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Atomistic origins of material removal rate anisotropy in mechanical polishing of diamond crystal
Carbon 99 (2016) 186e194
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Atomistic origins of material removal rate anisotropy in mechanical polishing of diamond crystal W.J. Zong*, X. Cheng, J.J. Zhang** Center for Precision Engineering, Harbin Institute of Technology, Harbin, 150001, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 August 2015 Received in revised form 25 November 2015 Accepted 1 December 2015 Available online 13 December 2015
In this work, molecular dynamics simulation is employed to represent the diamond polishing. Radial distribution function and coordination number analyses are further performed to reveal the underlying atomistic origins of the removal rate anisotropy. The results show that the lattice distortion is inevitable as the diamond substrate suffers from the mechanically induced effects, which produces an amorphous layer on the surface. In the amorphization, the perfect diamond cubic transforms to some non-diamond phases, including the amorphous sp0, sp1, sp2 and sp3 hybridized structures and well-arranged sp2 structures. However, the dominant phases are sp2 and amorphous sp3 phases. More interestingly, it is found that the removal rate strongly depends on the proportion of sp2 hybridizations to amorphous sp3 structures. In the ‘hard’ direction, phase transformation from amorphous sp3 to sp2 is difficult, and therefore a low proportion of sp2 to amorphous sp3 appears, which results in a small removal rate. In the ‘soft’ direction, phase transformation from amorphous sp3 to sp2 has less resistance, and a higher proportion output, which gives a greater removal rate. The variation laws as revealed above confirm that the removal rate anisotropy in diamond polishing is derived from the concentration of sp2 hybridizations in the as-created amorphous layer and debris. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction As the hardest engineering material known in the world, diamond crystal has the unmatched wear resistance and excellent chemical stability [1], and thus it has been considered as an ideal tooling material in nanometric cutting [2,3], nano-indentation [4,5], nano-scratching [6], and etc. However, it is difficult to smoothen the surface of diamond crystal, and some special polishing processes are required for fulfilling such objective [7], among which the mechanical polishing is one of the most favorable and popular solutions [2]. During mechanical polishing of diamond crystal, the anisotropy of material removal rate appears inevitably, which heavily depends on the crystalline orientation of polished diamond surface. However, the underlying mechanisms of this undesirable feature are still not answered satisfactorily. And
* Corresponding author. Harbin Institute of Technology, P.O. Box 413, Harbin, 150001, PR China. ** Corresponding author. Harbin Institute of Technology, P.O. Box 413, Harbin, 150001, PR China. E-mail addresses: [email protected] (W.J. Zong), [email protected] (J.J. Zhang). http://dx.doi.org/10.1016/j.carbon.2015.12.001 0008-6223/© 2015 Elsevier Ltd. All rights reserved.
therefore, many interesting works had been performed to try to reveal the possible mechanisms. Tolkowshy observed the microscopic morphology of debris that left on the polished surface of diamond crystal by using the optical microscope, and he put forward a microscopic cleavage theory to explain the anisotropy of wear rate [8]. Couto et al. investigated the polished surface with scanning tunneling microscopy, and they claimed that the surface layer of diamond crystal is removed in fractures or micro-chips as the polishing is performed along the ‘hard’ direction [9]. Moreover, they also proposed a nanometric groove dependent theory to interpret the material removal mechanism in polishing along the ‘soft’ direction [10]. Grillo and Field collected the worn debris from the polished diamond surface, and subsequently they analyzed them with transmission electron microscopy and electron energy loss spectroscopy in a scanning transmission electron microscope. They finally proposed a novel mechanism to expatiate the material removal in diamond polishing, i.e. phase transformation from the perfect diamond cubic to the amorphous sp2 and sp1 hybridized carbons [11]. Gogotsi et al. conducted the indentation experiments on diamond surface corroborated by micro-Raman spectroscopy. They confirmed that the plastic deformation induced phase transformation in diamond
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is a very common feature of wear, and the non-cubic diamond polytypes include lonsdaleite, graphitic carbon, and possibly new phases of carbon [12]. van Bouwelen claimed that there is no elastic energy as the plastic deformation takes place in diamond crystal. Conversely, rehybridization of carbon atom dominates once the stored deformation energy of CeC bond exceeds its energy barrier, i.e. 5.5ev [13]. Pastewka et al. proposed a concept of pilot-atom to describe the amorphization of diamond. They concluded that the anisotropy of amorphization rate is derived from the probability that the pilot-atom drive the surface atom to depart from its crystalline position to form the amorphous atom [14]. Fairchild et al. explored the amorphization of diamond crystal by ion implantation and molecular dynamics (MD) simulation. They declared that the amorphization of diamond carbon is strain driven. When the force-induced strain in diamond reaches a critical value of 16%, the diamond lattice collapses. And resultantly, the amorphous nondiamond phases come into being [15]. In addition to the material removal mechanisms, the friction behaviors of diamond had also been discussed. Jarvis et al. carried out a lot of ab-initio quantum-mechanical simulations to investigate the nano-asperity scratching on the diamond {110} surface. They suggested that the observed anisotropy of wear rate is due to the difference in the atomistic deformation of bond angle. In scratching along the ‘soft’ direction, the bond angle deforms on a few diamonds CeC bonds at the same time, which produces the large enough localized stress to break the deformed diamond bonds and drive the amorphization. In scratching along the ‘hard’ direction, however, the deformation of bond angle is not localized, and the stress distributes over a large number of diamond bonds, which finally leads to the ‘large-area’ subsurface damages [16]. Grillo, Field and van Bouwelen paid great attentions to the friction and wear properties when the diamond {100} surface was polished in different orientations. According to the experimental observations, they discovered that the wear happens more easily in polishing along the ‘soft’ direction, which outputs a large friction coefficient. However, the friction coefficient is relative small and keeps invariably in polishing along the ‘hard’ direction [17]. Gao et al. conducted nano-scratching in an atomic force microscope and MD simulation to examine the single-asperity friction behavior on the diamond {001} and {111} planes. They found that the friction force has a significant dependence on the crystalline orientations [18]. Zong et al. employed MD simulation to investigate the formation of amorphous carbons as the frictional sliding is performed on the diamond {100} surface [19]. They declared that the frictional sliding will inevitably trigger the amorphization of diamond carbons on the substrate surface, and the amorphization rate has a negative correlation with the resistance force of the abrasive in sliding. For instance, the greater amorphization rate appears in sliding along the ‘soft’ direction due to the smaller resistance force. Furthermore, some physical models had also been established to explain the anisotropy of removal rate. Klein and Cardinale proposed a Poisson's ratio model. According to this model, only when the Poisson's ratio in the polishing direction and that in the orthogonal direction approach the maximum on a smoothened plane, then the current polishing direction is the so-called ‘soft’ direction [20]. van Bouwelen and van Enckevort presented a periodic bond chain (PBC) model, which suggests the ‘soft’ direction when the inner product between the polishing direction vector and the PBC vector is not more than 0.7 and the ‘hard’ direction when the inner product is not less than 0.9 [21]. Based on Tolkowshy's work [8], Yuan et al. claimed that the variable removal rate has a great dependence on the inclination angle, i.e. the angle between the as-polished surface and the {111} cleavage plane. The larger the inclination angle is, the more the cleavage happens, and resultantly the higher the removal rate is [22]. Zong et al. put forward a
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brittleeductile transition model to describe the material removal mechanism of diamond crystal in mechanical polishing. As expected, the critical depths of cut for brittleeductile transition on different planes and directions of sliding were employed to quantitatively compare the anisotropy of removal rate, which suggests that the bigger the critical depth of cut is, the higher the removal rate does. The removal rate ratio of any one direction to the others is equal to the ratio of their critical depths of cut [23]. In summary, previous work as outlined above had paid great attentions to the removal rate anisotropy in diamond polishing, including the macroscopic observations in experiments and the microscopic descriptions in theory. However, a satisfactory explanation at the atomic scale is still unavailable. Therefore, MD simulation, radial distribution function calculation and coordination number analysis are fulfilled in this work to reveal the atomistic origins of the removal rate anisotropy of diamond crystal in mechanical polishing. 2. Molecular dynamics modeling In order to represent the diamond polishing procedure, nanoindentation and single-asperity nano-scratching coupled MD simulations are performed in this work. The configuration of MD simulation model consists of a monocrystalline diamond substrate (with {100} or {110} free surface) and a spherical grit, as shown in Fig. 1. The substrate has a dimension of 16.05 nm, 7.13 nm and 16.05 nm in X, Y and Z directions, respectively. The substrate consists of three types of atoms, i.e. boundary atoms, thermostat atoms and Newton atoms. The boundary atoms are fixed in three directions to restrict any rigid motion of the substrate. To maintain a constant environment temperature of 293 K for the simulation system, the velocities of thermostat atoms are frequently rescaled. The abrasive grit is modeled as a rigid sphere with a radius of 2.14 nm. The atomic interactions between carbon atoms in diamond substrate and spherical grit are described by the Tersoff potential. The Verlet algorithm is employed and the time step used for integration is 0.5 fs. The carbon atoms in the as-created substrate are first relaxed to their equilibrium configurations at 293 K by using the Nose-Hoover thermostat for 25 ps. Then the relaxed substrate is subjected to the mechanical polishing by using the spherical grit. As pictorially shown in Fig.1, the polishing process consists of two stages, as initial penetration along the negative Y direction and following scratching along the <100>direction (i.e. the ‘soft’ direction) or the <110>direction (i.e. the ‘hard’ direction) of the diamond substrate. The two stages are both performed in displacement-controlled mode, as the grit moves with the same constant velocity of 200 m/s. The penetration depth and scratching length are configured as 1.67 nm and 6.44 nm, respectively. 3. Results and discussions 3.1. RDF analysis In statistical mechanics, the radial distribution function (RDF) in a system of particles (such as atoms, molecules, and etc.) describes how density varies as a function of distance from a reference particle, which is usually employed to characterize the order degree of particle system. In order to evaluate the order degree of diamond carbons under mechanical polishing, the calculation of RDF at different stages is performed for the carbon atoms near the topmost surface in this work. The calculation results are presented in Fig. 2. In this work, the carbon atoms in the as-created diamond substrate are firstly relaxed in the initial 50000 time steps for each simulation. From 50000 to 67800 time steps, nano-indentation
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Fig. 1. Schematic illustration of MD model: a) in nano-indentation; b) in nano-scratching (A color version of this figure can be viewed online).
Fig. 2. RDF analysis for the {100} diamond substrate at different simulation stages: a) polishing in the <100> direction; b) polishing in the <110> direction (A color version of this figure can be viewed online).
simulation is performed. And subsequently, single-asperity nanoscratching is fulfilled in the time steps from 67800 to 132200.
Finally, unloading of the abrasive grit is carried out in the following 17800 steps.
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Therefore, it can be clearly seen from Fig. 2 that after the initial relaxation the first sharp peak of the diamond substrate always appears at a distance of 0.155 nm, regardless of the crystalline orientations, which implies that the distance of any first-neighbor atoms is equal to the bond length of diamond CeC. Such consistency suggests that the diamond carbon atoms still arrange orderly and compactly after the initial relaxation. Once the nanoindentation is performed, the RDF intensity of sharp peaks reduces visibly, as indicated by the blue lines shown in Fig. 2. The same observations can also be achieved as the diamond substrate suffers from the nano-scratching, as indicated by the red lines highlighted in Fig. 2. Moreover, the sharp peaks of the first-, second- and third-neighbor atoms notably shift to the left in the nanoindentation and nano-scratching. For example, as shown in the close-up of Fig. 2 (a), the interatomic distance of first sharp peak decreases from 0.155 nm to 0.151 nm, and three distinct sub-peaks appear at 0.148 nm, 0.15 nm and 0.154 nm. In the higher-order neighbor atoms, however, the leveling-off tendency of RDF peaks becomes more prominent. As a useful evidence, the comparable peak shifts in the lower-order neighbor atoms and the smoothing of RDF peaks in the higher-order neighbor atoms can reveal two facts. One is the distortion of diamond lattice, and the other is the variation of coordination number of diamond carbons. In terms of previous work [13e15], the distortion of diamond crystal under mechanical polishing in this work can be explained as follows. As the abrasive grit penetrates into the diamond substrate, carbon atoms on the topmost surface are subjected to the repulsive force of grit atoms, which inevitably introduces the hydrostatic stress inside the crystal lattice of the diamond substrate. With the ever-increasing penetration of grit, the carbon atoms under the grit begin to be compressed, which leads to a gradual decrement in the interatomic distance, as demonstrated by the peak shifting of the lower-order neighbor atoms shown in Fig.2, i.e. that the strain energy is stored in the form of compression deformation. When the stored strain energy exceeds a critical value, i.e. 5.5 eV that is not high enough to cause the plastic deformation [13], it will be released through the breakage of CeC bonds. Consequently, the ordered and compact diamond cubic structures will transform to the disordered and sparse carbon structures, i.e. the non-diamond phases. In the subsequent nano-scratching, the compression induced lattice distortion also takes place in the topmost surface layer of the diamond substrate, which completes until the abrasive grit unloads. 3.2. Coordination number analysis Fig. 2 has revealed the lattice distortion of the diamond substrate that happens in mechanical polishing. Due to the distortion of diamond lattice, many non-diamond carbons come into being. In order to distinguish the chemical compositions of those nondiamond carbons in the newly created surface layer and debris, the coordination number analysis is carried out in this work. Fig. 3 pictorially presents the distribution of carbon atoms with different coordination numbers as the polishing is performed along the <100>direction on the {100} substrate. In this figure, all the snapshots are captured at 130000 time steps. It can be seen from Fig. 3 that the freshly generated debris and surface layer are both composed of carbon atoms with coordination numbers of 1, 2, 3 and 4, which correspond to the sp0, sp1, sp2 and sp3 hybridizations, respectively. As demonstrated in Fig. 3 a) and b), the sp0 and sp1 hybrided carbon atoms are both disordered and amorphous. For the sp2 hybridizations, most of them are disorder and amorphous, such as the carbon atoms residing in the debris and the as-generated surface layer. However, a fraction of sp2 hybridizations seem to be ordered, which locate at the initial press-in position and are
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highlighted with the white circles, as shown in Fig. 3c). For the sp3 hybrided carbons, the ordered ones are the diamond cubic, and the disordered ones are amorphous too. More interestingly, the same chemical compositions can always be observed on different crystalline planes and directions of polishing. Therefore, it can be concluded that phase transformation or lattice distortion of diamond crystal takes place inevitably in mechanical polishing the diamond substrate, which is independent upon the crystalline orientation of the as-polished surface. In phase transition, the perfect diamond sp3 hybridizations transform to not only the amorphous sp0, sp1, sp2 and sp3 hybridized structures, but also the well-arranged sp2 phases, which is consistent with the previous observations in experiment [11,15,24,25] and findings in MD simulation [14,15,19,24]. On the other side, Fig. 3 further shows that the amounts of sp0 and sp1 hybridized phases are quite trivial. In contrast, the dominant non-diamond carbons are the sp2 hybridized structures and amorphous sp3 hybridizations, and the amounts of which are comparable. 3.3. Atomistic origins of the removal rate anisotropy In order to reveal the underlying atomistic origins of the anisotropic removal rate as observed in mechanical polishing the diamond substrate, the coordination number dependent analyses are also performed in this work to classify the carbon atoms in the newly created surface layer and debris. Fig. 4 presents the amounts of non-diamond carbons with different coordination numbers that sampled at 130000 iteration steps. The total amounts of nondiamond carbons generated in polishing on different planes and orientations are listed in Table 1. It should be noted that all the data in Table 1 are also collected at 130000 time steps. According to the classifications of non-diamond carbons in Fig. 4 and the total numbers of non-diamond carbons in Table 1, it can be found that on the {100} substrate the amounts of sp2 and amorphous sp3 hybridizations and the total number of non-diamond carbons produced in polishing along the <100>direction are both larger than that produced in polishing along the <110>direction. Such observations agree well with the fact that on the {100} plane the higher removal rate appears in polishing along the ‘soft’ <100>direction. On the {110} substrate, however, different variation laws are observed, i.e. that the greater amounts of sp2 and amorphous sp3 hybridizations and the total number of nondiamond carbons appear in polishing along the ‘hard’ <110>direction, not in the ‘soft’ <100>direction. Such observations obviously conflict with the appearance of low removal rate in the ‘hard’ <110>direction. From the viewpoint of diamond lattice structure, the atomistic origins of the above observations can be easily interpreted, i.e. that the formation of non-diamond carbons in polishing is heavily dependent on the arrangement periods of diamond carbon atoms, including the planar period and atomic distance of layer-to-layer, as the pictorial descriptions shown in Table 1. For example, on the {100} substrate, the planar arrangement period of carbon atoms is a/2 in the <100>direction, which is about 0.7 times the period in the <110>direction. As a result, the total non-diamond carbons as produced in the <100>direction are approximately 1.4 times the non-diamond carbons as produced in the <110>direction. Moreover, such atomistic origins can also well answer the variation law of non-diamond carbons as observed on the {110} substrate. That is to say, under the same polishing conditions, the diamond surface having a smaller planar arrangement period in the sliding direction of the abrasive grit and a shorter atomic distance of layer-to-layer creates much more non-diamond carbons, in particular the sp2 and amorphous sp3 phases. According to the atomistic explanations above, it can be concluded that the amount of the as-created non-
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Fig. 3. Carbon atoms with different hybridizations in the debris and the freshly generated surface layer as the spherical grit scratches along the <100> direction of the {100} substrate. (Atoms color description: sp0-blue, sp1-orange, sp2-green, sp3-violet) (A color version of this figure can be viewed online).
diamond carbons is not responsible for the removal rate anisotropy of diamond crystal in mechanical polishing. Fig. 5 presents the time evolution of the amounts of sp2 hybridized carbons and amorphous sp3 hybridizations as the polishing is performed in different directions and on different planes. It can be clearly seen from Fig. 5 that much more non-diamond carbons or sp2 and amorphous sp3 hybridizations appear on the {110} substrate when the abrasive grit is about to complete the
penetration, i.e. corresponding to a simulation time of 33.5 ps. This can be attributed to the larger atom density on the {110} plane. With the advance of the abrasive grit in sliding, the sp2 hybridized phases will increase quickly, which is independent on the crystalline orientations. To be different, however, the amorphous sp3 hybridized structures are invariable, as shown in Fig. 5 b) and c), or increase slightly, as shown in Fig. 5 a) and d). Such observations can be explained as follows.
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5000
b)
a)
4500
4000
along the <100> direction
3500
along the <110> direction
Amount of carbon atoms
Amount of carbon atoms
4500
3000 2500 2000 1500
4000
along the <100> direction
3500
along the <110> direction
3000 2500 2000 1500
1000
1000
500
500
0
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sp0
sp1
sp2
0
amorphous sp3
sp0
sp1
sp2
amorphous sp3
Fig. 4. Amounts of non-diamond carbons with different coordination numbers sampled at 130000 time steps: a) {100} substrate; b) {110} substrate. (A color version of this figure can be viewed online).
Table. 1 Lattice parameters of diamond and non-diamond carbons as generated in polishing. Crystalline plane
{100}
{110}
Crystalline orientation
Plane view of atomic arrangement
<100> ‘soft’ <110> ‘hard’
<100> ‘soft’ <110> ‘hard’
Atomic arrangement period in plane
layer to layer
Total number of non-diamond carbons
a 2
a 4
7822
pffiffiffi 2a 2
a 4
5694
a
pffiffiffi 2a 4
5457
pffiffiffi 2a 2
pffiffiffi 2a 4
8121
a is the diamond lattice constant, and a ¼ 0.356683nm [19]
As revealed in previous work [13e15], when the diamond substrate suffers from the mechanically induced effects, such as compression and scratching, the diamond CeC bonds will store the strain energy in the form of compression deformation. Once the stored strain energy exceeds 5.5 eV, the breakage of diamond CeC bonds takes place to release the excessive strain energy. In this case, phase transformation from the perfect diamond cubic to the amorphous sp3 structure appears firstly. Due to the frequent storage and release of strain energy on the CeC bonds, the broken CeC bonds become more and more, which leads to the appearance of sp2, sp1 and sp0 hybridized structures. As revealed in the MD simulations in this work, the carbon atoms will undergo much intenser deformation in scratching than that in indentation. This means that the scratch of the abrasive grit introduces more efficient transformation from the amorphous sp3 structures to the hybridized phases with lower coordination numbers, e.g. the sp2, sp1 and sp0 hybridizations. As the dominant phases with little coordination
number, therefore, the sp2 hybridized carbons increase quickly with the advance of the abrasive grit in sliding. As the transient phases, however, the sp3 hybridized carbons keep invariably or grow up slightly. According to the observations in Fig. 5 and the explanations above, it can be inferred that the content of sp2 phases or amorphous sp3 hybridizations may be the essential factor causing the removal rate anisotropy of diamond crystal in mechanical polishing. Moreover, Pastewka et al. [14] declared that the removal rate anisotropy of diamond crystal relies on the thickness of the ascreated amorphous layer in mechanical polishing. A bigger thickness of amorphous layer corresponds to a higher removal rate. In our MD simulations, the same phenomena are also observed in polishing the {100} substrate, which can be found in Table 2. From Table 2, it can be seen that an amorphous layer thickness of 4.40 nm comes into being as the abrasive grit slides along the ‘soft’ <100>direction of the {100} substrate, but a thickness of 3.37 nm
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a)
4500 4000
amorphous sp3 hybridization
b)
2
sp hybridization
3500
amorphous sp3 hybridization 3000
sp2 hybridization
Amount of carbon atoms
Amount of carbon atoms
3500 3000 2500 2000 1500 1000
2500
2000
1500
1000
500
500
0
0
33.5 35 37.5 40 42.5 45 47.5 50 52.5 55 57.5 60 62.5 65
33.5 35 37.5 40 42.5 45 47.5 50 52.5 55 57.5 60 62.5 65
Time (ps)
Time (ps) 3500
amorphous sp3 hybridization
Amount of carbon atoms
3000
d)
5000 4500
sp2 hybridization
amorphous sp3 hybridization sp2 hybridization
4000
Amount of carbon atoms
c)
2500
2000
1500
1000
3500 3000 2500 2000 1500 1000
500
500 0
0 33.5 35 37.5 40 42.5 45 47.5 50 52.5 55 57.5 60 62.5 65
Time (ps)
33.5 35 37.5 40 42.5 45 47.5 50 52.5 55 57.5 60 62.5 65
Time (ps)
Fig. 5. Amounts of sp2 and amorphous sp3 hybridizations vs. simulation time: a) {100} <100>; b) {100} <110>; c) {110} <100>; d) {110} <110 > (A color version of this figure can be viewed online).
appears in sliding along the ‘hard’ <110>direction. However, no comparable differences can be observed in the amorphous layer thickness when the abrasive grit slides on the {110} substrate. As shown in Table 2, the predicted values are 4.28 nm and 4.61 nm in sliding along the ‘soft’ and ‘hard’ directions, respectively. The obvious inconsistencies as observed above suggest that the theory of amorphous layer thickness still has no access to satisfactorily interpret the atomistic origins of the removal rate anisotropy in diamond polishing, although Pastewka's hypothesis is effective on some typical facets, e.g. the {100} plane in this work. Therefore in this work, a chemical composition-dependent hypothesis accounting for the proportion of sp2 hybridized structures to amorphous sp3 hybridizations is firstly put forward to understand the atomistic origins of the removal rate anisotropy in mechanical polishing of diamond crystal. In the light of the newly proposed hypothesis, the proportion of sp2 hybridizations to amorphous sp3 hybridizations that residing in the as-created amorphous layer and debris varies as the diamond polishing is performed along different directions and on different planes. In polishing along the ‘soft’ direction, phase transformation from amorphous sp3 structures to sp2 hybridized structures has little resistance, which produces a high proportion of sp2 to amorphous sp3. In contrast, a low proportion appears in polishing along the ‘hard’ direction. In accordance with the wear rates as observed in experiment, it can be predicted that the greater the proportion of sp2 to amorphous sp3 in the newly created surface layer and debris, the higher the removal rate in polishing. This is because a higher content of sp2 hybrided phases will soften the materials in the newly created surface layer much more, which is more favorable for
the material removal in the followed sliding of the abrasive grit. In order to validate the proposed hypothesis, the amounts of sp2 structures and amorphous sp3 hybridizations sampled at different simulation times are employed to calculate the proportions of sp2 to amorphous sp3. The original data can be found in Fig. 5, and the calculated proportions are pictorially shown in Fig. 6. In Fig. 6, it can be seen that the polished diamond substrates have no significant differences in the proportions of sp2 to amorphous sp3 at the initial stage. As demonstrated in Fig. 5, however, the sp2 hybridizations will increase quickly with the advance of the abrasive grit, which is independent on the orientation of the polished diamond surface. And subsequently, a strong anisotropy of the proportion appears when the simulation time is more than 42.5 ps, as highlighted in Fig. 6. In this case, the high proportion of sp2 to amorphous sp3 always emerges in polishing along the ‘soft’ direction, which can be observed on both the {100} and {110} substrates. As discussed above, the higher the proportion of sp2 to amorphous sp3, the softer the materials in the newly created surface layer, and resultantly the greater the material removal rate. Apparently, the results as disclosed in Fig. 6 agree well with the wear rate as observed in experiment, i.e. that both the {100} and {110} surfaces have a far greater wear rate in polishing along the ‘soft’ direction than that producing along the ‘hard’ direction [23]. Moreover, when the diamond substrates are all polished along the ‘soft’ direction, the {110} substrate presents a visibly larger proportion of sp2 to amorphous sp3 than that of the {100} substrate. Such variation law also has an excellent correlation with the experimental finding, i.e. that the {110} plane has a much greater wear rate than the {100} plane in polishing along the ‘soft’ direction
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Table. 2 Thickness of amorphous layer and distribution of non-diamond carbons as nano-scratching are performed in different directions and on different plane. Crystalline orientation
Thickness of amorphous layer [Å]
{100}<100>
44.05
{100}<110>
33.74
{110}<100>
42.80
{110}<110>
46.10
Distribution of non-diamond carbons in amorphous layer (yellow-sp2, blue-amorphous sp3)
good consistency with the observations in experiment, which powerfully validates that the proportion of sp2 hybridizations to amorphous sp3 phases in the as-created non-diamond carbons plays a dominant role in determining the removal rate anisotropy of diamond crystal in mechanical polishing.
4. Conclusions This work aims to reveal the underlying atomistic origins of the removal rate anisotropy in mechanical polishing the diamond crystal. According to the observations in molecular dynamics simulation, radial distribution function analysis and coordination number analysis, some important conclusions can be drawn as follows.
Fig. 6. The proportion of sp2 hybridizations to amorphous sp3 structures vs. simulation time (A color version of this figure can be viewed online).
[23]. To be evident, the variation laws as revealed in Fig.6 all have a
1) Lattice distortion is inevitable as the diamond substrate suffers from the mechanical polishing. Due to the mechanically induced compression and scratching, the perfect diamond cubic carbons will transform to some non-diamond phases, i.e. that an amorphous layer comes into being through phase transformation, which is composed of the amorphous sp0, sp1, sp2 and sp3 hybridizations and well-arranged sp2 structures. Among the as-
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created non-diamond carbons, however, the dominant structures are sp2 and amorphous sp3 hybridizations. 2) The material removal rate is heavily dependent on the proportion of sp2 hybridized structures to amorphous sp3 hybridizations in the newly created surface layer and debris. The observed laws validate that the greater the proportion of sp2 to amorphous sp3 is in the newly created surface layer and debris, the higher the material removal rate does in polishing. Acknowledgements The authors would like to thank the Natural Science Foundation of China (No. 51175127) and the Fundamental Research Funds for the Central Universities (No. HIT.BRETIII.201412) for the support of this work. Furthermore, this work was also supported by the Major Special Subject of High-end CNC Machine Tools and Basic Manufacturing Equipment Science and Technology of China (No. 2011ZX04004-031). References [1] J.E. Field, The mechanical and strength properties of diamond, Rep. Prog. Phys. 75 (2012) 126505. [2] W.J. Zong, Z.Q. Li, T. Sun, K. Cheng, D. Li, S. Dong, The basic issues in design and fabrication of diamond cutting tools for ultra-precision and nanometric machining, Int. J. Mach. Tools Manuf. 50 (4) (2010) 411e419. [3] S. Goel, X.C. Luo, A. Agrawal, R.L. Reuben, Diamond machining of silicon: a review of advances in molecular dynamics simulation, Int. J. Mach. Tools Manuf. 88 (2015) 131e164. [4] Ke Chen, W.J. Meng, G.B. Sinclair, Size dependence of the plane-strain response of single-crystal Al to indentation by diamond wedges, Acta Mater. 60 (2012) 4879e4887. [5] K.D. Bouzakis, M. Pappa, G. Maliaris, N. Michailidis, Fast determination of parameters describing manufacturing imperfections and operation wear of nanoindenter tips, Surf. Coat. Tech. 215 (2013) 218e223. [6] A.G. Khurshudov, K. Kato, H. Koide, Nano-wear of the diamond AFM probing tip under scratching of silicon, studied by AFM, Tribol. Lett. 2 (1996) 345e354. [7] E.L.H. Thomas, G.W. Nelson, S. Mandal, J.S. Foord, O.A. Williams, Chemical mechanical polishing of thin film diamond, Carbon 68 (2014) 473e479.
[8] M. Tolkowsky, Research on the Abrading, Grinding or Polishing of Diamonds [D. Sc. Thesis], University of London, London, 1920. [9] M.S. Couto, W.J.P. van Enckevort, B. Wichman, M. Seal, Scanning tunneling microscopy of polished diamond surfaces, Appl. Surf. Sci. 62 (4) (1992) 263e268. [10] M.S. Couto, W.J.P. van Enckevort, M. Seal, On the mechanism of diamond polishing in the soft directions, J. Hard Mater. 5 (2) (1994) 31e47. [11] S.E. Grillo, J.E. Field, The polishing of diamond, J. Phys. D. Appl. Phys. 30 (2) (1997) 202e209. [12] Y.G. Gogotsi, A. Kailer, K.G. Nickel, Pressure-induced phase transformations in diamond, J. Appl. Phys. 84 (3) (1998) 1299e1304. [13] F.M. van Bouwelen, Diamond polishing from different angles, Diam. Relat. Mater. 9 (3) (2000) 925e928. [14] L. Pastewka1, S. Moser, P. Gumbsch, M. Moseler, Anisotropic mechanical amorphization drives wear in diamond, Nat. Mater. 10 (2011) 34e38. [15] B.A. Fairchild, S. Rubanov, D.W. Lau, M. Robinson, I. Suarez-Martinez, N. Marks, A.D. Greentree, D. McCulloch, S. Prawer, Mechanism for the amorphisation of diamond, Adv. Mater. 24 (15) (2012) 2024e2029. rez, F.M. van Bouwelen, M.C. Payne, Microscopic mechanism [16] M.R. Jarvis, R. Pe for mechanical polishing of diamond (110) surfaces, Phys. Rev. Lett. 80 (16) (1998) 3428e3431. [17] S.E. Grillo, J.E. Field, F.M. van Bouwelen, Diamond polishing: the dependency of friction and wear on load and crystal orientation, J. Phys. D Appl. Phys. 33 (8) (2000) 985e990. [18] G. Gao, R.J. Cannara, R.W. Carpick, J.A. Harrison, Atomic-scale friction on diamond: a comparison of different sliding directions on (001) and (111) surfaces using MD and AFM, Langmuir 23 (10) (2007) 5394e5405. [19] N. Yang, W.J. Zong, Z.Q. Li, T. Sun, Amorphization anisotropy and the internal of amorphous layer in diamond nanoscale friction, Comp. Mater. Sci. 95 (2014) 551e556. [20] C.A. Klein, G.F. Cardinale, Young's modulus and Poisson's ratio of CVD diamond, Diam. Relat. Mater. 2 (5) (1993) 918e923. [21] F.M. van Bouwelen, W.J.P. van Enckevort, A simple model to describe the anisotropy of diamond polishing, Diam. Relat. Mater. 8 (1999) 840e844. [22] Z.J. Yuan, Y.X. Yao, M. Zhou, Q.S. Bai, Lapping of single crystal diamond tools, Ann. CIRP 52 (2003) 285e288. [23] W.J. Zong, D. Li, K. Cheng, T. Sun, H.X. Wang, Y.C. Liang, The material removal mechanism in mechanical lapping of diamond cutting tools, Int. J. Mach. Tools Manuf. 45 (2005) 783e788. [24] W.J. Zong, J.J. Zhang, Y. Liu, T. Sun, Achieving ultra-hard surface of mechanically polished diamond crystal by thermo-chemical refinement, Appl. Surf. Sci. 316 (2014) 617e624. [25] Y.G. Gogotsi, A. Kailer, K.G. Nickel, Transformation of diamond to graphite, Nature 401 (1999) 663e664.
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Atomistic origins of material removal rate anisotropy in mechanical polishing of diamond crystal W.J. Zong*, X. Cheng, J.J. Zhang** Center for Precision Engineering, Harbin Institute of Technology, Harbin, 150001, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 August 2015 Received in revised form 25 November 2015 Accepted 1 December 2015 Available online 13 December 2015
In this work, molecular dynamics simulation is employed to represent the diamond polishing. Radial distribution function and coordination number analyses are further performed to reveal the underlying atomistic origins of the removal rate anisotropy. The results show that the lattice distortion is inevitable as the diamond substrate suffers from the mechanically induced effects, which produces an amorphous layer on the surface. In the amorphization, the perfect diamond cubic transforms to some non-diamond phases, including the amorphous sp0, sp1, sp2 and sp3 hybridized structures and well-arranged sp2 structures. However, the dominant phases are sp2 and amorphous sp3 phases. More interestingly, it is found that the removal rate strongly depends on the proportion of sp2 hybridizations to amorphous sp3 structures. In the ‘hard’ direction, phase transformation from amorphous sp3 to sp2 is difficult, and therefore a low proportion of sp2 to amorphous sp3 appears, which results in a small removal rate. In the ‘soft’ direction, phase transformation from amorphous sp3 to sp2 has less resistance, and a higher proportion output, which gives a greater removal rate. The variation laws as revealed above confirm that the removal rate anisotropy in diamond polishing is derived from the concentration of sp2 hybridizations in the as-created amorphous layer and debris. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction As the hardest engineering material known in the world, diamond crystal has the unmatched wear resistance and excellent chemical stability [1], and thus it has been considered as an ideal tooling material in nanometric cutting [2,3], nano-indentation [4,5], nano-scratching [6], and etc. However, it is difficult to smoothen the surface of diamond crystal, and some special polishing processes are required for fulfilling such objective [7], among which the mechanical polishing is one of the most favorable and popular solutions [2]. During mechanical polishing of diamond crystal, the anisotropy of material removal rate appears inevitably, which heavily depends on the crystalline orientation of polished diamond surface. However, the underlying mechanisms of this undesirable feature are still not answered satisfactorily. And
* Corresponding author. Harbin Institute of Technology, P.O. Box 413, Harbin, 150001, PR China. ** Corresponding author. Harbin Institute of Technology, P.O. Box 413, Harbin, 150001, PR China. E-mail addresses: [email protected] (W.J. Zong), [email protected] (J.J. Zhang). http://dx.doi.org/10.1016/j.carbon.2015.12.001 0008-6223/© 2015 Elsevier Ltd. All rights reserved.
therefore, many interesting works had been performed to try to reveal the possible mechanisms. Tolkowshy observed the microscopic morphology of debris that left on the polished surface of diamond crystal by using the optical microscope, and he put forward a microscopic cleavage theory to explain the anisotropy of wear rate [8]. Couto et al. investigated the polished surface with scanning tunneling microscopy, and they claimed that the surface layer of diamond crystal is removed in fractures or micro-chips as the polishing is performed along the ‘hard’ direction [9]. Moreover, they also proposed a nanometric groove dependent theory to interpret the material removal mechanism in polishing along the ‘soft’ direction [10]. Grillo and Field collected the worn debris from the polished diamond surface, and subsequently they analyzed them with transmission electron microscopy and electron energy loss spectroscopy in a scanning transmission electron microscope. They finally proposed a novel mechanism to expatiate the material removal in diamond polishing, i.e. phase transformation from the perfect diamond cubic to the amorphous sp2 and sp1 hybridized carbons [11]. Gogotsi et al. conducted the indentation experiments on diamond surface corroborated by micro-Raman spectroscopy. They confirmed that the plastic deformation induced phase transformation in diamond
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is a very common feature of wear, and the non-cubic diamond polytypes include lonsdaleite, graphitic carbon, and possibly new phases of carbon [12]. van Bouwelen claimed that there is no elastic energy as the plastic deformation takes place in diamond crystal. Conversely, rehybridization of carbon atom dominates once the stored deformation energy of CeC bond exceeds its energy barrier, i.e. 5.5ev [13]. Pastewka et al. proposed a concept of pilot-atom to describe the amorphization of diamond. They concluded that the anisotropy of amorphization rate is derived from the probability that the pilot-atom drive the surface atom to depart from its crystalline position to form the amorphous atom [14]. Fairchild et al. explored the amorphization of diamond crystal by ion implantation and molecular dynamics (MD) simulation. They declared that the amorphization of diamond carbon is strain driven. When the force-induced strain in diamond reaches a critical value of 16%, the diamond lattice collapses. And resultantly, the amorphous nondiamond phases come into being [15]. In addition to the material removal mechanisms, the friction behaviors of diamond had also been discussed. Jarvis et al. carried out a lot of ab-initio quantum-mechanical simulations to investigate the nano-asperity scratching on the diamond {110} surface. They suggested that the observed anisotropy of wear rate is due to the difference in the atomistic deformation of bond angle. In scratching along the ‘soft’ direction, the bond angle deforms on a few diamonds CeC bonds at the same time, which produces the large enough localized stress to break the deformed diamond bonds and drive the amorphization. In scratching along the ‘hard’ direction, however, the deformation of bond angle is not localized, and the stress distributes over a large number of diamond bonds, which finally leads to the ‘large-area’ subsurface damages [16]. Grillo, Field and van Bouwelen paid great attentions to the friction and wear properties when the diamond {100} surface was polished in different orientations. According to the experimental observations, they discovered that the wear happens more easily in polishing along the ‘soft’ direction, which outputs a large friction coefficient. However, the friction coefficient is relative small and keeps invariably in polishing along the ‘hard’ direction [17]. Gao et al. conducted nano-scratching in an atomic force microscope and MD simulation to examine the single-asperity friction behavior on the diamond {001} and {111} planes. They found that the friction force has a significant dependence on the crystalline orientations [18]. Zong et al. employed MD simulation to investigate the formation of amorphous carbons as the frictional sliding is performed on the diamond {100} surface [19]. They declared that the frictional sliding will inevitably trigger the amorphization of diamond carbons on the substrate surface, and the amorphization rate has a negative correlation with the resistance force of the abrasive in sliding. For instance, the greater amorphization rate appears in sliding along the ‘soft’ direction due to the smaller resistance force. Furthermore, some physical models had also been established to explain the anisotropy of removal rate. Klein and Cardinale proposed a Poisson's ratio model. According to this model, only when the Poisson's ratio in the polishing direction and that in the orthogonal direction approach the maximum on a smoothened plane, then the current polishing direction is the so-called ‘soft’ direction [20]. van Bouwelen and van Enckevort presented a periodic bond chain (PBC) model, which suggests the ‘soft’ direction when the inner product between the polishing direction vector and the PBC vector is not more than 0.7 and the ‘hard’ direction when the inner product is not less than 0.9 [21]. Based on Tolkowshy's work [8], Yuan et al. claimed that the variable removal rate has a great dependence on the inclination angle, i.e. the angle between the as-polished surface and the {111} cleavage plane. The larger the inclination angle is, the more the cleavage happens, and resultantly the higher the removal rate is [22]. Zong et al. put forward a
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brittleeductile transition model to describe the material removal mechanism of diamond crystal in mechanical polishing. As expected, the critical depths of cut for brittleeductile transition on different planes and directions of sliding were employed to quantitatively compare the anisotropy of removal rate, which suggests that the bigger the critical depth of cut is, the higher the removal rate does. The removal rate ratio of any one direction to the others is equal to the ratio of their critical depths of cut [23]. In summary, previous work as outlined above had paid great attentions to the removal rate anisotropy in diamond polishing, including the macroscopic observations in experiments and the microscopic descriptions in theory. However, a satisfactory explanation at the atomic scale is still unavailable. Therefore, MD simulation, radial distribution function calculation and coordination number analysis are fulfilled in this work to reveal the atomistic origins of the removal rate anisotropy of diamond crystal in mechanical polishing. 2. Molecular dynamics modeling In order to represent the diamond polishing procedure, nanoindentation and single-asperity nano-scratching coupled MD simulations are performed in this work. The configuration of MD simulation model consists of a monocrystalline diamond substrate (with {100} or {110} free surface) and a spherical grit, as shown in Fig. 1. The substrate has a dimension of 16.05 nm, 7.13 nm and 16.05 nm in X, Y and Z directions, respectively. The substrate consists of three types of atoms, i.e. boundary atoms, thermostat atoms and Newton atoms. The boundary atoms are fixed in three directions to restrict any rigid motion of the substrate. To maintain a constant environment temperature of 293 K for the simulation system, the velocities of thermostat atoms are frequently rescaled. The abrasive grit is modeled as a rigid sphere with a radius of 2.14 nm. The atomic interactions between carbon atoms in diamond substrate and spherical grit are described by the Tersoff potential. The Verlet algorithm is employed and the time step used for integration is 0.5 fs. The carbon atoms in the as-created substrate are first relaxed to their equilibrium configurations at 293 K by using the Nose-Hoover thermostat for 25 ps. Then the relaxed substrate is subjected to the mechanical polishing by using the spherical grit. As pictorially shown in Fig.1, the polishing process consists of two stages, as initial penetration along the negative Y direction and following scratching along the <100>direction (i.e. the ‘soft’ direction) or the <110>direction (i.e. the ‘hard’ direction) of the diamond substrate. The two stages are both performed in displacement-controlled mode, as the grit moves with the same constant velocity of 200 m/s. The penetration depth and scratching length are configured as 1.67 nm and 6.44 nm, respectively. 3. Results and discussions 3.1. RDF analysis In statistical mechanics, the radial distribution function (RDF) in a system of particles (such as atoms, molecules, and etc.) describes how density varies as a function of distance from a reference particle, which is usually employed to characterize the order degree of particle system. In order to evaluate the order degree of diamond carbons under mechanical polishing, the calculation of RDF at different stages is performed for the carbon atoms near the topmost surface in this work. The calculation results are presented in Fig. 2. In this work, the carbon atoms in the as-created diamond substrate are firstly relaxed in the initial 50000 time steps for each simulation. From 50000 to 67800 time steps, nano-indentation
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Fig. 1. Schematic illustration of MD model: a) in nano-indentation; b) in nano-scratching (A color version of this figure can be viewed online).
Fig. 2. RDF analysis for the {100} diamond substrate at different simulation stages: a) polishing in the <100> direction; b) polishing in the <110> direction (A color version of this figure can be viewed online).
simulation is performed. And subsequently, single-asperity nanoscratching is fulfilled in the time steps from 67800 to 132200.
Finally, unloading of the abrasive grit is carried out in the following 17800 steps.
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Therefore, it can be clearly seen from Fig. 2 that after the initial relaxation the first sharp peak of the diamond substrate always appears at a distance of 0.155 nm, regardless of the crystalline orientations, which implies that the distance of any first-neighbor atoms is equal to the bond length of diamond CeC. Such consistency suggests that the diamond carbon atoms still arrange orderly and compactly after the initial relaxation. Once the nanoindentation is performed, the RDF intensity of sharp peaks reduces visibly, as indicated by the blue lines shown in Fig. 2. The same observations can also be achieved as the diamond substrate suffers from the nano-scratching, as indicated by the red lines highlighted in Fig. 2. Moreover, the sharp peaks of the first-, second- and third-neighbor atoms notably shift to the left in the nanoindentation and nano-scratching. For example, as shown in the close-up of Fig. 2 (a), the interatomic distance of first sharp peak decreases from 0.155 nm to 0.151 nm, and three distinct sub-peaks appear at 0.148 nm, 0.15 nm and 0.154 nm. In the higher-order neighbor atoms, however, the leveling-off tendency of RDF peaks becomes more prominent. As a useful evidence, the comparable peak shifts in the lower-order neighbor atoms and the smoothing of RDF peaks in the higher-order neighbor atoms can reveal two facts. One is the distortion of diamond lattice, and the other is the variation of coordination number of diamond carbons. In terms of previous work [13e15], the distortion of diamond crystal under mechanical polishing in this work can be explained as follows. As the abrasive grit penetrates into the diamond substrate, carbon atoms on the topmost surface are subjected to the repulsive force of grit atoms, which inevitably introduces the hydrostatic stress inside the crystal lattice of the diamond substrate. With the ever-increasing penetration of grit, the carbon atoms under the grit begin to be compressed, which leads to a gradual decrement in the interatomic distance, as demonstrated by the peak shifting of the lower-order neighbor atoms shown in Fig.2, i.e. that the strain energy is stored in the form of compression deformation. When the stored strain energy exceeds a critical value, i.e. 5.5 eV that is not high enough to cause the plastic deformation [13], it will be released through the breakage of CeC bonds. Consequently, the ordered and compact diamond cubic structures will transform to the disordered and sparse carbon structures, i.e. the non-diamond phases. In the subsequent nano-scratching, the compression induced lattice distortion also takes place in the topmost surface layer of the diamond substrate, which completes until the abrasive grit unloads. 3.2. Coordination number analysis Fig. 2 has revealed the lattice distortion of the diamond substrate that happens in mechanical polishing. Due to the distortion of diamond lattice, many non-diamond carbons come into being. In order to distinguish the chemical compositions of those nondiamond carbons in the newly created surface layer and debris, the coordination number analysis is carried out in this work. Fig. 3 pictorially presents the distribution of carbon atoms with different coordination numbers as the polishing is performed along the <100>direction on the {100} substrate. In this figure, all the snapshots are captured at 130000 time steps. It can be seen from Fig. 3 that the freshly generated debris and surface layer are both composed of carbon atoms with coordination numbers of 1, 2, 3 and 4, which correspond to the sp0, sp1, sp2 and sp3 hybridizations, respectively. As demonstrated in Fig. 3 a) and b), the sp0 and sp1 hybrided carbon atoms are both disordered and amorphous. For the sp2 hybridizations, most of them are disorder and amorphous, such as the carbon atoms residing in the debris and the as-generated surface layer. However, a fraction of sp2 hybridizations seem to be ordered, which locate at the initial press-in position and are
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highlighted with the white circles, as shown in Fig. 3c). For the sp3 hybrided carbons, the ordered ones are the diamond cubic, and the disordered ones are amorphous too. More interestingly, the same chemical compositions can always be observed on different crystalline planes and directions of polishing. Therefore, it can be concluded that phase transformation or lattice distortion of diamond crystal takes place inevitably in mechanical polishing the diamond substrate, which is independent upon the crystalline orientation of the as-polished surface. In phase transition, the perfect diamond sp3 hybridizations transform to not only the amorphous sp0, sp1, sp2 and sp3 hybridized structures, but also the well-arranged sp2 phases, which is consistent with the previous observations in experiment [11,15,24,25] and findings in MD simulation [14,15,19,24]. On the other side, Fig. 3 further shows that the amounts of sp0 and sp1 hybridized phases are quite trivial. In contrast, the dominant non-diamond carbons are the sp2 hybridized structures and amorphous sp3 hybridizations, and the amounts of which are comparable. 3.3. Atomistic origins of the removal rate anisotropy In order to reveal the underlying atomistic origins of the anisotropic removal rate as observed in mechanical polishing the diamond substrate, the coordination number dependent analyses are also performed in this work to classify the carbon atoms in the newly created surface layer and debris. Fig. 4 presents the amounts of non-diamond carbons with different coordination numbers that sampled at 130000 iteration steps. The total amounts of nondiamond carbons generated in polishing on different planes and orientations are listed in Table 1. It should be noted that all the data in Table 1 are also collected at 130000 time steps. According to the classifications of non-diamond carbons in Fig. 4 and the total numbers of non-diamond carbons in Table 1, it can be found that on the {100} substrate the amounts of sp2 and amorphous sp3 hybridizations and the total number of non-diamond carbons produced in polishing along the <100>direction are both larger than that produced in polishing along the <110>direction. Such observations agree well with the fact that on the {100} plane the higher removal rate appears in polishing along the ‘soft’ <100>direction. On the {110} substrate, however, different variation laws are observed, i.e. that the greater amounts of sp2 and amorphous sp3 hybridizations and the total number of nondiamond carbons appear in polishing along the ‘hard’ <110>direction, not in the ‘soft’ <100>direction. Such observations obviously conflict with the appearance of low removal rate in the ‘hard’ <110>direction. From the viewpoint of diamond lattice structure, the atomistic origins of the above observations can be easily interpreted, i.e. that the formation of non-diamond carbons in polishing is heavily dependent on the arrangement periods of diamond carbon atoms, including the planar period and atomic distance of layer-to-layer, as the pictorial descriptions shown in Table 1. For example, on the {100} substrate, the planar arrangement period of carbon atoms is a/2 in the <100>direction, which is about 0.7 times the period in the <110>direction. As a result, the total non-diamond carbons as produced in the <100>direction are approximately 1.4 times the non-diamond carbons as produced in the <110>direction. Moreover, such atomistic origins can also well answer the variation law of non-diamond carbons as observed on the {110} substrate. That is to say, under the same polishing conditions, the diamond surface having a smaller planar arrangement period in the sliding direction of the abrasive grit and a shorter atomic distance of layer-to-layer creates much more non-diamond carbons, in particular the sp2 and amorphous sp3 phases. According to the atomistic explanations above, it can be concluded that the amount of the as-created non-
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Fig. 3. Carbon atoms with different hybridizations in the debris and the freshly generated surface layer as the spherical grit scratches along the <100> direction of the {100} substrate. (Atoms color description: sp0-blue, sp1-orange, sp2-green, sp3-violet) (A color version of this figure can be viewed online).
diamond carbons is not responsible for the removal rate anisotropy of diamond crystal in mechanical polishing. Fig. 5 presents the time evolution of the amounts of sp2 hybridized carbons and amorphous sp3 hybridizations as the polishing is performed in different directions and on different planes. It can be clearly seen from Fig. 5 that much more non-diamond carbons or sp2 and amorphous sp3 hybridizations appear on the {110} substrate when the abrasive grit is about to complete the
penetration, i.e. corresponding to a simulation time of 33.5 ps. This can be attributed to the larger atom density on the {110} plane. With the advance of the abrasive grit in sliding, the sp2 hybridized phases will increase quickly, which is independent on the crystalline orientations. To be different, however, the amorphous sp3 hybridized structures are invariable, as shown in Fig. 5 b) and c), or increase slightly, as shown in Fig. 5 a) and d). Such observations can be explained as follows.
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5000
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Fig. 4. Amounts of non-diamond carbons with different coordination numbers sampled at 130000 time steps: a) {100} substrate; b) {110} substrate. (A color version of this figure can be viewed online).
Table. 1 Lattice parameters of diamond and non-diamond carbons as generated in polishing. Crystalline plane
{100}
{110}
Crystalline orientation
Plane view of atomic arrangement
<100> ‘soft’ <110> ‘hard’
<100> ‘soft’ <110> ‘hard’
Atomic arrangement period in plane
layer to layer
Total number of non-diamond carbons
a 2
a 4
7822
pffiffiffi 2a 2
a 4
5694
a
pffiffiffi 2a 4
5457
pffiffiffi 2a 2
pffiffiffi 2a 4
8121
a is the diamond lattice constant, and a ¼ 0.356683nm [19]
As revealed in previous work [13e15], when the diamond substrate suffers from the mechanically induced effects, such as compression and scratching, the diamond CeC bonds will store the strain energy in the form of compression deformation. Once the stored strain energy exceeds 5.5 eV, the breakage of diamond CeC bonds takes place to release the excessive strain energy. In this case, phase transformation from the perfect diamond cubic to the amorphous sp3 structure appears firstly. Due to the frequent storage and release of strain energy on the CeC bonds, the broken CeC bonds become more and more, which leads to the appearance of sp2, sp1 and sp0 hybridized structures. As revealed in the MD simulations in this work, the carbon atoms will undergo much intenser deformation in scratching than that in indentation. This means that the scratch of the abrasive grit introduces more efficient transformation from the amorphous sp3 structures to the hybridized phases with lower coordination numbers, e.g. the sp2, sp1 and sp0 hybridizations. As the dominant phases with little coordination
number, therefore, the sp2 hybridized carbons increase quickly with the advance of the abrasive grit in sliding. As the transient phases, however, the sp3 hybridized carbons keep invariably or grow up slightly. According to the observations in Fig. 5 and the explanations above, it can be inferred that the content of sp2 phases or amorphous sp3 hybridizations may be the essential factor causing the removal rate anisotropy of diamond crystal in mechanical polishing. Moreover, Pastewka et al. [14] declared that the removal rate anisotropy of diamond crystal relies on the thickness of the ascreated amorphous layer in mechanical polishing. A bigger thickness of amorphous layer corresponds to a higher removal rate. In our MD simulations, the same phenomena are also observed in polishing the {100} substrate, which can be found in Table 2. From Table 2, it can be seen that an amorphous layer thickness of 4.40 nm comes into being as the abrasive grit slides along the ‘soft’ <100>direction of the {100} substrate, but a thickness of 3.37 nm
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a)
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Time (ps)
Fig. 5. Amounts of sp2 and amorphous sp3 hybridizations vs. simulation time: a) {100} <100>; b) {100} <110>; c) {110} <100>; d) {110} <110 > (A color version of this figure can be viewed online).
appears in sliding along the ‘hard’ <110>direction. However, no comparable differences can be observed in the amorphous layer thickness when the abrasive grit slides on the {110} substrate. As shown in Table 2, the predicted values are 4.28 nm and 4.61 nm in sliding along the ‘soft’ and ‘hard’ directions, respectively. The obvious inconsistencies as observed above suggest that the theory of amorphous layer thickness still has no access to satisfactorily interpret the atomistic origins of the removal rate anisotropy in diamond polishing, although Pastewka's hypothesis is effective on some typical facets, e.g. the {100} plane in this work. Therefore in this work, a chemical composition-dependent hypothesis accounting for the proportion of sp2 hybridized structures to amorphous sp3 hybridizations is firstly put forward to understand the atomistic origins of the removal rate anisotropy in mechanical polishing of diamond crystal. In the light of the newly proposed hypothesis, the proportion of sp2 hybridizations to amorphous sp3 hybridizations that residing in the as-created amorphous layer and debris varies as the diamond polishing is performed along different directions and on different planes. In polishing along the ‘soft’ direction, phase transformation from amorphous sp3 structures to sp2 hybridized structures has little resistance, which produces a high proportion of sp2 to amorphous sp3. In contrast, a low proportion appears in polishing along the ‘hard’ direction. In accordance with the wear rates as observed in experiment, it can be predicted that the greater the proportion of sp2 to amorphous sp3 in the newly created surface layer and debris, the higher the removal rate in polishing. This is because a higher content of sp2 hybrided phases will soften the materials in the newly created surface layer much more, which is more favorable for
the material removal in the followed sliding of the abrasive grit. In order to validate the proposed hypothesis, the amounts of sp2 structures and amorphous sp3 hybridizations sampled at different simulation times are employed to calculate the proportions of sp2 to amorphous sp3. The original data can be found in Fig. 5, and the calculated proportions are pictorially shown in Fig. 6. In Fig. 6, it can be seen that the polished diamond substrates have no significant differences in the proportions of sp2 to amorphous sp3 at the initial stage. As demonstrated in Fig. 5, however, the sp2 hybridizations will increase quickly with the advance of the abrasive grit, which is independent on the orientation of the polished diamond surface. And subsequently, a strong anisotropy of the proportion appears when the simulation time is more than 42.5 ps, as highlighted in Fig. 6. In this case, the high proportion of sp2 to amorphous sp3 always emerges in polishing along the ‘soft’ direction, which can be observed on both the {100} and {110} substrates. As discussed above, the higher the proportion of sp2 to amorphous sp3, the softer the materials in the newly created surface layer, and resultantly the greater the material removal rate. Apparently, the results as disclosed in Fig. 6 agree well with the wear rate as observed in experiment, i.e. that both the {100} and {110} surfaces have a far greater wear rate in polishing along the ‘soft’ direction than that producing along the ‘hard’ direction [23]. Moreover, when the diamond substrates are all polished along the ‘soft’ direction, the {110} substrate presents a visibly larger proportion of sp2 to amorphous sp3 than that of the {100} substrate. Such variation law also has an excellent correlation with the experimental finding, i.e. that the {110} plane has a much greater wear rate than the {100} plane in polishing along the ‘soft’ direction
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Table. 2 Thickness of amorphous layer and distribution of non-diamond carbons as nano-scratching are performed in different directions and on different plane. Crystalline orientation
Thickness of amorphous layer [Å]
{100}<100>
44.05
{100}<110>
33.74
{110}<100>
42.80
{110}<110>
46.10
Distribution of non-diamond carbons in amorphous layer (yellow-sp2, blue-amorphous sp3)
good consistency with the observations in experiment, which powerfully validates that the proportion of sp2 hybridizations to amorphous sp3 phases in the as-created non-diamond carbons plays a dominant role in determining the removal rate anisotropy of diamond crystal in mechanical polishing.
4. Conclusions This work aims to reveal the underlying atomistic origins of the removal rate anisotropy in mechanical polishing the diamond crystal. According to the observations in molecular dynamics simulation, radial distribution function analysis and coordination number analysis, some important conclusions can be drawn as follows.
Fig. 6. The proportion of sp2 hybridizations to amorphous sp3 structures vs. simulation time (A color version of this figure can be viewed online).
[23]. To be evident, the variation laws as revealed in Fig.6 all have a
1) Lattice distortion is inevitable as the diamond substrate suffers from the mechanical polishing. Due to the mechanically induced compression and scratching, the perfect diamond cubic carbons will transform to some non-diamond phases, i.e. that an amorphous layer comes into being through phase transformation, which is composed of the amorphous sp0, sp1, sp2 and sp3 hybridizations and well-arranged sp2 structures. Among the as-
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created non-diamond carbons, however, the dominant structures are sp2 and amorphous sp3 hybridizations. 2) The material removal rate is heavily dependent on the proportion of sp2 hybridized structures to amorphous sp3 hybridizations in the newly created surface layer and debris. The observed laws validate that the greater the proportion of sp2 to amorphous sp3 is in the newly created surface layer and debris, the higher the material removal rate does in polishing. Acknowledgements The authors would like to thank the Natural Science Foundation of China (No. 51175127) and the Fundamental Research Funds for the Central Universities (No. HIT.BRETIII.201412) for the support of this work. Furthermore, this work was also supported by the Major Special Subject of High-end CNC Machine Tools and Basic Manufacturing Equipment Science and Technology of China (No. 2011ZX04004-031). References [1] J.E. Field, The mechanical and strength properties of diamond, Rep. Prog. Phys. 75 (2012) 126505. [2] W.J. Zong, Z.Q. Li, T. Sun, K. Cheng, D. Li, S. Dong, The basic issues in design and fabrication of diamond cutting tools for ultra-precision and nanometric machining, Int. J. Mach. Tools Manuf. 50 (4) (2010) 411e419. [3] S. Goel, X.C. Luo, A. Agrawal, R.L. Reuben, Diamond machining of silicon: a review of advances in molecular dynamics simulation, Int. J. Mach. Tools Manuf. 88 (2015) 131e164. [4] Ke Chen, W.J. Meng, G.B. Sinclair, Size dependence of the plane-strain response of single-crystal Al to indentation by diamond wedges, Acta Mater. 60 (2012) 4879e4887. [5] K.D. Bouzakis, M. Pappa, G. Maliaris, N. Michailidis, Fast determination of parameters describing manufacturing imperfections and operation wear of nanoindenter tips, Surf. Coat. Tech. 215 (2013) 218e223. [6] A.G. Khurshudov, K. Kato, H. Koide, Nano-wear of the diamond AFM probing tip under scratching of silicon, studied by AFM, Tribol. Lett. 2 (1996) 345e354. [7] E.L.H. Thomas, G.W. Nelson, S. Mandal, J.S. Foord, O.A. Williams, Chemical mechanical polishing of thin film diamond, Carbon 68 (2014) 473e479.
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