Damage evolution and removal behaviors of GaN crystals involved in double-grits grinding

Two kinds of MD models for double-grits interacted grinding of GaN crystals were established using LAMMPS software. Both models consisted of a workpiece with a dimensions of 27.5 nm × 20 nm × 10 nm and two hemispherical abrasives with a radius of 3 nm. Three kinds of atoms were used in both the abrasive and workpiece models, namely, boundary, thermostat, and Newtonian atoms. The atomic positions in the boundary layer were fixed to prevent the workpiece from translating under the action of the grinding force. The coupling constant of the thermostat was selected to be 0.1 ps. The interacted distance of the two abrasives perpendicular to the grinding direction is called the transverse interacted distance, L_a . The interacted distance of the two abrasives along the grinding direction is called the radial interacted distance, L_b . Figure 1(a) shows the first model in which both L_a and L_b (=6 nm) are nonzero. Figure 1(b) shows the second model, in which only L_a is nonzero. All the grinding simulations were performed on the (0001) plane and along the [11–20] direction. The grinding depth, grinding length and speed were set as 2 nm, 17 nm, and 50 m·s⁻¹, respectively. The relaxation and grinding processes of the abrasives and work material were simulated in the NVT and NVE ensembles, respectively. The two abrasives cut the workpiece simultaneously during the simulation.

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The Tersoff potential is a three-body potential function that can accurately describe the length, angle, and energy of a bond between atoms, thereby providing a realistic description of covalent bonded materials [60, 61]. The Tersoff potential shown in equation (1) was used to model the interaction between the ions in GaN crystals [62],

$$\begin{align}{E_{{\text{GaN}}}} = \mathop {\mathop \sum \nolimits }\limits_{i > j} {f_c}\left( {{r_{ij}}} \right)\left[ {V_{ij}^R\left( {{r_{ij}}} \right) - \overline {{B_{ij}}} V_{ij}^A\left( {{r_{ij}}} \right)} \right]\end{align} \tag{ 1 }$$

where f_c (r), $V_{ij}^A$, $V_{ij}^R$, and ${\overline B _{ij}}$ denote the cut-off function, attractive energy, repulsive energy, and bond-order parameter, respectively. The values of the key parameters in the Tersoff potential are detailed in [62].

The interaction of C ions in diamond abrasives was described by the LCBOP potential [63] given in equation (2),

$$\begin{align}{E_{\text{C}}} = \frac{1}{2}\sum\limits_{i,j}^N V_{ij}^{{\,\text{tot}}} = \frac{1}{2}\sum\limits_{i,j}^N \left[ {{f_c}\left( {{r_{ij}}} \right)V_{ij}^{{\text{SR}}} + \left( {1 - {f_c}\left( {{r_{ij}}} \right)} \right)V_{ij}^{{\,\text{LR}}}} \right]\end{align} \tag{ 2 }$$

where $V_{ij}^{{\,\text{tot}}}$, V^SR, and V^LR denote the total pair interaction, short-range section, and long-range section, respectively. The values of the key parameters in the LCBOP potential are detailed in [63].

In addition, the C–N and C–Ga interactions were described by the 12/6 Lenard–Jones potential [34] given in equation (3),

$$\begin{align}E = 4\varepsilon \left[ {{{\left( {\frac{\sigma }{r}} \right)}^{12}} - {{\left( {\frac{\sigma }{r}} \right)}^6}} \right],r < {r_c}\end{align} \tag{ 3 }$$

where denotes the attractive well depth, r_c denotes the cut-off radius whose value is 0.25 nm, and σ denotes the interparticle distance.

To investigate the influence of the interacted distance on material deformation and removal characteristics, simulations were carried out on interactive double-grit grinding with different interaction distances according to the scheme presented in table 1. Given the computational difficulty of running MD simulations with the dimensions of an actual grinding process, we reduced both the size and spacing of the abrasives by the same multiple. For L_b = 0, a minimum L_b of 6 nm was needed to prevent interference between the two abrasives. In addition, a simulation on single-grit grinding was performed as a control. During the simulation, the additional kinetic energy generated by the movement of atoms along the grinding direction was removed to ensure the accuracy of the simulation results. The simulation results were analyzed using OVITO visualization software.

To validate the simulated results, an grinding experiment was performed on monocrystalline GaN using a ultraprecision self-rotating grinder, as shown in figure 2. The GaN specimen was 10.5 mm long, 10 mm wide, and 0.35 mm thick. To ensure that the GaN specimen was not damaged during preparation for the grinding test, CMP was performed on the specimen to achieve a surface roughness below 2.0 nm in Ra. Ceramic bonded diamond grinding wheels with mesh size of #8000 and diamater of 125 mm were used in the grinding experiment. The rotational speeds of the wheel and workpiece were 1500 and 100 r·min⁻¹, respectively. The feed rate was 12 μm·min⁻¹. Oil coolants were used in grinding process to decrease the grinding temperature and wheel wear. After the grinding test, an TEM sample of the ground subsurface was prepared by using a focused ion beam, and the subsurface damage was analyzed by the cross-sectional TEM method. The accelerating voltage, TEM linear resolution, high-resolution TEM (HR-TEM), TEM magnification, and scanning transmission electron microscopy (STEM) magnification of the TEM (Talos F200x, USA) are 200 kV, 0.14 nm, 0.1 nm, 25–1500 000, and 150–2300 000, respectively.

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Equation (4) [21] was used to calculate the uncut chip thickness d_g under the grinding conditions used in this study as 0–17.8 nm:

$$\begin{align}{d_g} = 2.44{R_g}{\left( {\frac{{{f_s}r{n_w}}}{{\pi {d_s}{b_s}\gamma n_s^2}}} \right)^{0.4}}\end{align} \tag{ 4 }$$

where d_g is the uncut chip thickness, R_g is the abrasive radius, f_s is the feed speed, r is the distance from the workpiece center, n_w is the rotational speed of the work material, d_s is the outer diameter of the wheel, b_s is the width of the wheel, γ is the volume content of the abrasives, and n_s is the wheel rotational speed.

Grinding force is an important index for evaluating the machining effect during the grinding process, and indirectly reflects the material removal process and interaction between the abrasives and workpiece. Figure 3 shows the grinding forces under different interacted conditions. Both figures 3(a) and (b) indicate that as the grinding length increases, the grinding force increases and then stabilizes. Therefore, the average grinding force at the stable grinding stage can be used to analyze the influence of the interacted distance on the grinding force. Figure 3(a) also shows that the grinding force is smaller for the second abrasive than the first abrasive because of the elimination of coupling actions between the two abrasives. Figure 3(c) shows that for L_b = 6 nm and increasing L_a , the grinding force increases and then stabilizes. This result is obtained because increasing L_a weakens the coupling between the two abrasives, increasing the contact area between the workpiece and abrasives. Figure 3(d) shows that for noninterfering abrasives, there is a specific L_a at which there is no discernible coupling between the abrasives and the grinding force is approximately twice that of a single grit, that is, L_a has no discernible effect on the grinding force.

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Figure 4 shows the influence of the transverse interacted distance on the coefficient of friction during double-grits grinding of GaN crystals. In this study, the coefficient of friction is defined as the ratio of the tangential force exerted by the abrasive along the grinding direction to the normal force exerted by the abrasive. In figure 4(a), for L_b = 6 nm and increasing L_a , the coefficient of friction decreases and then increases. The atomic displacements shown in the inset images indicate for L_a below 3 nm, the contact area between the workpiece and abrasives increases with L_a . However, there is no discernible increase in the number of atoms that have accumulated in front of the abrasives because of the elimination of coupling between abrasives, which results in the gradual decrease of the coefficient of friction. For L_a above 3 nm, as L_a increases, the effect of eliminating the coupling between abrasives weakens and the number of atoms that have accumulated in front of the abrasives increases, resulting in the gradual increase of the coefficient of friction. Figure 4(b) shows that for L_b = 0 nm, L_a has no discernible effect on the coefficient of friction. Selecting appropriate interacted distances can effectively reduce the friction between the workpiece and abrasives below that of single-grit grinding while ensuring efficient material removal, providing a feasible approach to the wheel design of ordered abrasives.

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The stress investigated in this study corresponds to the von Mises stress, which was calculated by the spatial average method. Figure 5 presents the stress distributions for different transverse interacted distances when the radial interacted distance is 6 nm. The average stress induced by the second abrasive during double-grit grinding (∼49.5–57.5 GPa) is smaller than that induced during single-grit grinding (∼58.1 GPa) because of the elimination of the coupling to the first abrasive. When the transverse interacted distance is 1 nm, the average stress induced by the second abrasive is 14.8% lower than the average stress induced during single-grit grinding. As the transverse interacted distance increases, the coupling removal of the first abrasive weakens, causing the stress induced by the second abrasive to gradually increase and approach that induced during single-grit grinding.

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Figure 6 presents the stress distributions under different transverse interacted distances when the radial interacted distance is 0 nm. When the transverse interacted distance is 6 nm, large stresses in the workpiece are mainly concentrated between the two abrasives as well as below the abrasives because of the pushing action of these abrasives. As the transverse interacted distance increases, the coupling effect between the abrasives gradually weakens. Therefore, the stress on the subsurface gradually decreases, and the large stress is gradually transferred to the region below the two abrasives. In addition, the number of chips accumulated between the two abrasives gradually increases with the transverse interacted distance. A very low stress is exerted on the chips because the abrasives no longer push on the material after the chips form.

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It is crucial that MD simulations accurately predict material damage phenomena. Therefore, it is particularly important to determine the subsurface damage mechanism of GaN crystals during interactive double-grit grinding. The machining scale in an MD simulation is considerably smaller than the depth of the brittle-to-ductile transition region in GaN crystals. Thus, the simulated subsurface damage is plastic damage, as shown in figure 7. The simulated results demonstrate that the plastic damage of GaN crystals induced by double-grits grinding is dominated by the amorphous transition, high-pressure phase transition, dislocations, stacking faults, and lattice distortions. The atoms in the chips and groove surfaces have high energy and weak structural stability and are therefore most prone to amorphization [64, 65]. The results of Zhang et al [66] and Jiang et al [67] lead to the conclusion that the maximum stress induced by machining does not occur at the ground surface underneath the abrasive but at a certain distance from the ground surface in the plastic zone. Therefore, the high-pressure phase transition zone lies below the amorphous layer. The plastic zone is surrounded by a large number of stacking faults and dislocations because of the effect of subsurface stress at the boundary of the plastic zone [68, 69]. To eliminate the interference of elastic deformation on the identification of lattice distortion, we selected an area far away from the abrasive after elastic recovery to identify the lattice distortion. Therefore, the results presented in figure 7(h) were confirmed to be lattice distortion rather than elastic deformation. Figure 7(i) shows the phase transition path from hexagonal GaN to cubic GaN that occurs during the grinding process. It can be observed that the high pressure caused by the abrasive destroys the atomic arrangement and lattice structure. The high pressure induced by the abrasive destroys the atomic arrangement and lattice structure. The barrier to the phase transition is overcome by the generation of unstable intermediate phases between the hexagonal and cubic structures. As the pressure increases, the content of hexagonal GaN gradually decreases and the content of cubic GaN gradually increases and then stabilizes. An experiment was performed to confirm the simulation results.

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An experiment was performed to characterize the ground subsurface to validate the MD simulation results of the effect of coupling between abrasives on material damage and removal during grinding. Figure 8 shows the bright field (BF) TEM images of damage behaviors of the ground subsurface. The diffraction spots shown in figure 8(d) indicate that the original GaN substrate is a perfect single crystal with a zone axis of [11–20]. Figure 8(a) indicates that the ductile subsurface does not contain cracks and brittle fractures, and a plastic damage layer lies 200 nm beneath the ground surface. Figures 8(b) and (c) show that high-density stacking faults and dislocations are one of the main forms of plastic damage that occurs in GaN crystals during grinding. The main plastic deformation zone lies above the stacking fault and dislocation zones, which is similar to the subsurface damage induced by the quasi-static scratching [33]. To understand the essence of the main plastic deformation zone, more HR-TEM experiments need to be performed to characterize the main plastic deformation zone. The stacking faults generated under a high strain rate differ from those generated by low-strain-rate nanoscratching [33]. Only high-density stacking faults parallel to the (0001)-orientation plane are generated during the low strain-rate nanoscratch test. Figures 8(b) and (c) and (e) show that in addition to the stacking faults parallel to the (0001)-orientation plane, high-density stacking faults parallel to the {-1101} and {1-101} directions are generated during grinding. This phenomenon occurs because compared to low-strain-rate nanoscratching, grinding generates a considerably higher strain rate, which induces a higher stress on the subsurface and activates crystal-plane slip along more crystal directions.

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Figure 9 shows the HR-TEM images of the ground subsurface morphology. Figures 9(a) and (b) prove that surface amorphization is one of the main types of plastic damages in monocrystalline GaN induced by ultra-precision grinding, and figure 9(c) further confirms the existence of the high-density stacking faults. Similar to the simulated results, the surface atoms have relatively high energy and weak structural stability, producing an amorphization layer on the ground surface. The force exerted by the abrasives generates a shear stress along the close-packed plane that destroys the stacking sequence, generating stacking faults. As shown in figure 9(d), the interplanar spacings and included angles demonstrate that cubic GaN is generated by the high-pressure phase transition behavior. Figures 9(e) and (f) prove that dislocations and lattice distortions are also main forms of plastic damages induced in the grinding process. Lattice distortions increase the internal energy of materials and hinder dislocation slip. The TEM micrographs presented in figures 8 and 9 indicate that the forms of plastic damages from the ground surface to the subsurface are amorphous atoms, phase transition atoms, and a combination of dislocations and stacking faults. The aforementioned experimental results agree well with the MD results, which indicates that the simulated results are reliable.

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The subsurface damage depth is one of the important indicators for evaluating the surface integrity during the ultra-precision machining of brittle materials [70, 71]. In this study, all the amorphous atoms, phase transition atoms, dislocations, stacking faults, and lattice distortions underneath the residual surface are regarded as subsurface damages. Therefore, the subsurface damage depth is defined as the distance from the residual surface to the deepest damage. Figure 10 presents the effect of the transverse interacted distance on the subsurface damage depth. Compared with the interacted distance in only one direction, the interacted distance in both radial and transverse directions achieved the shallower subsurface damage. When the radial interacted distance is 6 nm, the damage depth of the ground subsurface increases as the transverse interacted distance increases. The stress analysis in figure 5 demonstrates that increasing transverse interacted distance leads to an increase in the grinding stress of the second abrasive, resulting in an increase in the subsurface damage depth. However, there is no clear correlation between the transverse interacted distance and subsurface damage depth for the radial interacted distance of 0 nm.

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Figure 11 shows the numbers of amorphous atoms under different interacted distances. As shown in figure 11(a), when the radial interacted distance is 6 nm, the number of amorphous atoms increases as the transverse interacted distance increases. This occurred because increasing transverse interacted distance can improve the material removal volume and grinding stress of the second abrasive, resulting in an increase in the number of amorphous atoms. As shown in figure 11(b), when the radial interacted distance is 0 nm, amorphous atoms increase and then decrease as the transverse interacted distance increases. When the transverse interacted distance is below 8 nm, as the transverse interacted distance increases, material removal volume and chip deformation increase, resulting in an increase in the number of amorphous atoms. However, when the transverse interacted distance is above than 8 nm, the grinding stress decreases as the transverse interacted distance increases, resulting in a decrease in the number of amorphous atoms.

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Figures 12 and 13 show the numbers of phase transition atoms of cubic GaN and dislocation lengths under different interacted distances, respectively. It can be found that there is no clear correlation between the transverse interacted distance and number of atoms in the phase transition and dislocation length. This occurred because the high-pressure phase transition and dislocation length are determined by the stress and material removal volume. For a constant radial interacted distance and increasing transverse interacted distance, the stress decreases and then gradually stabilizes, whereas the material removal volume increases and then stabilizes. Therefore, transverse interacted distance is not monotonically related to the number of atoms in the phase transition and dislocation length.

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Figure 14 shows that the amorphization transition is the main form of damage behaviors in abrasive wear, such that the proportion of abrasive amorphization can be used as a measure of the damage degree of the abrasives [72, 73]. The morphologies of the abrasives after grinding show more severe amorphization damage at the flank face than that at the rake face. The high elastic recovery rate of the residual GaN material under a high contact stress during grinding [74, 75] makes the flank face prone to friction after grinding than the rake face, resulting in severe wear of the flank face. As shown in figure 14(a), when the radial interacted distance is 6 nm, the amorphization proportion of the first abrasive is larger than that of the second abrasive for the same scratch lengths. As the transverse interacted distance increases, the amorphization proportion gradually increases and then stabilizes. This result is obtained because the elimination of coupling to the first abrasive reduces the volume of material removed by the second abrasive and the elastic recovery depth of the residual materials, effectively reducing the contact stress and flank wear induced by the elastic recovery of the residual materials. The stress generated by the second abrasive also suppresses the elastic recovery of the residual materials of the first abrasive, reducing the flank wear of the first abrasive compared to that of single-grit grinding. As shown in figure 14(b), when the radial interacted distance is 0 nm, there is no clear correlation between the transverse interacted distance and amorphization proportion of abrasive atoms, and the amorphization proportion of the first abrasive is close to that of the second abrasive.

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