Atomistic Insights into the Running-in, Lubrication, and Failure of Hydrogenated Diamond-Like Carbon Coatings

Abstract

The tribological performance of hydrogenated diamond-like carbon (DLC) coatings is studied by molecular dynamics simulations employing a screened reactive bond-order potential that has been adjusted to reliably describe bond-breaking under shear. Two types of DLC films are grown by CH₂ deposition on an amorphous substrate with 45 and 60 eV impact energy resulting in 45 and 30% H content as well as 50 and 30% sp³ hybridization of the final films, respectively. By combining two equivalent realizations for both impact energies, a hydrogen-depleted and a hydrogen-rich tribo-contact is formed and studied for a realistic sliding speed of 20 m s⁻¹ and loads of 1 and 5 GPa. While the hydrogen-rich system shows a pronounced drop of the friction coefficient for both loads, the hydrogen-depleted system exhibits such kind of running-in for 1 GPa, only. Chemical passivation of the DLC/DLC interface explains this running-in behavior. Fluctuations in the friction coefficient occurring at the higher load can be traced back to a cold welding of the DLC/DLC tribo-surfaces, leading to the formation of a transfer film (transferred from one DLC partner to the other) and the establishment of a new tribo-interface with a low friction coefficient. The presence of a hexadecane lubricant leads to low friction coefficients without any running-in for low loads. At 10 GPa load, the lubricant starts to degenerate resulting in enhanced friction.

Appendix

1.1 Pressure Coupling Algorithm

MD simulations only probe short-wavelength behavior and thus only model a representative element of the whole tribo-system, in our case the contact of two asperities. Since such a system is always open, the choice of boundary conditions, both thermal and mechanical, is crucial. In order to provide a realistic mechanical boundary, the distance between the two sliding surfaces needs to adjust according to the local pressure. Inertia and elastic moduli of the bulk material, which is not explicitly included in our MD simulations, resist this adjustment. By simply imposing a normal pressure on the simulation cell, these inertial and elastic contributions to pressure fluctuation within the representative cell are ignored. Hence, fluctuations will be suppressed leading to improper conditions within the representative volume element. On the other hand, fixing the distance of the two sliding partners can also lead to improper conditions due to stress accumulation within the sample. Here, we assume that the process of adjusting the bulk separation is dominated by the inertia of the sliding partners. Fixing the 0.3 nm top- and bottommost atoms, and increasing these rigid layers’ total mass M, models inertia effects (see Fig. 2). The finite periodic cell introduces short-wavelength fluctuations with a characteristic time scale of t _c = l v ⁻¹ into the system, where v is the sliding velocity and l is the repetition length. We thus damp the normal movement of the top rigid layer with total mass M by adding a normal force of F _z  = F _ext − γv _z . Here, v _z is the rigid layer’s normal velocity and F _ext is given by F _ext = p A, where A is the cross section of the cell parallel to the sliding direction and p the target pressure.

A guide to choose the free parameters M and γ can be obtained by estimating the response of the bulk separation, i.e., the separation of the top and bottom rigid slab of atoms, during sliding. Let us approximately decompose the normal response of the molecular simulation cell into a linear elastic component with spring constant k and an additional fluctuating force F _int. The force F _int(t) fluctuates with zero mean and is due to the sliding contact’s local topography and chemistry—it includes all contributions which are not captured by the linear elastic component. The distance h _z (t) of the two sliding partners then evolves according to the differential equation

$$ M{\frac{\partial^2}{\partial t^2}} h_z(t) = F_{\text {int}}(t) - kh_z(t) - \gamma{\frac{\partial}{\partial t}}h_z(t) + F_{\text {ext}},$$

(2)

which is identical to that of a damped harmonic oscillator. Fourier transformation immediately yields the transfer function in frequency space

$$ f(\omega) = \left| {\frac{h_z(\omega)}{F_{\text {int}}(\omega)}} \right| = {\frac{1}{ \sqrt{ ( M \omega^2 - k )^2 + (\gamma\omega)^2}}}$$

(3)

which describes the response of the separation distance h _z to the fluctuating force F _int as a function of frequency ω. The high-frequency limit of F _int(ω) is unknown a priori; however, we know that fluctuations with a characteristic time scale of t _c are introduced due to the periodic boundary conditions. All frequencies above ω_c = 2πt ⁻¹_c should not lead to a change in bulk separation and thus a change in the system’s integral density. We expect phase-transformations in the sliding partners, which should be able to change the bulk separation, to occur at frequencies below ω_c.

Two conditions are imposed: The system should be driven in the anharmonic limit to avoid resonances without overdamping; all frequency above and including ω_c should be cut-off. The first condition leads to

$$ \gamma=\sqrt{2Mk}. $$

(4)

We fix the second parameter by choosing f(ω_c) = p _c f(0) where the empirical cut-off parameter p _c is set to p _c = 1%. This gives a total mass of

$$ M=k\omega_{\text {c}}^{-2}\sqrt{p_{\text {c}}^{-2}-1}.$$

(5)

The resulting transfer function with the appropriate parameters for our systems is shown in the inset of Fig. 2. Frequencies up to half the recurrence frequency ω_c are efficiently damped. A movement of the two sliding partners is however not hindered as we confirmed by checking the normal pressure in the system, which reaches the prescribed value after typically 5 ns.

The considerations which lead to the mass M and dissipation constant γ should be regarded as order-of-magnitude considerations only. When going to larger sample sizes more sophisticated schemes will be necessary which also include the elastic response of the bulk material [44]. However, we expect that the elastic response of the bulk material which is explicitly included in our MD simulations supplies sufficient elasticity when the aspect ratio of the cell size along the sliding direction to the cell size perpendicular to the sliding plane is smaller than unity.