.8852
SystemBefore dopingAfter 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
γ (J/m2)5.10864.8852

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.

The essence of grain growth is a process of grain boundary migration. Under normal circumstances, this grain grows gradually and slowly, which is called normal growth. However, some factors (such as fine impurity particles, deformation texture, etc.) will hinder the normal growth of grains. Reducing the driving force of grain boundary migration is an important way to hinder grain growth. The calculation formula of the driving force of grain boundary migration is
$P=γ(1R1+1R2)$
(4)

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 [25], 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 [26].

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.

Fig. 6
Fig. 6
Close modal
Fig. 7
Fig. 7
Close modal

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 [27], 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.

Fig. 8
Fig. 8
Close modal

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.

Fig. 9
Fig. 9
Close modal

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.

Fig. 10
Fig. 10
Close modal
Table 2

Mulliken’s population of Co2 and its nearby atoms

ModelWC/WC-CoWC/WC-Co/Y
SystemPopulation
Co2-W1/430.270.27
Co2-W22/640.14
Co2-W26/680.260.22
Co2-W30/720.260.28
Co2-W500.100.14
Co2-C61−0.12−0.16
Co2-Co30.200.22
ModelWC/WC-CoWC/WC-Co/Y
SystemPopulation
Co2-W1/430.270.27
Co2-W22/640.14
Co2-W26/680.260.22
Co2-W30/720.260.28
Co2-W500.100.14
Co2-C61−0.12−0.16
Co2-Co30.200.22

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 [28]. 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.

We use cellular automata to simulate the grain growth process of cemented carbide. In this simulation, the cell adopts a square cell. In the cell space, the nucleation core is formed randomly, and the nucleation core continues to grow until the grain occupies the space. The dislocation density difference between the crystalline grains and original grains provides a driving force for the growth of new grains, which makes the new grains grow continuously until the driving force decreases to zero where the new grains stop growing, or in contact with other new grains, both grains stop growing in the contact part [29]. It is found that the grain boundary migration speed correlates with the temperature and the activation energy of grain boundary migration. The formula of grain boundary migration velocity is given as follows [3032]:
$G=G0exp(−QactRT)$
(5)
where G0 is the constant, Qact is the activation energy, R is the gas constant, usually taken as 8.31 J/mol/K, and T is the absolute temperature.
The grain growth rate v is directly proportional to the grain boundary mobility and the driving force of grain growth, which can be expressed as
$v=kexp(−QactRT)⋅γd$
(6)
where k is a constant, d is the average diameter of the grain, and γ is the interface energy.
In order to analyze the effect of interface properties on grain growth, we give the same values to parameters such as temperature and strain rate. The adsorption energy can be regarded as the maximum activation energy for interface migration. The formula of adsorption energy can be expressed as
$E=E1+E2−E1/2$
(7)
where E1,2 is the energy of the surface structure WC (0 0 0 1) and WC(1 −2 1 0)-Co or WC(1 −2 1 0)-Co/Y. E1/2 is the total energy of the adsorbed structure.

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.

Fig. 11
Fig. 11
Close modal

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.

Fig. 12
Fig. 12
Close modal

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.

Fig. 13
Fig. 13
Close modal

## 5 Conclusions

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:

1. 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.

2. 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.

3. 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.

4. 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.

## Acknowledgment

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.

## References

1.
Yang
,
Q. M.
,
Deng
,
D. F.
,
Li
,
J. Z.
,
Chen
,
L. Y.
,
Guo
,
S. D.
,
Liu
,
J.
, and
Chen
,
H.
,
2019
, “
Fabrication and Mechanical Properties of WC-10Co Cemented Carbides With Plate-Like WC Grains
,”
J. Alloys Compd.
,
803
, pp.
860
865
.
2.
Zhang
,
W. B.
,
Liu
,
X. Z.
,
Chen
,
Z. H.
,
Chen
,
D.
, and
Peng
,
C.
,
2015
, “
Latest Development of WC-Co Cemented Carbide
,”
Chin. J. Rare Met.
,
39
(
2
), pp.
178
186
.
3.
Pellan
,
M.
,
2015
, “
Development of Grain Boundaries and Phase Boundaries in WC-Co Cemented Carbides
,”
Université Grenoble Alpes
.
4.
Zhong
,
Y.
,
Zhu
,
H.
,
Shaw
,
L. L.
, and
,
R.
,
2011
, “
The Equilibrium Morphology of WC Particles–A Combined Abinitio and Experimental Study
,”
Acta Mater.
,
59
(
9
), pp.
3748
3757
.
5.
Yang
,
Y.
,
Luo
,
L. M.
,
Zan
,
X.
,
Zhu
,
X. Y.
,
Zhu
,
L.
, and
Wu
,
Y. C.
,
2021
, “
Study on Preparation and Properties of WC-8Co Cemented Carbide Doped With Rare Earth Oxide
,”
Int. J. Refract. Met. Hard Mater
,
98
, p.
105536
.
6.
Liu
,
S.
,
Huang
,
Z. L.
,
Liu
,
G.
, and
Yang
,
G. B.
,
2006
, “
Preparing Nano-Crystalline Rare Earth Doped WC/Co Powder by High Energy Ball Milling
,”
Int. J. Refract. Met. Hard Mater.
,
24
(
6
), pp.
461
464
.
7.
Wang
,
Y. L.
,
Wang
,
Y.
, and
Xie
,
X. H.
,
2019
, “
Research Progress of Rare Earth Cemented Carbide
,”
Nonferrous Met. Sci. Eng.
,
10
(
5
), pp.
106
112
.
8.
Dai
,
Z.
,
Lin
,
C. G.
, and
Lin
,
Z. K.
,
2013
, “
Effect of Rare Earth on Microstructure of WC-8Co Alloy Remelted by Zinc Melting
,”
Chin. J. Rare Met.
,
3
, pp.
359
364
.
9.
Zhang
,
L.
,
Shan
,
C.
,
Cheng
,
X.
,
Ma
,
J.
, and
Xiong
,
X. J.
,
2010
, “
Challenges to Conventional Theory of Grain Growth Inhibition of Cemented Carbide and Approach for the Breakthrough
,”
Cemented Carbide
,
27
(
5
), pp.
306
310
. (In Chinese).
10.
Lin
,
C.
, and
Yuan
,
G.
,
2005
, “
Effects of Rare Earths on the Microstructure of Nano-Grained WC-VC-10Co Hardmetals
,”
Proceedings of the 16th International Plansee Seminar
,
Reutte, Austria
,
Jan. 1
, Plansee Holding AG, Vol. 2, pp.
363
377
.
11.
Kawakami
,
M.
,
,
O.
, and
Hayashi
,
K.
,
2005
, “
Segregation Amount of Dopants at WC/Co Interface in Cr3C2 and VC + Cr3C2-Doped WC-Co Submicron-Grained Hardmetals
,”
Proceedings of the 16th International Plansee Seminar
,
Reutte, Austria
,
Jan. 1
, Plansee Holding AG, Vol. 2, pp.
653
667
.
12.
Delanoë
,
A.
, and
Lay
,
S.
,
2009
, “
Evolution of the WC Grain Shape in WC-Co Alloys During Sintering: Effect of Cr
,”
Int. J. Refract. Met. Hard Mater.
,
27
(
2
), pp.
189
197
.
13.
Delanoë
,
A.
, and
Lay
,
S.
,
2009
, “
Evolution of the WC Grain Shape in WC–Co Alloys During Sintering: Effect of C Content
,”
Int. J. Refract. Met. Hard Mater.
,
27
(
1
), pp.
140
148
.
14.
Weidow
,
J.
,
Andrén
,
H. O.
,
Bo
,
J.
, and
Zackrisson
,
J.
,
2009
, “
Analysis of Interfaces in WC-Co With Cubic Carbide Additions
,”
17th Plansee Seminar
,
Reutte, Austria
,
June 1
, Vol. 2, pp.
1
8
.
15.
Jaffrey
,
D.
,
Lee
,
J. W.
, and
Browne
,
J. D.
,
1980
, “
Co-WC Pseudobinary Eutectic Reaction
,”
Powder Metall.
,
23
(
3
), pp.
140
144
.
16.
Christensen
,
M.
, and
Wahnström
,
G.
,
2004
, “
Effects of Cobalt Intergranular Segregation on Interface Energetics in WC–Co
,”
Acta Mater.
,
52
(
8
), pp.
2199
2207
.
17.
Zhao
,
X. B.
,
Zhang
,
J.
,
Liu
,
S.
,
Zhao
,
C. C.
,
Wang
,
C. X.
,
Ren
,
X. J.
, and
Yang
,
Q. X.
,
2016
, “
Investigation on Grain Refinement Mechanism of Ni-Based Coating With LaAlO3 by First-Principles
,”
Mater. Des.
,
110
, pp.
644
652
.
18.
Xu
,
C. H.
,
Ai
,
X.
,
Huang
,
C. Z
, and
Deng
,
J.X.
,
1997
, “
Effect of Rare Earth on Microstructure and Mechanical Properties of Cemented Carbide Tool Materials
,”
Chin. Rare Earths
,
18
(
3
), pp.
55
60
.
19.
Hao
,
Z. P.
,
Liu
,
R.
,
Fan
,
Y. H.
, and
Wang
,
L. L.
,
2019
, “
First-Principles Calculations of a New Half-Metallic Heusler Alloy FeCrAs
,”
J. Alloys Compd.
,
820
, p.
153118
.
20.
Perdew
,
J. P.
,
Burke
,
K.
, and
Ernzerhof
,
M.
,
1998
, “
,”
Phys. Rev. Lett.
,
77
(
18
), pp.
3865
3868
.
21.
Zavodinsky
,
V. G.
,
2011
, “
Cobalt Layers Crystallized on the WC(100) Surface: Spin-Polarized AB Initio Study
,”
Int. J. Refract. Met. Hard Mater.
,
29
(
2
), pp.
184
187
.
22.
Jin
,
N.
,
Yang
,
Y. Q.
,
Luo
,
X.
,
Liu
,
S.
,
Xiao
,
Z. Y.
,
Guo
,
P. F.
, and
Huang
,
B.
,
2015
, “
First-Principles Calculation of W/WC Interface: Atomic Structure, Stability and Electronic Properties
,”
Appl. Surf. Sci.
,
324
, pp.
205
211
.
23.
Li
,
Y. F.
,
Gao
,
Y. M.
,
Xiao
,
B.
,
Min
,
T.
,
Ma
,
S. Q.
, and
Yi
,
D. W.
,
2011
, “
Theoretical Calculations on the Adhesion, Stability, Electronic Structure, and Bonding of Fe/WC Interface
,”
Appl. Surf. Sci.
,
257
(
13
), pp.
5671
5678
.
24.
Christensen
,
M.
,
Dudiy
,
S.
, and
Wahnström
,
G.
,
2002
, “
First-Principles Simulations of Metal-Ceramic Interface Adhesion: Co/WC Versus Co/TiC
,”
Phys. Rev. B
,
65
(
4
), p.
045408
.
25.
Sun
,
B. D.
,
Han
,
Y. F.
, and
Wang
,
J.
,
2012
, “
Development of Grain Refinement in Aluminium Field
,”
Mater. Sci. Forum
,
706–709
, pp.
402
407
.
26.
Hao
,
Z. P.
,
Qiu
,
Y.
,
Fan
,
Y. H.
, and
Fu
,
W. C.
,
2021
, “
Theoretical Calculation and Analysis of New Rare Earth Cemented Carbide Based on First-Principles
,”
Int. J. Refract. Met. Hard Mater.
,
101
, p.
105688
.
27.
Hao
,
Z. P.
,
Liu
,
R.
,
Fan
,
Y. H.
, and
Qiu
,
Y.
,
2021
, “
Ferromagnetic Exchange Mechanism and Martensitic Transformation of Heusler Alloy Based on D-Band Center Theory
,”
J. Magn. Magn. Mater.
,
523
, p.
167627
.
28.
Duan
,
C. Z.
, and
Qin
,
S. W.
,
2017
, “
Dynamic Recrystallization Kinetics Model of Hardened GCr15 Steel at High Temperature and High Strain Rate
,”
Heat Treat. Met.
,
42
(
2
), pp.
34
38
. (In Chinese).
29.
Xiao
,
H.
,
Xu
,
Y. C.
, and
Yan
,
Y. H.
,
2005
, “
Cellular Automaton Method for Simulation of Dynamic Recrystallization Process With Consideration of Grains Deformation
,”
China Mech. Eng.
,
16
(
24
), pp.
2245
2248
.
30.
Zhang
,
S. P.
, and
Xie
,
H. B.
,
2015
, “
Study on Grain Growth Behavior of SCM435 Austenite
,”
2015 National Symposium on Wire Rod and Small Section Steel
,
YiCang, China
,
Jan. 6
.
31.
Ashby
,
M. F.
, and
Easterling
,
K. E.
,
1978
, “
A First Report on Diagrams for Grain Growth in Welds
,”
Acta Metall.
,
30
(
11
), pp.
1969
1978
.
32.
Hu
,
H.
, and
Rath
,
B. B.
,
1970
, “
On the Time Exponent in Isothermal Grain Growth
,”
Metall. Trans.
,
1
(
11
), pp.
3181
3184
.