Molecular dynamics study on deformation behaviour of monocrystalline GaN during nano abrasive machining

Journal Pre-proofs Full Length Article Molecular dynamics study on deformation behaviour of monocrystalline GaN during nano abrasive machining Yongqiang Wang, Sai Tang, Jian Guo PII: DOI: Reference:

S0169-4332(20)30248-8 https://doi.org/10.1016/j.apsusc.2020.145492 APSUSC 145492

To appear in:

Applied Surface Science

Received Date: Revised Date: Accepted Date:

1 November 2019 17 January 2020 20 January 2020

Please cite this article as: Y. Wang, S. Tang, J. Guo, Molecular dynamics study on deformation behaviour of monocrystalline GaN during nano abrasive machining, Applied Surface Science (2020), doi: https://doi.org/ 10.1016/j.apsusc.2020.145492

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2020 Published by Elsevier B.V.

Molecular dynamics study on deformation behaviour of monocrystalline GaN during nano abrasive machining Yongqiang Wanga, Sai Tanga, Jian Guoa* aSchool

of Mechanical Engineering, University of South China, Hengyang, Hunan, 421001, P. R. China *Corresponding author. E-mail address: [email protected] (Jian Guo); Tel: +86 734 8282750 (Jian Guo)

Abstract Molecular dynamics simulations are carried out to investigate the nano abrasive machining of monocrystalline gallium nitride (GaN). Effects of the cutting velocity, depth of cut (DOC) and abrasive shape on the atomic strain, stress, temperature, cutting forces, and deformation layer are systematically investigated, aiming at understanding the deformation behaviour of monocrystalline GaN during nano abrasive machining. The results show that the strain, stress and temperature were increased by using the higher cutting velocity, the larger DOC or cub-octahedral abrasive. Being affected by both the average stress and the elasto-plastic deformation zone right ahead the diamond particle, the cutting forces increase with the increase in DOC but decrease under a larger cutting velocity, or when using a cub-octahedral abrasive. The deformation layer in the subsurface is insensitive to the cutting velocity, while impressively shrinks under a larger DOC or cub-octahedral abrasive used. As the stress and temperature rise, the use of higher cutting velocity, larger DOC or cub-octahedral abrasive would facilitate the nucleation of dislocation, phase transition and the development of pile-up. This work can enrich the understanding on the nanoscale deformation mechanism of monocrystalline GaN material during the ultra-precision machining process. Keywords: GaN; Nano abrasive machining; Molecular dynamics; Deformation

1

1. Introduction Gallium nitride (GaN), as the third generation of semiconductor, holds the centre of interest in industry and academia due to its unique properties, such as wide forbidden band, direct energy gap, high temperature and pressure resistance [1]. By virtue of these advantages, GaN-based devices have been widely used in blue/green/ultraviolet light emitting diodes (LEDs) [2,3], high electron mobility transistors [4,5], high power and frequency electronic devices [6,7], etc.

As crystal defect such as dislocations and lattice damage usually impairs photoelectric conversion efficiency [8], high-reliability and high-performance devices that fully realize the potential of GaN generally require the substrate has a global planarization surface with low lattice damage and thin deformation layer in the subsurface [9, 10]. Thereinto, nano abrasive machining, such as chemico-mechanical polishing (CMP) technique [11-14], is the prerequisite and common way to realize the surface planarization of GaN substrate, in which nano particle is usually used as abrasive to restrain lattice damage and improve surface finish. It is well known that CMP involves complex reciprocal action of chemical reaction and mechanical abrasion [15]. The deformation patterns (e.g. dislocation, phase transition, nanocrystal and amorphization, etc.) induced by the nanoscale mechanical interaction between the work material and abrasive particle during polishing have a direct effect on the surface and subsurface quality, and would also have a potential to enhance the chemical reaction, thus indirectly improving removal efficiency [16]. Therefore, systematically study on the deformation behaviour of monocrystalline GaN in a nano abrasive machining process can not only give an insight into the surface formation mechanism during polishing, but also provide a better understanding of the various material removal mechanisms involved. Nevertheless, the deformation behaviour and mechanism of monocrystalline GaN under nanoscale mechanical interaction are far from understood at present, which would to some extent restrict the further development of the process, especially in the case where the mechanical interaction is more dominant than the chemical effect. On

2

the other hand, owing to the inaccessibility of the nanoscale interaction between the work material and abrasive particle in the abrasive machining process, the deformation involved is really hard to be observed experimentally. It is hence necessary to find a feasible way to investigate the nanoscale deformation behaviour of monocrystalline GaN during the nano abrasive machining.

Molecular dynamic (MD) simulation, as a scientific algorithm, has been proven a powerful tool to study the nanoscale machining processes [17-20]. The implementation of MD simulation was first developed through the pioneering work of Alder and Wainwright in the late 1950s [21]. It was not until 1990 that Belak and Stowers [18] published a paper on the MD simulation of copper cutting process, which opened the prelude to the study of MD machining simulation. One year later, they also applied MD method in abrasive machining [22]. Since then, the MD simulation on abrasive machining has attracted the attention of many researchers. Rentsch et al. [23] presented the first simulation results on the pile-up phenomenon in abrasive machining. A new method to improve the model representation and to enhance the computation speed for a large MD model was also given in their work. Ye et al. [24] simulated the nano abrasive polishing of a copper surface using MD method. They focused on the mechanical abrasion aspect of material removal and found that dislocations and atomically rough planarized surface could be formed. Oluwajobi et al. [25] investigated the fundamentals of MD modelling involved abrasive machining and put forward some popular potentials used in MD modelling and algorithms to solve the equations encountered. Yang et al. [26] recently conducted MD simulation to study the self-rotation effect of abrasive particle in ultra-precision polishing. Their research results revealed that the deformation mechanism of monocrystalline copper is due to the formation and movement of dislocations. With the increase of abrasive self-rotation speed, the deformation mechanism would transit from cutting to plowing regimes. Additionally, regarding the removal mechanisms and deformation properties of different materials, MD nanometric machining simulations were also performed by some researchers. For example, Zhang et al. [19] discussed the deformation of monocrystalline silicon subjected to contact

3

sliding with the aid of the MD analysis. It was reported that amorphous transformation is the main deformation mechanism in silicon and the onset of such inelastic deformation can be well predicted by a stress criterion. Goel et al. [20] later used MD simulation to compare the nanometric cutting of monocrystalline and polycrystalline silicon. It was indicated that the propensity for amorphization is significantly higher in single crystal silicon than that in polysilicon, signifying that grain boundaries eases the deformation process. Li and Fang [27, 28] conducted MD simulation to investigate the mechanisms of subsurface damage and material removal of monocrystalline copper and Ni/Cu multilayers during a nanoscale high speed grinding and found a transition of deformation mechanisms depending on the competition between the dislocations and twinning. Komanduri et al. [29] systematically studied the nature of deformation of single crystal aluminum during nanometric cutting using MD simulation. They reported that the plastic deformation and dislocation ahead the tool were related to both the lattice orientation and cutting direction. Lu et al. [30] investigated the deformation behaviours of zirconia thin film on top of an zirconium substrate using MD nanoindentation simulation and determined the effect of the zirconia film on the mechanical properties of the zirconium substrate. Sharma et. al [31] studied the wear mechanism of single crystal diamond tool during nanocutting of copper beryllium under blunt and sharp edge configurations and indicated that blunt edge tool leads to smoother surface compared to the surface generated by sharp edge configuration. Zhu et al. [32] employed MD simulations to study the nanometric cutting process of Cu50Zr50 amorphous alloy. Their research results showed the plastic deformation of amorphous alloy is mainly due to the formation of shear transformation zones. More recently, MD nanoindentation and nanoscratch simulations of monocrystalline GaN were also conducted by Qian et al. [33, 34] and Xiang et al. [35]. Although the indentation response, the mechanism of plastic deformation and the tribological behaviour of monocrystalline GaN under a quasi-static loading condition were well demonstrated in the previous work, the systematically understanding of its deformation behaviour involving nano abrasive machining is still lacking, which inspires the motivations for our present research.

4

It is noted that, as the abrasive particles used in nano abrasive machining have nanoscale dimensions, the real DOC of abrasive should be generally less than the critical DOC of GaN material. This suggested that the material removal would fall in the ductile cutting regime [36] and the results of MD simulation on nanometric cutting could be applicable to understand the nano abrasive process. In addition, taking the complexity and stochastic characteristics of a multi-grits system into account, a tactic similar to a single point grinding experiment [37] was applied to perform a MD study on the nanometric cutting of wurtzite monocrystalline GaN with a single abrasive particle in this work, aiming at simplifying the problem. Effects of cutting velocity, DOC and abrasive shape on the machining performance were systematically investigated, from which information cannot be easily duplicated experimentally (e.g. atomic strain, atomic stress, atomic temperature, cutting forces and deformation conditions) could be obtained by simulation. Such information involving individual grit behavior could be used to synthesize the collective performance and analyze the mechanism of multi-abrasive system, so as to enrich the understanding about deformation behaviour and mechanism of monocrystalline GaN during an entire nano abrasive process, and definitely open up a potential to improve machining performance.

2. MD simulation details 2.1 Simulation model This work used a Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [38] to perform MD simulation. The simulated outputs were visualized and analysed by OVITO software [39]. Fig. 1 shows the established MD simulation model, which contains a cubic monocrystalline GaN workpiece and a rigid spherical diamond particle. According to Ref [33], the lattice constants used to build wurtzite GaN single crystal are a=3.191 Å, b=5.510 Å, and c=5.194 Å and another internal constant u that specifies the relative distance between the Ga- and N- sublattices along the [0001]-direction was taken to be 0.375, as shown in the right side of Fig. 1. The workpiece includes three types of atoms: boundary atoms, thermostat atoms, and

5

Newtonian atoms. The movement of the thermostat and Newtonian atoms obey the classical second Newton’s law whose equations of motion could be numerically integrated using the well-established Velocity-Verlet algorithm [40]. The simulation system was sufficiently relaxed by 30 ps prior to machining. The velocity rescaling method was applied on the thermostat atoms at every five time steps, serving to keep the system at a constant initial temperature and dissipate the generated heat during the machining process at a reasonable rate in accordance with the practical situation. Both the relaxation and cutting simulations were conducted in a microcanonical ensemble (NVE). The bottom atoms were kept spatially fixed to eliminate the rigid body motion of the workpiece. The side edges of the model were also imposed fixed boundary to maintain the symmetry of the lattice structure by reducing the edge effects [41], and avoid the distortion of the workpiece induced by the abrasive invasion which disagrees with the real machining conditions [42, 43] since the width used in this model was sufficient to conduct the simulation properly. Periodic boundary conditions (PBC) were applied along and orthogonal to the cutting direction, aiming at reducing the influence of variation in length scale and avoiding the phenomenon of “lost atoms” occurred occasionally in the simulation running since the difference between the simulations with and without PBC applied was acceptable.

2.2 Interatomic potential There are six different atomic interactions in this MD simulation: the interactions between atoms in the workpiece, i.e. Ga-Ga, Ga-N and N-N, the interactions between the diamond particle and the workpiece, i.e. C-Ga and C-N, and the interaction between atoms in the diamond particle C-C. Tersoff-Brenner bond-order potential was applied on Ga-Ga, Ga-N and N-N interactions since this potential has been proven to reproduce the geometric structure and mechanical properties of GaN accurately in previous work [33, 44].The interactions of C-Ga and C-N were described by Lennard-Jones potential [33], which is expressed as,   12   6  E  4      , r  r0  r    r 

(1)

6

where r the distance between two atoms; σ and ε the potential parameters for equilibrium distance and cohesive energy, respectively, whose values are calculated according to the long-range Vander Waals interaction [45] and listed in Table 1. The cut-off radius r0 in Lennard-Jones potential was taken to be 7.5 Å to ensure computational efficiency. The interaction between atoms (C-C) in the diamond particle was ignored as the diamond particle is treated as a rigid body in this work [46].

Fig. 1: MD simulation model of nano abrasive machining of wurtzite monocrystalline GaN. (The right side shows the unit cell used to build wurtzite GaN crystal [33]). Table 1: Lennard-Jones potential parameters for C-Ga and C-N interactions [33] Element

σ (Å)

ε (meV)

C-Ga

3.6919

8.4646

C-N

3.3677

3.7235

2.3 Simulation parameters The computational parameters used in this MD simulation are listed in Table 2. The size of the GaN workpiece was 24×14×8 nm3 with atom numbers of 225330. Spherical diamond particle and cub-octahedral diamond particle that has a negative rake angle with straight cutting edge were used as abrasive respectively, for the purpose of

7

evaluating the influence of grain shape. The spherical particle has a radius of 3 nm, with 19913 atoms, while the cub-octahedral particle has the equivalent size as the spherical particle, with 18938 atoms. The time step for numerical integration was 1 fs. The initial temperature was set as 293 K. Nanoscale machining was conducted along the [-2110] direction on (0001) crystal plane with a cutting distance of 16 nm. Different cutting velocities of 25, 50, 100 and 200 m/s and different DOCs of 0.5, 1.0, 1.5 and 2.0 nm were used to investigate the effects of cutting velocity and DOC.

2.4 Analysis methodology In this study, von Mises stress was calculated to clarify the shear-dependence deformation behaviour of GaN during atomic-level machining as [47, 48],

 Mises  3 xy2   yz2   xz2  



1  xx   yy 2   xx   zz 2   yy   zz 2 2



(2)

Where σxx, σyy, σzz, τxy, τxz and τyz are the stress components of each atom, which can be derived from the MD simulation result of LAMMPS. Table 2: Computational parameters used in MD machining simulation Materials

Workpiece: GaN

Dimensions (nm)

Cubic: 24×14×8

Number of atoms

225330

Time step (fs)

1

Initial temperature (K)

293

Cutting velocity (m/s)

25, 50, 100, 200

DOC (nm)

0.5, 1.0, 1.5, 2.0

Cutting distance (nm)

16

Cutting direction

[-2110]-direction on (0001) plane

Tool: diamond Spherical: R3, Cub-octahedral 19913, 18938

To quantify the plastic deformation at the atomic level, an atomic local shear strain analysis method proposed by Shimizu et al. [49] was employed in this work, where von Mises shear invariant was calculated as,

8

 iMises   xy2   yz2   xz2 



1  xx   yy 2   xx   zz 2   yy   zz 2 6



(3)

As a lowly ionic compound, GaN generally stabilizes in wurtzite (WZ, P63mc in space group) phase under ambient conditions [50], that is, in a perfect GaN single crystal, the coordination number (CN) of bulk and surface atoms should be 4 and 3, respectively. Once this rule is broken, it can be indicated that the primitive crystal structure has been collapsed. Then the phase transformation may occur in monocrystalline GaN, which can be identified according to the coordination analysis. It should be noted that there are some other analysis methods to identify structure alterations, such as Centrosymmetry Parameter (CSP) [51] and Common Neighbor Analysis (CNA) [51]. However, CSP fails when non-centerosymmetric wurtzite GaN crystal is concerned because it is defined only in a centrosymmetric crystal such as fcc and bcc [51] and CNA is time-consuming due to its complicated parameter calculation [52]. Accordingly, we chose coordination analysis with a cut-off radius of 2.15 Å in this work since it can identify defect patterns accurately and efficiently as proven by the previous work [33-35]. In addition, the automated “dislocation extraction algorithm” (DXA) [53, 54] was also used to identify dislocations and other crystal defects.

The temperature of the individual atom in the Newtonian layer was calculated based on the relationship between temperature and energy as [32], T

2 Ek dNk B

(4)

Where Ek the kinetic energy for a single atom which was derived from the simulation result of LAMMPS. d the spatial dimension taken to be 3 as this work conducted a three-dimensional simulation. N the number of atoms which was taken to be 1 for an individual atom. kB the Boltzman constant with the value of 1.3806504×10−23 J/K.

9

3. Results and discussion 3.1 General analysis of nano abrasive machining of GaN Fig. 2 shows the force histories and atomic displacement distributions during the machining simulation. In the initial stage, as the contact area between diamond particle and workpiece increases with the increase of cutting distance from 0 to 3 nm, the cutting forces, both normal and tangential forces, increase rapidly from 0 to ~560 nN, as shown in Fig. 2(a). It is clear in Fig. 2(a) that a semiwarhead-shaped deformation zone was formed ahead the diamond particle, with atomic displacement ranging from 2.15 to 8 Å. Our simulation showed that this zone was an elasto-plastic deformation zone (EPDZ) as it can be partially recovered after unloading. Generally, EPDZ is affected by both the development of dislocation and the contact of workpiece/tool, and has a great influence on cutting force, that is, the larger the EPDZ, the stronger cutting resistance the diamond particle is subjected, hence the greater the overall cutting force (see below for detailed discussion). As the diamond particle further advanced to 8 and 9.5 nm, slip traces induced by dislocation glide can be observed on both sides of the groove, as indicated by the yellow arrows in Fig. 2(b) and (c), suggesting that dislocations were well developed in the subsurface [35]. At the same time, with the propagation of dislocation, the potential energy stored in the atomic bonds, also known as the strain energy density macroscopically [55], was dissipated, thus resulting in the reduction of material strength and a contracted EPDZ. As a response to the reduction of material strength, the tangential force was slightly decreased, being similar to the pop-in event as observed in nanoindentation test [56]. Nevertheless, it seems that this response is only associated with the cutting direction because the normal force in the non-cutting direction continued to increase. It is interesting to note that the EPDZ expanded and the cutting forces increased as the cutting distance was further increased from 9.5 to 11 nm but with no obvious increase in slip traces on the (0001) plane (see Fig. 2(d)), which indicates the system is reaccumulating potential energy in the atomic bonds and preparing to evoke a new round of deformation [55]. Fig. 2 also shows that with the progress of machining, the atoms pile-up ahead the diamond particle and on both sides of the groove became severe, as indicated by the black arrows.

10

Fig. 3 shows the localized atomic displacement vector variation of wurtzite GaN single crystal with the progress of machining. As can be seen, the workpiece atoms right ahead the diamond particle mostly move along the cutting direction, i.e. [-2110] direction, due to the push of diamond particle. This part of atoms are the so-called stagnation region atoms [57], which contribute the greatest blockage to the cutting of diamond particle. On account of the hindrance of stagnation region atoms, other workpiece atoms in the vicinity of the contact zone of workpiece/tool are forced to deviate from the cutting direction, such as some move along the {1-100} planes (a major slip system of wurtzite GaN), following the slip direction of 1/3<1-210> [35], some move upward to free surface to form pile-up and the rest move towards the interior of the material along the {-2112} plane (another slip system [58]). It is also found that the atoms in the topmost of the workpiece contacted with the diamond particle had the longest displacement vectors, indicating the atoms migrate the furthest. With the progress of cutting, the diamond particle continued to move forward, leaving a large machined groove behind the tool. As a result, the workpiece atoms got more extent of freedom to move along other directions. Fig. 3(b) and (c) show that there are many atoms moving back towards the machined groove, from both sides of the cutting direction and at the bottom of the contact zone. In addition, the atoms that have already moved to the interior of the crystal bulk at the initial stage also migrate upward to the machined zone. The return of these atoms backward to the machined groove leads to the consequent elastic recovery [59] and the expansion of the machined surface. It should be stressed that there are obvious boundaries between the atom groups which move along different directions. With the progress of machining, these boundaries have the potential to eventually constitute the birthplace of some defects, such as dislocation or crack. The analysis of Fig. 3 suggested that localized atomic displacement of monocrystalline GaN was synergistically affected by the stagnation region and the slip systems.

Fig. 4 shows the evolution of the deformation layer with the machining progress. As can be seen from Fig. 4(a) to (c), the deformation layer significantly expanded as the

11

diamond particle moves forward. With the increase of cutting distance from 0 to 16 nm, the number of the atoms in the deformation layer increased from 0 to 10030, as shown in Fig. 4(d). The simulation showed that the majority of the deformation layer (‘Other’ shown in Fig. 4) lost the pristine long-range ordered atomic arrangement, suggesting the formation of amorphous substance. Also, as the cutting distance increased, nanocrystal with cubic diamond (CD) structure appeared in the deformation zone, as shown in Fig. 4(c), indicating a possible phase transition of GaN from wurtzite to the zinc-blende structure during a nano abrasive machining. It is known that zinc-blende GaN is metastable in normal conditions [60]. Presently, radio-frequency planar magnetron sputter deposition using low-pressured N2 gas [61] and epitaxial growth using excess Ga flux supply at low temperature [62] are two conventional approaches to obtain zinc-blende GaN. However, the pressure-induced phase transition from wurtzite to zinc-blende structure could be also expected at a finite temperature [63]. Accordingly, we thought that the resultant high pressure and temperature during nano abrasive machining could facilitate the transition of GaN from wurtzite to the zinc-blende phase.

12

Fig. 2: Force histories and top-viewed atomic displacement distributions with the advance of diamond particle: (a) 3, (b) 8, (c) 9.5 and (d) 11 nm. White dash lines signify the elastoplastic deformation zone (EPDZ, identified with the cut-off radius ranging from 2.15 to 8 Å), black arrows indicate the pile-up atoms and yellow arrows indicate the slip trace.

13

Fig. 3: Top and cross-sectional snapshots showing localized atomic displacement vectors variation under different cutting distances of (a) 3, (b) 6 and (c) 12 nm. (Note the length and direction of the arrow represent the relative size and direction of the displacement respectively. The vectors under cutting distance of 3 nm are calculated relative to those under 0 nm and the latter is calculated relative to the former)

14

Fig.4: The deformation layers under different cutting distances of (a) 3, (b) 6 and (c) 12 nm; (d) Atom number in deformed zone vs. cutting distance. Gray, blue, baby blue and light green represent other, cubic diamond (CD), 1st and 2nd CD neighbor atoms.

15

Fig. 5: Dislocation under different cutting distance of (a) 3, (b) 6 and (c) 12 nm and (d) dislocation length vs. cutting distance.

16

Fig. 5 shows the comparison of dislocations under different cutting distances, obtained by the DXA method. Apparently, with the increase of cutting distance from 0 to 16 nm, the dislocation significantly grew from 0 to 92 nm, as shown in Fig. 5(d). It should be noted that at the initial stage when the diamond particle advanced to 3 nm, there is no dislocation formation inside the bulk, as shown in Fig. 5(a), although the deformation has been produced in the subsurface (see Fig. 4(a)). This suggested that the average stress in the subsurface is insufficient to initiate dislocation in this stage. As the cutting distance increased to 6 nm, the stress was higher than the critical value to activate dislocation, and half dislocation loops propagating along the slip directions of 1/3<1-210> began to appear beneath the work surface, as shown in Fig. 5(b). It can be found that these half dislocation loops are composed of three segments, one is in parallel with the (0001) plane, and the other two nucleate from the (0001) plane, giving slip trace on the (0001) plane as observed in Fig. 2, and propagate vertically towards inside and eventually intersect with the parallel segment, thus merging into a “u-shaped” half loop. Xiang et al. [35] have suggested that these half dislocation loops could be preferentially evoked by the load acting on (0001) plane owing to the anisotropy with respect to the loading axis in wurtzite lattice. Moreover, the increase in cutting distance would also cause the diversification of dislocation type, as evidenced by the appearance of dislocations with Shockley partials b=1/3<1-100> and other unidentified dislocations, as shown in Fig. 5(c). Since dislocations with Shockley partials are generally around the intrinsic stacking fault formed on (0001) plane [35], it can be deduced that stacking fault developed as the machining progressed.

17

Fig. 6: Atomic distribution of different coordination numbers under different tool advances: (a) 3, (b) 6 and (c) 12 nm; (d) Number and (e) percentage of atoms of different coordination numbers evolved with progressive machining.

Fig. 6 are the snapshots showing the atomic distribution of different coordination numbers (CNs) with the progress of machining and the plots of atom number and percentage of different CNs against cutting distance. It is seen from Fig. 6(a) to (c),

18

atoms of CN=4 mostly distributed in the deformation layer right ahead the diamond particle. With the advance of cutting, the deformation layer expanded and the atoms numbers of different CNs all increased obviously, as shown in Fig. 6(d). Nevertheless, the variation trends of atomic percentage of different CNs are different. Fig. 6(e) shows the percentages of low coordinated atoms (CN=1 and 2) are very low while the atoms of the intermediate coordination (CN=3 and 4) hold an absolute majority in the deformation zone. At the beginning of the cutting, as the crystal had a relatively intact wurtzite structure, the atomic percentage of CN=4 was high, up to 74%, and the atoms of CN=3 which constitute the crystal surface ranked the second with a percentage of approximately 20%. When the diamond particle continued to advance, due to the variation in contact loading [64], the Ga-N bonds in the deformation layer were stretched or broken and tended to form a sparse amorphous structure with low coordination, thus could establish a new equilibrium. As a result, the atomic percentage of the wurtzite structure (CN=4) was decreased (see Fig.6 (b)), and the percentage of the amorphous phase atoms (refers to the atoms with CN=1, 2 and 3 only inside the crystal bulk) was increased, being in agreement with the finding in Fig. 4. Of course, in view of the rise of pressure and temperature during machining, the phase transition to other fourfold coordinated structure, such as cubic zinc-blende (CN=4) [63] as observed in Fig. 4, or even body-centered-tetragonal (CN=4) structure [65, 66] could be also possible. The compression-induced phase with a fivefold coordinated hexagonal structure (CN=5) was also identified in this simulation but with an extremely low percentage. It has been reported that the phase transition of monocrystalline GaN from wurtzite to fivefold coordinated hexagonal structure could be enhanced by high pressure, high compressive strain rate and very low temperature with the radial stretching motion of atoms [67]. Therefore, the high strain rate and stress arising from high cutting velocity used in nano abrasive machining could enable phase transition, but the room temperature and the slide motion of cutting applied in this simulation greatly decreased the transition ratio. This explains why CN=5 atoms can be traced but with very little percentage.

19

Fig. 7 shows the shear strain distributions in monocrystalline GaN under different cutting distance and the average strain (extracted from the deformation layer with a thickness of 1.5 nm right ahead the diamond particle) plotted against cutting distance. Each atom is colored according to their local von Mises shear invariant in the typical atomic configurations during nano abrasive machining. It is obvious that the shear strain greater than 0.5 mainly distributed in the pile-up and the topmost of the machined surface, demonstrating that severe plastic deformation occurred in these areas. As the diamond particle moved forward from 0 to 16 nm, the shear strain extended throughout the area that the diamond particle has scratched, as shown in Fig. 7(a) to (c), with its average value increasing rapidly at the initial stage, and then stabilizing at ~0.59, as shown in Fig. 7(d). Since the increase of atomic strain boosts the probability of bond breaking, we speculated that the increase in shear strain could facilitate the amorphization in the subsurface, as observed in Fig. 6.

The local von Mises stress distribution in monocrystalline GaN under different cutting distance and the corresponding average stress (extracted from the deformation layer with a thickness of 1.5 nm right ahead the diamond particle) evolved with the progressive cutting are illustrated in Fig. 8. It is clear that the stress higher than 120 GPa almost concentrated ahead and underneath the diamond particle, as show in Fig. 8(a) to (c). After the diamond particle has scratched through, the stress in the machined area decreased, but it would not disappear completely, thus forming the residual stress in the subsurface behind the tool. The average von Mises stress in the deformation layer soared up at the initial stage when the diamond particle slided from 0 to 4 nm, and then stabilized at approximately 70.3 GPa when the diamond particle further moved forward to 16 nm, as shown in Fig. 8(d). According to Fig. 5(d), the first dislocation event in the subsurface appeared at the cutting distance of 3.5 nm, combining with the average stress of approximately 64 GPa at this time, as shown in Fig. 8(d), we estimated that for cutting along the [-2110] lattice direction on the (0001) plane, the critical average stress that evokes the nucleation of dislocation should be approximately 64 GPa. This value has a corresponding resolved shear stress (RSS) of 19 GPa, being consistent with the

20

value reported in Ref [35]. RSS is also related to the development of dislocation and equals to the stress components of τxy and τxz in Eq. (2) for contact loading on (0001)-plane [35].

Fig. 7: Shear strain distribution under different tool advances of (a) 3, (b) 6 and (c) 12 nm; (d) Average stain vs. cutting distance.

21

Fig. 8: von Mises stress distribution under different tool advances of (a) 3, (b) 6 and (c) 12 nm; (d) Average stress vs. cutting distance.

22

Fig. 9: Temperature distribution under different tool advances of (a) 3, (b) 6 and (c) 12 nm; (d) Average temperature vs. cutting distance.

Fig. 9 shows the atomic temperature distribution in monocrystalline GaN with the progress of machining and the average temperature in the Newtonian layer plotted against cutting distance. The temperature higher than 1500 K mainly concentrated in the pile-up and the vicinity of the interface between the GaN workpiece and the diamond particle, as shown in Figs. 9(a) to (c). The increase in temperature was determined by the friction between the GaN workpiece and the diamond particle, which introduced a

23

great amount of heat into the neighbourhood of the workpiece/tool interface. Since the dissipation rate of heat was lower than its generation rate in this work in accordance with the practical situation, we can see that the high-temperature region expanded with the increase in the cutting distance, thus resulting in a growth in average temperature from 293 to 740 K, as shown in Fig. 9(d). Generally, the increased temperature would favour the amorphization of monocrystalline materials [68-70]. However, our simulation showed that when the contact loading is in absence, the raising temperature to 740 K is insufficient to trigger the amorphization of wurtzite GaN, while if contact loading exists, the higher the temperature, the more severe the amorphization. This suggests that the amorphization of wurtzite GaN during nano abrasive machining could be the coupled result of temperature and contact loading but with different contributions, that is, the contact loading plays a dominant role and the temperature rise only facilitates this process in the former presence.

3.2 Effect of machining parameters 3.2.1 Cutting velocity Fig. 10 plots the variation of average temperature, shear strain and von Mises stress versus the cutting distance under three different cutting velocities of 25, 50, and 200 m/s, respectively. After cutting a 13 nm distance, the average temperature of the Newtonian layer rose from 500 to 850 K when the cutting velocity increased from 25 to 200 m/s, as shown in Fig. 10(a). The increased cutting velocity suppresses the time to dissipate the extra frictional heat under the same cutting distance. The dissipated heat Qdissipate could be calculated as, Qdissipate  t

(5)

Where λ the dissipate rate, t the dissipate time. With t=s/v (where s the cutting distance and v the cutting speed), Eq. (5) can be rewritten as,

Qdissipate 

s v

(6)

Given a constant dissipate rate, it can be deduced that the dissipated heat at cutting

24

velocity of 25 m/s is 8 times that at 200 m/s. Hence, a greater temperature increment could be expected under a higher cutting speed. Additionally, when cutting with a low velocity, as the system dissipates more heat at the same cutting distance, a new thermal equilibrium would be built more quickly such that the temperature tends to level off after a relatively short cutting distance. For instance, when the cutting velocity is 25 m/s, the temperature stabilized after cutting for a 6 nm distance, while for cutting velocity 50 m/s used, it stabilized after cutting for an 8 nm distance. Nevertheless, it seems that the effect of cutting velocity on the average shear strain is insignificant. Following the rapid growth in the initial stage of machining, the average strain stabilized at 0.55 for a cutting velocity of 25 m/s, 0.59 for 50 m/s, and 0.58 for 200 m/s, respectively, as shown in Fig. 10(b), suggesting the increase in cutting velocity slightly promotes the plastic deformation in the contact region. The average stress showed almost the same trend as that observed on the average strain, with the stabilized values of 65.1 GPa for 25 m/s, 65.7 GPa for 50 m/s and 67.8 GPa for 200 m/s, as shown in Fig. 10(c), indicating an increased cutting velocity results in a more severe machining-induced hardening. It is known that the increase of strain and strain rate could lead to the increase of stress (i.e. the so-called strain and strain rate hardening), but the increase of temperature reduces stress contrarily (i.e. the thermal softening) [71]. Considering the increase in cutting velocity could cause the increase in strain (see Fig. 10(a)), strain rate and temperature (see Fig. 10(c)), we thought that the nano abrasive machining was actually determined by the competition among effects of strain hardening, strain rate hardening and thermal softening. Hence, the phenomenon that the average stress increases with the increased cutting velocity (range from 25 to 200 m/s in this work) indicated that the strain and strain rate hardening effects play a more significant role than thermal softening during machining of monocrystalline GaN.

25

Fig. 10: (a) Averaged temperature, (b) strain and (c) stress plotted against cutting distance under different cutting velocities of 25, 50 and 200 m/s.

26

Fig. 11: Cross-sectional snapshots showing the deformation layer from [0-110] direction under different cutting velocities of (a) 25, (b) 50 and (c) 200 m/s (Blue for cubic diamond, isabelline for hexagonal diamond, gray for other atoms); (d) Comparison of atom numbers for different lattice structures (Red for total deformed atoms) under different cutting velocities; (e) Statistics of the dislocation length under different cutting velocities. (DOC=1.5 nm).

27

Fig. 11 illustrates the deformation layer analyzed by the DXA method under different cutting velocities and the comparison of atom numbers for different lattice structures when the diamond particle advanced to 13 nm using a DOC of 1.5 nm. After machining at a velocity of 50 m/s, the thinnest deformation layer with a thickness of 2.5 nm was produced in the subsurface, in comparison to that of 3.2 nm for 25 m/s and that of 3.2 nm for 200 m/s, as shown in Figs. 11(a) to (c). Elastic recovery (ER) can be also identified in the machined region behind the diamond particle, which increased slightly from 0.7 nm for 25 m/s to 0.8 nm for 200 m/s (corresponding to the increase in ER ratio from 47% to 53%). Fig. 11(d) shows the deformed atom number was 14696 for 25 m/s, 15157 for 50 m/s and 14809 for 200 m/s, respectively, which demonstrates the cutting velocity has less influence on the overall deformation. When the cutting velocity was increased to 50 m/s (higher than the critical velocity of 45 m/s that distinguishes the high-speed cutting from the general cutting), a noticeable increase in the total number of the cubic diamond atoms was observed in the subsurface, suggesting that the transition to zinc-blende structure would be enhanced in high-speed cutting. Additionally, as the average stresses of three velocities used were all greater than the critical value (64 GPa) that could activate dislocation (see Fig. 10(c)), dislocations can be observed under all three cutting velocities, as shown in Fig. 11(e). The figure also showed that the increased cutting velocity favours the nucleation of dislocation as the dislocation length was increased from 21 to 26 nm as the cutting velocity increased from 25 to 200 m/s. This should be associated with speed-induced temperature rise (see Fig. 10(a)), which in turn leads to an increase in atomic kinetic energy and a decrease in the required energy for bonding break [46], thus developing more dislocations.

Fig. 12 shows that the increase of cutting velocity from 25 to 200 m/s resulted in a slight decrease of the average normal and tangential cutting forces from 825 to 735 nN and from 351 to 316 nN, respectively. It is interesting to note that although the average stress showed positive dependence on the cutting velocity (see Fig. 10(c)), the overall cutting forces decreased as the cutting velocity increases. According to the previous analysis, the increase of cutting velocity could evoke more dislocations nucleated in the

28

crystal (see Fig. 11(e)), and thus produce a contracted EPDZ as evidenced by Fig. 13, where the EPDZ was observed to decrease from 18496 atoms to 15572 atoms as the cutting velocity increased from 25 to 200 m/s. Since the multiplication (0.88) of the average stress increase rate (1.04) and the EPDZ reduction rate (0.85) is very close to the cutting force decrease rate, especially the tangential force decrease rate (0.90), we thought that the influence of the shrunk EPDZ prevails over that of the increased average stress, thus resulting in a slight reduction in the overall cutting forces.

Fig. 12: (a) Normal and (b) tangential force plotted against cutting distance under different cutting velocities of 25, 50 and 200 m/s.

29

Fig. 13: EPDZ after cutting a distance of 13 nm under different velocities of (a) 25, (b) 50 and (c) 200 m/s; (d) Atom number of EPDZ under different velocities.

Fig. 14 plots the atom number and percentage of different CNs against cutting velocity when the diamond particle moved forward to 13 nm with a DOC of 1.5 nm. Both the number and percentage of the low-coordinated atom (CN=1, 2 and 3) increased with the increase in cutting speed, while the atom with high coordination (CN=4) had an opposite trend, as shown in Fig. 14(a) and (b), demonstrating that the increase in cutting velocity would enhance the amorphization of monocrystalline GaN. As shown in Fig. 10(a) and (c), the amorphization should be ascribed to the velocity-induced rise of temperature and stress, which is considered to be the most direct factor responsible for the amorphization in nanoscale machining [68-71].

30

Fig. 14: (a) Number and (b) percentage of atoms of different coordination number plotted against cutting velocity.

Fig. 15 are the snapshots showing the pile-up under different cutting speeds and the atom number of pile-up plotted against cutting speed when the diamond particle moves forward to 13 nm with a cutting depth of 1.5 nm. It is found that as the cutting speed increased from 25 to 200 m/s, the height of the pile-up increased from 0.7 to 1.0 nm, as shown in Figs. 15(a) to (c), and the corresponding atom number grew from 667 to 1310, as shown in Fig. 15(d). According to the previous analysis, the temperature increased with the increase of cutting velocity. On the other hand, the increase of temperature is actually the increase of kinetic energy (see Eq. (4)), which suggested that the Ga-N covalent bond would become active and can be more easily broken with lower mechanical energy. Under such a circumstance, the wear resistance of GaN crystal

31

would be weakened and the plastic flow and chip formation are thus pronounced [46], being consistent with the analysis on the variation of strain (see Fig. 10(b)). Therefore, it is not surprising that a higher cutting velocity produced a larger pile-up.

Fig. 15: Snapshots showing pile-up under different cutting velocities of (a) 25, (b) 50 and (c) 200 m/s; (d) Atom number of pile-up under different velocities.

3.2.2 Depth of cut The average temperature, shear strain, and von Mises stress under different DOCs are plotted against cutting distance in Fig. 16. The cutting velocity used was 50 m/s. As shown in Fig. 16(a), the average temperature in the machining region increased from 300 to 740 K with an increase in DOC from 0.5 to 2 nm. As DOC increased, the frictional force increased, thus the heat generated from friction increased as well. With a constant heat dissipation rate, the temperature in the machining region is bound to rise. Also, as less frictional heat is generated from the smaller DOC used, a new balance

32

between heat generation and dissipation could be established sooner, thus the temperature in the machining region can stabilize more quickly under a smaller DOC than that under a greater DOC. The DOC has a significant effect on the average shear strain. The stabilized average shear strain impressively increased from 0.07 to 0.96 as DOC increased from 0.5 to 2.0 nm, as shown in Fig. 16(b), demonstrating plastic deformation would become severe under a greater DOC. The average stress positively depends on DOC. As shown in Fig. 16(c), the stabilized average stress were 50.4 GPa for DOC of 0.5 nm, 58.2 GPa for 1.0 nm and 70.3 GPa for 2.0 nm. According to the definition of strain rate, ε=v/w (where v the relative velocity between workpiece and tool, w the contact width between workpiece and tool) [72], the strain rate should decrease with the increased DOC because the cutting velocity v was constant and the contact width w increased with the increase in DOC in this case. This suggested that the strain rate hardening would get weaker as the DOC increased. At the same time, the thermal softening effect got stronger with the increase in DOC since the temperature was rising. Under such a circumstance, the increase in average stress with increased DOC should be mainly associated with strain hardening. Fig. 17 are the snapshots showing the deformation layer under different DOCs and the comparison of atom numbers for different lattice structures. Obviously, there is no deformation layer produced behind the diamond particle when the DOC of 0.5 nm was used, as shown in Fig. 17(a). The ER ratio of 100% suggested that the interaction between the GaN workpiece and the diamond particle falls in a pure elastic regime at this time. As the DOC further increased to 2 nm, the deformation layer expanded greatly to have a thickness up to 3.5 nm, but with a consequent reduction in ER ratio to 50%, as shown in Fig. 17(b) to (c). The total number of atoms in the deformation layer increased from 189 to 21035 with the increase of DOC from 0.5 to 2 nm, as shown in Fig. 17(d). Meanwhile, the rise of temperature and pressure caused by the increased DOC enhances the phase transition from wurtzite to zinc-blende structure, as evidenced by the remarkable growth of cubic diamond atoms (see Fig. 17(d)). It is also found that DOC had a great influence on the dislocation nucleation and evolution. The dislocation

33

significantly extended from 0 to 70 nm as the DOC increased from 0.5 to 2 nm, as shown in Fig. 17(e), which should be related to both stress and temperature. Since the average stresses for DOCs of 0.5 and 1 nm (50.4 GPa for 0.5 nm and 58.2 GPa for 1.0 nm, see Fig. 16(c)) are all less than the critical value (64 GPa, see Fig. 8(d)) that evokes the nucleation of dislocation, no dislocation was observed under these two depths, as shown in Fig. 17(e). Once the DOC increased to 2 nm, the average stress (70.3 GPa) exceeded the critical value, the dislocation thus greatly propagated. Additionally, the increase in temperature with the increase in DOC also promotes the development of dislocations, which could be considered as an assistant factor to obtain a longer dislocation under a greater DOC.

Fig. 18 plots the normal and tangential cutting forces against the cutting distance under different DOCs. It indicates that with the increase in DOC, the cutting forces significantly increased, with the average value increasing from 342 to 938 nN for normal force and from 19 to 529 nN for tangential force, as shown in Fig. 18(a) and (b). The increase in cutting forces should be associated with both the EPDZ and the average stress. On the one hand, the increased DOC would result in the expansion of the contact area of workpiece/tool, thus producing a larger EPDZ. Fig. 19 shows that when the DOC increased from 0.5 to 2 nm, EPDZ grew about 18 times with its atom number significantly increasing from 1470 to 26369. On the other hand, the increased DOC also resulted in an increase of 1.4 times on average stress, as shown in Fig. 16(c), thus giving an increase of 25 times in the multiplication of the average stress and the EPDZ. This rate is close to the growth rate of cutting force, especially the increase rate of tangential force (~27.8). It is therefore concluded that the increase in cutting forces should be the combined result of the increased stress and the expanded EPDZ.

34

Fig. 16: (a) Averaged temperature, (b) shear strain and (c) stress plotted against cutting distance under different DOCs of 0.5, 1.0 and 2.0 nm.

35

Fig. 17: Cross-sectional views of deformation layer from [0-110] direction under different DOCs of (a) 0.5, (b) 1.0 and (c) 2.0 nm (Blue for cubic diamond, isabelline for hexagonal diamond, gray for other atoms); Comparisons of (d) atom number of deformation layers (Red for total deformed atoms) and (e) dislocation length under different DOCs. Cutting velocity used was 50 m/s.

36

Fig. 18: (a) Normal and (b) tangential force plotted against cutting distance under different DOCs of 0.5, 1.0 and 2.0 nm. Fig. 20 plots the atom number and percentage of different CNs against DOC after the diamond particle moved forward to 13 nm with a cutting velocity of 50 m/s. Since the increased DOC gave the expansion of total deformation (see Fig. 17), the atom numbers of different CNs all increased with the increase in DOC, as shown in Fig. 20(a). On the other hand, on account of the rise of temperature and stress induced by the increased DOC (see Fig. 16), the amorphization of wurtzite GaN became severe with the increase in DOC. As a result, the percentage of CN=4 atom decreased from 97% for 0.5 nm DOC to 59% for 2 nm DOC, and the percentage of CN=3 atom increased from 3% for 0.5 nm DOC to 30% for 2 nm DOC, as shown in Fig. 20(b). Additionally, it seems that the compression-induced phase transition to fivefold hexagonal structure became weak with

37

the increased DOC, as evidenced by the decrease in the percentage of CN=5 atom from 5.8% to 0.9%, which could be attributed to the increased temperature [67].

Fig. 19: EPDZ after nano abrasive machining under different DOCs of (a) 0.5, (b) 1 and (c) 2 nm; (d) Atom number of EPDZ under different DOCs. Cutting distance was 13 nm.

Fig. 21 are the snapshots showing the pile-up under different DOCs and the atom number of pile-up plotted against DOC after the diamond particle moved forward to 13 nm at a cutting velocity of 50 m/s. It is found that when the depth of cutting was less than 1 nm, there was no obvious pile-up occurred ahead and on both sides of the diamond particle, as shown in Fig. 21(a) and (b), indicating that the minimum DOC for wurtzite monocrystalline GaN to form pile-up is approximately 1 nm, below which machining would fall in the sliding or ploughing regime. When the DOC increased to 2 nm, the pile-up expanded greatly, with its height increasing to 1.5 nm as shown in Fig. 21(c) and the atom number increasing to 2396, as shown in Fig. 21(d), demonstrating the machining has entered a stable stage. Generally, the increase in DOC could deteriorate the tribological situation in the work interface, thus raising friction

38

coefficient. Our simulation showed that an increase in friction coefficient from 0.054 to 0.561 with an increase in DOC from 0.5 to 2 nm. This enables more workpiece atoms to adhere to the diamond particle and thus migrate from the crystal interior to the free surface to form pile-up. In addition, as mentioned earlier, the decrease in bond strength caused by the increased temperature could also degrade the wear resistance of GaN material, thus further pronouncing pile-up under a higher friction condition.

Fig. 20: (a) Number and (b) percentage of atoms of different coordination number plotted against DOC.

39

Fig. 21: Snapshots showing pile-up under different DOCs of (a) 0.5, (b) 1.0 and (c) 2.0 nm; (d) Statistics of atom number of pile-up under different DOCs.

3.3 Effect of particle shape The simulations to evaluate the influence of grain shape using spherical and cub-octahedral diamond particles as abrasive were carried out under a constant cutting velocity of 50 m/s and DOC of 1.5 nm. The obtained average temperature, shear strain, and stress curves are plotted in Fig. 22. As can been seen in Fig. 22(a), the average cutting temperatures of the machining region using the two particles with different shapes were very closed, indicating that cutting using spherical and cub-octahedral diamond particles generated almost the same amount of frictional heat (see the detailed discussion below). The stabilized average shear strain was 0.59 for spherical particle and 0.58 for cub-octahedral particle, as shown in Fig. 22(b), demonstrating the effect of spherical and cub-octahedral diamond particles on the plastic deformation were similar. As shown in Fig. 22(c), the average stress using spherical particle stabilized at 65.7 GPa,

40

slightly higher than the value of 64.2 GPa from using cub-octahedral particle, suggesting that the use of cub-octahedral particle would alleviate machining-induced hardening during nano abrasive machining of wurtzite monocrystalline GaN.

Fig. 22: (a) Averaged temperature, (b) shear strain and (c) stress plotted against cutting distance using spherical and cub-octahedral diamond particles.

Fig. 23 are the snapshots showing the deformation layer after cutting 13 nm using

41

spherical and cub-octahedral particles and the corresponding statistical comparison of atom numbers for different lattice structures. The deformation layer produced after cutting using spherical particle was thicker than that obtained using cub-octahedral particle, with a thickness of 2.5 nm for the former in comparison to that of 1.3 nm for the latter, as shown in Fig. 23(a) and (b). It can be also found in this figure that the machined region behind the spherical particle elastically recovered more than that behind the cub-octahedral particle, with ER value of 0.7 for the former (corresponding ER ratio of 47%) and 0.2 nm for the latter (corresponding ER ratio of 13%). After cutting with a distance of 13 nm, the total number of atoms in the deformation layer was 15157 for spherical particle used, in comparison to that of 11484 for cub-octahedral particle used, as shown in Fig. 23(c). Both the deformation layer and elastic recover were affected by the compression acting on the GaN workpiece by the diamond particle (see the detailed disscusion below). Due to the reduction in pressure, the phase transition from wurtzite to zinc-blende structure for cutting using spherical particle was weaker than that for cutting using cub-octahedral particle, as evidenced by the decrease in cubic diamond atoms (also see Fig. 23(c)). Additionally, it seems that cutting using cub-octahedral particle was more conducive to the development of dislocation because the dislocation for cutting using cub-octahedral particle was longer than that for cutting using spherical particle, as shown in Fig. 23(d). Based on above simulation results, it can be concluded that cutting using cub-octahedral diamond particle, which has a negative rake angle with straight cutting edge, is more inclined to obtain a less damaged subsurface during the nano abrasive machining process.

42

Fig. 23: Cross-sectional views of deformation layer along [0-110] direction after cutting with a distance of 13 nm using (a) spherical and (b) cub-octahedral diamond particles (Blue for cubic diamond, isabelline for hexagonal diamond, gray for other atoms); Comparisons of (c) atom number of deformation layers (Red for total deformed atoms) and (d) dislocation length under different particle shapes.

43

Fig. 24: (a) Normal and (b) tangential force plotted against cutting distance using spherical and cub-octahedral diamond particles.

Fig. 24 plots the normal and tangential cutting forces against the cutting distance for spherical and cub-octahedral diamond particles used respectively. Obviously, the particle shape had a significant influence on the normal cutting forces, with the average value of 825 nN for cutting using spherical particle and 598 nN for cutting using cub-octahedral diamond particles in the stable cutting stage, as shown in Fig. 24(a). The higher normal force indicated that the compression acting on GaN workpiece by the spherical particle was stronger than that exerted by cub-octahedral particle. It is therefore not surprise that the subsurface would be damaged more severely by the the spherical particle, and thus the spherical particle produced the thicker deformation layer

44

and the stronger elastic recover (see Fig. 23(a) and (b)). However, the tangential forces were almost the same for the two diamond particles, with an average value of approximate 330 nN in the stable cutting stage, as shown in Fig. 24(b). This suggested that cutting using spherical and cub-octahedral particles had almost the same frictional situation, and thus generated the close amount of friction heat from the machining, supporting the temperature curve shown in Fig. 22(a).

Fig. 25: EPDZ after nano abrasive machining after cutting using spheric and cub-octahedral diamond particles; (d) Atom number of EPDZ using different particle shapes.

Fig. 25 are the snapshots showing EPDZ and the corresponding statistics of atom number after nano abrasive machining using spherical and cub-octahedral diamond particles. EPDZ produced by spherical particle was slightly smaller than that produced by cub-octahedral particle, with the atom number of 16938 for spherical particle and 14941 for cub-octahedral particle. The smaller EPDZ produced by cub-octahedral particle was related to the smaller contact area and the more dislocations evoked by

45

cub-octahedral particle, which thus in turn made the normal cutting force smaller, as shown in Fig. 24(a). Fig. 26 are the statistical comparison of the atom number and percentage of different CNs after cutting with a distance of 13 nm using spherical and cub-octahedral diamond particles. The atom numbers and percentages of CN=1, 2 and 3 for spherical particle were all smaller than those for cub-octahedral diamond particle, but the atom number and percentage of CN=4 for spherical particle were higher than those for cub-octahedral diamond particle, as shown in Fig. 26(a) and (b). This result indicated that cutting using a cub-octahedral diamond particle would intensify the amorphization of wurtzite GaN.

Fig. 26: (a) Number and (b) percentage of atoms of different coordination after cutting with a distance of 13 nm using spherical and cub-octahedral diamond particles.

Fig. 27 are the snapshots showing the pile-up after cutting with a distance of 13 nm

46

using spherical and cub-octahedral diamond particles and the corresponding statistical comparison of atom number. It was found that, when the spherical diamond particle was used as abrasive, the workpiece atoms slightly piled up ahead the tool and on both sides of the machined groove, with a height of 0.8 nm as shown in Fig. 26(a) and the atom number of 715 as shown in Fig. 26(c). But for cutting using cub-octahedral particle, most atoms removed from the workpiece formed a chip-like pile-up right ahead the rake surface of the abrasive, with a height of 1.7 nm as shown in Fig. 26(b) and the atom number of 1333 as shown in Fig. 26(c). This briefly remarked that cub-octahedral abrasive particle with straight cutting edge would have stronger cutting effect compared with spherical abrasive particle.

Fig. 27: (a) Snapshots showing pile-up after cutting 13 nm distance using spherical and cub-octahedral diamond particles and (d) the corresponding statistical comparison of atom number of pile-up.

47

4. Conclusions In this work, molecular dynamics simulations were performed to study the nano abrasive machining process of wurtzite monocrystalline GaN. Effects of cutting velocity and DOC on the deformation behaviour are systematically investigated. Detailed conclusions drawn from this study are summarized below.

(1) A semiwarhead-shaped elasto-plastic deformation zone was formed right ahead the diamond particle, which is associated with both the development of dislocation and the contact of workpiece/tool, and has a significant influence on the cutting forces. The localized atomic displacement was affected cooperatively by the stagnation region and slip systems, thus producing pile-up and elastic recovery. For cutting made on (0001) wurtzite monocrystalline GaN, half dislocation loops were preferentially evoked in the subsurface. The increased cutting distance would cause the diversification of dislocation types, such as partial dislocations along the slip directions of 1/3<1-210>, 1/3<1-100> and other unidentified dislocations. After nano abrasive machining, phase transitions from wurtzite to zinc-blende or even fivefold coordinated hexagonal structure, as well as the amorphization, were identified.

(2) The shear strain, the von Mises stress and the temperature all increased with the increase in cutting distance, cutting velocity and DOC. The critical average von Mises stress that could activate dislocation nucleation was estimated to be 64 GPa. The cutting velocity has little effect on the deformation layer, but the increase in DOC would greatly boost the deformation. The elastic recovery increased slightly with the increase in cutting velocity, but decreased significantly with the increase in DOC. Due to the stress and temperature rise, both the increase in cutting velocity and DOC could facilitate the nucleation of dislocation, phase transition and the development of pile-up. The overall cutting force decreased as the cutting velocity increased due to the contracted EPDZ, but increased with the increase in DOC owing to the inflated EPDZ and elevated stress.

48

(3) Compared with the spherical abrasive, the use of cub-octahedral abrasive that has a negative rake angle with straight cutting edge could reduce the strain, stress, force, the deformation layer, and the elastic recovery, but promote the dislocation, phase transition and the development of pile-up.

Acknowledgements This work was financially supported by the National Natural Science Foundation of China (Grant no. 51805240), the Natural Science Foundation of Hunan province (Grant no. 2018JJ2328), the Foundation of Education Department of the Hunan province (Grant no. 17C1368), and the China Scholarship Council (201808430059). The authors also thank HPC&S Centre in University of South China for the simulation running.

References [1]

M. Fujikane,T. Yokogawa, S. Nagao, R. Nowak, Nanoindentation study on insight of plasticity related to dislocation density and crystal orientation in GaN, Applied Physics Letters 101 (2012) 201901.

[2]

P. Pust, P.J. Schmidt, W. Schnick, A revolution in lighting, Nat. Mater. 14 (2015) 454.

[3]

J. Y. Tsao, M.H. Crawford, M.E. Coltrin, A.J. Fischer, D.D. Koleske, G. S. Subramania, G.T. Wang, J.J Wierer, R.F. Karlicek Jr., Toward smart and ultra-efficient solid-state lighting. Adv. Opt. Mater. 2 (9) (2014) 809-836.

[4]

F. Roccaforte, G. Greco, P. Fiorenza, F. Iucolano, An overview of normally-off GaN-based high electron mobility transistors, Materials 12 (10) (2019) 1599.

[5]

F. Zeng, J. X. An, G. Zhou, W. Li, H. Wang, T. Duan, L. Jiang, H. Yu, A comprehensive review of recent progress on GaN high electron mobility transistors: devices, fabrication and reliability. Electronics 7 (12) (2018) 377.

[6]

U.K. Mishra, L. Shen, T.E. Kazior, Y. Wu, GaN-based RF power devices and amplifiers. Proceedings of the IEEE 96 (2) (2008) 287-305.

[7]

G. Meneghesso, M. Meneghini, E. Zanoni, Gallium Nitride-Enabled High Frequency and High Efficiency Power Conversion; Springer: New York, NY, USA, 2018.

49

[8]

S.C. Jain, M. Willander, J. Narayan, R.V. Overstraeten, III-nitrides: growth, characterization, and properties, J. Appl. Phys 87 (3) (2000) 965-1006.

[9]

J. Guo, C. J. Qiu, H. L. Zhu, Y.Q. Wang. Nanotribological properties of Ga- and N-faced bulk gallium nitride surfaces determined by nanoscratch experiments, Materials 12 (2019) 2653.

[10] M.F. Doerner, W. D. Nix, A method for interpreting the data from depth-sensing indentation instruments, J. Mater. Res. 1 (4) (1986) 601-609. [11] J.L. Weyhera, S. Miillera, I. Grzegoryh, S. Porowskih, Chemical polishing of bulk and epitaxial GaN, Journal of Crystal Growth 182 (1997) 17-22 [12] P. R. Tavernier, T. Margalith, L. A. Coldren, S. P. DenBaars, D. R. Clarke, Chemical Mechanical Polishing of Gallium Nitride, Electrochemical and Solid-State Letters 5 (8) (2002) G61-G64. [13] S. Hayashi, T. Koga, M. S. Goorsky, Chemical mechanical polishing of GaN, J. Electrochem. Soc. 155 (2) (2008) 113-116. [14] C. Zou, P. Guoshun, G. Hua, L. Xu, Z. Yan, Y. Liu, In A study of surface defects of GaN during CMP process, 2015 International Conference on Planarization/CMP Technology (ICPT) (2015) 1-3. [15] H. Lee, H. Kasuga, H. Ohmori, H. Lee, H. Jeong, Application of electrolytic in-process dressing (ELID) grinding and chemical mechanical polishing (CMP) process for emerging hard-brittle materials used in light-emitting diodes, Journal of Crystal Growth 326 (2011) 140-146 [16] G.S. Zeng, N. Tansu, B.A. Krick. Moisture dependent wear mechanisms of gallium nitride, Tribology International 118 (2017) 120-127. [17] H. Aida, T. Doi, H. Takeda, H. Katakura, S. W. Kim, K. Koyama, T. Yamazaki, M. Uneda, Ultraprecision CMP for sapphire, GaN, and SiC for advanced optoelectronics materials, Current Applied Physics 12 (2012) S41-S46. [18] J. Belak, I. Stowers A molecular dynamics model of the orthogonal cutting process. Lawrence Livermore National Lab., Livermore (1990). [19] L. C. Zhang, H. Tanaka. Atomic scale deformation in silicon monocrystals induced by two-body and three-body contact sliding. Tribology International 31(8) (1998) 425-433. [20] G. Saurav, K. Andrii, S. Alexander, C. Graham, Influence of microstructure on

50

the cutting behaviour of silicon, Acta Materialia 105 (2016) 464-78. [21] B.J. Alder, T.E. Wainwright, Phase Transition for a Hard Sphere System, J Chem Phys 1208 (1957) 27 [22] J. Belak, I. F. Stowers, The Indentation and Scratching of a Metal Surface: A Molecular Dynamics Study, Fundamentals of Friction: Macroscopic and Microscopic, Singer, Pollock E, 220 (1991) 1-10 [23] R. Rentsch, I. Inasaki, Molecular Dynamics Simulation for Abrasive Processes, Annals of the CIRP 43(1) (1994) 327-330 [24] Y. Ye, R. Biswas, J.R. Morris, A. Bastawros, A. Chandra, Simulation of Nanoscale Polishing of Copper with Molecular Dynamics, Mat. Res. Soc. Symp. Proceedings Vol. 732E (2002) I4.8.1-6 [25] A.O. Oluwajobi, X. Chen, The Fundamentals of Modelling Abrasive Machining Using Molecular Dynamics, International Journal of Abrasive Technology 3(4) (2010) 354-381 [26] Y. Yang, H. Zhao, L. Zhang, M. Shao, H. Liu, H. Huang, Molecular dynamics simulation of self-rotation effects on ultra-precision polishing of single-crystal copper, AIP Advance 3 (2013) 102106 [27] J. Li, Q.H. Fang, Y.W. Liu, L.C. Zhang, A molecular dynamics investigation into the mechanisms of subsurface damage and material removal of monocrystalline copper subjected to nanoscale high speed grinding, Applied Surface Science 303 (2014) 331-343. [28] Q. Fang, Q. Wang, J. Li, X. Zeng, Y. Liu, Mechanisms of subsurface damage and material removal during high speed grinding processes in Ni/Cu multilayers using a molecular dynamics study, RSC Adv. 7 (2017) 42047-42055. [29] R. Komanduri, N. Chandrasekaran, L. M. Raff. MD Simulation of nanometric cutting of single crystal aluminum-effect of crystal orientation and direction of cutting, Wear 242 (2000) 60-88. [30] Z. Lu, A. Chernatynskiy, M. J. Noordhoek, S. B. Sinnott, S. R. Phillpot, Nanoindentation of ZrO2 and ZrO2/Zr systems by molecular dynamics simulation, Journal of Nuclear Materials 486 (2017) 250-266. [31] A. Sharma, D. Datta, R. Balasubramaniam, A molecular dynamics simulation of wear mechanism of diamond tool in nanoscale cutting of copper beryllium, The

51

International Journal of Advanced Manufacturing Technology 102 (2019) 731-745. [32] P. Z. Zhu, Q. Chen Qiu, F. Z. Fang, D. D. Yuan, X. C. Shen, Molecular dynamics simulations of nanometric cutting mechanismsof amorphous alloy, Applied Surface Science 317 (2014) 432-442 [33] Y. Qian, S. Deng, F. Shang, Q. Wan, Y. Yan, Dependence of tribological behavior of GaN crystal on loading direction: A molecular dynamics study, J. Appl. Phys. 126 (2019) 075108. [34] Y. Qian, F. Shang, Q. Wan, Y. Yan, A molecular dynamics study on indentation response of single crystalline wurtzite GaN, Journal of Applied Physics 124 (2018) 115102. [35] H. Xiang, H. Li, T. Fu, C. Huang, X. Peng, Formation of prismatic loops in AlN and GaN under nanoindentation, Acta Mater. 138 (2017) 131. [36] T.G. Bifano, T.A. Dow, R.O. Scattergood, Ductile-regime grinding: a new technology for machining brittle materials, Journal of Engineering for Industry 113 (1991) 184-189 [37] D. Axinte, P. Butler-Smith, C. Akgun, K. Kolluru, On the influence of single grit micro-geometry on grinding behavior of ductile and brittle materials, International Journal of Machine Tools & Manufacture 74 (2013) 12-18. [38] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117 (1995) 1-19. [39] A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO-the open visualization tool, Model Simul. Mater Sc. 18 (2010). [40] L. Verlet, Computer “Experiments” on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules, Physical Review 159 (1967) 98-103. [41] H. Dai, J. Chen, G. Liu, A numerical study on subsurface quality and material removal during ultrasonic vibration assisted cutting of monocrystalline silicon by molecular dynamics simulation, Mater. Res. Express 6 (2019) 065908 [42] L. N. Abdulkadir, K. Abou-El-Hossein, A. I. Jumare, M. M. Liman, T. A. Olaniyan, P. B. Odedeyi, Review of molecular dynamics/experimental study of diamond-silicon behavior in nanoscale machining, The International Journal of Advanced Manufacturing Technology (2018) 98:317-371

52

[43] W.C. D. Cheong, L. C. Zhang, Molecular dynamics simulation of phase transformations in silicon monocrystals due to nano-indentation, Nanotechnology 11 (2000) 173-180. [44] J. Nord, K. Albe, P. Erhart, K Nordlund, Modelling of compound semiconductors: analytical bondorder potential for gallium, nitrogen and gallium nitride, J. Phys.: Condens. Mat. 15 (2003) 5649. [45] S.L. Mayo, B. D. Olafson, W. A. Goddard, Dreiding: a generic force field for molecular simulations, J. Phys. Chem. 94 (1990) 8897. [46] Y. Isono, T. Tanaka, Three-dimensional molecular dynamics simulation of atomic scale precision processing using a pin tool. JSME International Journal, Series A: Mechanics and Material Engineering 40(3) (1997) 211-218. [47] S. Goel, X. Luo, R.L. Reuben, Shear instability of nanocrystalline silicon carbide during nanometric cutting. Appl. Phys. Lett. 100 (23) (2012) p231902. [48] G. LW Cross, Silicon nanoparticles: isolation leads to change, Nat. Nanotechnol. 6 (2011) 467-8 [49] F. Shimizu, S. Ogata, J. Li, Theory of Shear Banding in Metallic Glasses and Molecular Dynamics Calculations, Materials Transactions 48 (11) (2007) 2923-2927 [50] K. Sarasamak, A. J. Kulkarni, M. Zhou, S. Limpijumnong, Stability of wurtzite, unbuckled wurtzite, and rocksalt phases of SiC, GaN, InN, ZnO, and CdSe under loading of different triaxialities, Physical Rreview B 77 (2008) 024104. [51] A. Stukowski, Structure identification methods for atomistic simulations of crystalline materials, Modelling Simul Mater Sci Eng 20 (2012) 045021. [52] H. Tsuzuki, P. S. Branicio, J. P. Rino, Structural characterization of deformed crystals by analysis of common atomic neighborhood, Computer Physics Communications 177 (2007) 518-523 [53] A. Stukowski, V.V. Bulatov, A. Arsenlis, Automated identification and indexing of dislocations in crystal interfaces, Model Simul. Mater Sc. 20 (2012) 085007. [54] A. Stukowski, K. Albe, Extracting dislocations and non-dislocation crystal defects from atomistic simulation data, Model Simul. Mater Sc. 18 (2010) 085001. [55] Q.M. Li, strain energy density failure criterion, International Journal of Solids

53

and Structures 38 (38-39) (2001) 6997-7013 [56] Y.Q. Wu, S. Gao, H. Huang, The deformation pattern of single crystal β-Ga2O3 under nanoindentation, Materials Science in Semiconductor Processing 71 (2017) 321-325 [57] M. Lai, X.D. Zhang, F.Z. Fang, Study on critical rake angle in nanometric cutting, Appl Phys A 108 (2012) 809-818. [58] R. J. Wang, C. Y. Wang, Y. T. Feng, C. Tang, Mechanical responses of a-axis GaN nanowires under axial loads, Nanotechnology 29 (2018) 095707. [59] Y. Kondo, A. Tsukuda, A. Takada, S. Okada, Grinding Forces and Elastic Recovery in Ceramic Materials, Journal of the American Ceramic Society 77 (6) (1994) 1653-1654. [60] S. Strite, H. Morko, GaN, AIN, and InN: A review, Journal of Vacuum Science & Technology B 10 (1992) 1237. [61] J. H. Kim, H. H. Paul, Wurtzite to zinc-blende phase transition in gallium nitride thin films, Applied Physics Letters 84 (2004) 711 [62] B. M. Shi, M. H. Xie, H. S. Wu, Transition between wurtzite and zinc-blende GaN: An effect of deposition condition of molecular-beam epitaxy, Applied Physics Letters 89 (2006) 151921 [63] Y. Wu, J. Kang, Pressure induced wurtzite-to-zinc blende phase transition in ZnO at finite temperature, J. Mater. Res. 23 (12) (2008). [64] L.C. Zhang, I. Zarudi, Towards a deeper understanding of plastic deformation in mono-crystalline silicon, International Journal of Mechanical Sciences 43 (2001) 1985-1996 [65] J. Wang, A. J. Kulkarni, K. Sarasamak, S. Limpijumnong, F. J. Ke, M. Zhou, Molecular dynamics and density functional studies of a body-centered-tetragonal polymorph of ZnO, Physical Review B 76 (2007) 172103. [66] K. Jung, M. Cho, M. Zhou, Thermal and mechanical response of [0001]-oriented GaN nanowires during tensile loading and unloading, Journal of Applied Physics 112 (2012) 083522. [67] Y. Qian, F. Shang, Q. Wan, Y. Yan, Compression-induced phase transition of GaN bulk from wurtzite phase to five-fold coordination hexagonal phase, AIP Advances 7 (2017) 095312.

54

[68] P. Richet, P. Gillet, Pressure-induced amorphization of minerals: a review, Eur. J. Mineral. 9 (1997) 907-933. [69] M. Grimsditch, S. Popova, V. V. Brazhkin, R. N. Voloshin, Temperature-induced amorphization of SiO2 stishovite, Phys. Rev. B 50 (1994) 12984. [70] R. F. Boyer, The High Temperature (T>Tg) Amorphous Transition in Atactic Polystyrene, Journal of Polymer Science Part C: Polymer Symposia 14 (1) (1966) 267-281. [71] G.R. Johnson, W.H. Cook, A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, Proceedings of the 7th International Symposium on Ballistics, The Netherlands 21 (1983) 541-547. [72] Z. Ding, B. Li, S.Y. Liang, Maraging steel phase transformation in high strain rate grinding, Int J Adv Manuf Technol 80 (2015) 711-718.

55

*Highlights (for review)

Highlights



Nano abrasive machining of monocrystalline GaN is studied by molecular dynamics simulations.



Deformation of monocrystalline GaN is associated with both the propagation of dislocation and the contact of workpiece/tool.



Dislocation and phase transition are identified in the deformation layer of monocrystalline GaN after nano abrasive machining.



Pile-up and elastic recovery of monocrystalline GaN are affected by the stagnation region and slip system.



Effects of cutting velocity, depth of cut and abrasive shape on the deformation behavior are systematically investigated.

Graphical Abstract (for review)

Graphical abstract

*Author Contributions Section

Author Contribution Statement Yongqiang Wang: Conceptualization, Methodology, Software, Writing- Original draft preparation, Funding acquisition, Supervision. Sai Tang: Resources, Data curation, Investigation. Jian Guo: Methodology, Software, Writing- Reviewing and Editing, Investigation, Funding acquisition.

*Declaration of Interest Statement

Declaration of interests ☑The authors declare that they have no known competing financialinterestsor personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: