Experimental and Theoretical Investigation of Crystallographic Orientation Dependence of Nanoscratching of Single Crystalline Copper

In the present work, we perform experiments and molecular dynamics simulations to elucidate the underlying deformation mechanisms of single crystalline copper under the load-controlled multi-passes nanoscratching using a triangular pyramidal probe. The correlation of microscopic deformation behavior of the material with macroscopically-observed machining results is revealed. Moreover, the influence of crystallographic orientation on the nanoscratching of single crystalline copper is examined. Our simulation results indicate that the plastic deformation of single crystalline Cu under the nanoscratching is exclusively governed by dislocation mechanisms. However, there is no glissile dislocation structure formed due to the probe oscillation under the load-controlled mode. Both experiments and MD simulations demonstrate that the machined surface morphologies in terms of groove depth and surface pile-up exhibit strong crystallographic orientation dependence, because of different geometries of activated slip planes cutting with free surfaces and strain hardening abilities associated with different crystallographic orientations.


Introduction
Nanostructures with unique properties not only provide novel applications in fields of optoelectronics, sensors, transducers and biomedical sciences [1][2][3][4][5], but also are of significant fundamental research interests at the nanometer scale. Surface quality in terms of surface morphology and subsurface damage is one important issue governing potential application and performance of nanostructures [6][7][8]. Thus, how to fabricate nanostructures with ultra-fine surface finish becomes critical and challenging. The atomic force microscopy (AFM) probebased mechanical nanoscratching has been demonstrated to be one powerful fabrication technique for functional nanostructures [9][10]. To facilitate surface quality improvement of the as-fabricated nanostructures, a fundamental understanding of the underlying machining mechanisms involved in the probe-based nanoscratching process is essentially required.
Given the ultra-small material removal thickness, the properties of workpiece materials play increased even dominant role in the probe-based nanoscratching. For instance, nanocrystalline metals of unique chemical, physical and mechanical properties not only provide novel possibilities for the fabrication of advanced functional nanostructures [11], but also bring new challenges in understanding their nanoscratching mechanisms because of internal textured microstructures [12][13][14]. Due to comparable probe radius with average grain size, a typical scratching pass of nanocrystalline materials under the probe-based nanoscratching involves multiple grains of different crystallographic orientations. It's known that the mechanical properties of an anisotropic material vary with orientation, which consequently results in difficulty in obtaining a uniformly-machined surface quality over individual grains. Since the deformation of nanocrystalline materials at the grain level mainly relies on the orientation of individual grains, it's important to examine the effect of crystallographic orientation on the nanoscratching process. Previous experiments and molecular dynamics (MD) simulations of tension [15][16], compression [17], bending [18][19][20] and indentation [21][22] tests under the uniaxial stress state have well documented that the crystallographic orientation-dependent mechanical response of single crystalline face centered cubic (FCC) metals is determined by the activation of {111}<110> slip systems. However, the localized multi-axis stress state in nanoscratching causes more complex tribological response with respect to the crystallographic orientation than the uniaxial stress state, which thus requires new insights above previous documentation of the crystallography dependence. On the experimental side, it is found that there is rather limited information known about the influence of crystallographic orientation on the nanoscratching. Furthermore, the influence of scratching pass number on the crystallographic orientation dependence is largely unknown. On the theoretical side, although the effect of crystallographic orientation on the nanoscratching has been investigated by several MD simulations [23][24][25], most of which exclusively mimicked the nanoscratching under the displacement-controlled mode, i.e., probe penetrating into sample surface with constant velocities. However, the probe-based nanoscratching experiments are usually carried out in the loadcontrolled mode by applying constant normal load on the probe. Furthermore, most of the probes considered in previous MD simulations are conical-or spherical-shaped, which are significantly different from the triangular pyramidal geometry that is widely used in nanoscratching experiments. Those discrepancies of nanoscratching methodologies inevitably introduce uncertainties in the comparison between experimental data and simulation results.
Therefore, in the present work we conduct experiments and MD simulations of multi-passes nanoscratching of single crystalline copper. The experimental and theoretical methodologies of nanoscratching are mainly consistent with each other, as the nanoscratching tests are performed under the load-controlled mode using a triangular pyramidal probe. We elucidate the microscopic deformation mechanisms of single crystalline copper, and also reveal their correlations with the macroscopic machining results in terms of machining force and machined surface quality. We further examine the crystallographic orientation dependence of the nanoscratching.

Experiments
The probe-based nanoscratching experiments are carried out in a commercial AFM-based nanomachining system (Dimension Icon, Bruker Company, Germany). Particularly, the equipped Nanoman module in the AFM system is employed for the multi-passes scratching. Fig 1(A) illustrates the configuration of multi-passes nanoscratching experiment. Each scratching pass can be divided into three sequential phases, as first penetration, following scratching and final retraction, respectively. In the first phase of penetration, a pre-determined normal load F N is applied to the cantilever with a normal spring constant (K N ) of 275 N/m, which results in a diamond probe (PDNISP, Bruker Company, Germany) penetrating into the sample surface under the contact mode of the AFM. The triangular pyramidal diamond probe shown in Fig 1(B) has a radius of approximately 110 nm evaluated by the blind reconstruction method [26]. In the second phase of scratching the applied normal load (F N ) is maintained, and the probe driven by the piezoelectric ceramic transducer scratches 20 μm with a constant velocity of 3 μm/s along the direction highlighted by the red arrow shown in Fig 1(A), which leads to a straight groove of nanometer dimensions formed on the sample surface. To minimize the error of applied normal load between pre-determined and actual values, the scratching direction perpendicular to the cantilever is particularly chosen. In the third phase of retraction, the probe returns to its initial position prior to the first penetration with a constant velocity of 10 μm/s under the tapping mode of the AFM. In the present work, the number of scratching passes is fixed as 3 for each normal load. After completion of the multi-passes scratching, the machined sample surface is first ultrasonically washed in alcohol solution for 10 min to remove chips formed in the scratching process, and then subjected to imaging in the AFM under the tapping mode using a silicon nitride probe with a probe radius of 10 nm.
To reveal the crystallographic orientation dependence of material removal in the nanoscratching, three commercially-provided single crystalline copper samples with different surface orientations of (010), (110) and (111) are considered. The 2θ-diffraction angles obtained from the X-Ray diffraction for the (010)-, (110)-and (111)-oriented single crystalline copper are 50.4, 43.36 and 74.18 。 , respectively. All the three copper samples have the same dimension of 10 mm × 10 mm × 1 mm, and the measured surface roughness (R a ) is less than 5 nm. For each sample, six normal loads (20.6, 28.9, 37.2, 45.4, 53.7 and 61.9 μN) are considered.

Simulations
In addition to the nanoscratching experiments, MD simulations of load-controlled multipasses nanoscratching of single crystalline Cu(010), (110) and (111) surfaces are also performed by using the LAMMPS code with an integration timestep of 1 femtosecond [27].  and Z directions, and the bottom of the sample along Y direction is fixed in space. The atomic interactions in copper sample are described by an EAM potential developed for Cu [28], and the interactions between carbon atoms and copper atoms are described by the Morse potential [29].
Prior to the nanoscratching, the as-created samples are first equilibrated at 30 K in the NVT (constant number of atoms, volume and temperature) ensemble for 50 ps. Then the relaxed sample is subjected to the nanoscratching in the NVT ensemble at 30 K. The relative low temperature of 30 K is used to eliminate thermal effect on the nanoscratching [30]. To be consistent with experimental configuration, the multi-passes nanoscratching simulation also consists of three phases, as initial penetration along negative Y direction, following scratching along negative X direction and final retraction to its initial position before penetration, respectively. Both the penetration and scratching are carried out in the load-controlled mode by applying constant normal load on the probe. In the first phase of penetration with a duration of 20 ps, a normal load of 56 nN is applied to the probe. In the following scratching phase the constant normal load is maintained, while the probe scratches 16 nm on the sample surface with constant velocity of 100 m/s. In the final phase of retraction the applied normal load is fully released, and the probe first moves upwards along positive Y direction for 4 nm, and then return to its initial position along positive X direction. To make the computational time reasonable, a relative high scratching velocity is used in the present MD simulations, given the intrinsic limitation of the integration timestep to be in the order of the magnitude of fs. The common neighbor analysis (CNA) is employed to distinguish different types of defects generated in the samples [31]. The Ovito is utilized to visualize MD data and generate MD snapshots [32].   In the penetration phase, the increment of probe height is calculated by subtracting the probe height before penetration using the current height. For the first scratching pass, the magnitude of probe velocity first increases linearly accompanied by the probe approaching to the sample surface until the initial contact occurs, at which the increase of probe velocity reverses. However, the probe height continues to decrease due to the probe penetrating into the sample surface. Fig 4(A) shows that after the probe height reaches its lowest value, the probe first bounces upwards slightly and then fluctuates around a constant value, accompanied with the fluctuation of probe velocity around 0, indicating that the penetration is stable.  increment of probe height is calculated by subtracting the probe height before scratching using the current height. It is found that the probe height during the first scratching pass mainly keeps constant value and is lower than the value after the completion of penetration phase. Fig 4(D) shows that the scratching force first increases rapidly and then fluctuates around a constant value of 90 nN when scratching is stable. The strong fluctuation phenomena observed in Fig 4(D) can be attributed to dislocation nucleation events. Fig 4 also demonstrates that the scratching pass number has significant influence on the mechanical response of nanoscratching. In the penetration phase, the constant value of probe height, the maximum value of probe velocity and the slope of velocity decreasing increase with scratching pass number. In the following scratching phase, the bouncing back phenomenon is more pronounced for larger scratching pass number. For either the second or the third scratching pass, Fig 4(C) shows that the probe height first decreases slightly in the initial scratching length of 3 nm, but increases significantly in the rest of scratching length. Furthermore, for each scratching pass number, the penetration depth is decreasing with increasing scratching length. It is seen from Fig 4(C) that after completion of the scratching phase, the increment of probe height is 1.0 and 1.5 nm for the second and third scratching pass number, respectively. Accordingly, Fig 4(D) shows that the constant value of scratching force is nearly independent on the scratching pass.

Mechanisms of multi-passes nanoscratching
To reveal the underlying deformation mechanisms of single crystalline Cu(010), dynamic analysis of defect evolutions during the load-controlled multi-passes nanoscratching is carried out. Fig 5 presents representative MD snapshots of instantaneous defect structures during the nanoscratching process. For the single scratching pass, the deformation mechanisms of single crystalline Cu(010) can be summarized as follows: in the penetration phase, the defect-free material first undergoes first elastic deformation, followed by plastic deformation initiated by the nucleation of dislocations from the penetrated surface. In the plastic deformation the nucleated dislocations subsequently glide on {111} slip planes below the (010) free surface, and their reaction and cross-slip lead to the formation of sessile dislocation structures shown in Fig 5(A). However, there is no glissile dislocation structure such as prismatic dislocation loop formed, which is significantly different from previous MD simulations of the displacement-controlled penetration [30]. The discrepancy of dislocation structures between different penetration modes can be attributed to the oscillating displacement of the probe in the load-controlled mode, which releases accumulated plastic strain in the vicinity of the probe. In the following scratching phase, dislocation evolution is much more complex than that in the penetration phase because of more complex stress state of multi-axis. It is found from Fig 5(B) that while there are fresh dislocations nucleated from free surface in front of the probe due to the shear stress applied by the probe, dislocation annihilations occur at the free surface behind the probe because of the release of applied normal stress. Furthermore, there is still no glissile prismatic dislocation structures formed within the material in the scratching phase. Correspondingly, there are considerable displaced material accumulated on the sample surface, due to the glide of dislocations on {111} slip planes towards the surface and the annihilation of dislocation at the surface [30]. In the final retraction phase, the release of applied stress leads to considerable strain energy recovery, and the defect zone beneath the free surface shrinks slightly.
Be similar to the single scratching pass, the plastic deformation behavior of the Cu(010) under multi-passes nanoscratching is also dominated by dislocation mechanisms. However, Fig 5(C) and 5(D) demonstrate that the microscopic deformation behavior as well as the machining results is strongly dependent on the scratching pass number. In the penetration phase of multi-passes nanoscratching, the initiation of plastic deformation is governed by the motion of pre-existing dislocations beneath the scratched surface, instead of initial dislocation nucleation from the free surface. Since there are considerable sessile dislocations formed in the first scratching pass that act as barriers for dislocation motions, the strain hardening becomes more pronounced in the multi-passes nanoscratching. And the larger the scratching pass number, the more pronounced the strain hardening. Consequently, the probe height in the scratching phase is larger than the penetration phase, and increment of probe height increases with increasing scratching pass number, as shown in Fig 4(C).
It is also seen from Fig 3 that during the multi-passes nanoscratching the triangular pyramid-shaped probe is inclined, as compared to its original geometry. And the inclination angle increases with scratching pass number. To characterize the inclination of the probe, the initial configuration of the probe shown in Fig 6(A) is chosen as the reference to obtain the displacement magnitude of the probe after the nanoscratching. Fig 6(B) presents the atomic configuration of the probe colored by atomic displacement magnitudes after the third scratching pass, indicating that the inclination of the probe is composed of lateral displacement and radial rotation. And the atomic displacement magnitude of the probe increases with atomic height. The inclination of probe during the load-controlled multi-passes nanoscratching can be attributed to the heterogeneous deformation occurred within the material. It's should be noted that in the experiments, the slight rotation and oscillation of the probe are eliminated after each scratching pass because of the large normal spring constant of the cantilever.  Fig 9(A), 9 (B) and 9(C) present MD snapshots of cross-sectional view of groove profiles for the Cu(010), Cu(110) and Cu(111) after the 3rd scratching pass, respectively. It is found from Fig 9 that both the groove depth and the volume of surface pile up for the Cu(010) and Cu(110) are significantly larger than that for the Cu(111) [36]. Furthermore, while surface pile up is mainly accumulated on the left side of the groove for the Cu(010) and Cu(110), the material pile up  Above experiments and MD simulations demonstrate a strong crystallographic orientation dependence of single crystalline Cu under the load-controlled multi-passes nanoscratching, which can be attributed to different geometries of activated slip planes with free surface and strain hardening abilities for different crystallographic orientations. MD simulations reveal that the plastic deformation of single crystalline Cu under the nanoscratching is exclusively governed by dislocation slip on {111} plane in <110> direction at ambient temperature. While there are 12 crystallographically equivalent {111}<110> slip systems in FCC copper, the yielding accompanied by the dislocation nucleation will only begin on one slip system when the applied resolved shear stress on the system first reaches a critical value. The activation of slip systems can be determined by calculating the Schmid factor M = cos φ Ã cos λ, where φ and λ are the angle between the applied load direction and the slip plane normal and the angle  Orientation Dependence of Nanoscratching of Single Crystalline Copper between the applied load direction and the slip plane direction. In particular, the maximum Schmid factor indicates the primary slip system that carries the local deformation process.

Effect of crystal orientation on the nanoscratching
In the scratching phase of the nanoscratching, there are multi-axis stress components acting on the sample, the Schmid factor is divided into two components: (i) a scratching Schmid factor associated with frictional resistance along the negative X direction and (ii) a normal Schmid factor associated with normal pressure along the negative Y direction. Table 1 lists the calculated maximum Schmid factors for the three crystallographic orientations, indicating that the activation of primary slip system highly depends on the orientation of the crystal axes relative to the applied load direction. For the Cu(100), all the four {111} planes beneath the (010) free surface are primary slip planes. However, there are only two primary slip planes for either the Cu(110) or Cu(111). Specifically, the primary slip planes for the Cu(110) are (111) and (11-1), for the Cu(111) are (1-11) and (-111). Furthermore, the geometry of {111} slip planes cutting free surface varies with crystallographic orientation. Consequently, the morphology of scratched surface shows a strong dependence on crystallographic orientation, because the transportation of displaced material is primarily along the intersection between the primary slip plane and the scratched free surface [30,[37][38]. We also note that the probe geometry also has significant influence on the surface pile-up pattern, as the displaced materials mainly flow through the side face of the probe parallel to the scratching direction. It is also seen from Table 1 that there are at least two primary slip planes activated for each crystallographic orientation under the scratching phase. The multiple slips on neighboring slip planes resulting in dislocation multiplication, which leads to dislocations blocking the motion of each other because of the decreased average distance between them. Furthermore, the cross-slip and reaction of dislocations lead to formation of the sessile dislocation structures shown in Fig 3, which act as barriers to dislocation motion. Consequently, significant strain hardening occurs in the material, which leads to the decrease of scratching depth with increasing scratching number, given the maintained constant normal load. Furthermore, since the strain hardening is associated with the increase of dislocation density with plastic deformation due to multiplication, there is also a strong crystallographic orientation dependence of the strain hardening ability because of different primary slip systems for different crystallographic orientations.

Summary
In summary, we perform experiments and MD simulations of the load-controlled multi-passes nanoscratching of single crystalline copper using a triangle pyramidal probe, with an emphasis on the influence of crystallographic orientation on the nanoscratching. Our results show that dislocation slip is the dominant deformation mode operating in the plastic deformation of the Cu materials. However, there is no glissile dislocation structure formed thorough the nanoscratching process, because of the oscillation of the probe. While the plastic deformation of the material in the first scratching pass is initiated by the nucleation of fresh dislocation, the onset of plasticity in the multiple scratching passes is governed by the motion of pre-existing dislocations. The heterogeneous plastic deformation within the material leads to the inclination of the probe. It is found that both the surface pile-up height and groove depth have a strong dependence on the crystallographic orientation. While the surface pile up for either the Cu(010) or Cu(110) mainly resides on the left side of the groove, the surface pile up for the Cu(111) is symmetrically distributed along the groove. Moreover, the crystallographic orientation dependence of nanoscratching of single crystalline Cu is not influenced by the applied normal load. However, the inclination degree of the probe are larger for the Cu(010) than that for both the Cu (110) and Cu(111). Orientation Dependence of Nanoscratching of Single Crystalline Copper