(0001) Interfaces: A

Sep 21, 2010 - Advances in atomic-scale tribological mechanisms of solid interfaces. Jingyan Nian , Yifan Si , Zhiguang Guo. Tribology International 2...
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J. Phys. Chem. C 2010, 114, 17709–17719

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Slip Mechanisms of Hydroxylated r-Al2O3 (0001)/(0001) Interfaces: A First-Principles Molecular Dynamics Study Carolyn J. Carkner and Nicholas J. Mosey* Department of Chemistry, Queen’s UniVersity, Kingston, ON, Canada K7L 3N6 ReceiVed: June 16, 2010; ReVised Manuscript ReceiVed: August 24, 2010

First-principles molecular dynamics simulations are used to explore sliding along interfaces composed of different forms of hydroxylated (0001)/(0001) interfaces of R-alumina (Al2O3). The results demonstrate that a fully hydroxylated form of the interface is insensitive to changes in normal pressure, P. Meanwhile, partially hydroxylated interfaces undergo changes in structure when P is increased. The different interface structures exhibit different sliding mechanisms. The fully hydroxylated interface exhibits smooth sliding with low critical shear stresses. At low P, the partially hydroxylated interface takes part in a slip mechanism that is dominated by changes in hydrogen bonding across the interface, leading to larger critical shear stresses than observed for the fully hydroxylated system. At high P, the partially hydroxylated interface undergoes slip through a process involving the formation and dissociation of Al-O bonds across the interface, leading to high critical shear stresses and irreversibly changing the interface structure. The differences in the slip mechanisms for these systems are rationalized in terms of the electronic structures of the interfaces. As a whole, the study provides detailed insight regarding the relationship between interface structure, friction, and wear, and highlights the importance of fully chemically passivating surfaces to minimize friction and wear. I. Introduction Understanding the structural and chemical details of interfaces, and how these details change over time, is important in many areas of science and technology. For example, the conduction of heat and electricity in nanoscopic junctions is strongly affected by the chemical details of the interface.1,2 In addition, processes such as crack propagation and slip are affected by the structure of grain boundaries.3 Tribology, the study of friction and wear, is another area that is highly dependent on interface structure, which affects the ability of surfaces to slide past each other. For example, the relative orientations of the surfaces forming a contact significantly impact coefficients of friction.4,5 In addition, sliding-induced changes in the interface structure arising from processes ranging from plastic deformation to the formation of protective tribofilms can lead to effects ranging from large degrees of wear to wear inhibition.6-11 To better control friction and wear, and thus minimize the substantial economic and environmental impacts12 of these phenomena, it is necessary to have a more detailed understanding of the atomic-level mechanisms associated with sliding. Experiments aimed at understanding fundamental details of friction are often performed by using techniques such as the surface force apparatus,13 scanning probe microscopy,14,15 atomic force microscopy (AFM),16 and the quartz crystal microbalance.17 Such experiments have shed light on many fundamental aspects of friction. However, these techniques do not provide sufficient resolution in size and time to identify the specific atomic-level processes occurring when systems slide past one another. These processes can be very complex, involving changes in the chemical structure of the interface, and may have significant ramifications regarding friction and wear. * To whom correspondence should be addressed. E-mail: nicholas. [email protected].

Chemical simulation is a powerful alternative to experiment for modeling sliding contacts with atomic resolution, and has played a key role in understanding fundamental aspects of friction and lubrication. Numerous simulations of sliding contacts using force-field (FF) based molecular dynamics (MD) simulations have been reported.18-20 While these methods have provided detailed insights regarding aspects such as the relationship between friction and energy dissipation through hysteresis,21-23 the effects of different chemical structures on friction,24-26 and the relationship between third-body molecules and tribological processes,27,28 they are generally unable to describe the changes in chemical bonding that occur within sliding contacts in the presence of strong chemical interactions, or during processes such as wear. MD simulations employing reactive FFs have been employed for this purpose, and have shed light on details such as tribochemical processes,29 and the relationship between friction anisotropy, wear, and surface roughness.30 Recently, MD simulations of tribochemical processes using tight-binding density functional theory methods have also been reported, demonstrating how Mo-based nanostructures and molecules decompose to form protective films,31 how MoS2 sheets reduce friction within contacts composed of iron,32 and how conditions within sliding contacts can induce tribochemical transformations in phosphorus-based antiwear additives.33 To simulate the full range of chemical processes that can occur during sliding events, it is necessary to employ potentials based on a quantum mechanical treatment of the electronic structure;so-called quantum chemical methods. These methods have been used in the context of slip and shear, relying primarily on static calculations involving geometry optimizations and potential energy surface scans.34 These approaches have provided insight into many details associated with slip including the identification of slip directions in materials,35,36 the evaluation of shear strengths37,38 and friction coefficients,39,40 the effects of tribochemical reactions on friction and slip,41-43 and the

10.1021/jp1055478  2010 American Chemical Society Published on Web 09/21/2010

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Figure 1. Optimized structures of (a) the full-OH system, (b) the partial-OH model in the low-pressure (LP) phase, and (c) the partial-OH model in the high-pressure (HP) phase. Al, O, and H atoms are represented by large purple, small red, and smaller green spheres, respectively.

relationship between slip and the electronic structure across the interface.44,45 Recently, we reported first-principles MD (FPMD) simulations of hydroxylated (0001)/(0001) R-Al2O3 (alumina) interfaces which showed that bonding across the interface can have a significant impact on static friction.46 In the present study, we expand on that work by using FPMD simulations to explore the slip mechanisms of different forms of (0001)/(0001) R-Al2O3 interfaces. These interfaces are of interest given the widespread use of aluminum in technological applications, where surfaces are nearly always oxidized to alumina, which then reacts with water. Previous force-field based MD simulations of similar systems have shed light on details related to the friction coefficient and energy dissipation;21,47-50 however, those studies were not performed in a manner that accounts for changes in chemical bonding during sliding. The use of first-principles methods in the present study permits an investigation of the electronic structure during sliding, and allows for changes in bonding to occur. The results demonstrate that capturing such changes is necessary to provide a complete description of the system. Specifically, fully hydroxylated interfaces undergo smooth, wearless sliding with low friction. Models composed of partially hydroxylated interfaces exhibit slip mechanisms involving the formation and dissociation of bonds across the interface, leading to higher friction and wear. These differences are interpreted in terms of the strengths of the interactions across the interface, which is supported by analysis of the electronic structure. As a whole, these results suggest that fully hydroxylating the surfaces, or fully passivating the surfaces with other chemical groups, can be useful in the context of minimizing wear and friction. Although these results were obtained for specific models of alumina, they likely also apply to other materials with the corundum structure, e.g., Fe2O3, Cr2O3, and Ti2O3, as well as other hydroxylated interfaces in general. The remainder of this paper is as follows. The model systems and methods used are discussed in section II. The results are presented in section III, with investigations of the structure of the interface at different normal loads, the shear stresses associated with the sliding, the slip mechanisms, and the electronic structures of the interface. These results are discussed in section IV, and conclusions are presented in section V. II. Methods and Model Systems The simulations were performed with three different models for the hydroxylated (0001)/(0001) Al2O3 interface. The first model, referred to as “full-OH”, was formed by cleaving bulk Al2O3 (alumina) to yield two Al-terminated (0001) surfaces, and replacing all terminal Al3+ ions with three protons. This model has been employed previously in force-field based MD simulations of friction and slip on hydroxylated (0001)/(0001) Al2O3

interfaces.21,47,49,50 The optimized structure of this model is shown in Figure 1a. The second model explored will be designated “partial-OH”. This model was formed by cleaving bulk Al2O3 to yield two Al-terminated surfaces, adding an OH group to each Al3+ ion, and a proton to the next subsurface oxygen along [101j0]. This structure corresponds to the preferred form of a monolayer of water adsorbed dissociatively on an Al-terminated (0001) Al2O3 surface at monolayer coverages.51 This structure is shown in Figure 1b, and was found to exist when partial-OH was subjected to normal pressures, P, below 4 GPa. As such, it will be designated the low-pressure (LP) phase. For P > 4 GPa, the partial-OH system adopted the structure shown in Figure 1c, where each hydroxyl group has abstracted a proton from the opposite side of the interface, yielding two surfaces that are each covered by a monolayer of water. This structure will be designated the high-pressure (HP) phase. In all cases, the simulations were performed using 2 × 2 × 1 representations of the hexagonal unit cells for these systems, which were then treated with 3-D periodic boundary conditions. Examination of the optimized structures of the interface, as well as the structure of the systems during the MD simulations, showed that model systems are sufficiently thick to describe the behavior of the system during slip. Specifically, the distances between the interlayer distances between the outermost five atomic layers in each model exhibit values that remain within 0.025 Å or better of corresponding interlayer distances for bulk Al2O3, with only those atomic layers closer to the interface being significantly affected by hydroxylation and shear/slip (see the Supporting Information). Geometry optimizations and first-principles molecular dynamics (FPMD) simulations were performed with a version of the Quantum-Espresso software package that we modified to permit the application of constant strain and stress rates.52 The electronic structure was evaluated with density functional theory53,54 by using the exchange-correlation functional of Perdew, Burke, and Ernzerhof.55 The valence states were represented as plane waves expanded at the Γ-point to a kinetic energy cutoff of 30 Ry. The core states were represented by ultrasoft pseudopotentials56 using a kinetic energy cutoff of 180 Ry for the augmentation charges. The constant cutoff approach of Bernasconi et al.57 was used in all FPMD simulations. Tests showed that this methodology accurately reproduces previously reported experimental and calculated data regarding the crystal structure of Al2O3 (this work: |a| ) 4.792 Å, |c| ) 13.071 Å; experiment:58 |a| ) 4.759 Å, |c| ) 12.991 Å), (0001)-Al2O3 surface energy (this work: γ ) 1.58 J/m2; previous calculation:59 γ ) 1.49 J/m2), dissociation energy of H2O on (0001)Al2O3 (this work: 1.38 eV; previous calculation:60 1.44 eV), and Young’s modulus of Al2O3 along [0001] (this work: G ) 402 GPa; experiment:61 G ) 345 to 409 GPa). The dynamics were

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J. Phys. Chem. C, Vol. 114, No. 41, 2010 17711 on the (0001) plane of bulk Al2O3. The shear simulations were performed at values of P ranging from 0 to 10 GPa, which were maintained by allowing the height of the simulation cell to change according to PR dynamics. III. Results

Figure 2. General outline of the processes used to study compression and shear. Compression occurs by increasing the normal pressure, P, along the [0001] direction at a rate, Prate, of 5.0 GPa/ps. Shear is modeled by uniformly shearing the simulation cell along the [213j0] direction at a strain rate, δrate, of 1.0 Å/ps. δ is the shear distance and corresponds to the distance the top of the simulation cell has moved along the shear direction relative to its initial position and t represents time.

performed within the Car-Parrinello formalism,62 using a time step of 5.0 au (0.121 fs, 8268 time steps per ps of simulation) and an orbital mass of 400.0 au. The systems were equilibrated at 300 K with Nose-Hoover thermostats.63-65 Temperature controls were not used during the production portions of the simulations. Analysis of the temperature during the simulations indicated that the system temperature increased by at most 50 K prior to slip in the absence of temperature controls (see the Supporting Information). The systems were compressed and sheared during FPMD simulations to study their interface structures and shear strengths. Figure 2 provides a general outline of the compression and shear processes, and also provides definitions of key quantities. Compression was modeled by performing simulations in which the systems were subjected to increasing P along [0001]. This was achieved by employing the Parrinello-Rahman (PR) equations of motion66 to permit variations in the size of the simulation cell along this direction and changing the goal value of the σ33 component of the stress tensor at each step of the simulation as needed to increase P at a rate of 5.0 GPa/ps. The systems were sheared along [213j0] by altering the x and y components of c such that the top of the simulation cell moved along this direction at a rate of 1.0 Å/ps according to Lees-Edwards boundary conditions.67 This direction was selected based on experiments68 indicating that it is the preferred basal slip direction in bulk Al2O3 and potential energy scans

The calculations illustrate the different slip mechanisms that occur within the modeled hydroxylated (0001)/(0001) Al2O3 interfaces. The structures of these interfaces at different P are considered in section a. The shear stresses required to induce slip along these interfaces at different P are examined in section b. The structures of the systems during sliding are discussed in section c. The electronic structures of the interfaces at key points during the slip processes are explored in section d. a. Interface Structure during Compression. The full-OH and partial-OH systems were compressed by performing MD simulations in which P was increased from 0 to 20 GPa at a rate of 5 GPa/ps. This particular rate of compression was the slowest that could be reasonably considered with the available computational resources and is estimated to be approximately 500 times faster than compression rates experienced during actual asperity contacts, where typical sliding speeds of ∼10 m/s, asperity separations of ∼10 nm, and theoretical yield strengths of ∼10 GPa yield a compression rate of ∼10 GPa/ns during asperity collisions. Additional calculations showed that the compressive strength of bulk Al2O3 is ∼90 GPa, while the shear strength is in the range of 20 to 30 GPa, depending on the normal load. Thus, examining P ) 0 to 20 GPa covers a range of P that can be reasonably expected to be experienced at small length scales during asperity collisions. The changes in thickness of the simulation cells as a function of P are shown in Figure 3a. The data show that the thickness of the full-OH system decreases linearly with P, yielding an elastic modulus along [0001], E, of 252 GPa. By comparison, analogous simulations yield E ) 443 GPa for bulk alumina. The large modulus likely arises from repulsive interactions between the hydrogen atoms on either side of the interface. The simulations also showed that the structure of the full-OH interface is insensitive to P with no bonds forming or dissociating during compression, which is consistent with the linear relationship between thickness and P. The data for the partialOH system exhibit a break at P ≈ 4 GPa, which is due to the transition from the LP to HP phases shown in Figure 1, panels

Figure 3. (a) Simulation cell thickness versus pressure, P, for the full-OH and partial-OH systems. The thickness of the full-OH system decreases linearly with increasing P. The data for the partial-OH system exhibit a break at P ≈ 4 GPa and can be separated into two roughly linear regimes, corresponding to the LP and HP phases. The elastic moduli along [0001], E, are given in each regime. (b) Energy versus thickness for the full-OH system and the partial-OH system in the LP and HP phases. The energies are given relative to the most stable forms of the partial-OH and full-OH systems. The data show that the LP phase of partial-OH is more stable than the HP phase for thicknesses greater than ∼15.75 Å. For thicknesses below ∼15.75 Å, the LP and HP phase are equivalent.

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Figure 4. Shear stress, τ, versus shear distance, δ, for (a) the full-OH and (b) the partial-OH models with P ) 0, 2, 4, 6, 8, and 10 GPa. The values of τ for the full-OH system are low over the course of the entire sliding distance and do not differ significantly with P. The data for the partial-OH model exhibit a significant dependence on P. These differences are associated with the differences in the interface structure of the LP and HP phases of partial-OH. For P e 4 GPa, the interface is supported by hydrogen bonds during the initial phases of shearing, and the values of τ are comparatively low and do not exhibit a significant dependence on P. For P g 6 GPa, Al-O bonds form across the interface, leading to an apparent dependence on P, with the systems have large shear strengths of 5.7, 10.4, and 15.1 GPa for the simulations at P ) 6, 8, and 10 GPa, respectively.

b and c, respectively. Within each of these two phases, the thickness changes roughly linearly with P, yielding moduli of 35 and 304 GPa for the LP and HP phases, respectively. The large differences in these moduli can be attributed to the interface structure. In the LP phase, P is supported by hydrogen bonds, which are relatively compliant during compression. The load is also supported by O-H interactions in the HP phase; however, in this case, the interactions are between the hydrogen atoms in water molecules adsorbed on one side of the interface and subsurface oxygens within the Al2O3 slab on the opposite side of the interface. Since alumina is not very compliant, this results in a much higher modulus than the LP phase. These results demonstrate that changes in the interface structure can have significant effects on mechanical properties. The energies of the optimized structures of the full-OH and partial-OH systems are given in Figure 3b as a function of cell thickness. The results are consistent with those of the MD simulations given in Figure 3a. Specifically, the full-OH system is most stable at a thickness of 13.75 Å, is weakly bound with an interface energy of 0.237 J/m2, and is strongly repulsive upon compression, which is consistent with the high compressive modulus. Data are given for both the LP and HP phases of the partial-OH system. The LP phase has an energetically preferred thickness of 16.75 Å and is lower in energy than the HP phase for larger thicknesses. The LP phase exhibits a slow increase in energy upon compression from its minimum energy thickness, which is consistent with the low modulus for this system mentioned above. Upon compression to 15.50 Å, the data for the LP phase overlap with those for the HP phase, which is consistent with the compression-induced transformation between these phases during the MD simulations. The HP phase exhibits an energetic minimum at a thickness of 15.25 Å and is strongly repulsive for lower thicknesses. This is consistent with the large elastic modulus for this system. The attractive interactions across the interface for the HP phase are stronger than those for the LP phase, with the phases exhibiting interface energies of 0.794 and 0.396 J/m2, respectively. This difference arises because the HP phase has 16 hydrogen bonds across the interface while the LP phase has only 8 hydrogen bonds. b. Shear Stresses. The full-OH and partial-OH systems were sheared as described in section II with P ) 0, 2, 4, 6, 8, and 10 GPa. These values of P are sufficient to study the behavior of

both the LP and HP phases of partial-OH and will shed light on the effects of normal load on sliding and shear within the full-OH system. The systems were sheared along the [213j0] direction, which led to sliding along the interface spanning the (0001) plane. The shear stresses, τ, along the [213j0] direction are plotted in Figure 4 as a function of the shear distance, δ, where δ is defined as the distance the top of the simulation cell has moved along [213j0] relative to its initial position. Plots of τ versus δ are given in Figure 4a for the full-OH system. A close examination of the data shows that τ tends to increase linearly over small ranges of δ before reaching a maximum value, dropping quickly, and increasing linearly again. This is evident from the data obtained with P ) 10 GPa, where τ exhibits peaks at δ ≈ 1.0, 2.8, and 4.5 Å. The structural changes responsible for this behavior are discussed in later sections. Despite the periodic increases in τ, the data suggest that sliding on the full-OH interface occurs easily for all P, with τ < 4 GPa over the entire range of δ considered. The data for the partial-OH systems are shown in Figure 4b. The systems in the LP phase, i.e., when P e 4 GPa, all behave similarly, with each system exhibiting a linear increase in τ during the initial stages of shear before reaching a maximum shear stress, corresponding to a shear strength, τc, of ∼3 GPa when δ ≈ 1.0 Å. After overcoming this maximum, each system in the LP phase exhibits τ that oscillates around 0 GPa before increasing linearly again when δ ≈ 2.5 Å. A maximum value of τ ) 5 GPa is reached when δ ≈ 4.0 Å. Each system in the HP phase, i.e., when P g 6 GPa, also exhibits a linear increase in τ from the onset of shear before reaching a maximum value and decreasing suddenly. However, the values of τc are much larger than those for the systems in the LP phase, and the sudden drops in τ are more apparent. In addition, the values of τc for the HP phase varied with P, with τc ) 5.7, 10.4, and 15.1 GPa when P ) 6, 8, and 10 GPa, respectively. The differences between the full-OH system, the partial-OH system in the LP phase, and the partial-OH system in the HP phase demonstrate that differences in interface structure can have significant effects on τ. These differences can be understood in terms of the atomic and electronic structures of these interfaces, and changes to these structures through the formation and

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Figure 5. Structures of the full-OH and partial-OH models during shear. Al, O, and H atoms are designated as large purple, small red, and smaller green spheres, respectively. Oxygen atoms directly above and below the interface are designated as orange and blue spheres, respectively, in panels b, c, and d. (a) The full-OH system with P ) 0 GPa at δ ) 0.0, 2.0, and 4.0 Å. This structure exhibits no changes in interface structure during sliding. (b) Partial-OH with P ) 0 GPa at δ ) 0.0, 1.6, and 4.7 Å. The structures exhibit changes in the interactions across the interface, with a change in hydrogen bonding occurring between δ ) 0.0 and 1.6 Å, and the formation of Al-O bonds between δ ) 1.6 and 4.7 Å. (c) Oxygen and hydrogen atoms directly above and below the interface in the partial-OH model with P ) 0 GPa at δ ) 0.0, 1.6, and 4.7 Å. These structures illustrate the changes in hydrogen bonding across the interface with shear. (d) Partial-OH with P ) 0 GPa at δ ) 0.0, 3.9, and 5.2 Å. The structures show that Al-O bonds form during shear between δ ) 0.0 and 3.9 Å, these bonds then dissociate between δ ) 3.9 and 5.2 Å, with many of the oxygen atoms initially bonded to the upper surface before slip being bonded to the lower surface after slip and vice versa. Note that each structure represents a simulation cell that has been repeated twice along the a and b lattice vectors.

dissociation of chemical bonds during sliding, which are discussed in the following sections. c. Atomic Structure during Shear. Structures representing the full-OH model at different stages of shear with P ) 0 GPa are shown in Figure 5a. Analogous structures were observed in simulations of this system performed with higher values of P. As a whole, the structures indicate that a separation exists between the two sides of the interface during sliding. This allows the system to slide smoothly, which is consistent with the low values of τ in Figure 4a. The main structural changes that occurred are due to reorientations of the OH groups. Specifically, OH groups pointing inward from opposite sides of the interface

repel each other and inhibit sliding. To overcome this repulsion, and allow sliding to continue, these inward-pointing OH groups reorient to lie parallel to the plane of the interface. No other changes in the structure of the interface occurred during sliding. Structures of the partial-OH LP phase at different stages of shear with P ) 0 GPa are shown in Figure 5b. Similar structures were observed during the simulations with P ) 2 and 4 GPa. The structures show that the two sides of the interface interact through hydrogen bonds until δ ) 4.7 Å, when Al-O bonds form across the interface. The changes in the hydrogen bonds are more clearly illustrated by Figure 5c, which plots the OH groups in the interface looking along the [0001j] direction. The

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Figure 6. Changes in Al-O distances as a function of shear distance for the partial-OH system at P ) 10 GPa. (a) Distances between oxygen atoms originally bonded to the upper surface (in orange in Figure 5d) and the Al3+ ions immediately on either side of the interface at P ) 10 GPa. (b) Distances between oxygen atoms originally bonded to the lower surface (in blue in Figure 5d) and the Al3+ ions immediately on either side of the interface at P ) 10 GPa. Collectively, panels a and b demonstrate the formation and dissociation of Al-O bonds across the interface during shear and sliding within the HP phase of partial-OH.

structures show that the hydrogen bonds are initially aligned approximately along the [112j0] direction. A change in the orientation of these bonds occurs upon shearing to δ ) 1.6 Å, with the hydrogen bonds becoming aligned along [011j0]. The change in the orientation occurs through the dissociation of four hydrogen bonds;specifically, those involving a hydrogen atom bonded to the lower surface and an oxygen bonded to the upper surface. The formation of Al-O bonds that occurs at δ ) 4.7 Å involves additional changes in the orientations of the hydrogen bonds, with these bonds exhibiting a “zigzag” structure within the (0001) plane. Structures associated with slip during the simulation of the HP phase with P ) 10 GPa are shown in Figure 5d. As noted above, the optimized structure of the HP phase (Figure 1c) has a monolayer of water molecules on each side of the interface. The structure at δ ) 0.0 Å in Figure 5d shows that proton transfer across the interface occurs at finite temperature, and that the water molecules (or hydroxyl groups) are interdigitated. This allows the terminal oxygen atoms on a given side of the interface to move close to the terminal Al3+ ions on the opposite surface. During shear, this leads to the formation of Al-O bonds across the interface, as shown by the structure with δ ) 3.9 Å. The slip process itself involves the dissociation of the Al-O bonds bridging the interface, which is apparent from the structure in Figure 5d at δ ) 5.2 Å. The formation and dissociation of the Al-O bonds across the interface in the HP phase at P ) 10 GPa irreversibly changed the connectivity of the atoms within the interface. The details of this process are illustrated by Figure 6, panels a and b, which plot the distances between the oxygen atoms within the interface and the Al3+ ions immediately on either side of the interface. The data in Figure 6a correspond to the distances involving oxygen atoms initially bonded to Al3+ ions in the lower surface of the interface. The data show that bonds between these oxygen atoms and the lower surface are present from the onset of shear, with Al-O bonds forming with the upper surface between δ ) 3.0 and 4.0 Å. A total of four bonds were formed, corresponding to one additional bond per Al3+ ion immediately on the upper side of the interface. Analogous results are shown by the data in Figure 6b, which plots the Al-O distances involving the oxygen atoms initially bonded to the upper surface. Overall, these data show that eight additional Al-O bonds were formed, leading to the structure at δ ) 3.9 Å in Figure 5c. These Al-O bonds persisted until slip occurred when δ ) 5.0 Å. At that

point, four Al-O bonds dissociated on either side of the interface. A close examination of the data, however, illustrates a novel process in which most of the oxygen atoms that were initially bonded to the lower surface end up bonded to the upper surface, and vice versa. This is also apparent through a comparison of the structures at δ ) 3.9 and 5.0 Å in Figure 5d, where the oxygens initially bonded to the upper and lower surfaces are designated with different colors. Overall, this demonstrates that the HP phase does not slide through a process that simply involves groups on either side of the interface moving past each other, but rather involves a significant change in the chemical connectivity of the interface. The effects of this slip process on friction and wear are discussed further in section IV. Similar slip mechanisms were observed during the simulations of the HP phase of partial-OH with P ) 6 and 8 GPa, although different numbers of Al-O bonds formed and dissociated during those simulations. The different numbers of Al-O bonds formed when the HP phase of the partial-OH system was sheared at different P is the origin of the different τc reported for these systems in section b. As discussed in a recent study of this system, the differences in the number of bonds formed within the HP phase is not due to a dependence on P, but rather related to the instantaneous structure and dynamics of the system.46 Instead, the main conclusions to be drawn from the simulations of the HP phase of partial-OH is that sliding involves the formation and dissociation of Al-O bonds across the interface. d. Electronic Structure during Shear. The results presented above have focused primarily on mechanical properties and atomic structure. Ultimately, however, the forces required to initiate and maintain sliding depend on the strength of interactions acting across the interface. These interactions depend to a large extent on the distribution of electron density in the system. In addition, changes in the atomic structure of the interface arise from a redistribution of electron density during the formation and dissociation of chemical bonds. In this section, the electronic structures of the different model systems are investigated at different stages of sliding to shed light on the observed shear stresses and slip mechanisms. The valence electron density distribution of the full-OH system is shown in Figure 7a at different stages of shear. The data clearly indicate a lack of electron density across the interface at all values of δ, which indicates a lack of chemical bonding across the interface. This is consistent with the results

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Figure 7. Valence electron densities of the full-OH and partial-OH systems during shear. Al, O, and H atoms are denoted as large purple, small red, and smaller green spheres, respectively. Yellow surfaces correspond to the valence electron density plotted at an isosurface value of 0.05 au. (a) Full-OH system at P ) 0 GPa and δ ) 0.0, 2.0, and 4.0 Å. The plots show a lack of electron density across the slip interface. (b) Partial-OH system at P ) 0 GPa and δ ) 0.0, 1.6, and 4.7 Å. Electron density bridging the interface is evident at δ ) 0.0 and 1.6 Å and corresponds to hydrogen bonding. Electron density corresponding to Al-O bonds spanning the interface is evident at δ ) 4.7 Å. (c) Partial-OH system at P ) 10 GPa and δ ) 0.0, 3.9, and 5.2 Å. Electron density corresponding to hydrogen bonds and Al-O interactions are present across the interface at each shear distance. These results are consistent with the observed slip mechanisms and shear strengths.

presented above, where the full-OH model has a low interface energy, undergoes slip with small applied shear stresses, and does not undergo significant changes in structure during the slip process. Electron density plots for the partial-OH system in the LP phase at P ) 0 GPa are given in Figure 7b. The plots with δ ) 0.0 and 1.6 Å show electron density spanning the interface, which can be correlated with the positions of the hydrogen bonds that were shown above to undergo changes during the slip processes, contributing to the shear strength of the interface. The electron density distribution at δ ) 4.7 Å in Figure 7b is consistent with the formation of Al-O bonds across the interface. The electron density distributions of the partial-OH HP phase at P ) 10 GPa and δ ) 0.0, 3.9, and 5.2 Å are given in Figure 7c. In all cases, substantial electron density extends across the interface, leading to significant attractive (bonding) interactions. The presence of density bridging the interface when δ ) 0.0 Å demonstrates how the formation of Al-O bonds can occur readily within this system, since there are already significant interactions between the Al3+ ions and oxygen atoms involved in the formation of those bonds. The density distributions at δ ) 3.9 and 5.2 Å are consistent with the arrangements of Al-O bonds in Figure 5d, once again confirming the presence of chemical bonds across the interface.

The results presented above shed light on how differences in the structures of hydroxylated (0001)/(0001) interfaces of Al2O3 affect sliding. In what follows, the results are summarized briefly to provide a clear description of the slip mechanisms for each model system. The relationship between these mechanisms and friction and wear are also explored. Such information may be of practical use in the context of lubricating devices containing these types of interfaces. While the results have been obtained through simulations of models derived from Al2O3, it is noted that many other technologically relevant materials including oxides of Ti, V, Cr, and Fe have the same stoichiometry and structure as alumina. In addition, many other materials form hydroxylated interfaces that may undergo similar processes during slip. The data in section IIIb regarding the full-OH system show that τ is low (ranging between 0 and 4 GPa) throughout the range of δ considered, yet exhibits periodic increases and drops. The low values of τ can be understood in terms of the electronic structure, which shows a lack of electron density across the interface, suggesting the absence of strong bonding interactions. Indeed, the slip mechanism for the full-OH system simply involves the reorientation of OH groups on either side of the interface due to repulsive interactions during sliding, as described in section IIIc. These repulsive interactions and subsequent changes in OH group orientation are responsible for the observed increases and decreases in τ for this system. The structural details in Figure 5a indicate that sliding does not alter the chemical connectivity within the slabs forming the interface, and instead the surfaces slide smoothly past each other. This notion is supported by Figure 8a, which plots the average displacements, ∆r, of the Al3+ ions immediately on either side of the interface within the (0001) plane from their positions at the start of the simulation. Under smooth sliding conditions, the ions in the bottom slab should remain at ∆r ) 0 Å, while those in the top slab should be at ∆r ) δ. The data exhibit these relationships, indicating that the full-OH system does indeed undergo smooth sliding at all P considered. The details of the electronic structure show that electron density spans the interface of the LP phase of the partial-OH structure throughout sliding, indicating that chemical interactions holding the interface together may play a role during sliding. These effects are evident from the data in Figure 4b, which show that the LP phases of the partial-OH models exhibit two peaks in τ of ∼3.0 and 5.0 GPa when δ ≈ 1.0 and 4.0 Å. These peaks are larger than those for the full-OH system, where interactions across the interface were minimal, and are associated with the dissociation and reorientation of hydrogen bonds discussed in section IIIc. These results indicate that during the initial stages of shear, the LP phase of partial-OH exhibits a slip mechanism that is dominated by changes in hydrogen bonds across the interface. The shear strain in this regime is accommodated primarily within the interface, and the slabs actually slide smoothly. This is demonstrated by the data in Figure 8b with P e 4 GPa, which show that the ∆r values of the upper and lower slabs follow values consistent with smooth sliding. As noted in section IIIc, the peak in τ at δ ≈ 4.0 Å for partialOH at P ) 0 GPa was followed by the formation of Al-O bonds across the interface (as shown in Figure 5a). The formation of these bonds alters the sliding mechanism to one involving the formation and dissociation of Al-O bonds, as opposed to changes in hydrogen bonding. To explore this process further, the simulations with P ) 0 GPa were continued until δ reached 8.0 Å. The results exhibited a peak of τ ) 6.6

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Figure 8. Average distances, ∆r, of the Al3+ ions immediately above (open symbols) and below (closed symbols) the interface for (a) full-OH and (b) partial-OH with P ) 0, 2, 4, 6, 8, and 10 GPa. Dashed lines are provided to indicate the ideal positions of the ions assuming smooth slip. For both systems, the ideal values for smooth sliding correspond to ∆r ) 0 Å and ∆r ) δ for the ions in the bottom and top layers, respectively. Smooth sliding behavior is exhibited by the full-OH system at all P and partial-OH at P ) 0, 2, and 4 GPa. The partial-OH system at P ) 6, 8, and 10 GPa exhibits deviations from ideally smooth sliding. As discussed in the text, the deviations from ideal behavior for the HP phase at P ) 6 and 8 GPa are due to irreversible changes in the structure of the slabs forming the interface.

Figure 9. (a) Partial-OH LP at P ) 0 GPa and δ ) 8.0 Å. The interface has largely recovered the structure it had prior to the onset of shear. (b) Partial-OH HP at P ) 6 GPa and δ ) 3.4 Å before slip involving the dissociation of Al-O bonds has occurred. (c) Partial-OH HP at P ) 6 GPa and δ ) 4.0 Å after slip involving the dissociation of Al-O bonds has occurred. A comparison of the structures in parts b and c indicates how slip leads to irreversible changes in the positions of the Al3+ ions denoted with arrows. Essentially, the ions marked with the arrows are aligned with each other in part b, but have become separated along the slip direction in part c. Note that each structure represents a simulation cell that has been repeated twice along the a and b lattice vectors.

GPa at δ ≈ 7.2 Å, corresponding to the dissociation of the Al-O bonds. This process yielded an interface structure similar to that of the original partial-OH LP interface (see Figure 9a), suggesting a periodic slip mechanism in which hydrogen bonding dominates in the early stages of sliding, followed by the formation and dissociation of the Al-O bonds, and then returning to a state in which hydrogen bonds are the only interactions present across the interface. The data in section IIId show that significant chemical interactions are present across the interface in the HP phase of partial-OH due to substantial electron density spanning the interface. These interactions lead to the formation and dissociation of Al-O bonds throughout sliding, which is evident from the structures in Figure 5d. The changes in bonding have significant effects on τ, with the HP phase exhibiting τc between 5.7 and 15.1 GPa depending upon the number of Al-O bonds formed across the interface. To further explore sliding along the HP interface of the partial-OH model, the simulation of the HP phase with P ) 10 GPa was continued until δ ) 8.0 Å. The results demonstrated that additional processes involving the formation and dissociation of Al-O bonds across the interface occurred, but did not lead to a structure reminiscent of that observed when δ ) 0.0 Å. As such, the HP phase does not undergo a periodic sliding mechanism that regenerates the initial interface, as in the case of the LP phase, but rather takes part in a sliding mechanism that continually involves the formation and dissociation of Al-O bonds. This inhibits the ability of

the system to undergo smooth sliding, and instead the HP phase exhibits behavior that is consistent with a stick-slip mechanism. This is evident from the data in Figure 8b for P ) 10 GPa, where the ∆r values deviate from those expected for smooth sliding during the “stick” phase before rapidly returning to the ideal values after slip. This behavior is not exhibited for the HP phase at P ) 6 and 8 GPa, where changes in the structure of the slabs lead to deviations from the behavior expected during smooth sliding. These changes in structure are discussed further below. The different interfaces exhibit significantly different shear strengths, with τc ) 2.0 to 4.0 GPa for full-OH, 3.0 to 6.6 GPa for the LP phase of partial-OH, and 5.7 to 15.1 GPa from the HP phase of partial-OH depending on the particular slip event and value of P. The shear strengths are directly related to the friction force, F, with F ) τcA, where A is the cross-sectional area of the interface. On this basis, one can determine that the values of F associated with each interface are ordered as Ffull-OH < Fpartial-OH, LP < Fpartial-OH, HP. This is consistent with recent force-field based MD simulations of hydroxylated (0001)/(0001) Al2O3 interfaces, which show that partial hydroxylation leads to an increase in friction.47,50 Fitting the data obtained in the present study to F ) F0 + µL yields static friction coefficients of µ ) 0.039 and 0.280 for the full-OH and LP phases of the partial-OH system, respectively. A friction coefficient was not obtained for the HP phase of partial-OH, since the data could not be fit accurately to a linear expression due to the variable

Slip Mechanisms of Alumina number of bonds formed across the interface at different P. The friction coefficient of 0.039 for the full-OH system is identical with that reported in earlier force-field based MD simulations.47 No data are available for comparison of the friction coefficient for the LP phase, but it is within the range of coefficients reported for smooth (µ ) 0.08) and rough (µ ) 0.33 to 0.52) alumina surfaces sliding in air.69 In real systems, of course, the specific values of F observed also depend on factors that are not incorporated into these calculations such as the number of asperities in contact and the roughness of the surface. Nonetheless, the predicted trends in F are consistent with the presence and strength of the bonding interactions across the interface, suggesting that one should minimize these interactions through chemical modification of the surface. In the present study, this is achieved through full hydroxylation, which limits the ability of the system to form hydrogen bonds and Al-O bonds across the interface. Similar effects could likely be achieved by fully passivating the surfaces with other chemical groups that reduce attractive interactions across the interface. It is also of interest to investigate the abilities of the different interfaces to resist wear. The simulations performed in this study employed a constant number of particles, and thus wear cannot occur through the removal of material. Instead, wear is investigated in the context of irreversible changes in the structure of the interface. As noted above, the full-OH system undergoes smooth sliding without any change in the chemical connectivity of the interface. This is true at values of P up to and including 10 GPa and is likely also the case at higher P, since the data in Figure 1a suggest that interface structure persists at higher normal loads. The LP phase of partial-OH did not undergo any change in chemical connectivity aside from the dissociation of hydrogen bonds during the slip events that involve the reorientation of the hydrogen bonds. The slip event at δ ≈ 7.2 Å involving the dissociation of Al-O bonds led to changes in the bonding between the hydroxyl groups and the remainder of the slab, but this was due to changes in which specific hydroxyl groups were bonded to which particular Al3+ ions, as opposed to an irreversible change in the structure of the underlying material, with the slabs retaining the structure of bulk alumina. The HP phase of partial-OH slides through the formation and dissociation of Al-O bonds and thus alters the chemical connectivity of the interface. As noted in section IIIc, at P ) 10 GPa this system undergoes a mechanism in which most of the hydroxyl groups initially bonded to the bottom surface of the interface become bonded to the top slab, and vice versa. This process actually prevents slip from affecting the chemical structure of the underlying alumina slabs, thereby permitting wearless sliding. This behavior is evident from Figure 8b, where the ∆r values collected with P ) 10 GPa return to the ideal curves for smooth sliding after slip occurs at δ ) 5.0 Å. Wearless slip was not observed, however, for the HP phase at P ) 6 and 8 GPa. In each case, one or more of the Al3+ ions within the surface moved from its equilibrium position in bulk alumina as a result of changes in Al-O bonding across the interface. This is evident through a comparison of the structures in panels b and c of Figure 9, which show the HP phase with P ) 8 GPa before and after slip, with arrows indicating the Al3+ ions that have moved irreversibly. Essentially, the Al3+ ions indicated with arrows were aligned before slip, but have become separated along the slip direction after slip. Overall, these data suggest that the full-OH system is best able to minimize wear, although wearless slip can occur in some cases with the partial-OH models. These observations are consistent

J. Phys. Chem. C, Vol. 114, No. 41, 2010 17717 with the fact that there are no bonding interactions across the interface in the full-OH model, thus providing little ability for sliding to damage the surfaces. Once again, these results suggest that chemical passivation of the surfaces is important in terms of minimizing wear. V. Conclusions In this study, quantum chemical methods were used to investigate different forms of the hydroxylated (0001)/(0001) Al2O3 interface under conditions of compression and shear. The results demonstrate that the interface structure can be sensitive to the normal pressure, P, and that differences in the interface structure lead to different slip mechanisms and shear strengths. Analyses of the atomic and electronic structures of the systems during sliding indicate that the differences in the behaviors of the model systems can be interpreted in terms of the strengths of the interactions across the interface. The full-OH structure is insensitive to P and undergoes smooth sliding under shear conditions. The slip mechanism involves the reorientation of OH groups as the surfaces slide past one another, yet does not involve any changes in the connectivity of the system. The partial-OH model undergoes a change from the LP to HP phases when P ) 4 GPa. The LP phase exhibits a slip mechanism involving changes in hydrogen bonds, as well as the formation and dissociation of Al-O bonds. This process is found to be periodic with the system reverting to the initial LP structure after shearing through a distance of δ ) 7.2 Å. The HP phase exhibits a slip mechanism involving the formation and dissociation of Al-O bonds and does not return to the original structure over the range of δ considered in the simulations. The differences in the shear strengths of the interfaces suggest that the friction associated with these systems will be in the order of Ffull-OH < Fpartial-OH, LP < Fpartial-OH, HP. The full-OH system undergoes smooth sliding without wear. The LP phase of the partial-OH phase also exhibits wearless sliding in the calculations, yet the formation and dissociation of Al-O bonds during the slip mechanisms certainly suggests that wear may be possible. The slip mechanism for the HP phase of partial-OH involves a change in the chemical connectivity in the interface and leads to irreversible changes in structure, corresponding to wear. As such, the results suggest that the full-OH system is best suited to minimizing friction and wear. This insight, as well as the fundamental details associated with the slip process, may prove useful in developing strategies for lubricating hydroxylated surfaces. Acknowledgment. Financial support from the Natural Sciences and Engineering Research Council (NSERC) of Canada Discovery Grant Program and the Ontario Ministry of Research and Innovation’s Early Researcher Award Program is gratefully acknowledged. C.J.C. is thankful for support in the form of an Undergraduate Student Research Award from NSERC. Computing resources were provided by the Shared Hierarchical Academic Research Computing Network (SHARCNET) and the Re´saue Que´be´cois de Calcul de Haute Performance (RQCHP). Supporting Information Available: Discussion of model thicknesses, temperatures during the simulations, and optimized structures of simulated systems. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Fahlman, M.; Crispin, A.; Crispin, X.; Henze, S. K. M.; de Jong, M. P.; Osikowicz, W.; Tengstedt, C.; Salaneck, W. R. Electronic Structure

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