Effect of water film on the plastic deformation of monocrystalline copper

Abstract

The mechanical behavior of nanoscale materials is strongly influenced by the working conditions. The corresponding research about plastic properties, however, is very limited especially in liquid environments. In this work, the effect of a water film on the plastic deformation of monocrystalline copper (Cu) is performed by a nanoindentation process using molecular dynamics simulations. The results indicate that the water film induces strong fluctuation of the load–indentation depth curves and increase of the load at the same indentation depth. The plastic deformation of monocrystalline Cu is obviously strengthened due to the water film facilitating dislocation propagation sufficiently into the inner Cu substrate. In addition, the mechanism of plasticity response to the nanoindentation process is discussed based on the interaction force. The results reveal that with the water film thickness increasing, the interaction force between the indenter and monocrystalline Cu exhibits obvious delay and its value is significantly smaller compared with that of the nanoindentation without a water film. The water molecules under and around the indenter transmit the force stemming from the indenter to the Cu substrate, which strengthens the dislocation propagation into the inner substrate but blocks the dislocation propagation to the surface, leading to a larger plastic deformation of monocrystalline Cu. In addition, the effect tendency of the water film on the nanoindentation property of the Cu substrate slows down rather than increases continuously once the thickness is large enough. Our findings can help us to understand more thoroughly the plastic deformation mechanism of nanomaterials under liquid or humid conditions.

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Introduction

With the rapid development of ultra-precision manufacture of miniaturized components, metallic devices on a micro- and nano-scale are increasingly significant in many modern technologies.^1,2 As one crucial material of metallic devices, thin films or nanolayer systems have entered into a wide range of applications, such as medical sensors, micro-/nano-electromechanical systems (MEMS/NEMS), aerospace and optical devices.^1–4 The mechanical behavior of metallic thin films of nanometer size under different working conditions, especially under humid or liquid conditions, strongly influences the working reliability and service life of metallic devices.⁵ Therefore, it is pressing to characterize the mechanical behavior of thin films for further research and wide industrial applications.

Nanoindentation is one of the few ways to study and measure the mechanical properties of thin film materials, particularly the plastic deformation of materials at fine scales.^3,6–8 Experimentally, an increasing number of efforts have been made in nanoindentation research, such as determination of the hardness and elastic modulus from load–displacement,⁶ measurement of stress and strain,⁷ investigation of size effects and stochastic behavior of nanoindentation pop in and pop out,^9,10 nanoindentation strain-rate jump tests,¹¹ and analysis of nanoindentation creep.¹² In addition, molecular dynamics (MD) simulation provides invaluable physical insight into the plastic deformation behavior of materials due to the fast developments in computer technology.¹³ Liang et al. proposed an MD study to find the microstructure origin of the elastic–plastic response of a copper Cu substrate during nanoindentation.¹⁴ Gao et al. presented a simulation study of nanoindentation of iron to understand dislocation generation and reactions.¹⁵ Saraev and Miller aimed to elucidate details of plastic deformation and the underlying deformation mechanisms during nanoindentation of Cu thin films with epitaxial nickel coatings.¹⁶ Sun et al. simulated the effect of residual stress on surface hardness and incipient plasticity of monocrystalline Cu thin films.¹⁷ Consequently, experiments and simulations have facilitated the probing of changes in mechanical properties and provided better understanding of the plastic deformation mechanism. However, almost all of the research neglects the actual experimental or working conditions.

Moreover, it is well known that the importance of environmental effects in the plasticity of metallic materials should not be underestimated, particularly when materials work in liquid or water environments at the micro- and nano-scale.^18–20 Mann et al. placed an indenter and sample in an enclosed space modified by silica gel and water,²¹ and they further reported a new type of experiment attempting to investigate wear phenomena for asperity size indentations of BCC metals immersed in aqueous HCl and distilled water.⁵ However, until now the experiments of the liquid conditions impacting the plastic deformation behavior have been very limited, while a corresponding simulation has not yet been found, especially for nano-scale metallic materials. Thus, exploring and understanding the influences of liquid on the plastic deformation of materials is a key issue and should be settled immediately.

In the present work, MD simulations are implemented to investigate the effects of the water film on the nanoindentation process of monocrystalline Cu. Emphasis is put on analysis of the plasticity and dislocation evolution under different water film thicknesses, and on discussion of the mechanism of incipient plasticity in terms of interatomic interaction. This study contributes a better and detailed understanding of material deformation and the correlated characteristics.

Modeling and simulation details

In this study, the MD simulations are performed using the large-scale atomic/molecular massively parallel simulator (LAMMPS).²² As shown in Fig. 1, the schematic model is composed of a spherical diamond indenter, a water film and a defect-free monocrystalline Cu workpiece along the Z axis. The indenter with a radius of 2.53 nm, consisting of 11 954 atoms with a perfect diamond atomic lattice, is positioned initially at a height of 2 nm above the water film. The Cu workpiece, assumed to be a perfect FCC metal, contains 750 400 atoms within a lattice size of 68a × 68a × 40a, where a = 0.3615 nm is the lattice constant of Cu. The crystal orientations of both the Cu workpiece and the diamond indenter along the X, Y and Z axes are [100], [010] and [001].

Fig. 1 Schematic of the MD simulation model for nanoindentation on the Cu (001) surface with a water film.

The Cu workpiece includes three zones: the boundary zone, thermostat zone and Newtonian zone. In the Newtonian and thermostat zones, the motion of the atoms obeys the classical Newton’s second law and is integrated through a Velocity-Verlet algorithm with a time step of 1 fs. Four layers of atoms at the bottom of the workpiece are the boundary atoms, which are kept fixed in their initial lattice positions to reduce the boundary effects. The thermostat zone, consisting of four layers of atoms, is adopted to imitate the heat dissipation properly. Periodic boundary conditions are imposed in the X and Y directions and a temperature of 300 K is applied initially in the workpiece for all MD simulations. Before starting the indentation, a relaxation process of 50 ps is carried out to optimize the system energy. Displacement control by positioning the indenter is used during the loading process along the [001] crystal orientation, and the velocity of displacement control is kept as a constant of 0.05 nm ps⁻¹ similar to that used by other works,^1,13 before reaching the largest indentation depth h = 2 nm.

It is vital to select an accurate and efficient potential energy for MD study. The embedded atom method (EAM) potential proposed by Mishin et al. provides a more realistic description of metallic cohesion and avoids ambiguity inherited by volume dependency,^23–26 which is employed to define the interaction between Cu atoms. The Morse potential is adopted to depict the interaction between the Cu atoms and C atoms of the diamond indenter,²⁷ whose potential energy function is expressed as

where D = 0.1 eV is the cohesive energy, α = 1.7 Å⁻¹ is the elastic modulus, and r₀ = 2.2 Å and r are the interatomic equilibrium distance and instantaneous distance, respectively. The cutoff radius of 0.4 nm is selected for the Morse potential to make all MD simulations efficient and precise. The C–C interaction is omitted because of the treatment of a rigid body. The rigid TIP4P model comprising three fixed point charges and one Lennard-Jones center is applied to simulate the condensed phase of the water film.^24,28 The interactions of H atoms in water molecules with other types of atoms are neglected due to the weak influence of H atoms.²⁴ The Cu–O and C–O interactions are described by the Lennard-Jones (12-6) potential, and the Lorentz–Berthelot mixing rules are employed to obtain the relevant parameters as shown in Table 1.^24,29–31 Further validation of potentials is provided in the ESI.†

Table 1 Parameters of the Lennard-Jones potential for different atomic pairs

Interatomic pair	ε (kcal mol^−1)	δ (nm)	Cutoff radius (nm)
O–O	0.1554	0.31655	0.6
Cu–O	0.2708	0.28877	0.5
C–O	0.1	0.3275	0.5

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To discern defects in the Cu workpiece, the centro-symmetry parameter (CSP) is incorporated to visualize the dislocation.³² In addition, the dislocation extraction algorithm (DXA), a computational analysis technique developed by Stukowski,^15,33 is also used to identify dislocation defects by converting all identified dislocations into continuous lines and computing their Burgers vectors in a fully automated fashion. The open visualization tool (Ovito) is used to visualize the simulation results.³⁴

Load–depth curves and dislocation evolution processes

In this section, the properties of the elastic–plastic response caused by a diamond indenter loading on the monocrystalline Cu workpiece are illustrated with the analysis of the load–indentation depth curves and dislocation evolution, when the water film thickness (H) is increased from H = 0 (no water) to H = 4 nm. Here, the load is defined as the total normal force of the indenter interacting with the water film and the monocrystalline Cu workpiece. As expected, in Fig. 2 the load–indentation curve exhibits nearly smooth elastic behavior at a small indentation depth of less than 0.25 nm during the nanoindentation without the water film. This result is consistent with simulated results,^14,17,35 but in strong conflict with published experiments following the Hertzian relation.³⁶ Liang et al. also found the deviation and attributed it to the comparable size of the indenter and indentation depth in simulations.¹⁴ With the increase in displacement, the load–indentation depth curve for the nanoindentation without a water film exhibits a sudden load drop and a strain burst due to the plastic deformation. However, as the water film exists on the Cu workpiece, the load–indentation depth curves (in Fig. 2) show a strongly fluctuant characteristic. Therefore, it is difficult to identify the elastic regime and a clear sudden load drop under the existence of a water film. This can be understood because the influence of the surface tension of water film on the total load force cannot be neglected, and meanwhile the discontinuous distribution of water molecules at the nanoscale leads to the fluctuant interaction between the water film and indenter. Moreover, we find that the load increases in proportion to the water film thickness in a range of H = 0 to H = 3 nm at the same indentation depth. A similar conclusion was obtained by Mann et al. where the indentation experiments of GaAs and tungsten were performed in distilled water and HCl solution.^5,21 This result suggests that the variation of the load may stem from the changing interaction of the Cu–C atoms induced by the penetrating of water molecules during indentation. Then, the difference between the load–indentation depth curves becomes ambiguous when the water film thickness is greater than or equal to 3 nm (i.e. the water film just overwhelms the spherical indenter), especially at the end of the indentation process. Similarly, Ren et al.²⁴ stressed that the growth rate of the water-to-tip force slows down once the thickness is larger than 3 nm. This means that when the water film is thick enough, the contribution of the water film to the load tends to slow down and the influence of the water film on the nanoindentation property may remain in a steady state.

Fig. 2 Load–indentation depth curves under different water film thicknesses (H).

As is well known, the load–indentation depth behavior demonstrates the elastic–plastic response, which is correlated with the development of the dislocation structure beneath the indenter. Thus, we need to indicate the dislocation evolution processes at the stage of plastic deformation of monocrystalline Cu. As shown in Fig. 3, a sequence of atomic configurations depicts the evolution processes of the dislocation structure throughout nanoindentation with various water film thicknesses. Small Cu atom clusters appear beneath the indenter at the final stage of elastic deformation, which can be regarded as the nucleated dislocation embryos.^2,4,17 As the penetration of the indenter increases beyond a critical depth, a pair of Shockley partial dislocations, bounding the stacking fault domains represented by yellow and green atoms for clarity, nucleates and evolves in the {111} slip planes (when h = 0.3 nm as shown in Fig. 3).^14,17 This corresponds to the point of highest stress concentration in the sudden load drop regime of the load–indentation depth curve (in Fig. 2). Those Shockley pairs grow and propagate to interact with the workpiece surface and many new nucleated dislocations represented by brown atoms in Fig. 3. Consequently, a stair-rod dislocation (loop) and a Lomer–Cottrell lock are formed (when h = 0.4 nm and h = 0.6 nm as shown in Fig. 3), corresponding to the relaxation and the subsequent rise of stress at the stage of the sudden load drop as shown in Fig. 2.

Fig. 3 Snapshots of embryonic plasticity evolution under different water film thicknesses (H): (a) no water, (b) H = 1 nm, (c) H = 2 nm, and (d) H = 3 nm. Red represents the surface and dislocation atoms, green and yellow represent the first nucleated dislocation embryos, and brown represents the subsequent nucleated dislocations.

Furthermore, it can be observed from Fig. 3 that, at the same indentation depth, the thicker the water film on the monocrystalline Cu workpiece is, the larger the area and depth of the initial Shockley pairs become. This suggests that the water film facilitates sufficient propagation of the Shockley pairs at the same depth. On the contrary, the initial dislocations propagate slightly and entangle themselves with a great quantity of new dislocations during the nanoindentation without the water film as shown in Fig. 3(a). The difference in dislocation propagation demonstrates that the existence of the water film probably causes the change in the form of force transfer between different atoms, which will be discussed in depth in the next section.

The dislocation snapshots viewed from the bottom and front of the Cu workpiece with different water film thickness are presented in Fig. 4. Observed from the bottom view, the dislocation bounding the stacking fault atoms looks like a flower. Similar dislocation structures were found by Ziegenhain et al. in nanoindentation of FCC metals;^35,37 also, Gao et al. investigated the defect formation at various stages of the indentation of iron (BCC metal) and showed analogous dislocations.¹⁵ When the indentation depth exceeds a value of around h = 0.8 nm, the load–indentation depth curves transform into the strain burst producing the obvious stress fluctuation shown in Fig. 2. As a result, a large number of new dislocations nucleate and then they interact and entangle with each other. Thus many dislocations move from the bottom of the indenter to a deeper position in the Cu substrate along the {111} slip planes. At the same time, the interaction between dislocations promotes the dislocation loop to form and move away from the indentation, as shown in Fig. 4. We also find that the increase of the water film thickness leads to the dislocations further generating and extending in the Cu substrate, whereas, detailed comparison shows that the increase rate of dislocation gradually slows down with the thickening of the water film. For instance, the difference in dislocation structure becomes very small as the water film overwhelms the indenter (H ≥ 3 nm), as shown in Fig. S1 (ESI†).

Fig. 4 Snapshots of dislocation evolution in the plastic region viewed from the bottom (above) and front (below), under different water film thicknesses (H): (a) no water, (b) H = 1 nm, (c) H = 2 nm, and (d) H = 3 nm. Red represents the surface and dislocation atoms and blue represents stack faults.

The aforementioned characteristics of dislocation in monocrystalline Cu are in agreement with other simulation results reported in the literature, such as the nucleation of a new dislocation,^15,35 the formation of a dislocation loop,^1,37 and the development of the defect structure on {111} fault planes.¹⁴ Here, particularly worth mentioning is that the formation and movement of the dislocation loop are not perfectly symmetric in this simulation, especially under a thicker water film and larger indentation. However, the indenter is perfectly spherical and the load is symmetric in all loading directions. This symmetry bifurcation should be attributed to the stochastic nature of nucleating events at the beginning of the strain burst as explained by Liang et al.¹⁴

To further reveal the effect of the water film on the plastic properties of monocrystalline Cu, the dislocation line length is introduced to describe the dislocation density in a certain volume in Fig. 5. It can be seen that the dislocation line length increases with the indentation depth, and also increases in proportion to the thickness of the water film, which is consistent with the dislocation increasing as shown in Fig. 3 and 4. Meanwhile, the further increase in water film thickness (H ≥ 3 nm) has a slight effect on the dislocation line length, consistent with the results in Fig. S4 (ESI†). In detail, the increasing tendency of the dislocation line length in the quasi-elastic regime (indentation depth h < 0.3 nm) and incipient plastic regime (0.3 nm < h < 0.8 nm) seems to be smaller than that in the strain burst regime (h > 0.8 nm). The feature of change in the dislocation line length reflects the evolution of the dislocation microstructure beneath the contact surface.

Fig. 5 Dislocation line length vs. indentation depth under different water film thicknesses (H).

Discussion on the plastic deformation mechanism

It is necessary to discuss the plastic deformation mechanism to illustrate the plastic response of monocrystalline Cu to the nanoindentation process, combined with the above analyses of the load–indentation depth curves and the dislocation evolution under the effect of the water film. Firstly, the interaction force between the indenter and the Cu workpiece is calculated and shown in Fig. 6. In this figure, we can see that when the Cu workpiece surface is covered by the water film, the interaction force between the indenter and monocrystalline Cu exhibits an obvious delay and its value is significantly smaller compared with that of the nanoindentation without the water film. The increase in the water film thickness results in the enhancement of the corresponding indentation depth at which the first nonzero interaction force occurs, but weakens the interaction force between the indenter and monocrystalline Cu at the same indentation depth.

Fig. 6 The interaction force between the indenter and monocrystalline Cu with different water film thickness (H). The insets show the partial configuration around the indenter for the water film thicknesses of H = 2 nm with various indentation depths. Color coding: grey, C atoms; red, O atoms; white, H atoms; brown, Cu atoms.

In addition, the partial configurations around the indenter for the simulation system with a water film thickness of H = 2 nm are extracted in Fig. 6, and the number of water molecules inside the indentation is also calculated and shown in Fig. 7. Here, when the coordination of the oxygen atom is located in the indentation, the water molecule is considered to be inside the indentation, otherwise the water molecule is outside the indentation. The insets indicate that at the early stage of nanoindentation a great quantity of water molecules occupy a large space between the indenter and the Cu workpiece, which is enough to prevent the indenter from interacting with the Cu workpiece. Gradually, a part of the water molecules between the indenter and the Cu surface are pressed into the indentation, and there are more water molecules to be pressed into the indentation when the water film thickness increases. Thus, the number of water molecules inside the indentation increases quickly with the increase of the indentation depth and water film thickness, as shown in Fig. 7. Therefore, the interaction force between the indenter and the Cu workpiece still remains at zero even when the indentation depth reaches h = 0.6 nm. Then, when the load of the indenter becomes large enough, the penetration of water molecules around the indenter into the indentation becomes difficult. Thus, the increase in the number of water molecules inside the indentation slows down, and the water molecules already inside the indentation are dispersed, as shown in Fig. 7 and the insets in Fig. 6, causing the interaction between the indenter and the Cu workpiece to start to increase (see Fig. 6). In addition, the increasing trend of water molecule numbers with water film thickness becomes gentle once the thickness is greater than or equal to 3 nm. This is mainly attributed to the tiny or constant increase in the interactive area of the indenter with the water film when the indenter is overwhelmed by the water film, which induces a decreased difference in the Cu–indenter interaction force (Fig. 6).

Fig. 7 Number of water molecules inside the indentation under different water film thicknesses (H).

All these findings suggest that the water film has a seriously impeding effect on the contact between the indenter and monocrystalline Cu. In general, we can infer from the impeding effect of the water film that the indentation should be smaller and the atomic defects beneath the indenter should be lesser in comparison with the nanoindentation without the water film. However, this inference is contrary to the facts illustrated in Fig. 2–5. Furthermore, the interaction force between the indenter and the water film and that between the Cu workpiece and the water film are calculated and shown in Fig. S2 and S3 (ESI†). It can be seen that the two interaction forces manifest a very approximate tendency with the varying indentation depth, and also the low relative error of the two interaction forces (Table S2 and Fig. S4, ESI†) means that the water film undoubtedly plays an important role in the force delivery from the load of the indenter to the plastic deformation of the Cu substrate.

Thus, in order to further reveal the role of the water film in the nanoindentation process, the interaction force between the indenter and the water molecules inside and outside the indentation is calculated as shown in Fig. 8 and 9. As shown in Fig. 8, the interaction force between the indenter and the water molecules inside the indentation exhibits a linear increase with the indentation depth increasing, and is almost free of the water film thickness before the indentation reaches h = 0.8 nm. Meanwhile, the interaction force between the indenter and the water molecules outside the indentation increases from a large value before its subsequent decrease. Actually, the increase of the two interaction forces is accompanied by the nucleation and propagation of a large amount of dislocations, especially under conditions of a thicker water film, as shown in Fig. 3. Therefore, at the early stage of the plastic deformation, these water molecules beneath the indenter, acting as a medium of force delivery, transmit their force stemming from the indenter to the Cu workpiece, though there is no direct contact between the indenter and the Cu workpiece.

Fig. 8 The interaction force between the indenter and the water molecules inside the indentation.

Fig. 9 The interaction force between the indenter and the water molecules outside the indentation.

As a consequence, with the continuous penetrating of the indenter, more and more dislocations nucleate and grow under the indenter, leading to larger plastic deformation of the Cu substrate as shown in Fig. 2–5. On the other hand, those water molecules outside the indentation also transmit the force to the Cu surface around the indentation, which blocks the dislocation propagation from the subsurface to the surface but enhances the dislocation propagation in the inner substrate. Therefore, there are large differences in the process of dislocation propagation among these nanoindentations with different water film thicknesses as illustrated in Fig. 3.

With the continuing penetration of the indenter into the Cu workpiece, the contact between the indenter and the water molecules outside the indentation decreases, resulting in the decrease of their interaction force shown in Fig. 9. At the same time, a great amount of dislocations nucleate and interact with themselves, causing the increase of the load, which disperses some water molecules inside the indentation into the space between the deformed Cu atoms.

Hence, the interaction force between the indenter and the water molecules decreases after a gradual inflection point as shown in Fig. 8, whereas the direct contact between the indenter and the Cu atoms increases. It is notable that the increasing tendency of the interaction force becomes slow when the water film is thicker than 3 nm, which validates these results as shown in Fig. 5–7. Based on these results, we can easily conclude that the water film indeed facilitates the plastic deformation through the force delivery.

Conclusion

In this work, the effect of the water film, covering the monocrystalline Cu (001) surface, on the plastic deformation behavior is studied using MD simulations. We can draw the conclusion that the water film has an important influence on the incipient plasticity of monocrystalline Cu, affecting the load–indentation depth curves and dislocation structure. Compared with the nanoindentation without the water film, the load–indentation depth curves show a strongly fluctuant characteristic and a larger load force at the same indentation depth for the nanoindentation with the water film. The water film facilitates the sufficient propagation of the initial Shockley pair at the same depth, whereas the initial dislocations propagate restrictedly and entangle themselves with a great quantity of new dislocations during the nanoindentation without the water film. When the indentation depth exceeds a value of approximately h = 0.8 nm, the water film facilitates a large number of dislocations to move from the bottom of the indenter to a deeper position in the Cu substrate along the {111} slip planes, which is inconsistent with the nanoindentation without the water film. The change in the dislocation line length quantitatively reflects the evolution of the dislocation structure.

Furthermore, the plastic deformation mechanism is discussed to illustrate the plastic response of monocrystalline Cu to the nanoindentation process by analyzing the interaction force. With the increase of the water film thickness, the interaction force between the indenter and monocrystalline Cu exhibits an obvious delay and its value is significantly smaller compared with the nanoindentation without the water film, suggesting that the water film plays an important role in the force delivery from the load of the indenter to the deformation of the Cu substrate. At an early stage of plasticity, these water molecules beneath the indenter transmit the force stemming from the indenter to the Cu workpiece, leading to larger plastic deformation of the Cu substrate. Meanwhile, those water molecules outside the indentation also transmit the force to the Cu surface around the indentation, blocking the dislocation propagation from the inner substrate to the surface but facilitating the dislocation propagation into the deeper substrate. Hence, the water film indeed facilitates the plastic deformation of monocrystalline Cu through the force delivery. However, the effect of the water film on the nanoindentation behavior of the Cu substrate tends to be steady rather than increase continuously as the thickness is large enough, such as the water film overwhelming the indenter. It is worthy to mention that the load rate or indentation velocity is also an important factor influencing the nanoindentation property of the material under the existence of the water film, and we will try our best to study this aspect in the future. Based on this, it is helpful for us to more thoroughly understand the plastic deformation mechanism of nanomaterials under liquid or humid conditions.

Acknowledgements

This work was supported by the National Natural Science Foundation of China [grant numbers 51375364, 51375359].

References

1. G. Z. Voyiadjis and M. Yaghoobi, Mater. Sci. Eng., A, 2015, 634, 20–31.
2. L. Zhang, H. Zhao, L. Dai, Y. Yang, X. Du, P. Tang and L. Zhang, RSC Adv., 2015, 5, 12678–12685.
3. P. Hansson, Procedia Mater. Sci., 2014, 3, 1093–1098.
4. L. Li, W. Song, M. Xu, A. Ovcharenko and G. Zhang, Comput. Mater. Sci., 2015, 98, 105–111.
5. A. B. Mann and J. B. Pethica, Langmuir, 1996, 12, 4583–4586.
6. W. C. Oliver and G. M. Pharr, J. Mater. Res., 1992, 7, 1564–1583.
7. S. Pathak and S. R. Kalidindi, Mater. Sci. Eng., R, 2015, 91, 1–36.
8. D. A. Lucca, K. Herrmann and M. J. Klopfstein, CIRP Ann.–Manuf. Technol., 2010, 59, 803–819.
9. J. R. Morris, H. Bei, G. M. Pharr and E. P. George, Phys. Rev. Lett., 2011, 106, 165502.
10. D. Chrobak, N. Tymiak, A. Beaber, O. Ugurlu, W. W. Gerberich and R. Nowak, Nat. Nanotechnol., 2010, 6, 480–484.
11. V. Maier, K. Durst, J. Mueller, B. Backes, H. W. Höppel and M. Göken, J. Mater. Res., 2011, 26, 1421–1430.
12. S. Yang, Y. W. Zhang and K. Zeng, J. Appl. Phys., 2004, 95, 3655–3666.
13. B. Yang, B. Zheng, X. Hu, K. Zhang, Y. Li, P. He and Z. Yue, Comput. Mater. Sci., 2016, 114, 172–177.
14. H. Y. Liang, C. H. Woo, H. Huang, A. H. W. Ngan and T. X. Yu, Philos. Mag., 2003, 83, 3609–3622.
15. Y. Gao, C. J. Ruestes and H. M. Urbassek, Comput. Mater. Sci., 2014, 90, 232–240.
16. D. Saraev and R. Miller, Acta Mater., 2006, 54, 33–45.
17. K. Sun, W. Shen and L. Ma, Comput. Mater. Sci., 2014, 81, 226–232.
18. Surface Effects in Crystal Plasticity, ed. R. M. Latanision and J. T. Fourier, Noordorf, Leyden, 1977, Nano Advanced Study Institutes Series E; Applied Science, No. 17.
19. S. V. Hainsworth and T. F. Page, J. Mater. Sci., 1994, 29, 5529–5540.
20. S. V. Hainsworth and T. F. Page, Surf. Coat. Technol., 1994, 68, 571–575.
21. A. B. Mann, J. B. Pethica, W. D. Nix and S. Tomiya, in Thin Films: Stresses and Mechanical Properties, V, ed. S. P. Baker, P. Børgesen, P. H. Townsend, C. A. Ross and C. A. Volkert, Materials Research Society, Pittsburgh, PA, 1995, vol. 356, p. 271.
22. S. Plimpton, J. Comput. Phys., 1995, 117, 1–19.
23. Y. Mishin, M. J. Mehl, D. A. Papaconstantopoulos, A. F. Voter and J. D. Kress, Phys. Rev. B: Condens. Matter Mater. Phys., 2001, 63, 224106.
24. J. Ren, J. Zhao, Z. Dong and P. Liu, Appl. Surf. Sci., 2015, 346, 84–98.
25. P. Z. Zhu, Y. Z. Hu, T. B. Ma and H. Wang, Appl. Surf. Sci., 2010, 256, 7160–7165.
26. H. M. Khan and S. G. Kim, J. Mech. Sci. Technol., 2011, 25, 2111–2120.
27. P. Morse, Phys. Rev., 1929, 34, 57–64.
28. J. L. F. Abascal and C. Vega, J. Chem. Phys., 2005, 123, 234505.
29. D. Boda and D. Henderson, Mol. Phys., 2008, 106, 2367–2370.
30. A. K. Al-Matar and D. A. Rockstraw, J. Comput. Chem., 2003, 25, 660–668.
31. T. Werder, J. H. Walther, R. L. Jaffe, T. Halicioglu and P. Koumoutsakos, J. Phys. Chem. B, 2003, 107, 1345–1352.
32. C. L. Kelchner, S. J. Plimpton and J. C. Hamilton, Phys. Rev. B: Condens. Matter Mater. Phys., 1998, 58, 11085–11088.
33. A. Stukowski and K. Albe, Modell. Simul. Mater. Sci. Eng., 2010, 18, 085001.
34. A. Stukowski, Modell. Simul. Mater. Sci. Eng., 2010, 18, 015012.
35. G. Ziegenhain, H. M. Urbassek and A. Hartmaier, J. Appl. Phys., 2010, 107, 061807.
36. B. Kracke and B. Damaschke, Appl. Phys. Lett., 2000, 77, 361–363.
37. G. Ziegenhain, A. Hartmaier and H. M. Urbassek, J. Mech. Phys. Solids, 2009, 57, 1514–1526.

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Footnote

† Electronic supplementary information (ESI) available: Interaction force between monocrystalline Cu and a water film (Fig. S1), and that between an indenter and a water film (Fig. S2), and the relative error of the two interaction forces (Table S1 and Fig. S3). See DOI: 10.1039/c6ra17126e

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