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Investigation on tensile behaviors of diamond-like carbon films
Journal of Non-Crystalline Solids 443 (2016) 8–16
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Investigation on tensile behaviors of diamond-like carbon films Lichun Bai c, Narasimalu Srikanth a, Hong Wu b, Yong Liu b, Bo Liu c, Kun Zhou c,⁎ a b c
Interdisciplinary Graduate School, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, People's Republic of China School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
a r t i c l e
i n f o
Article history: Received 30 November 2015 Received in revised form 28 March 2016 Accepted 30 March 2016 Available online xxxx Keywords: Diamond-like carbon sp2 cluster propagation sp3 network degradation Failure mechanism Graphitization
a b s t r a c t The lubrication performance of diamond-like carbon films is significantly influenced by their deformations under loading. However, their deformation mechanisms are unclear so far due to their nanoscale thicknesses and complex microstructures. In this study, these mechanisms are explored by investigating the tensile response of the DLC films via molecular dynamics simulations. The atomic strain localizations are observed, and the regions where they occur are dominated by sp2 clusters. These clusters relax the film at small tensile-strains by releasing its residual energies. The sp3-sp2 transitions are present at large tensile-strains and prefer to occur in the strainlocalized regions. This preference significantly improves the graphitization level in these regions and thus promotes the sp2 clusters to propagate. The propagation severely damages the sp3 networks and leads to the failure of the film. This research suggests that reductions of heterogeneities such as existences of large-sized sp2 clusters may be useful to delay the film failure by suppressing the initial strain localizations. It is demonstrated that the propagation of sp2 clusters for the DLC films can be induced by their deformation besides the high friction temperature in their wear tests. This demonstration can help to improve the understanding of their trigological mechanisms. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Amorphous solids are materials that lack the long-range order characteristics of crystals and thus exhibit disordered microstructures [1,2]. The linear defects and dislocations which support plasticity in crystals are inappropriate for interpreting the deformation mechanisms of amorphous solids. As a result, these mechanisms always attract attentions, and many significant discoveries have been made in the past decades [3–5]. It was found that amorphous solids exhibit localizations of atomic strains and atomic stresses when subjected to external forces. Domains in which the localizations occur are usually ill-packed and have high free-volumes due to low local densities and liquid-like properties [6–8]. Since the plasticity or localized shear transformations are initiated in these domains, they are commonly regarded as defects [5]. For metallic glasses, the evolutions of these domains can even induce the presence of shear bands which improve ductility of materials [9]. Diamond-like carbon (DLC) films are amorphous solids that combine carbon atoms by hybridized sp3, sp2, and sp bonds [10,11]. These films exhibit excellent mechanical properties and good wear resistances, and are widely used as solid lubrication films. Lubricities of DLC films are dominated by sp3-sp2 rehybridization transitions (also named graphitization) with the passivation of surface dangling bonds ⁎ Corresponding author. E-mail address: [email protected] (K. Zhou).
http://dx.doi.org/10.1016/j.jnoncrysol.2016.03.025 0022-3093/© 2016 Elsevier B.V. All rights reserved.
by other atoms or molecules [12–15]. Recent theoretical works showed that strains can largely induce the sp3-sp2 transitions and strain localizations are observed to play a crucial role in the lubricities of DLC films when the dangling bonds inside them lack efficient passivation [12,14, 16–21]. Since both the strain-induced bond transition and the strain localization are closely related to structural evolutions of DLC films, these works indicate that the understanding of the film deformation mechanisms is of significant importance. So far, few studies have been conducted on these deformation mechanisms, mainly due to the huge experimental difficulties in directly observing the microstructural evolutions of DLC films because of their nanoscale thicknesses [10,15,22]. Moreover, previous theoretical works mainly focused on the evolution of atoms at the sliding interface in the wear test [12,14,23] instead of the deformation of the whole film. In view of the many similar properties such as the disorder distributions of atoms and the absence of dislocations shared by most of the amorphous solids, their common theories can provide useful points to investigate the deformation mechanisms of DLC films [3–5]. For example, the strain localizations may be used to understand the sp3-sp2 transitions [6], and the free-volume theory reminds that sp2 atoms or clusters may act as defects due to their larger atomic volumes as compared with those of sp3 atoms [7,8]. In the present study, the deformation process of DLC films under tensile loading is explored via molecular dynamics (MD) simulation. The evolutions of microstructures are studied in detail, and the effect of strains on the plasticity and graphitization is investigated. Since the
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DLC films are comprised of pure C atoms without other doping elements, the results are applicable for non-hydrogenated DLC films especially those with high fraction of sp3 C atoms.
2. Modelling The MD simulation is performed by the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [24]. Atomic interactions in DLC films are described by the Tersoff potential which is effective and accurate for carbon systems [25]. Its cutoff distance is set as 2.1 Å. The initial atomic configurations of DLC films are generated by using the melting and quenching procedure, since it can help to easily obtain their realistic structures [26–29]. During this generation procedure, periodic conditions are applied along all three directions. At the beginning, a diamond-crystalline structure containing 29,504 atoms is created with a lattice parameter of 3.6 Å. The system is then heated from 300 K to the temperature above the melting point of crystalline diamond in the canonical NVT ensemble [30]. At the maximum temperature, the system is thermally equilibrated for 20 ps. It is cooled down with a quenching rate of 1000 K/ps to 300 K. This rate can promote the relaxation of the film structure and make it most realistic [26,31]. The systemic volume is subsequently adjusted at zero pressure by the isothermal–isobaric NPT ensemble to reduce the residual stress. The temperature in the NVT and NPT ensembles is adjusted by the Nose-Hoover method. The final dimensions of the system are 167.2, 74.6 and 15.6 Å along x, y and z-directions, respectively. The density of the obtained DLC film is about 3.02 g/cm3. A tensile test of the obtained DLC film is performed along the xdirection at 300 K, as shown in Fig. 1. Periodic conditions are applied along the x and z-directions. During the tensile test, the strain rate is set as 0.002 ps−1. The molecular visualization is conducted by using the software VMD and OVITO [32,33]. The structural properties of the DLC film are studied by evaluating its radial distribution function (RDF), pair distribution function (PDF) and bond angle distribution [32,34]. Moreover, the coordination numbers of atoms are calculated based on a cutoff distance of 1.90 Å by regarding four-fold and threefold atoms as being sp3 and sp2 bonded, respectively [26]. This distance corresponds to the first minimum in the RDF of DLC films. In the deformation of amorphous solids, their structural changes commonly occur in regions where atomic volume strains and atomic shear strains localize [3,9]. Due to the significance of these two strains, they are evaluated as in the reference [35] to interpret the microstructural evolutions of DLC films. The effect of atomic strains on the film structure is further investigated by the clusters analysis.
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3. Results 3.1. Stress-strain curves and potential energy evolution Fig. 2 shows the obtained stress vs. strain curve. When the tensilestrain initially increases, the stress increases linearly, indicating a linear and reversible elastic deformation process. The slope of the linear curve gives the elastic modulus, as about 539 GPa which agrees well with those reported in the experimental study [36]. As the tensile-strain increases, the stress-strain curve becomes nonlinear and exhibits a decreasing slope. The nonlinear deformation also called inelasticity is usually irreversible. As the strain increases further to about 0.21, the stress reaches a maximum value, i.e., the ultimate tensile strength of the DLC film, after which it fractures immediately. Stress-strain curves of reverse tests which are conducted by compressing DLC films from tensile-strains of 0.05 and 0.16 are also presented in Fig. 2, respectively. The stress in the reversed test is lower than that in the tensile test at the same strain. This reveals that the film microstructures change during the tensile tests. The potential energy evolutions of the DLC films in the tensile test as well as in the reversed tests are shown in Fig. 3. In the tensile test, when the tensile-strain increases initially, the potential energy increases slowly. However, it increases rapidly at high tensile-strains. This rapid increase is attributed to that the huge tensile stress causes the atoms to deviate far from their balanced locations in the potential landscape [37]. When the ultimate tensile strength is reached, the maximum potential energy is obtained, followed by a sharp drop due to the film failure. In the reversed tests, the potential energy is lower than that in the tensile tests at any given strain. The lower potential energy is usually caused by microstructure relaxation or transformation, depending on the initial tensile-strains. At a small initial tensile-strain of 0.05, the potential energy of the film monotonically decreases as it is compressed and reaches a minimum value at zero tensile-strain where the potential energy for the tensile test is also the minimal. The monotonic decrease of the potential energy during the reverse test for the initial tensile-strain of 0.05 indicates that small initial tensile-strains can only cause the structural relaxation of films instead of their structural transformations [38,39]. On the contrast, at a large initial tensile-strain of 0.16, the potential energy of the DLC film first decreases and then increases as it is compressed, showing a nonmonotonic behavior. Minimum of the potential energy is reached at the tensile-strain of about 0.03 rather than at the zero tensile-strain. Such nonmonotonic behavior indicates there is a microstructure transformation caused by the large initial tensile-strain. Such transformation will be further illustrated below. The potential energy evolutions of DLC films
Fig. 1. Illustration of MD models for tensile test of DLC film.
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Fig. 2. Stress-strain curves for the tensile test and reverse tests of DLC films.
in the reverse tests with different initial strain show good consistence with those of metallic glasses [7], demonstrating that amorphous solids tend to share similar mechanical response to external loading. 3.2. Microstructure analysis It has been reported that the fraction of sp3 atoms Fsp3 and the fraction of sp2 atoms Fsp2 of carbon materials usually reflect their microstructural and mechanical properties [11]. To study the structural changes of the DLC film in the tensile test, the evolution of Fsp3 and Fsp2 is investigated and shown in Fig. 4a. When the tensile-strain is smaller than 0.05, both Fsp3 and Fsp2 keep almost constant. With the increasing tensile-strain, Fsp3 decreases but Fsp2 increases significantly. Moreover, the larger the tensile-strain, the faster Fsp3 and Fsp2 change. The evolution of Fsp3 and Fsp2 demonstrates that the film structure keeps stable at small tensile-strains but experiences dramatic transformations at high tensile-strains. Such structural transformation implies that the graphitization of DLC films can be induced by the high strain besides the high temperature, keeping consistent with recent studies [12, 14]. The dependence of film structures on tensile-strains corresponds well with the results shown by the potential energy evolution of reversed tests in Fig. 3. The bond angle distribution in carbon materials is useful to demonstrate their structural properties. The crystalline diamond has a bond angle of about 109°, while that of graphite is 120° [40]. As a result, the graphitization of diamond structures can lead to the shift of bond angles from 109° to 120°. The bond angle distributions of the DLC film are presented in Fig. 4b. At zero tensile-strain, a bond-angle peak located between 109° and 120° is observed, thus indicating a mixture of sp3 and sp2 atoms. When the tensile-strain increases up to 0.05, the bond angle distribution broadens slightly but the location of its peak keeps
unchanged. This demonstrates that under the small tensile-strain the bonds are only distorted and few sp3-sp2 transitions are induced. With the tensile-strain increasing to 0.16, the bond angle distribution broadens further and shifts to the higher angle side, revealing the sp3sp2 transitions and thus the structural transformation, i.e., the graphitization of the DLC film. The structural changes of DLC films can be further characterized by the radius distribution functions (RDFs) [31]. Fig. 5 shows the RDFs for all the carbon atoms. Only two nearest peaks are observed, which indicates the short-range order of the DLC film. At zero tensile-strain, the first nearest neighbor peak locates at 1.52 Å. The second nearest neighbor peak locates at 2.6 Å and has a small satellite peak at about 2.1 Å. The satellite peak is caused by the cut-off radius of the Tersoff potential and also termed as “false peak” in literature [41,42]. This is supported by the fact that this satellite peak does not shift with the increase of strain. When the tensile-strain increases, all other peaks shift to the right, indicated by the dashed line in the figure. The shifted peaks imply the increased atomic-distances. In addition, the heights of peaks decrease but their widths increase. This is attributed to the influence of atomic stresses and strains, as pointed out by Srolovitz et al [8]. At large tensile-strains, a shoulder peak located at about 1.82 Å appears near the first nearest neighbor peak. This presence of the shoulder peak demonstrates that more and more atomic bonds are severely stretched as the tensile-strain increases. Highly stretched bonds are unstable and break easily at large strains [14], causing structural changes of the DLC films. Investigating the evolution of these bonds can help to understand the structural transformation of the DLC films. In the DLC films, there mainly exist three types of bonds, namely, the bonds between the sp3 atoms, those between the sp2 atoms, and those between the sp2 and sp3 ones. These bonds are named as sp3-sp3, sp2-sp2 and sp2-sp3 bonds for short in the following discussion. To identify which bond type is most unstable and thus contribute most to the presence of the shoulder peak of the first nearest peak in RDF, three types of PDFs are calculated for the pair of sp2 atoms, the pair of sp3 atoms, and the pair of atoms in which one is sp2 bonded and the other is sp3 bonded, respectively. Similarly, these PDFs are named as sp2-sp2, sp3-sp3 and sp2-sp3 PDFs for short. The calculated PDFs are shown in Fig. 6. Two main peaks exist in all the PDFs and the location of the first nearest peaks is approximately the C\\C bond length of the DLC films. The change of these first peaks in PDFs usually gives information about the formation or breaking of the three types of bonds introduced above. At zero tensile-strain, the first peaks in all the PDFs are smooth and almost symmetrical about their central lines. When the tensile-strain increases to 0.05, a new peak protrudes out from the right shoulder of the first peak for both the sp3-sp3 and the sp2-sp3 PDFs. However, the sp2-sp2 PDF keeps almost unchanged. The appearance of the shoulder peaks implies that part of the sp3-sp3 bonds and sp2-sp3 bonds is
Fig. 3. Potential energy evolutions of DLC films during the tensile test and reverse tests.
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Fig. 4. (a) Evolution of the fractions of sp3 and sp2 atoms during the tensile tests; (b) bond angle distribution of DLC films with different tensile-strains.
stretched and tends to have a larger bond length. When the tensilestrain increases up to 0.16, the intensities of both the shoulder peaks for the sp3-sp3 and sp2-sp3 PDFs increase and the peak intensity of the former is higher. Moreover, a similar shoulder peak starts to form for the sp2-sp2 PDF but with a much weaker intensity than those of the shoulder peaks for the sp3-sp3 and sp2-sp3 PDFs. The rise of the shoulder peaks and the increase of their intensities with the increasing tensile-strain for the sp3-sp3 and sp2-sp3 RDFs indicate that the tensile deformation of the DLC films is mainly realized by the stretching of the sp3-sp3 and sp2-sp3 bonds. This is in good consistency with previous study which reported that in the deformation of DLC films sp3-sp3 and sp2-sp3 bonds become unstable and break firstly while all sp2-sp2 bonds stay intact [14]. The different mechanical response of sp2-sp2 bonds is because they are stabilized due to the hyperconjugation effect which enhances their bond strengths [43], and thus large tensile-strains is required to get them stretched. The different mechanical responses of the bonds also well explain the sp3-sp2 transition shown in Fig. 4 and the dependence of the bond fractions Fsp3 and Fsp2 on the tensile-strain. At small tensile-strains, the rise of the weak shoulder peaks indicates that a few sp3-sp3 and sp2sp3 bonds are stretched and become unstable, which can only induce a small number of sp3-sp2 transitions and thus both Fsp3 and Fsp2 keep almost constant. At large tensile-strains, the significant increase of the shoulder peak intensities reveals the breakings of a large quantity of stretched bonds which lead to lots of sp3-sp2 transitions and thus the increase of Fsp2 and decrease of Fsp3.
Fig. 5. Radius distribution functions (RDFs) of DLC films in the tensile test.
3.3. Atomic deformation analysis In the deformation of amorphous solids, volume strains of atoms can help to characterize variances of their free volume, and their shear strains are significant to demonstrate their propensity to participate in local inelastic transformation [44]. Contours of atomic volume strains and atomic shear strains in the DLC film are given in Fig. 7. The strain localizations are observed, and the regions with high atomic volume strains generally possess high atomic shear strains. When the tensilestrain increases, these regions expand due to the increase of the overall atomic strains. In addition, the shear bands occurring in the deformation of metallic glasses [5,45] are absent in the DLC films in present simulations. This may be due to the differences between covalent bonds and metallic bonds. The mechanisms of the absence of shear bands in the DLC films will be discussed later in Discussion section. The distributions of atoms in terms of their atomic volume strains and atomic shear strains are given in Fig. 8a–b. It is found that the sp2 atoms and sp3 atoms exhibit different distributions. In general, sp2 atoms dominate in the regions of both high atomic volume and shear strains. This is because the sp2 atoms have lower volume densities than the sp3 bonded ones and thus possess larger free-volumes which promotes atoms to rearrange easily under deformations [4,6]. Moreover, the smaller atomic elastic modulus of sp2 atoms also contribute to their larger atomic strains [46,47]. Therefore, the regions in which atomic strains are localized should mainly be occupied by the sp2 atoms. Due to their capabilities to bear large strains, they can be regarded as plasticity carriers in DLC films. The analysis of the atomic strain in relation to the bond deformation shown by the RDFs in Fig. 6 shows that the sp2 atoms have larger atomic strain than the sp3 atoms although the bonds of these sp2 atoms are less elongated than those of the sp3 atoms. This may be due to the fact that the atomic strain of one atom is determined not only by the lengths of its bonds with its surrounding atoms but also the angles between these bonds. The sp2 bonds can rotate easily to release the stress due to their high rotation flexibility and thus exhibit small elongations but large angle rotations in the presence of external loading. In contrast, the sp3 bonds have high rotation rigidity and thus mostly deform through bond elongation [46]. Since stretched bonds break easily at high atomic strains, it is reasonable to assume that the sp3-sp2 transitions mainly occur in the strain-localized regions. This assumption is verified by Fig. 8c–d which shows the distributions of atomic strains of new sp2 atoms generated from the sp3-sp2 transitions. These atoms generally have both higher atomic volume strains and atomic shear strains than those of all the atoms in the DLC film (Fig. 8a–b). As a result, sp3-sp2 transitions are localized and can increase the number of sp2 atoms and thus the graphitization level in the strain-localized regions. The high fractions of sp2 atoms in these regions can degrade their local mechanical properties [46]. When the tensile-strain increases, it causes larger localized strains and thus the expansions of these regions. These expansions can induce continuous degradations of mechanical properties of DLC films by
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Fig. 6. PDFs of atoms in the DLC film during the tensile test for (a) the pair of sp2 atoms, (b) the pair of sp3 atoms, and (c) the pair of atoms in which one is sp2 bonded and the other is sp3 bonded.
inducing more transitions. Consequently, the DLC films fracture when their degraded structures fail to bear the external tensile loading. In the strain-localized regions, influences of atomic shear strains and atomic volume strains on the sp3-sp2 transitions are coupled. This is due to that the transitions induced by high atomic shear strains can result in lower local densities and larger atomic volumes, thereby increasing the atomic volume strains. On the other hand, the high atomic volume strain may cause the transitions due to the atom-volume differences between sp3 and sp2 atoms and subsequently influence the atomic shear strains. The role of the two types of atomic strains on the sp3-sp2 transition can be explored by monitoring the unstable sp3 atoms that will become sp2 bonded and thus the new sp2 atoms when the tensile-strain increases. The distribution of these unstable sp3 atoms in terms of their atomic volume strains and atomic shear strains is given in Fig. 8e–f. Compared with all the sp3 atoms in the DLC film (Fig. 8a–b), these unstable sp3 atoms exhibit similar distribution of the atomic volume strain with a slight preference in the small range, while major of them have large atomic shear strains. The similar distribution of atomic volume strains indicates the independence of the sp3-sp2 transition on them. However, the large atomic shear strains imply that their higher values are needed to overcome the barrier in the transitions. As a result, it can be concluded that the atomic shear strains instead of the atomic volume strains dominate the sp3-sp2 transitions.
Fig. 7. Contours of (a) atomic volume strains and (b) atomic shear strains in the DLC film at tensile-strain of 0.18.
4. Discussions The stretched sp3-sp3 and sp2-sp3 bonds are unstable and break easily due to their larger bond lengths than those of the sp2-sp2 bonds. This has also been previously verified by density functional theory (DFT) calculations [21]. Since the bond elongations are induced by atomic strains, one might assume that atoms with the stretched bonds should be highly strained. To evaluate this assumption, distributions of these atoms in terms of their atomic strains are further studied. Surprisingly, the results show that these atoms have the atomic-strain distribution similar to that of the other atoms in the DLC film. Therefore, the bond elongations are independent of atomic strains and may be determined by complicated atomic-environments such as bonding states of atom neighbors [29]. As discussed above, the stretched-bond breakings and the sp3-sp2 transitions are dominated by atomic shear strains instead of atomic volume strains. This is consistent with previous experimental studies [16, 20]. In experiments, it was found that sp3 structures are unstable at high shear strains but only exhibit cell-size changes at high volume strains. The significance of atomic shear strains is attributed to that they can cause a rearrangement of the neighbors of sp3 atoms and thus the formation of the π bonds and graphite-like layer structures with the sp2 networks [18,19]. The atomic volume strains may play roles in increasing the distances between atoms and thus decreasing their local densities, and lowering the energy barriers for the sp3-sp2 transitions triggered by the atomic shear strain. Gilman has previously predicted that the critical atomic shear strain for the transitions is around 0.08 [17,48]. The prediction is consistent with the results in Fig. 8f where all the unstable sp3 atoms which will experience sp3-sp2 transitions with increased tensile-strains possess the shear strains higher than this critical value. The localized atomic strains in the DLC film promote the localizations of sp3-sp2 transitions which increase the graphitization level in the strain-localized regions. As a result, the atom structures in these regions can be almost treated as sp2 clusters. Expands of these regions at high tensile-strains can cause the propagations of the sp2 clusters, because the newly generated sp2 atoms due to the sp3-sp2 transitions tend to connect with the existed clusters due to the delocalization properties of π bonds [29]. To verify the propagations of sp2 clusters, their distributions are at the tensile-strains of zero and 0.18 are is analyzed (Fig. 9), respectively. With the increasing tensile-strain, the number of large-sized clusters significantly increases. Since the strength of the sp2 clusters is much lower than that of the sp3 networks, the propagations of these sp2 clusters highly weaken the mechanical properties of DLC films [46].
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Fig. 8. Distribution of carbon atoms in term of (a) atomic volume strain and (b) atomic shear strain for DLC films; distribution of new sp2 atoms obtained by transitions in terms of (c) atomic volume strain and (d) atomic shear strain at the tensile strain of 0.18; distribution of unstable sp3 atoms in terms of (e) atomic volume strain and (f) atomic shear strain when the tensile-strain increases from 0.18 to 0.184.
Therefore, it can be stated that the strain-induced propagations of sp2 clusters are responsible for the film failure. This statement shares many similarities with the clusters model of DLC films developed by Robertson et al [49,50]. In this model, mixtures of sp3 and sp2 atoms
tend to segregate into sp2 clusters embedded in a sp3 matrix which determines the mechanical properties. Fig. 9a also shows that as the tensile-strain increases, the number of sp2 clusters with small sizes especially those contain single atoms
Fig. 9. Distribution of (a) small-sized and (b) large-sized sp2 clusters at different tensile-strains. The size of a cluster is defined as the count of sp2 atoms in it.
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decreases while the number of sp2 clusters with large sizes increases. This phenomenon is due to the fact that new sp2 atoms are generated between small sp2 clusters and gradually connect them. As they are connected, they merge together and form large sp2 clusters. Therefore, the sp3 atoms whose neighbors are mainly sp2 bonded may have stretched bonds and easily experience the sp3-sp2 transitions. This is proved by collecting the coordination number of nearest neighbors of new sp2 atoms before their transitions. Besides spatial distributions in strain-localized regions, the sp2 clusters exhibit chain-like arrangements instead of graphite-like rings, although sizes of these clusters become large at large tensile strains. A clear graphical depiction of the chain-like arrangements can be obtained by using the metric as reported by Majmudar [51] and Bassett [52]. This chain-like arrangement may be due to the high fraction of sp3 atoms in DLC films [53,54]. Such arrangement may also be due to the absence of torsional energy term for rotations of π bonds in the Tersoff potential [53], since this term can make sp2 structures be planar by tailoring their relative stability and thus induce the formation of graphite-like structure [55]. The relation between bonding environment of neighbor atoms and sp3-sp2 transitions of sp3 atoms indicates that these transitions are not only influenced by atomic strains (Fig. 8e–f) but also affected by the local bonding environment. This keeps consistent with directional properties of covalent bonds. This relation can also help to demonstrate the absence of shear bands in DLC films. The strain localizations are present in DLC films as well as in metallic glasses, due to their amorphous structures. In the metallic glasses, atoms near the strain-localized region are rearranged freely along the plane of maximum shear under forces of their neighbors, due to the non-directional properties of metallic bonds [56]. Such rearrangements can make different strain-localized regions merged and induce the presence of shear bands along the plane, since the rearranged atoms are easily deformed. In DLC films, however, most of atom arrangements (sp3-sp2 transitions) are randomly distributed instead of distributed along the plane of maximum shear, due to the fact that the arrangement of atoms are influenced not only by the forces of their neighbors but also by bonding environment of their neighbors. Such random arrangements further induce that the strainlocalized regions in the DLC film are hardly merged to form a band. This can be verified from Fig. 7 which shows that most of the strainlocalized regions are isolated from each other even at the high tensile strain of 0.18. This can also be verified from the failure configuration of DLC film that shows a fracture perpendicular to the tensile axis instead of along the plane of maximum shear. Such configuration is a common failure configuration for many covalent amorphous solids. Therefore, these explanations about the absence of shear bands in the DLC films should be also applicable for deformations of other covalent amorphous materials. The propagation of sp2 clusters can greatly damage the networks formed by sp3 atoms. Evolution of such networks can also be analyzed by counting the number of sp3 clusters with different sizes at the tensile strains of zero and 0.18, N0 and N0.18 (Table 1). With the increase of tensile strain, the number of small-sized sp3 clusters in such networks greatly increases; however, the number of atom in the largest cluster decreases. This indicates that the branches of the largest clusters before the tensile test are cut off by the increased strain via inducing the transition of sp3 atoms from sp3 to sp2 bonding. Since the largest sp3 cluster undertakes the highest external stress, it can be regarded as a backbone in the DLC film. The reduction of its branches can highly weaken the mechanical properties of the film. Fig. 10 shows that the increase of tensile strain can significantly degrade this cluster. At the large tensile strain of 0.18, many voids are formed, and they should be filled by the sp2 clusters or the small-sized sp3 clusters. The increase of tensile strain can further enlarge these voids. In the largest void, the failure of the DLC film is observed to be initiated at the tensile strain of 0.21. Therefore, the degradation of the largest sp3 cluster directly leads to the film failure.
Table 1 Influence of the tensile strain on the sp3 clusters. Cluster size
N0
N0.18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 19 21 22 28 33 37 45 226 11,568 13,745
397 110 53 20 11 6 2 3 3 3 0 0 1 2 0 1 0 0 0 0 0 0 1 0 0 1
552 155 71 31 21 17 7 5 6 4 4 2 1 2 1 1 1 1 2 1 1 1 0 1 1 0
Generally, it can be seen that both the sp2 cluster propagation and the film failure are determined by the atomic strain localizations. These localizations definitely exist due to the heterogeneous distribution of the sp2 atoms inside the DLC films. Such heterogeneities form during the fabrication of the DLC films due to the fact that, sp2 atoms prefer to gather and form small clusters instead distribute randomly and evenly in the sp3 matrix because of the delocalization characteristic of π bonds [54,57]. It can be seen that the sp2 clusters exhibit unique behaviors in the tensile test. At small tensile-strains, the originally existed sp2 clusters are responsible for the structural relaxations of DLC films by relieving
Fig. 10. Atomic configuration of the largest sp3 cluster with the tensile strain of (a) zero, (b) 0.10 and (c) 0.18. The voids in this cluster are filled by sp2 clusters or small-sized sp3 clusters.
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their internal strain energies (Fig. 3). At large tensile-strains, the merges and propagations of sp2 clusters weaken the strength of films and thus lead to their failures. Therefore, it can be concluded the sp2 clusters in DLC films behave similarly to the dislocations or defects in crystals. This conclusion keeps consistent with previous studies [49,50,58], although they were focused on the electronic properties. Moreover, since the sp2 clusters dominate the regions with low local densities and large free volumes in DLC films, this conclusion is also supported by the free-volume theory which states that such regions act as plastic defects in amorphous solids [59]. The understanding of the behaviors of sp2 clusters in the deformation of DLC films can further guide their future applications. It is recommended that reducing heterogeneities of DLC films such as existences of large-sized sp2 clusters may be efficient in delaying film failures by suppressing the initial atomic-strain localizations. By summarizing the discussions above, the whole deformation process of DLC films in the tensile tests can be well described. When the tensile-strain initially increases, atomic strains are localized in the regions dominated by sp2 clusters. These clusters can efficiently relax the film structure by relieving residual strain energies, which prevents the sp3-sp2 transitions. When the tensile-strain further increases to be high, the stretched sp3-sp3 and sp2-sp3 bonds in or near the strainlocalized regions break. The bond breakings induce the sp3-sp2 transitions and the propagations of sp2 clusters. These propagations significantly weaken the mechanical strengths of DLC films and lead to their failures when the ultimate tensile strength is reached. The deformation mechanisms of DLC films can help to interpret their tribological behaviors. In the wear tests of these films, their surface asperities experience high strains. Such high strains can cause the sp2 clusters to merge and propagate inside these asperities and gradually weaken their strengths. The asperities subsequently drop from film surfaces, forming wear debris dominated by sp2 clusters. Transfer of these debris to the counterpart surface are induced by the interfacial adhesion between DLC film and counterpart and leads to the formation of transfer films which have graphite-like layer structures and isolate the DLC film and the counterpart. As a result, the lateral sliding of counterpart mainly occurs as shear deformations of the transfer films. In this case, π bonds in the graphite-like layer structures bear the high vertical load, and the absence of interlayer σ bonds leads to reductions of tangential friction forces with passivations of dangling carbon bonds by particles such as hydrogen molecules [12,13,15,22,60]. Due to low temperature in present simulation, the obtained deformation mechanisms of DLC films can be valid to explain their graphitization mechanisms in their running-in period when the friction temperature is low. It should be noted that the propagations of sp2 clusters have been reported in the wear tests of DLC films by employing the analysis of Raman spectrum and transmission electron micrographs [15,61]. However, such propagations are commonly believed to be determined by the high friction temperature in these tests since it can easily cause the transitions of C atoms from sp3 to sp2 bonding. The present study demonstrates that the propagations can happen during the yielding of surface asperities of DLC films in their running-in stages before the occurrence of the high friction temperature. Therefore, this demonstration may help to improve the understanding of their tribological mechanisms. 5. Conclusions The deformation mechanisms of DLC films are investigated by conducting a tensile test via MD simulations. At small tensile-strains, the fraction of sp2 atoms Fsp2 and the fraction of sp3 atoms Fsp3 keep constant, but the film structures are relaxed. With the increasing tensilestrain, Fsp3 decreases but Fsp2 increases, indicating the occurrence of sp3-sp2 transitions. When the ultimate tensile strength of the DLC film is reached, it subsequently fails. The atomic strains analysis indicates that the transitions are dominated by atomic shear strains instead of
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atomic volume strains. Moreover, the transitions prefer to occur in regions where atomic strains are localized. It is found that these regions are dominated by sp2 atoms due to their low local densities and low elastic modulus. As a result, the sp3-sp2 transitions are also localized in these regions and thus enhance their graphitization levels, leading to propagations of sp2 clusters. The disappearances of small-sized sp2 clusters indicate that the sp3 atoms which are located between sp2 clusters easily experience the sp3-sp2 transitions in the cluster propagations. The large-sized sp2 clusters can weaken the mechanical strengths of DLC films and thus lead to their failures when the degraded structures cannot bear the tensile stress as high as ultimate tensile strengths. Therefore, sp2 clusters can be regarded as defects, keeping consistent with the free-volume theory and previous structural models of DLC films. The results imply that reducing heterogeneities such as existences of large-sized sp2 clusters may be useful to delay film failures by suppressing the initial atomic strain localizations. Moreover, the present study demonstrates that the propagations of sp2 clusters for DLC films can be induced by their deformation besides the high friction temperature in their wear tests. This demonstration can help to improve the understanding of their tribological mechanisms. Acknowledgements This work is financially supported by Ministry of Education (Academic Research Fund TIER 1-RG128/14), Singapore. LB acknowledges the Interdisciplinary Graduate School of Nanyang Technological University, Singapore for providing the Research Student Scholarship. References [1] Z. Lu, J. Li, H. Shao, H. Gleiter, X. Ni, The correlation between shear elastic modulus and glass transition temperature of bulk metallic glasses, Appl. Phys. Lett. 94 (2009) 91907. [2] Z. Lu, J. Li, Correlation between average melting temperature and glass transition temperature in metallic glasses, Appl. Phys. Lett. 94 (2009) 1913. [3] W. Liu, H. Ruan, L. Zhang, On the plasticity event in metallic glass, Philos. Mag. Lett. 93 (2013) 158–165. [4] Y. Cheng, J. Ding, E. Ma, Local topology vs. atomic-level stresses as a measure of disorder: correlating structural indicators for metallic glasses, Mater. Res. Lett. 1 (2013) 3–12. [5] S. Takeuchi, K. Edagawa, Atomistic simulation and modeling of localized shear deformation in metallic glasses, Prog. Mater. Sci. 56 (2011) 785–816. [6] Y. Cheng, E. Ma, Indicators of internal structural states for metallic glasses: local order, free volume, and configurational potential energy, Appl. Phys. Lett. 93 (2008) 051910. [7] D. Srolovitz, V. Vitek, T. Egami, An atomistic study of deformation of amorphous metals, Acta Metall. 31 (1983) 335–352. [8] D. Srolovitz, T. Egami, V. Vitek, Radial distribution function and structural relaxation in amorphous solids, Phys. Rev. B 24 (1981) 6936. [9] T. Egami, Atomic level stresses, Prog. Mater. Sci. 56 (2011) 637–653. [10] L. Bai, G. Zhang, Z. Lu, Z. Wu, Y. Wang, L. Wang, P. Yan, Tribological mechanism of hydrogenated amorphous carbon film against pairs: a physical description, J. Appl. Phys. 110 (2011) 033521. [11] L. Bai, G. Zhang, Z. Wu, J. Wang, P. Yan, Effect of different ion beam energy on properties of amorphous carbon film fabricated by ion beam sputtering deposition (IBSD), Nucl. Instrum. Methods Phys. Res., Sect. B 269 (2011) 1871–1877. [12] T.-B. Ma, L.-F. Wang, Y.-Z. Hu, X. Li, H. Wang, A shear localization mechanism for lubricity of amorphous carbon materials, Sci. Rep. 4 (2014). [13] Y. Liu, A. Erdemir, E. Meletis, An investigation of the relationship between graphitization and frictional behavior of DLC coatings, Surf. Coat. Technol. 86 (1996) 564–568. [14] T. Kunze, M. Posselt, S. Gemming, G. Seifert, A.R. Konicek, R.W. Carpick, L. Pastewka, M. Moseler, Wear, plasticity, and rehybridization in tetrahedral amorphous carbon, Tribol. Lett. 53 (2014) 119–126. [15] Y. Liu, E. Meletis, Evidence of graphitization of diamond-like carbon films during sliding wear, J. Mater. Sci. 32 (1997) 3491–3495. [16] Y.G. Gogotsi, A. Kailer, K.G. Nickel, Pressure-induced phase transformations in diamond, J. Appl. Phys. 84 (1998) 1299–1304. [17] J.J. Gilman, Mechanism of shear-induced metallization, Czechoslov. J. Phys. 45 (1995) 913–919. [18] H. Chacham, L. Kleinman, Instabilities in diamond under high shear stress, Phys. Rev. Lett. 85 (2000) 4904. [19] A. De Vita, G. Galli, A. Canning, R. Car, A microscopic model for surface-induced diamond-to-graphite transitions, Nature 379 (1996) 523–526. [20] Y.G. Gogotsi, A. Kailer, K.G. Nickel, Materials: transformation of diamond to graphite, Nature 401 (1999) 663–664.
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Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Investigation on tensile behaviors of diamond-like carbon films Lichun Bai c, Narasimalu Srikanth a, Hong Wu b, Yong Liu b, Bo Liu c, Kun Zhou c,⁎ a b c
Interdisciplinary Graduate School, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, People's Republic of China School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
a r t i c l e
i n f o
Article history: Received 30 November 2015 Received in revised form 28 March 2016 Accepted 30 March 2016 Available online xxxx Keywords: Diamond-like carbon sp2 cluster propagation sp3 network degradation Failure mechanism Graphitization
a b s t r a c t The lubrication performance of diamond-like carbon films is significantly influenced by their deformations under loading. However, their deformation mechanisms are unclear so far due to their nanoscale thicknesses and complex microstructures. In this study, these mechanisms are explored by investigating the tensile response of the DLC films via molecular dynamics simulations. The atomic strain localizations are observed, and the regions where they occur are dominated by sp2 clusters. These clusters relax the film at small tensile-strains by releasing its residual energies. The sp3-sp2 transitions are present at large tensile-strains and prefer to occur in the strainlocalized regions. This preference significantly improves the graphitization level in these regions and thus promotes the sp2 clusters to propagate. The propagation severely damages the sp3 networks and leads to the failure of the film. This research suggests that reductions of heterogeneities such as existences of large-sized sp2 clusters may be useful to delay the film failure by suppressing the initial strain localizations. It is demonstrated that the propagation of sp2 clusters for the DLC films can be induced by their deformation besides the high friction temperature in their wear tests. This demonstration can help to improve the understanding of their trigological mechanisms. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Amorphous solids are materials that lack the long-range order characteristics of crystals and thus exhibit disordered microstructures [1,2]. The linear defects and dislocations which support plasticity in crystals are inappropriate for interpreting the deformation mechanisms of amorphous solids. As a result, these mechanisms always attract attentions, and many significant discoveries have been made in the past decades [3–5]. It was found that amorphous solids exhibit localizations of atomic strains and atomic stresses when subjected to external forces. Domains in which the localizations occur are usually ill-packed and have high free-volumes due to low local densities and liquid-like properties [6–8]. Since the plasticity or localized shear transformations are initiated in these domains, they are commonly regarded as defects [5]. For metallic glasses, the evolutions of these domains can even induce the presence of shear bands which improve ductility of materials [9]. Diamond-like carbon (DLC) films are amorphous solids that combine carbon atoms by hybridized sp3, sp2, and sp bonds [10,11]. These films exhibit excellent mechanical properties and good wear resistances, and are widely used as solid lubrication films. Lubricities of DLC films are dominated by sp3-sp2 rehybridization transitions (also named graphitization) with the passivation of surface dangling bonds ⁎ Corresponding author. E-mail address: [email protected] (K. Zhou).
http://dx.doi.org/10.1016/j.jnoncrysol.2016.03.025 0022-3093/© 2016 Elsevier B.V. All rights reserved.
by other atoms or molecules [12–15]. Recent theoretical works showed that strains can largely induce the sp3-sp2 transitions and strain localizations are observed to play a crucial role in the lubricities of DLC films when the dangling bonds inside them lack efficient passivation [12,14, 16–21]. Since both the strain-induced bond transition and the strain localization are closely related to structural evolutions of DLC films, these works indicate that the understanding of the film deformation mechanisms is of significant importance. So far, few studies have been conducted on these deformation mechanisms, mainly due to the huge experimental difficulties in directly observing the microstructural evolutions of DLC films because of their nanoscale thicknesses [10,15,22]. Moreover, previous theoretical works mainly focused on the evolution of atoms at the sliding interface in the wear test [12,14,23] instead of the deformation of the whole film. In view of the many similar properties such as the disorder distributions of atoms and the absence of dislocations shared by most of the amorphous solids, their common theories can provide useful points to investigate the deformation mechanisms of DLC films [3–5]. For example, the strain localizations may be used to understand the sp3-sp2 transitions [6], and the free-volume theory reminds that sp2 atoms or clusters may act as defects due to their larger atomic volumes as compared with those of sp3 atoms [7,8]. In the present study, the deformation process of DLC films under tensile loading is explored via molecular dynamics (MD) simulation. The evolutions of microstructures are studied in detail, and the effect of strains on the plasticity and graphitization is investigated. Since the
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DLC films are comprised of pure C atoms without other doping elements, the results are applicable for non-hydrogenated DLC films especially those with high fraction of sp3 C atoms.
2. Modelling The MD simulation is performed by the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [24]. Atomic interactions in DLC films are described by the Tersoff potential which is effective and accurate for carbon systems [25]. Its cutoff distance is set as 2.1 Å. The initial atomic configurations of DLC films are generated by using the melting and quenching procedure, since it can help to easily obtain their realistic structures [26–29]. During this generation procedure, periodic conditions are applied along all three directions. At the beginning, a diamond-crystalline structure containing 29,504 atoms is created with a lattice parameter of 3.6 Å. The system is then heated from 300 K to the temperature above the melting point of crystalline diamond in the canonical NVT ensemble [30]. At the maximum temperature, the system is thermally equilibrated for 20 ps. It is cooled down with a quenching rate of 1000 K/ps to 300 K. This rate can promote the relaxation of the film structure and make it most realistic [26,31]. The systemic volume is subsequently adjusted at zero pressure by the isothermal–isobaric NPT ensemble to reduce the residual stress. The temperature in the NVT and NPT ensembles is adjusted by the Nose-Hoover method. The final dimensions of the system are 167.2, 74.6 and 15.6 Å along x, y and z-directions, respectively. The density of the obtained DLC film is about 3.02 g/cm3. A tensile test of the obtained DLC film is performed along the xdirection at 300 K, as shown in Fig. 1. Periodic conditions are applied along the x and z-directions. During the tensile test, the strain rate is set as 0.002 ps−1. The molecular visualization is conducted by using the software VMD and OVITO [32,33]. The structural properties of the DLC film are studied by evaluating its radial distribution function (RDF), pair distribution function (PDF) and bond angle distribution [32,34]. Moreover, the coordination numbers of atoms are calculated based on a cutoff distance of 1.90 Å by regarding four-fold and threefold atoms as being sp3 and sp2 bonded, respectively [26]. This distance corresponds to the first minimum in the RDF of DLC films. In the deformation of amorphous solids, their structural changes commonly occur in regions where atomic volume strains and atomic shear strains localize [3,9]. Due to the significance of these two strains, they are evaluated as in the reference [35] to interpret the microstructural evolutions of DLC films. The effect of atomic strains on the film structure is further investigated by the clusters analysis.
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3. Results 3.1. Stress-strain curves and potential energy evolution Fig. 2 shows the obtained stress vs. strain curve. When the tensilestrain initially increases, the stress increases linearly, indicating a linear and reversible elastic deformation process. The slope of the linear curve gives the elastic modulus, as about 539 GPa which agrees well with those reported in the experimental study [36]. As the tensile-strain increases, the stress-strain curve becomes nonlinear and exhibits a decreasing slope. The nonlinear deformation also called inelasticity is usually irreversible. As the strain increases further to about 0.21, the stress reaches a maximum value, i.e., the ultimate tensile strength of the DLC film, after which it fractures immediately. Stress-strain curves of reverse tests which are conducted by compressing DLC films from tensile-strains of 0.05 and 0.16 are also presented in Fig. 2, respectively. The stress in the reversed test is lower than that in the tensile test at the same strain. This reveals that the film microstructures change during the tensile tests. The potential energy evolutions of the DLC films in the tensile test as well as in the reversed tests are shown in Fig. 3. In the tensile test, when the tensile-strain increases initially, the potential energy increases slowly. However, it increases rapidly at high tensile-strains. This rapid increase is attributed to that the huge tensile stress causes the atoms to deviate far from their balanced locations in the potential landscape [37]. When the ultimate tensile strength is reached, the maximum potential energy is obtained, followed by a sharp drop due to the film failure. In the reversed tests, the potential energy is lower than that in the tensile tests at any given strain. The lower potential energy is usually caused by microstructure relaxation or transformation, depending on the initial tensile-strains. At a small initial tensile-strain of 0.05, the potential energy of the film monotonically decreases as it is compressed and reaches a minimum value at zero tensile-strain where the potential energy for the tensile test is also the minimal. The monotonic decrease of the potential energy during the reverse test for the initial tensile-strain of 0.05 indicates that small initial tensile-strains can only cause the structural relaxation of films instead of their structural transformations [38,39]. On the contrast, at a large initial tensile-strain of 0.16, the potential energy of the DLC film first decreases and then increases as it is compressed, showing a nonmonotonic behavior. Minimum of the potential energy is reached at the tensile-strain of about 0.03 rather than at the zero tensile-strain. Such nonmonotonic behavior indicates there is a microstructure transformation caused by the large initial tensile-strain. Such transformation will be further illustrated below. The potential energy evolutions of DLC films
Fig. 1. Illustration of MD models for tensile test of DLC film.
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Fig. 2. Stress-strain curves for the tensile test and reverse tests of DLC films.
in the reverse tests with different initial strain show good consistence with those of metallic glasses [7], demonstrating that amorphous solids tend to share similar mechanical response to external loading. 3.2. Microstructure analysis It has been reported that the fraction of sp3 atoms Fsp3 and the fraction of sp2 atoms Fsp2 of carbon materials usually reflect their microstructural and mechanical properties [11]. To study the structural changes of the DLC film in the tensile test, the evolution of Fsp3 and Fsp2 is investigated and shown in Fig. 4a. When the tensile-strain is smaller than 0.05, both Fsp3 and Fsp2 keep almost constant. With the increasing tensile-strain, Fsp3 decreases but Fsp2 increases significantly. Moreover, the larger the tensile-strain, the faster Fsp3 and Fsp2 change. The evolution of Fsp3 and Fsp2 demonstrates that the film structure keeps stable at small tensile-strains but experiences dramatic transformations at high tensile-strains. Such structural transformation implies that the graphitization of DLC films can be induced by the high strain besides the high temperature, keeping consistent with recent studies [12, 14]. The dependence of film structures on tensile-strains corresponds well with the results shown by the potential energy evolution of reversed tests in Fig. 3. The bond angle distribution in carbon materials is useful to demonstrate their structural properties. The crystalline diamond has a bond angle of about 109°, while that of graphite is 120° [40]. As a result, the graphitization of diamond structures can lead to the shift of bond angles from 109° to 120°. The bond angle distributions of the DLC film are presented in Fig. 4b. At zero tensile-strain, a bond-angle peak located between 109° and 120° is observed, thus indicating a mixture of sp3 and sp2 atoms. When the tensile-strain increases up to 0.05, the bond angle distribution broadens slightly but the location of its peak keeps
unchanged. This demonstrates that under the small tensile-strain the bonds are only distorted and few sp3-sp2 transitions are induced. With the tensile-strain increasing to 0.16, the bond angle distribution broadens further and shifts to the higher angle side, revealing the sp3sp2 transitions and thus the structural transformation, i.e., the graphitization of the DLC film. The structural changes of DLC films can be further characterized by the radius distribution functions (RDFs) [31]. Fig. 5 shows the RDFs for all the carbon atoms. Only two nearest peaks are observed, which indicates the short-range order of the DLC film. At zero tensile-strain, the first nearest neighbor peak locates at 1.52 Å. The second nearest neighbor peak locates at 2.6 Å and has a small satellite peak at about 2.1 Å. The satellite peak is caused by the cut-off radius of the Tersoff potential and also termed as “false peak” in literature [41,42]. This is supported by the fact that this satellite peak does not shift with the increase of strain. When the tensile-strain increases, all other peaks shift to the right, indicated by the dashed line in the figure. The shifted peaks imply the increased atomic-distances. In addition, the heights of peaks decrease but their widths increase. This is attributed to the influence of atomic stresses and strains, as pointed out by Srolovitz et al [8]. At large tensile-strains, a shoulder peak located at about 1.82 Å appears near the first nearest neighbor peak. This presence of the shoulder peak demonstrates that more and more atomic bonds are severely stretched as the tensile-strain increases. Highly stretched bonds are unstable and break easily at large strains [14], causing structural changes of the DLC films. Investigating the evolution of these bonds can help to understand the structural transformation of the DLC films. In the DLC films, there mainly exist three types of bonds, namely, the bonds between the sp3 atoms, those between the sp2 atoms, and those between the sp2 and sp3 ones. These bonds are named as sp3-sp3, sp2-sp2 and sp2-sp3 bonds for short in the following discussion. To identify which bond type is most unstable and thus contribute most to the presence of the shoulder peak of the first nearest peak in RDF, three types of PDFs are calculated for the pair of sp2 atoms, the pair of sp3 atoms, and the pair of atoms in which one is sp2 bonded and the other is sp3 bonded, respectively. Similarly, these PDFs are named as sp2-sp2, sp3-sp3 and sp2-sp3 PDFs for short. The calculated PDFs are shown in Fig. 6. Two main peaks exist in all the PDFs and the location of the first nearest peaks is approximately the C\\C bond length of the DLC films. The change of these first peaks in PDFs usually gives information about the formation or breaking of the three types of bonds introduced above. At zero tensile-strain, the first peaks in all the PDFs are smooth and almost symmetrical about their central lines. When the tensile-strain increases to 0.05, a new peak protrudes out from the right shoulder of the first peak for both the sp3-sp3 and the sp2-sp3 PDFs. However, the sp2-sp2 PDF keeps almost unchanged. The appearance of the shoulder peaks implies that part of the sp3-sp3 bonds and sp2-sp3 bonds is
Fig. 3. Potential energy evolutions of DLC films during the tensile test and reverse tests.
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Fig. 4. (a) Evolution of the fractions of sp3 and sp2 atoms during the tensile tests; (b) bond angle distribution of DLC films with different tensile-strains.
stretched and tends to have a larger bond length. When the tensilestrain increases up to 0.16, the intensities of both the shoulder peaks for the sp3-sp3 and sp2-sp3 PDFs increase and the peak intensity of the former is higher. Moreover, a similar shoulder peak starts to form for the sp2-sp2 PDF but with a much weaker intensity than those of the shoulder peaks for the sp3-sp3 and sp2-sp3 PDFs. The rise of the shoulder peaks and the increase of their intensities with the increasing tensile-strain for the sp3-sp3 and sp2-sp3 RDFs indicate that the tensile deformation of the DLC films is mainly realized by the stretching of the sp3-sp3 and sp2-sp3 bonds. This is in good consistency with previous study which reported that in the deformation of DLC films sp3-sp3 and sp2-sp3 bonds become unstable and break firstly while all sp2-sp2 bonds stay intact [14]. The different mechanical response of sp2-sp2 bonds is because they are stabilized due to the hyperconjugation effect which enhances their bond strengths [43], and thus large tensile-strains is required to get them stretched. The different mechanical responses of the bonds also well explain the sp3-sp2 transition shown in Fig. 4 and the dependence of the bond fractions Fsp3 and Fsp2 on the tensile-strain. At small tensile-strains, the rise of the weak shoulder peaks indicates that a few sp3-sp3 and sp2sp3 bonds are stretched and become unstable, which can only induce a small number of sp3-sp2 transitions and thus both Fsp3 and Fsp2 keep almost constant. At large tensile-strains, the significant increase of the shoulder peak intensities reveals the breakings of a large quantity of stretched bonds which lead to lots of sp3-sp2 transitions and thus the increase of Fsp2 and decrease of Fsp3.
Fig. 5. Radius distribution functions (RDFs) of DLC films in the tensile test.
3.3. Atomic deformation analysis In the deformation of amorphous solids, volume strains of atoms can help to characterize variances of their free volume, and their shear strains are significant to demonstrate their propensity to participate in local inelastic transformation [44]. Contours of atomic volume strains and atomic shear strains in the DLC film are given in Fig. 7. The strain localizations are observed, and the regions with high atomic volume strains generally possess high atomic shear strains. When the tensilestrain increases, these regions expand due to the increase of the overall atomic strains. In addition, the shear bands occurring in the deformation of metallic glasses [5,45] are absent in the DLC films in present simulations. This may be due to the differences between covalent bonds and metallic bonds. The mechanisms of the absence of shear bands in the DLC films will be discussed later in Discussion section. The distributions of atoms in terms of their atomic volume strains and atomic shear strains are given in Fig. 8a–b. It is found that the sp2 atoms and sp3 atoms exhibit different distributions. In general, sp2 atoms dominate in the regions of both high atomic volume and shear strains. This is because the sp2 atoms have lower volume densities than the sp3 bonded ones and thus possess larger free-volumes which promotes atoms to rearrange easily under deformations [4,6]. Moreover, the smaller atomic elastic modulus of sp2 atoms also contribute to their larger atomic strains [46,47]. Therefore, the regions in which atomic strains are localized should mainly be occupied by the sp2 atoms. Due to their capabilities to bear large strains, they can be regarded as plasticity carriers in DLC films. The analysis of the atomic strain in relation to the bond deformation shown by the RDFs in Fig. 6 shows that the sp2 atoms have larger atomic strain than the sp3 atoms although the bonds of these sp2 atoms are less elongated than those of the sp3 atoms. This may be due to the fact that the atomic strain of one atom is determined not only by the lengths of its bonds with its surrounding atoms but also the angles between these bonds. The sp2 bonds can rotate easily to release the stress due to their high rotation flexibility and thus exhibit small elongations but large angle rotations in the presence of external loading. In contrast, the sp3 bonds have high rotation rigidity and thus mostly deform through bond elongation [46]. Since stretched bonds break easily at high atomic strains, it is reasonable to assume that the sp3-sp2 transitions mainly occur in the strain-localized regions. This assumption is verified by Fig. 8c–d which shows the distributions of atomic strains of new sp2 atoms generated from the sp3-sp2 transitions. These atoms generally have both higher atomic volume strains and atomic shear strains than those of all the atoms in the DLC film (Fig. 8a–b). As a result, sp3-sp2 transitions are localized and can increase the number of sp2 atoms and thus the graphitization level in the strain-localized regions. The high fractions of sp2 atoms in these regions can degrade their local mechanical properties [46]. When the tensile-strain increases, it causes larger localized strains and thus the expansions of these regions. These expansions can induce continuous degradations of mechanical properties of DLC films by
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Fig. 6. PDFs of atoms in the DLC film during the tensile test for (a) the pair of sp2 atoms, (b) the pair of sp3 atoms, and (c) the pair of atoms in which one is sp2 bonded and the other is sp3 bonded.
inducing more transitions. Consequently, the DLC films fracture when their degraded structures fail to bear the external tensile loading. In the strain-localized regions, influences of atomic shear strains and atomic volume strains on the sp3-sp2 transitions are coupled. This is due to that the transitions induced by high atomic shear strains can result in lower local densities and larger atomic volumes, thereby increasing the atomic volume strains. On the other hand, the high atomic volume strain may cause the transitions due to the atom-volume differences between sp3 and sp2 atoms and subsequently influence the atomic shear strains. The role of the two types of atomic strains on the sp3-sp2 transition can be explored by monitoring the unstable sp3 atoms that will become sp2 bonded and thus the new sp2 atoms when the tensile-strain increases. The distribution of these unstable sp3 atoms in terms of their atomic volume strains and atomic shear strains is given in Fig. 8e–f. Compared with all the sp3 atoms in the DLC film (Fig. 8a–b), these unstable sp3 atoms exhibit similar distribution of the atomic volume strain with a slight preference in the small range, while major of them have large atomic shear strains. The similar distribution of atomic volume strains indicates the independence of the sp3-sp2 transition on them. However, the large atomic shear strains imply that their higher values are needed to overcome the barrier in the transitions. As a result, it can be concluded that the atomic shear strains instead of the atomic volume strains dominate the sp3-sp2 transitions.
Fig. 7. Contours of (a) atomic volume strains and (b) atomic shear strains in the DLC film at tensile-strain of 0.18.
4. Discussions The stretched sp3-sp3 and sp2-sp3 bonds are unstable and break easily due to their larger bond lengths than those of the sp2-sp2 bonds. This has also been previously verified by density functional theory (DFT) calculations [21]. Since the bond elongations are induced by atomic strains, one might assume that atoms with the stretched bonds should be highly strained. To evaluate this assumption, distributions of these atoms in terms of their atomic strains are further studied. Surprisingly, the results show that these atoms have the atomic-strain distribution similar to that of the other atoms in the DLC film. Therefore, the bond elongations are independent of atomic strains and may be determined by complicated atomic-environments such as bonding states of atom neighbors [29]. As discussed above, the stretched-bond breakings and the sp3-sp2 transitions are dominated by atomic shear strains instead of atomic volume strains. This is consistent with previous experimental studies [16, 20]. In experiments, it was found that sp3 structures are unstable at high shear strains but only exhibit cell-size changes at high volume strains. The significance of atomic shear strains is attributed to that they can cause a rearrangement of the neighbors of sp3 atoms and thus the formation of the π bonds and graphite-like layer structures with the sp2 networks [18,19]. The atomic volume strains may play roles in increasing the distances between atoms and thus decreasing their local densities, and lowering the energy barriers for the sp3-sp2 transitions triggered by the atomic shear strain. Gilman has previously predicted that the critical atomic shear strain for the transitions is around 0.08 [17,48]. The prediction is consistent with the results in Fig. 8f where all the unstable sp3 atoms which will experience sp3-sp2 transitions with increased tensile-strains possess the shear strains higher than this critical value. The localized atomic strains in the DLC film promote the localizations of sp3-sp2 transitions which increase the graphitization level in the strain-localized regions. As a result, the atom structures in these regions can be almost treated as sp2 clusters. Expands of these regions at high tensile-strains can cause the propagations of the sp2 clusters, because the newly generated sp2 atoms due to the sp3-sp2 transitions tend to connect with the existed clusters due to the delocalization properties of π bonds [29]. To verify the propagations of sp2 clusters, their distributions are at the tensile-strains of zero and 0.18 are is analyzed (Fig. 9), respectively. With the increasing tensile-strain, the number of large-sized clusters significantly increases. Since the strength of the sp2 clusters is much lower than that of the sp3 networks, the propagations of these sp2 clusters highly weaken the mechanical properties of DLC films [46].
L. Bai et al. / Journal of Non-Crystalline Solids 443 (2016) 8–16
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Fig. 8. Distribution of carbon atoms in term of (a) atomic volume strain and (b) atomic shear strain for DLC films; distribution of new sp2 atoms obtained by transitions in terms of (c) atomic volume strain and (d) atomic shear strain at the tensile strain of 0.18; distribution of unstable sp3 atoms in terms of (e) atomic volume strain and (f) atomic shear strain when the tensile-strain increases from 0.18 to 0.184.
Therefore, it can be stated that the strain-induced propagations of sp2 clusters are responsible for the film failure. This statement shares many similarities with the clusters model of DLC films developed by Robertson et al [49,50]. In this model, mixtures of sp3 and sp2 atoms
tend to segregate into sp2 clusters embedded in a sp3 matrix which determines the mechanical properties. Fig. 9a also shows that as the tensile-strain increases, the number of sp2 clusters with small sizes especially those contain single atoms
Fig. 9. Distribution of (a) small-sized and (b) large-sized sp2 clusters at different tensile-strains. The size of a cluster is defined as the count of sp2 atoms in it.
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decreases while the number of sp2 clusters with large sizes increases. This phenomenon is due to the fact that new sp2 atoms are generated between small sp2 clusters and gradually connect them. As they are connected, they merge together and form large sp2 clusters. Therefore, the sp3 atoms whose neighbors are mainly sp2 bonded may have stretched bonds and easily experience the sp3-sp2 transitions. This is proved by collecting the coordination number of nearest neighbors of new sp2 atoms before their transitions. Besides spatial distributions in strain-localized regions, the sp2 clusters exhibit chain-like arrangements instead of graphite-like rings, although sizes of these clusters become large at large tensile strains. A clear graphical depiction of the chain-like arrangements can be obtained by using the metric as reported by Majmudar [51] and Bassett [52]. This chain-like arrangement may be due to the high fraction of sp3 atoms in DLC films [53,54]. Such arrangement may also be due to the absence of torsional energy term for rotations of π bonds in the Tersoff potential [53], since this term can make sp2 structures be planar by tailoring their relative stability and thus induce the formation of graphite-like structure [55]. The relation between bonding environment of neighbor atoms and sp3-sp2 transitions of sp3 atoms indicates that these transitions are not only influenced by atomic strains (Fig. 8e–f) but also affected by the local bonding environment. This keeps consistent with directional properties of covalent bonds. This relation can also help to demonstrate the absence of shear bands in DLC films. The strain localizations are present in DLC films as well as in metallic glasses, due to their amorphous structures. In the metallic glasses, atoms near the strain-localized region are rearranged freely along the plane of maximum shear under forces of their neighbors, due to the non-directional properties of metallic bonds [56]. Such rearrangements can make different strain-localized regions merged and induce the presence of shear bands along the plane, since the rearranged atoms are easily deformed. In DLC films, however, most of atom arrangements (sp3-sp2 transitions) are randomly distributed instead of distributed along the plane of maximum shear, due to the fact that the arrangement of atoms are influenced not only by the forces of their neighbors but also by bonding environment of their neighbors. Such random arrangements further induce that the strainlocalized regions in the DLC film are hardly merged to form a band. This can be verified from Fig. 7 which shows that most of the strainlocalized regions are isolated from each other even at the high tensile strain of 0.18. This can also be verified from the failure configuration of DLC film that shows a fracture perpendicular to the tensile axis instead of along the plane of maximum shear. Such configuration is a common failure configuration for many covalent amorphous solids. Therefore, these explanations about the absence of shear bands in the DLC films should be also applicable for deformations of other covalent amorphous materials. The propagation of sp2 clusters can greatly damage the networks formed by sp3 atoms. Evolution of such networks can also be analyzed by counting the number of sp3 clusters with different sizes at the tensile strains of zero and 0.18, N0 and N0.18 (Table 1). With the increase of tensile strain, the number of small-sized sp3 clusters in such networks greatly increases; however, the number of atom in the largest cluster decreases. This indicates that the branches of the largest clusters before the tensile test are cut off by the increased strain via inducing the transition of sp3 atoms from sp3 to sp2 bonding. Since the largest sp3 cluster undertakes the highest external stress, it can be regarded as a backbone in the DLC film. The reduction of its branches can highly weaken the mechanical properties of the film. Fig. 10 shows that the increase of tensile strain can significantly degrade this cluster. At the large tensile strain of 0.18, many voids are formed, and they should be filled by the sp2 clusters or the small-sized sp3 clusters. The increase of tensile strain can further enlarge these voids. In the largest void, the failure of the DLC film is observed to be initiated at the tensile strain of 0.21. Therefore, the degradation of the largest sp3 cluster directly leads to the film failure.
Table 1 Influence of the tensile strain on the sp3 clusters. Cluster size
N0
N0.18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 19 21 22 28 33 37 45 226 11,568 13,745
397 110 53 20 11 6 2 3 3 3 0 0 1 2 0 1 0 0 0 0 0 0 1 0 0 1
552 155 71 31 21 17 7 5 6 4 4 2 1 2 1 1 1 1 2 1 1 1 0 1 1 0
Generally, it can be seen that both the sp2 cluster propagation and the film failure are determined by the atomic strain localizations. These localizations definitely exist due to the heterogeneous distribution of the sp2 atoms inside the DLC films. Such heterogeneities form during the fabrication of the DLC films due to the fact that, sp2 atoms prefer to gather and form small clusters instead distribute randomly and evenly in the sp3 matrix because of the delocalization characteristic of π bonds [54,57]. It can be seen that the sp2 clusters exhibit unique behaviors in the tensile test. At small tensile-strains, the originally existed sp2 clusters are responsible for the structural relaxations of DLC films by relieving
Fig. 10. Atomic configuration of the largest sp3 cluster with the tensile strain of (a) zero, (b) 0.10 and (c) 0.18. The voids in this cluster are filled by sp2 clusters or small-sized sp3 clusters.
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their internal strain energies (Fig. 3). At large tensile-strains, the merges and propagations of sp2 clusters weaken the strength of films and thus lead to their failures. Therefore, it can be concluded the sp2 clusters in DLC films behave similarly to the dislocations or defects in crystals. This conclusion keeps consistent with previous studies [49,50,58], although they were focused on the electronic properties. Moreover, since the sp2 clusters dominate the regions with low local densities and large free volumes in DLC films, this conclusion is also supported by the free-volume theory which states that such regions act as plastic defects in amorphous solids [59]. The understanding of the behaviors of sp2 clusters in the deformation of DLC films can further guide their future applications. It is recommended that reducing heterogeneities of DLC films such as existences of large-sized sp2 clusters may be efficient in delaying film failures by suppressing the initial atomic-strain localizations. By summarizing the discussions above, the whole deformation process of DLC films in the tensile tests can be well described. When the tensile-strain initially increases, atomic strains are localized in the regions dominated by sp2 clusters. These clusters can efficiently relax the film structure by relieving residual strain energies, which prevents the sp3-sp2 transitions. When the tensile-strain further increases to be high, the stretched sp3-sp3 and sp2-sp3 bonds in or near the strainlocalized regions break. The bond breakings induce the sp3-sp2 transitions and the propagations of sp2 clusters. These propagations significantly weaken the mechanical strengths of DLC films and lead to their failures when the ultimate tensile strength is reached. The deformation mechanisms of DLC films can help to interpret their tribological behaviors. In the wear tests of these films, their surface asperities experience high strains. Such high strains can cause the sp2 clusters to merge and propagate inside these asperities and gradually weaken their strengths. The asperities subsequently drop from film surfaces, forming wear debris dominated by sp2 clusters. Transfer of these debris to the counterpart surface are induced by the interfacial adhesion between DLC film and counterpart and leads to the formation of transfer films which have graphite-like layer structures and isolate the DLC film and the counterpart. As a result, the lateral sliding of counterpart mainly occurs as shear deformations of the transfer films. In this case, π bonds in the graphite-like layer structures bear the high vertical load, and the absence of interlayer σ bonds leads to reductions of tangential friction forces with passivations of dangling carbon bonds by particles such as hydrogen molecules [12,13,15,22,60]. Due to low temperature in present simulation, the obtained deformation mechanisms of DLC films can be valid to explain their graphitization mechanisms in their running-in period when the friction temperature is low. It should be noted that the propagations of sp2 clusters have been reported in the wear tests of DLC films by employing the analysis of Raman spectrum and transmission electron micrographs [15,61]. However, such propagations are commonly believed to be determined by the high friction temperature in these tests since it can easily cause the transitions of C atoms from sp3 to sp2 bonding. The present study demonstrates that the propagations can happen during the yielding of surface asperities of DLC films in their running-in stages before the occurrence of the high friction temperature. Therefore, this demonstration may help to improve the understanding of their tribological mechanisms. 5. Conclusions The deformation mechanisms of DLC films are investigated by conducting a tensile test via MD simulations. At small tensile-strains, the fraction of sp2 atoms Fsp2 and the fraction of sp3 atoms Fsp3 keep constant, but the film structures are relaxed. With the increasing tensilestrain, Fsp3 decreases but Fsp2 increases, indicating the occurrence of sp3-sp2 transitions. When the ultimate tensile strength of the DLC film is reached, it subsequently fails. The atomic strains analysis indicates that the transitions are dominated by atomic shear strains instead of
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atomic volume strains. Moreover, the transitions prefer to occur in regions where atomic strains are localized. It is found that these regions are dominated by sp2 atoms due to their low local densities and low elastic modulus. As a result, the sp3-sp2 transitions are also localized in these regions and thus enhance their graphitization levels, leading to propagations of sp2 clusters. The disappearances of small-sized sp2 clusters indicate that the sp3 atoms which are located between sp2 clusters easily experience the sp3-sp2 transitions in the cluster propagations. The large-sized sp2 clusters can weaken the mechanical strengths of DLC films and thus lead to their failures when the degraded structures cannot bear the tensile stress as high as ultimate tensile strengths. Therefore, sp2 clusters can be regarded as defects, keeping consistent with the free-volume theory and previous structural models of DLC films. The results imply that reducing heterogeneities such as existences of large-sized sp2 clusters may be useful to delay film failures by suppressing the initial atomic strain localizations. Moreover, the present study demonstrates that the propagations of sp2 clusters for DLC films can be induced by their deformation besides the high friction temperature in their wear tests. This demonstration can help to improve the understanding of their tribological mechanisms. Acknowledgements This work is financially supported by Ministry of Education (Academic Research Fund TIER 1-RG128/14), Singapore. LB acknowledges the Interdisciplinary Graduate School of Nanyang Technological University, Singapore for providing the Research Student Scholarship. References [1] Z. Lu, J. Li, H. Shao, H. Gleiter, X. Ni, The correlation between shear elastic modulus and glass transition temperature of bulk metallic glasses, Appl. Phys. Lett. 94 (2009) 91907. [2] Z. Lu, J. Li, Correlation between average melting temperature and glass transition temperature in metallic glasses, Appl. Phys. Lett. 94 (2009) 1913. [3] W. Liu, H. Ruan, L. Zhang, On the plasticity event in metallic glass, Philos. Mag. Lett. 93 (2013) 158–165. [4] Y. Cheng, J. Ding, E. Ma, Local topology vs. atomic-level stresses as a measure of disorder: correlating structural indicators for metallic glasses, Mater. Res. Lett. 1 (2013) 3–12. [5] S. Takeuchi, K. Edagawa, Atomistic simulation and modeling of localized shear deformation in metallic glasses, Prog. Mater. Sci. 56 (2011) 785–816. [6] Y. Cheng, E. Ma, Indicators of internal structural states for metallic glasses: local order, free volume, and configurational potential energy, Appl. Phys. Lett. 93 (2008) 051910. [7] D. Srolovitz, V. Vitek, T. Egami, An atomistic study of deformation of amorphous metals, Acta Metall. 31 (1983) 335–352. [8] D. Srolovitz, T. Egami, V. Vitek, Radial distribution function and structural relaxation in amorphous solids, Phys. Rev. B 24 (1981) 6936. [9] T. Egami, Atomic level stresses, Prog. Mater. Sci. 56 (2011) 637–653. [10] L. Bai, G. Zhang, Z. Lu, Z. Wu, Y. Wang, L. Wang, P. Yan, Tribological mechanism of hydrogenated amorphous carbon film against pairs: a physical description, J. Appl. Phys. 110 (2011) 033521. [11] L. Bai, G. Zhang, Z. Wu, J. Wang, P. Yan, Effect of different ion beam energy on properties of amorphous carbon film fabricated by ion beam sputtering deposition (IBSD), Nucl. Instrum. Methods Phys. Res., Sect. B 269 (2011) 1871–1877. [12] T.-B. Ma, L.-F. Wang, Y.-Z. Hu, X. Li, H. Wang, A shear localization mechanism for lubricity of amorphous carbon materials, Sci. Rep. 4 (2014). [13] Y. Liu, A. Erdemir, E. Meletis, An investigation of the relationship between graphitization and frictional behavior of DLC coatings, Surf. Coat. Technol. 86 (1996) 564–568. [14] T. Kunze, M. Posselt, S. Gemming, G. Seifert, A.R. Konicek, R.W. Carpick, L. Pastewka, M. Moseler, Wear, plasticity, and rehybridization in tetrahedral amorphous carbon, Tribol. Lett. 53 (2014) 119–126. [15] Y. Liu, E. Meletis, Evidence of graphitization of diamond-like carbon films during sliding wear, J. Mater. Sci. 32 (1997) 3491–3495. [16] Y.G. Gogotsi, A. Kailer, K.G. Nickel, Pressure-induced phase transformations in diamond, J. Appl. Phys. 84 (1998) 1299–1304. [17] J.J. Gilman, Mechanism of shear-induced metallization, Czechoslov. J. Phys. 45 (1995) 913–919. [18] H. Chacham, L. Kleinman, Instabilities in diamond under high shear stress, Phys. Rev. Lett. 85 (2000) 4904. [19] A. De Vita, G. Galli, A. Canning, R. Car, A microscopic model for surface-induced diamond-to-graphite transitions, Nature 379 (1996) 523–526. [20] Y.G. Gogotsi, A. Kailer, K.G. Nickel, Materials: transformation of diamond to graphite, Nature 401 (1999) 663–664.
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