Effect of CaF₂@SiO₂ on Si₃N₄/TiC Composite Ceramic Materials: Molecular Dynamics Analysis and Material Preparation

Abstract

Molecular dynamics simulations allow to investigate the microscopic evolution of a structure, and can also point the way to tool material design. In this paper, the effect of adding CaF₂ and CaF₂@SiO₂ on the Si₃N₄/TiC system is studied using molecular dynamics simulations. The results show that the system with the addition of CaF₂@SiO₂ to the model has a higher hardness than the system with the addition of CaF₂. In order to obtain the optimum parameters for self-lubricating ceramic tools, the effect of adding different amounts of CaF₂@SiO₂ on the Si₃N₄/TiC system was investigated. The Si₃N₄/TiC/CaF₂@SiO₂ system achieved optimum mechanical properties when four CaF₂@SiO₂ were included in the model. By analyzing the effect of the sintering temperature on the system, it was deduced that the hardness achieved a maximum value of 15.89 GPa and the modulus of elasticity reached 132.53 GPa when the sintering temperature was at 2073 K. Based on this sintering parameter, the Si₃N₄/TiC/CaF₂@SiO₂ composite ceramic tool material was experimentally prepared with the mechanical properties of 15.66 GPa hardness and 128.08 GPa modulus of elasticity. The experimental results were consistent with the simulation results.

1. Introduction

Si₃N₄-based ceramics have become one of the most promising ceramics due to their high hardness, corrosion resistance, temperature resistance, and chemical stability [1,2,3]. Therefore, they are often used as ideal materials for cutting tools in the field of mechanical engineering. Toughening and reinforcement of ceramic materials can be achieved by improving the manufacturing process and introducing reasonable toughening mechanisms such as particle dispersion, whisker toughening, and synergistic effects of several mechanisms [4,5]. Studies have shown that the addition of composite materials, such as TiC, to ceramic matrix materials improves the mechanical properties of the ceramic materials [6,7,8]. The improvement in toughness of Si₃N₄/TiC nanocomposite ceramics is mainly achieved through mechanisms such as dispersion toughening of nano-TiC particles and pull-out, bridging, and crack deflection of long columnar whisker-like β-Si₃N₄ grains [9]. In addition, the Si₃N₄/TiC ceramic tools are less frictional in dry cutting due to the absence of solid lubricants.

Researchers have deduced that adding a solid lubricant, such as CaF₂, to ceramic tools can reduce tool wear [10,11,12]. Due to the relatively low mechanical properties of CaF₂, a direct addition of CaF₂ to self-lubricating ceramic tools can significantly reduce their mechanical properties [13,14,15]. With the rapid development of surface technology, the addition of nanoparticles with a core–shell structure can effectively improve the mechanical properties of ceramic materials and maintain good lubricity [16,17,18]. For instance, Chen et al. [19,20] prepared CaF₂@Al₂O₃ nanoparticles using a non-uniform nucleation method, and then developed Al₂O₃/Ti(C,N)/CaF₂@Al₂O₃ composite ceramic tools. Wu et al. [21,22] prepared Al₂O₃/(W,Ti)C ceramic tools with h-BN@Ni coated powder and showed that the friction coefficient and wear rate of the tools were lower than those of Al₂O₃/(W,Ti)C/h-BN. The ethyl ester (TEOS) method was also used to prepare ceramic materials with CaF₂@SiO₂-coated nanoparticles. The mechanical properties, friction, and wear resistance were significantly improved compared to ceramics with directly added CaF₂ nanoparticles [23].

For composite ceramic materials, the interface is an extremely important component of the composite, determining whether the matrix and reinforcing particles can fully exploit their role to form an optimal composite [24]. The molecular dynamics simulations outperform the conventional laboratory methods in the interfacial analysis and understanding of the nanostructure of materials at the atomic scale. Sazgar A et al. [25] used molecular dynamics methods to study the interfacial behavior of Al/α-Al₂O₃ composites under tensile and shear loading. Shen et al. [26] used molecular dynamics methods to study the cohesion of the Cu-Fe interface performance. For the study of interfaces between ceramic materials, Zhou et al. [27] studied the interfacial energy and diffusion phenomena of the Al₂O₃(012)-SiC(011) interfacial model using a molecular dynamics approach. The results showed that the Al₂O₃(012)-SiC(011) interfacial model had the highest interfacial bond strength and the strongest resistance to grain boundary crack extension at 1500 K. Therefore, it is important to study the interface of composite ceramic materials to enhance their performance. However, few previous studies on the interface of Si₃N₄-based composite ceramic materials exist.

The sintering densification process of ceramic materials is closely related to the sintering temperature and sintering pressure. In addition, the sintering parameters significantly affect the microstructure of ceramic tool materials and the mechanical properties of ceramic materials [28,29]. Fang et al. [30] conducted computer simulations of the sintering process of single-phase and two-phase ceramics using a two-dimensional hexagonal lattice model. Hao et al. [31] simulated the microstructure evolution of defect-free three-phase nanocomposite ceramic tool materials at sintering temperatures of 1500, 1600, and 1700 °C and sintering pressures of 0, 20, and 30 MPa. The simulation results show that the grain growth rate increases with the increase in the sintering temperature, and the simulated results are all consistent with the experiments. In order to investigate the mechanical and grain boundary sintering properties of Si₃N₄/TiC/CaF₂@SiO₂ ceramic tool materials, a better approach consists of studying them from the microstructure.

Molecular dynamics simulation methods can study the evolution of microstructure to optimize the preparation process, reduce the R&D costs, and improve the R&D efficiency. There are no studies on Si₃N₄/TiC-based ceramic materials with the addition of solid lubricants using molecular dynamics. In this paper, the effect law of CaF₂ addition on the mechanical properties of Si₃N₄/TiC/CaF₂ composites was first investigated using the molecular dynamics method. The effect law of CaF₂@SiO₂ addition on the mechanical properties of Si₃N₄/TiC/CaF₂@SiO₂ composites was then investigated using the molecular dynamics method. Finally, the Si₃N₄/TiC/CaF₂@SiO₂ composites were experimentally prepared according to the optimal parameters of the preparation process obtained from the simulations, and the accuracy of the simulations was verified.

2. Objectives and Methods

2.1. Molecular Dynamics Simulations

2.1.1. CaF₂ Crystal Surfaces with Different Surface Layer Atoms

The CaF₂ proto-cell model was built in the Visualizer interface of the Materials Studio simulation software (Figure 1). By cutting along the (111) crystalline face of the CaF₂ protocell model, the outermost vertex parameter (Top) is 0, 0.25, 0.50, 0.75, and 1.00, the geometric parameters of the surface are a = b = 3.86 Å, α = 120.00°, and the thickness parameter (Thickness) is 1. For ease of presentation, the five models are denoted by Models 1 to 5, respectively.

2.1.2. CaF₂@SiO₂ Crystalline Surfaces at Different Concentrations

In addition, an SiO₂ proto-cell model was developed in the visualizer interface. The initial values of the SiO₂ lattice constants are set to a = b = c = 7.16 Å and α = β = γ = 90.00°, where the yellow color indicates Si atoms and the red color indicates O atoms. Using the constructed CaF₂ model, a spherical CaF₂ molecular structure model with a radius of 5 Å is built. An SiO₂ model with a radius of 10 Å is built, then the region of the model with a radius of 5 Å is considered, and the selected SiO₂ is removed, thus obtaining a toroidal SiO₂ model. Combining the spherical CaF₂ structural model with a radius of 5 Å with the toroidal SiO₂ model yields a radius of 10 Å, with the outermost layer of SiO₂ and the inner layer of CaF₂ in a spherical model.

To study the effect of CaF₂@SiO₂ concentration on Si₃N₄/TiC, three CaF₂@SiO₂ structural models with different concentrations were developed. For ease of presentation, the three models with different concentrations are denoted by models 6 to 8. CaF₂@SiO₂ structural models 3, 4, and 5 are placed in models 6, 7, and 8, respectively. Figure 2 shows the initial structural model of CaF₂@SiO₂.

2.1.3. Initial Model of Si₃N₄/TiC/CaF₂

To minimize the mismatch rate, it was necessary to separately expand the crystals. 12 × 3 was chosen for the Si₃N₄ (110) crystal plane, 12 × 3 for the TiC (100) crystal plane, and 9 × 9 for the CaF₂ (111) crystal plane, creating the initial structural model shown in Figure 3.

2.1.4. Initial Model of Si₃N₄/TiC/CaF₂@SiO₂

On the 3D modelling platform visualizer, the Si₃N₄ (110) crystal plane was selected as 12 × 3 for layer 1 of the initial model, the TiC (100) crystal plane was selected as 12 × 3 for layer 3 of the initial model. In addition, the CaF₂@SiO₂ built in 2.1.2 was used as layer 2, and a 15 Å vacuum layer was added to the upper layer of layer 3. The initial structure of each model is shown in Figure 4.

2.2. Simulation Process

Both materials were calculated using Forcite, the molecular dynamics module of Materials Studio software, with periodic boundary conditions. The model was first optimized for geometry and accuracy with Ultrafine, and then placed in an NVE system with a simulation time of 100 ps. It has been shown that Si₃N₄ composite ceramic tools have the highest density and best overall mechanical properties at a pressure of 32 MPa. Therefore, 32 MPa was chosen as the sintering pressure in this study [32]. The model was again subjected to molecular dynamics calculations at NPT with a simulation time of 500 ps and temperatures of 1673, 1773, 1873, 1973, and 2073 K. The model was annealed at half the sintering temperature and at 500 K, with a pressure of 0 MPa. The time step was 1 fs and the force field was Universal to the force field (which is detailed by Universal), in order to describe the interaction between the atoms. Finally, the model was analyzed to study its mechanical properties.

2.3. Experimentation

According to the simulation results, the optimum mechanical properties of Si₃N₄/TiC/CaF₂@SiO₂ were achieved at a process parameter of 32 MPa and a temperature of 2073 K. Therefore, The Si₃N₄/TiC/CaF₂@SiO₂ composite ceramic tool material was prepared experimentally at a pressure of 32 MPa, a temperature of 2073 K, and a holding time of 15 min, with Si₃N₄/TiC as the base material, CaF₂@SiO₂ nano-coated particles as the solid lubricant, and Al₂O₃ and Y₂O₃ as the sintering aids. The specific grouping of materials is shown in

Table 1. Material grouping ratios for Si₃N₄/TiC/CaF₂@SiO₂ ceramic tools.

Material	Si3N4	TiC	CaF2@SiO2	Al2O3	Y2O3
components (vol.%)	72	10	10	3	5

. The raw material powder used is shown in

Table 2. Raw materials Si₃N₄, TiC, Al₂O₃, Y₂O₃ CaF₂@SiO₂.

Material	Manufacturer	Particle Size
Si3N4	Qinhuangdao Yi Nuo high-tech material development Co., LTD	0.5–1 μm
TiC	Qinhuangdao Yi Nuo high-tech material development Co., LTD	0.5–1 μm
Al2O3	Qinhuangdao Yi Nuo high-tech material development Co., LTD	0.5 μm
Y2O3	Sinopharm Group Chemical reagent Co., LTD	0.5 μm
CaF2@SiO2	self-developed	40–60 nm (The SiO2 shell is 10 nm)

.

The preparation process of Si₃N₄/TiC/CaF₂@SiO₂ composites is as follows: firstly, the Si₃N₄, TiC, Al₂O₃, and Y₂O₃ powders are weighed, and the measured powders are added to an appropriate amount of anhydrous ethanol for ultrasonic dispersion and stirring, then the components are mixed with continuous ultrasonic stirring. The resulting suspension and the CaF₂@SiO₂ prepared in advance are poured into a ball mill jar for ball milling, the resulting mixture is placed under a vacuum drying oven for drying, the dried raw material is placed in a sieve and the sieved powder is loaded into a graphite mold for pre-pressing and forming. Finally, it is put into a dual power SPS plasma sintering machine (SPS-625HF) for sintering.

The mechanical properties of the prepared Si₃N₄/TiC/CaF₂@SiO₂ composite ceramic tool materials were tested. The hardness was measured using a Vickers hardness tester (Shanghai Taiming Optical Instruments Co., Ltd., Model HVS-30ZC/LCD), the modulus of elasticity was measured using the bending method, and the microstructure of the specimens was observed using a scanning electron microscope (Zeiss, Germany, SUPRA 55).

3. Results and Discussion

3.1. Interfacial Work of Adhesion

3.1.1. Interfacial Adhesion Work of Si₃N₄/TiC/CaF₂

The adhesion work can be used to describe the bonding strength of the interface. The larger the value of its adhesion work, the higher the bonding strength of the interface, and therefore the bonding strengths of the interface can be compared according to the adhesion work. The calculation formula of the adhesion work of the interface of each model is given by:

$${\mathrm{E}}_{\mathrm{a}\mathrm{d}}=\left({\mathrm{E}}_{{\mathrm{S}\mathrm{i}}_3{\mathrm{N}}_4}^{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{b}}+{\mathrm{E}}_{\mathrm{T}\mathrm{i}\mathrm{C}}^{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{b}}+{\mathrm{E}}_{{\mathrm{C}\mathrm{a}\mathrm{F}}_2}^{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{b}}-{\mathrm{E}}_{{\mathrm{S}\mathrm{i}}_3{\mathrm{N}}_4/\mathrm{T}\mathrm{i}\mathrm{C}/{\mathrm{C}\mathrm{a}\mathrm{F}}_2}^{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}}\right)/\mathrm{A}$$

(1)

where ${\mathrm{E}}_{\mathrm{a}\mathrm{d}}$ is the interface adhesion work, ${\mathrm{E}}_{{\mathrm{S}\mathrm{i}}_3{\mathrm{N}}_4}^{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{b}}$ is the energy of Si₃N₄ that builds the interface, ${\mathrm{E}}_{\mathrm{T}\mathrm{i}\mathrm{C}}^{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{b}}$ is the energy of TiC that builds the interface, ${\mathrm{E}}_{{\mathrm{C}\mathrm{a}\mathrm{F}}_2}^{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{b}}$ is the energy of the CaF₂ that builds the interface, and A is the interface area.

Figure 5 shows the interfacial adhesion work obtained by each model of Si₃N₄/TiC/CaF₂ by molecular dynamics calculation. It can be seen that the interface bonding type also has a great influence on the adhesion work. The adhesion work of each model shows a trend of gradually increasing with the temperature increase. This is because the atoms near the interface gain more energy and get closer to each other through diffusion when the temperature increases. The interactions between these atoms become stronger, and some pairs of atoms create new bonds. The curve shows a linear relationship with the temperature increase.

3.1.2. Interfacial Adhesion Work of Si₃N₄/TiC/CaF₂@SiO₂

The interfacial adhesion work of the Si₃N₄/TiC/CaF₂@SiO₂ model is computed as:

$${\mathrm{E}}_{\mathrm{a}\mathrm{d}}=\left({\mathrm{E}}_{{\mathrm{S}\mathrm{i}}_3{\mathrm{N}}_4}^{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{b}}+{\mathrm{E}}_{\mathrm{T}\mathrm{i}\mathrm{C}}^{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{b}}+{\mathrm{E}}_{{\mathrm{C}\mathrm{a}\mathrm{F}}_2@{\mathrm{S}\mathrm{i}\mathrm{O}}_2}^{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{b}}-{\mathrm{E}}_{{\mathrm{S}\mathrm{i}}_3{\mathrm{N}}_4/\mathrm{T}\mathrm{i}\mathrm{C}/{\mathrm{C}\mathrm{a}\mathrm{F}}_2@{\mathrm{S}\mathrm{i}\mathrm{O}}_2}^{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}}\right)/\mathrm{A}$$

(2)

where ${\mathrm{E}}_{\mathrm{a}\mathrm{d}}$ is the interfacial adhesion work, ${\mathrm{E}}_{{\mathrm{S}\mathrm{i}}_3{\mathrm{N}}_4}^{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{b}}$ is the energy of the Si₃N₄ building the interface, ${\mathrm{E}}_{\mathrm{T}\mathrm{i}\mathrm{C}}^{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{b}}$ is the energy of the TiC building the interface, ${\mathrm{E}}_{{\mathrm{C}\mathrm{a}\mathrm{F}}_2@{\mathrm{S}\mathrm{i}\mathrm{O}}_2}^{\mathrm{s}\mathrm{l}\mathrm{a}\mathrm{b}}$ is the energy of the CaF₂@SiO₂ building the interface, and A is the area of the interface.

Figure 6 shows the interfacial adhesion work of each model of Si₃N₄/TiC/CaF₂@SiO₂. It can be seen from Figure 6 that the interfacial adhesion work of each simulation shows a trend of gradually increasing with the temperature increase. The interfacial adhesion work of each model of Si₃N₄/TiC/CaF₂@SiO₂ is slightly higher than that of Si₃N₄/TiC/CaF₂ interface adhesion work. It can also be seen that the bonding strength and system stability of the Si₃N₄/TiC/CaF₂@SiO₂ interface are stronger than those of Si₃N₄/TiC/CaF₂.

3.2. Geometry and Interface Analysis

3.2.1. Geometric Structure and Interface Analysis of Si₃N₄/TiC/CaF₂

Table 3. Model 1 Dimensions.

T (K)	a (Å)	b (Å)	c (Å)	V (Å3)	α (°)	β (°)	γ (°)
	36.22	37.75	78.76	107,665.88	90.00	90.00	100.00
1673	37.61	38.94	60.20	88,248.27	93.28	85.21	90.00
1773	37.61	38.94	60.10	88,282.70	93.33	87.03	90.00
1873	37.61	38.94	60.00	88,334.29	93.21	87.29	90.00
1973	37.61	38.94	59.98	88,318.10	92.42	87.42	89.99
2073	37.61	38.94	60.00	88,350.93	93.22	87.49	89.99

,

Table 4. Model 2 Dimensions.

T (K)	a (Å)	b (Å)	c (Å)	V (Å3)	α (°)	β (°)	γ (°)
	36.22	37.75	76.88	105,102.60	90.00	90.00	100.00
1673	37.61	38.93	57.19	84,206.60	88.73	90.63	89.99
1773	37.61	38.93	57.20	84,209.56	88.70	89.95	90.00
1873	37.61	38.93	57.21	84,198.62	88.75	91.75	89.99
1973	37.61	38.93	57.18	84,214.14	88.53	89.90	89.99
2073	37.61	38.93	57.18	84,264.59	88.56	90.07	89.99

,

Table 5. Model 3 Dimensions.

T (K)	a (Å)	b (Å)	c (Å)	V (Å3)	α (°)	β (°)	γ (°)
	36.22	37.75	76.88	105,102.60	90.00	90.00	100.00
1673	37.61	38.93	57.38	84,067.07	94.67	90.82	90.00
1773	37.61	38.93	57.28	84,125.16	93.09	91.74	89.99
1873	37.61	38.93	57.44	84,026.12	95.14	93.27	89.99
1973	37.61	38.93	57.39	84,251.84	95.17	90.71	90.00
2073	37.61	38.93	57.41	84,077.66	94.75	92.02	90.00

,

Table 6. Model 4 Dimensions.

T (K)	a (Å)	b (Å)	c (Å)	V (Å3)	α (°)	β (°)	γ (°)
	36.22	37.75	78.17	106,863.4	90.00	90.00	100.00
1673	37.61	38.93	57.25	84,041.69	90.76	92.86	89.99
1773	37.61	38.93	57.21	83,958.71	90.44	91.72	89.99
1873	37.61	38.93	57.20	84,078.24	90.70	92.24	90.00
1973	37.61	38.93	57.21	84,061.70	91.28	91.75	90.00
2073	37.61	38.93	57.24	84,041.39	90.75	91.99	89.99

and

Table 7. Model 5 Dimensions.

T (K)	a (Å)	b (Å)	c (Å)	V (Å3)	α (°)	β (°)	γ (°)
	36.22	37.75	78.17	106,863.40	90.00	90.00	100.00
1673	37.61	38.93	57.33	83,638.48	88.51	85.86	89.99
1773	37.61	38.93	57.37	83,643.17	87.45	86.80	90.00
1873	37.61	38.93	57.40	83,807.61	87.72	85.82	90.00
1973	37.61	38.93	57.39	83,769.17	88.69	85.21	90.00
2073	37.61	38.93	57.16	83,750.62	89.33	84.93	89.99

show the model sizes of the Si₃N₄/TiC/CaF₂ models after molecular dynamics calculations. It can be seen that all the models show the phenomenon of shrinkage. Among them, in the a and b directions, the size changes little, while the size decreases in the c direction. The different interface structures constructed by each model lead to different degrees of deformation after molecular dynamics calculation, and the degrees of deformation of α, β, and γ are also different.

Figure 7 shows a cross-sectional view of each model at a temperature of 1873 K after kinetic calculations. It can be seen that the atomic layers at the model interface are displaced to a large extent in the direction perpendicular to the interface, which results in a large change in the size of the model in the c-direction. In addition, a layer misalignment of the atomic layers occurs. It can be seen from Figure 7 that the layer misalignment phenomenon is more pronounced in models 1, 2, and 4. The TiC atomic layer closer to the interface has a larger chirality, the first layer shrinks inwards as a whole, the C-Ti bond length increases, and the C-Ti-C bond angle slightly increases. The second layer is more stable and the atoms away from the interface layer have a smaller relaxation. It can also be deduced that the CaF₂ layer as a whole moves closer to the underlying Si₃N₄ layer, the CaF₂ layer and the underlying Si₃N₄ layer mix with each other, while the CaF₂ layer and the upper TiC layer maintain a distance of 3–4 Å. Finally, the layering phenomenon is clear.

3.2.2. Geometric Structure and Interface Analysis of Si₃N₄/TiC/CaF₂@SiO₂

Table 8. Model 6 Dimensions.

T (K)	a (Å)	b (Å)	c (Å)	V (Å3)	α (°)	β (°)	γ (°)
	35.00	40.00	110.20	154,273.15	90.00	90.00	90.00
1673	37.61	38.94	71.20	105,017.93	82.90	81.51	90.00
1773	37.61	38.92	71.13	105,007.51	81.46	80.88	90.00
1873	37.61	38.93	71.41	104,956.46	82.00	81.78	90.00
1973	37.61	38.94	71.70	105,110.01	81.25	80.14	89.99
2073	37.61	38.94	69.95	105,028.65	82.72	84.23	89.99

,

Table 9. Model 7 Dimensions.

T (K)	a (Å)	b (Å)	c (Å)	V (Å3)	α (°)	β (°)	γ (°)
	35.00	40.00	111.73	156,421.11	90.00	90.00	90.00
1673	37.61	38.93	70.94	119,229.28	97.39	83.40	90.00
1773	37.61	38.94	72.38	119,349.82	99.15	82.47	89.99
1873	37.61	38.93	71.57	119,128.23	101.38	88.65	89.99
1973	37.61	38.93	71.20	119,278.74	96.75	84.81	90.00
2073	37.61	38.93	71.73	119,317.77	99.73	90.11	89.99

and

Table 10. Model 8 Dimensions.

T (K)	a (Å)	b (Å)	c (Å)	V (Å3)	α (°)	β (°)	γ (°)
	35.00	40.00	125.16	175,225.03	90.00	90.00	90.00
1673	37.57	38.99	84.57	121,478.64	96.89	81.06	90.00
1773	37.61	38.93	81.82	121,488.58	98.23	82.62	90.00
1873	37.61	38.94	79.96	121,467.63	97.81	81.08	90.00
1973	37.61	38.94	80.43	121,375.85	96.34	81.09	89.99
2073	37.61	38.93	79.69	121,653.44	96.56	79.73	90.00

show the model dimensions after molecular dynamics calculations for models 6 to 8. It can be seen that each model shows shrinkage after the molecular dynamics calculations. In the a direction, each model size increases, while in the b and c directions, each model size contracts, and the contraction in the c direction is more obvious. In the α direction, each model shows an increase, in the β direction, each model has a large change, and in the γ direction, each model undergoes a small change.

Figure 8 shows the cross-section of each model after simulation. It can be seen that the thickness of the vacuum layer in all the models is reduced, the positions of Si₃N₄ and TiC atoms perpendicular to the interface are greatly changed, and model 6 has a relatively clear deformation. In addition, the CaF₂@SiO₂ spheres migrated to the lower Si₃N₄. The relaxation of Si₃N₄ and TiC atoms near the interface is larger, while the relaxation of Si₃N₄ and TiC atoms far from the interface is smaller. The first and second layers shrink inward, while the third layer is more stable. In the model, the lower interface of TiC is clearly separated from the middle layer, maintaining the interlayer distance of 2–3 A, while the upper interface of Si₃N₄ is not clearly stratified with the middle layer. This is due to the fact that the interface of TiC is saturated with Ti-C bond, which has no effect on the interlayer, while the interface of Si₃N₄ is free N atom and unsaturated Si-N bond, which has a greater impact on the interlayer than the interface of TiC.

3.3. Mechanical Properties

3.3.1. Mechanical Properties Analysis of Si₃N₄/TiC/CaF₂

The bulk modulus B, shear modulus G, and Young’s modulus E of each Si₃N₄/TiC/CaF₂ model are shown in Figure 9. As the parameter of the outermost vertex of the CaF₂ crystalline surface increases from 0.0 to 1.0, the bulk and shear moduli of the corresponding models increase, and the elastic modulus of each model varies with the temperature increase. Among the models, model 1 has the lowest bulk modulus, which indicates that the system is easily compressed. This demonstrates that the model with the outermost vertex parameter (Top) of the crystal plane taking 0 is not conducive to the mechanical properties of the Si₃N₄/TiC/CaF₂ material. In model 5, the material achieves the highest bulk modulus and the strongest average chemical bond, indicating that the system is resistant to deformation. Similarly, the shear modulus and Young’s modulus in model 5 are the highest among the models, which indicates that the system is most resistant to shear deformation.

The ratio of bulk modulus B to shear modulus G can be used to measure the ductility and brittleness of a material. A high (low) B/G corresponds to the ductility (brittleness) of the material, and the value used as the dividing node is 1.75. It can be seen from Figure 10 that the B/G ratios of the Si₃N₄/TiC/CaF₂ models calculated in this paper are all below 1.75, ranging from 1.2 to 1.4. This indicates that the molecules of the models are able to calculate the hardness. On the other hand, this is the opposite of the B/G ratio, showing a trend of increasing and then decreasing with the temperature increase, while the hardness attains the highest values at 1873 K and 1973 K. The results show that either too high or too low temperatures have a negative effect on the mechanical properties, and the optimum sintering temperatures are obtained from 1873 K to 1973 K.

3.3.2. Mechanical Properties Analysis of Si₃N₄/TiC/CaF₂@SiO₂

The bulk modulus B, shear modulus G, and Young’s modulus E of each model of Si₃N₄/TiC/CaF₂@SiO₂ are shown in Figure 11. The bulk modulus and shear modulus of model 6 and model 7 are significantly higher than those of model 8. In models 6 and 7, the bulk modulus shows an overall tendency to decrease with the temperature increase. In addition, the shear modulus of model 6 fluctuates more with the temperature increase, the Young’s modulus first decreases and then increases, while the shear modulus of model 7 shows an overall tendency to decrease with the temperature increase, and the Young’s modulus gradually decreases. In model 8, the bulk modulus, shear modulus, and Young’s modulus all tend to decrease and then increase with the temperature increase, with the minimum value of bulk modulus being obtained at 1873 K and the minimum values of shear modulus and Young’s modulus being obtained at 1773 K. It can be deduced that the mechanical properties of models 6 and 7 are better than those of model 8.

The B/G and hardness Hv of each model of Si₃N₄/TiC/CaF₂@SiO₂ are shown in Figure 12. It can be seen that the B/G ratios of each model of Si₃N₄/TiC/CaF₂@SiO₂ are all lower than 1.75, indicating that the calculated models belong to brittle materials after molecular dynamics calculation. In models 6 and 7, the hardness shows a tendency to increase with the temperature increase. In model 6, the hardness first rapidly increases and then slowly increases with the temperature increase. The maximum value of hardness is obtained at 2073 K with a value of 13.72 GPa. In model 8, the hardness shows a trend of increasing and then decreasing with the temperature increase. The maximum value of hardness is obtained at 1873 K with a value of 14.13 GPa. In model 7, the hardness first slowly increases and then rapidly increases with the temperature increase, with a maximum value of 15.89 GPa at 2073 K, which is higher than the value in models 6 and 8, where the modulus of elasticity is 132.53 GPa.

Compared with the Si₃N₄/TiC/CaF₂ simulation system, it can be seen that the addition of the coated structure CaF₂@SiO₂ to the Si₃N₄/TiC matrix improves the interface bonding strength and slightly improves the hardness. When the content of CaF₂@SiO₂ in the model is different, the mechanical properties of the model are also different. At the sintering temperature of 2073 K, when the amount of CaF₂@SiO₂ is 4, that is, when the proportion of CaF₂@SiO₂ is 10 vol%, the model hardness reaches the maximum value.

3.4. Phase Analysis and Microstructure of Si₃N₄/TiC/CaF₂@SiO₂ Composite Ceramic Material

As can be seen in Figure 13a, as the sintering temperature rises, the sintering agent dissolves into the liquid phase, Si₃N₄ particles are rearranged in the liquid phase, and ceramic materials increase density. When the temperature reaches a certain degree of formation, some of the α-Si₃N₄ dissolves into the liquid phase where the solubility is high, and when the saturation of β-Si₃N₄ is reached, new β-Si₃N₄ precipitates out of the liquid phase. Finally, the β-Si₃N₄ grains began to grow and when the sintering temperature reached 1800 °C, Si₃N₄ reacted with TiC to form SiC and TiC₀.₇N₀.₃ in.

The fracture SEM photographs and energy spectra of the Si₃N₄/TiC/CaF₂@SiO₂ composite ceramic tool material are shown in Figure 13b. It can be seen from the SEM photographs in Figure 13c that the material is densely sintered with no obvious porosity. The Si₃N₄/TiC/CaF₂@SiO₂ composite ceramic material has two different fracture modes (along-crystal fracture and through-crystal fracture), contributing to the mechanical properties.

The prepared Si₃N₄/TiC/CaF₂@SiO₂ composite ceramic tool material was selected as the specimen for XRD analysis. It can be seen from Figure 13 that the diffraction peaks of α-Si₃N₄ and β-Si₃N₄ are very clear as the main crystalline phases. Diffraction peaks of SiC and TiC₀.₇N₀.₃ can also be clearly observed.

3.5. Mechanical Properties of Si₃N₄/TiC/CaF₂@SiO₂ Composite Ceramic Tool Materials

The mechanical properties of the sintered Si₃N₄/TiC/CaF₂@SiO₂ composite ceramic tool material were tested with a hardness of 15.66 GPa and a modulus of elasticity of 128.08 GPa. The results of the comparison between the simulated and experimental values are shown in

Table 11. Simulated and experimental values of the mechanical properties of Si₃N₄/TiC/CaF₂@SiO₂ composite ceramic materials.

	Simulated Values	Experimental Values	Error Value
Hardness (GPa)	15.89	15.66	0.23
Elastic modulus (GPa)	132.53	128.08	4.45

. It can be seen that the simulated and experimental values are consistent.

4. Conclusions

As the addition of solid lubricants can improve the mechanical properties of ceramic materials, this paper studies the effect of CaF₂ and CaF₂@SiO₂ addition on Si₃N₄/TiC materials using molecular dynamics. Different CaF₂ and CaF₂@SiO₂ models were developed to analyze the effects on the material interface as well as the mechanical properties. Based on the simulation results, the optimum sintering parameters for the Si₃N_4/TiC/CaF₂@SiO₂ material were obtained: a temperature of 2073 K at a pressure of 32 MPa. Based on these sintering parameters, the Si₃N₄/TiC/CaF₂@SiO₂ composite ceramic tool material was experimentally prepared and the mechanical properties were tested.

(1) The interfacial atomic layer is displaced to a greater extent in the direction perpendicular to the interface, and the atomic layer undergoes a phenomenon of layer dislocation. The TiC atomic layer closer to the interface has a larger amount of chirality, the first layer shrinks inwards as a whole, the C-Ti bond length increases, and the C-Ti-C bond angle slightly increases.

(2) When the type of atomic bonding at the interface between CaF₂ and the Si₃N₄ and TiC models is different, the corresponding elastic constants and elastic moduli are also different. The addition of CaF₂ leads to a decrease in the hardness of the system.

(3) The mechanical properties of the Si₃N₄/TiC/CaF₂@SiO₂ models differed when CaF₂@SiO₂ was added in different amounts. The model achieved optimum mechanical properties when the addition of CaF₂@SiO₂ in the model was 4. The hardness of the material increased with the temperature increase. It was 15.89 GPa when the temperature was 2073 K, while the modulus of elasticity was 132.53 GPa.

(4) The Si₃N₄/TiC/CaF₂@SiO₂ composite ceramic tool material was experimentally prepared with mechanical properties of 15.66 GPa hardness and 128.08 GPa modulus of elasticity, that are slightly lower than the simulated values. The SEM photograph at the fracture shows a mixed mode of along-crystal fracture and through-crystal fracture, which contributes to the mechanical properties.