Robust structural superlubricity under gigapascal pressures

The study investigates how structurally superlubric (SSL) interfaces withstand extreme mechanical loading, specifically gigapascal-level pressures. SSL, predicted in the 1990s and later termed by Müser, arises from atomic-scale structural incommensurability and has been demonstrated across length scales, speeds, and materials, especially in vdW-layered systems such as graphite. While SSL shows ultralow friction and essentially no wear, its reliability under extreme pressures relevant to applications remains unclear. Conventional wear theories (Archard’s progressive wear model; atom-by-atom attrition for microscopic contacts) suggest wear scales with load and sliding distance, implying inevitable material loss. However, recent SSL experiments show long wear-free sliding, challenging progressive wear in this regime. Graphite interfaces are known to be stable under tens of GPa before phase transitions, motivating the question: what is the upper bound of pressure for SSL stability and what mechanisms trigger breakdown beyond it? The authors aim to probe SSL robustness and identify the critical pressure for wear activation (P_cr) in self-mated graphite/graphite and non-self-mated tungsten/graphite contacts, and to elucidate the microscopic mechanisms behind SSL breakdown.

Prior work established SSL theoretically (Hirano, Sokoloff; Müser) and experimentally in incommensurate graphite contacts (Dienwiebel et al.), with extensions to micro- and macro-scales, high speeds, high pressures, and heterojunctions (e.g., graphene/h-BN). Archard’s progressive wear model predicts wear volume proportional to load and sliding distance and has been linked to atom-by-atom attrition at micro/nano scales. Nonetheless, SSL contacts have shown wear-free sliding over 100 km at low pressures (MPa range), suggesting that progressive wear may not apply in SSL. Graphite interfaces remain stable under tens of GPa before sp2–sp3 transitions, implying potentially high SSL breakdown pressures. The literature also indicates that contaminants and environmental factors can affect SSL but can be managed; and that contact roughness at SSL scales is low, making single-asperity or single-contact models relevant. Theoretical studies on metal/graphene interfaces show varied interaction strengths and bonding behavior, indicating potential differences between self-mated and non-self-mated SSL contacts under pressure.

Experiments and simulations were combined.

• Experimental platforms:
  • Home-built loading system enabling 0.1–10 mN normal loads with closed-loop control and in-situ optical microscopy (OM) monitoring. Sliding speed 10 µm/s, reciprocating.
  • Contacts studied: (i) self-mated graphite/graphite (mesa/substrate setup); (ii) non-self-mated tungsten tip/graphite substrate.
  • Sample preparation: Graphite mesa (6 µm × 6 µm) etched from HOPG with 100 nm SiO2 cap for stiffness and handling; graphite substrate exfoliated (normal flake graphite) onto Si/300 nm SiO2. Tungsten tips etched in 5 M KOH, ultrasonically cleaned (acetone, alcohol, DI water). Surface crystallinity assessed via EBSD; roughness via AFM/OM. Tips characterized by SEM/AFM; RMS roughness <0.3 nm and nanometer-scale smoothness.
  • Graphite/graphite tests: Pre-clean substrate region (26 µm × 14 µm); then sliding at center under maximum pressure P ≈ 9.45 GPa achieved by 10 mN load, 10 µm reciprocating amplitude, 10 µm/s; total distance 10 mm over 5×10^2 cycles. Friction measured with a two-dimensional force sensor (lateral resolution ~80 nN; normal load mN range). Raman used to detect defects (D peak at 1350 cm^-1). AFM tapping mode for wear morphology; resolution 0.1 µm × 0.1 µm × 1 nm.
  • Tungsten/graphite tests: Increasing load sequence 0.1, 0.2, 0.5, 1, 2, 3, 5, 7, 9, 10 mN; sliding amplitude 30 µm, speed 10 µm/s. Protocol: slide at P = 3.74 GPa (Region I), increase to P = 5.07 GPa and move tip along a trace, then slide at P = 5.07 GPa (Region II). Monitoring by OM; AFM post-characterization. Tests stopped on visible wear or at 10^6 cycles (0.6 m total distance). Friction coefficient measured ~10^-3; shear strength ~10 MPa.
  • Environmental conditions: Ambient; pre-cleaning to reduce adsorbates; SSL friction largely robust to atmosphere; contaminants swept to edges during pre-cleaning.
• Computations:
  • DFT (VASP) with PBE-GGA, plane-wave cutoff 520 eV; vacuum 4 nm; Monkhorst-Pack k-grid density 3 Å^-1; energy/force convergence 0.1 meV/atom and 0.01 eV/Å. Supercells: WO3/graphite ((√2×√2)R45 reconstructed WO3(001) with graphite; misfit ~3%), and W(001)/graphite (misfit ~2%). Two graphene layers (AB) and 2–4 metal/oxide layers; PBC in-plane.
  • Breakdown pressure determined from peak in pressure–displacement curves by approaching counterfaces; shear characteristics from lateral displacement calculations. Electron localization function (ELF) computed to assess interfacial electronic coupling. Metals screened (Os, W, Re, Ni, Co, Ta, Hf, Ti, Zr; also Cu, Au, Ag) for P_cr and failure modes; correlations with materials properties (bulk modulus, first ionization energy).
  • MD (LAMMPS): Graphite modeled with all-atom optimized potential; vdW via LJ 12-6 (cutoff 1.2 nm). Structures minimized; shear applied by moving tungsten layer at 20 m/s; T = 0.1 K via Nosé-Hoover; graphene edges fixed. Simulations of wrinkle formation and tear initiation under elevated interfacial coupling (reduced distance ~2.5 Å; shear strength ~5.22 GPa).

• Self-mated graphite/graphite contact:
  • Maintains SSL up to at least P ≈ 9.45 GPa (maximum accessible), with ultralow friction stress (~20 kPa) and friction coefficient ~10^-5 between 1–6 GPa; friction nearly pressure-independent.
  • No detectable wear after 10 mm sliding over 5×10^2 cycles under 9.45 GPa; AFM resolution 0.1 µm × 0.1 µm × 1 nm implies wear rate < 1×10^-10 mm^3/N·m. Raman showed no D peak at 1350 cm^-1, indicating absence of atomic-scale defects.
• Non-self-mated tungsten/graphite contact:
  • Friction coefficient ~10^-3; measured shear strength ~10 MPa (higher than graphite/graphite, likely due to adhesion).
  • Wear-free up to P = 3.74 GPa for long sliding (0.6 m, up to 10^6 cycles limit); wear initiates at P = 5.07 GPa, observed as tearing of graphite layers from onset.
  • Critical pressure P_cr > 3.74 GPa experimentally for oxidized tungsten tip (WO3 surface).
• Mechanism of breakdown (WO3/graphite):
  • DFT predicts breakdown at P_cr ≈ 3.50 GPa via pressure-assisted interfacial O–C bond formation. ELF between nearest O–C increases from <0.1 (vdW) at P < 1.7 GPa to 0.27 near P_cr (ionic character), and to 0.79 beyond P_cr (covalent bonding).
  • Shear strength low (<0.14 GPa) below P_cr; jumps to ~3.65 GPa after bonding forms.
  • MD shows step-wear: pressure-assisted bonding triggers shear-induced wrinkle formation and tearing, consistent with experimental AFM of torn step edges; deformation localizes near contact edges (shear-lag behavior).
• Graphite/graphite mechanism and defects:
  • Graphite vdW interfaces are stable up to tens of GPa before sp2→sp3 transitions; within accessible 9.45 GPa, no interfacial bonds form and wear is not activated.
  • Introducing vacancies (argon plasma) reduces P_cr to ~0.4 GPa; wear manifests as tearing, supporting the same step-wear mechanism.
• Bare W/graphite vs WO3/graphite:
  • DFT predicts higher P_cr ≈ 5.4 GPa for bare W(001)/graphite. Transition in coupling mediated by charge transfer rather than covalent bonding, leading to higher pressure tolerance.
• Materials screening and correlations:
  • Two classes of non-self-mated contacts: (i) Cu/Au/Ag/graphite with P_cr ~ O(100 GPa), but practical limit set by metal strength (plasticity) well below; (ii) Os, W, Re, Ni, Co, Ta, Hf, Ti, Zr/graphite that fail by covalent bond formation with lower P_cr (max ~9.78 GPa for Os/graphite).
  • Breakdown pressure correlates strongly with bulk modulus (B; r ≈ 0.95) and first ionization energy (IE; r ≈ 0.90). Metals with higher B and IE resist electronic coupling transitions and bonding at the interface.
  • SSL interface breakdown pressures can exceed the intrinsic strength of contacting materials, highlighting SSL robustness.

The results directly address the central question of SSL stability under extreme pressures. Self-mated graphite interfaces sustain SSL with no detectable wear up to 9.45 GPa, contradicting progressive wear expectations and supporting a step-wear picture: below a critical pressure, material loss is not activated. In non-self-mated tungsten/graphite contacts, the observed transition from wear-free behavior at 3.74 GPa to immediate wear at 5.07 GPa pinpoints a P_cr bracket and validates the step-wear mechanism. First-principles calculations connect the mechanical transition to a change in interfacial electronic coupling: pressure-assisted bonding (WO3/graphite) or pressure-enhanced charge transfer (W/graphite) increases shear strength and enables shear-driven tearing. The strong correlation of P_cr with bulk modulus and ionization energy unifies structural (elastic stiffness) and electronic (reactivity) determinants of interface stability, enabling predictive material selection. These insights imply that SSL-enabled systems can operate under gigapascal pressures if interfacial bonding is avoided (e.g., by choosing less reactive, stiffer metals or controlling oxidation), and that device functions could be reconfigured via pressure without incurring wear below P_cr. Speed and temperature, known to affect friction and reaction rates, likely modulate P_cr by altering the activation of pressure-assisted bonding, suggesting design trade-offs for applications.

This work demonstrates that structural superlubricity can be robustly maintained under gigapascal pressures. Self-mated graphite/graphite contacts exhibit wear-free sliding up to at least 9.45 GPa, while non-self-mated tungsten/graphite contacts remain wear-free up to ~3.7 GPa and fail above ~5 GPa. The breakdown follows a step-wear mechanism: pressure-assisted interfacial bonding (or charge-transfer-mediated coupling) dramatically increases shear strength and triggers shear-induced tearing of atomic layers. First-principles and MD simulations corroborate experiments, and materials screening reveals that breakdown pressures correlate strongly with bulk modulus and first ionization energy, providing design guidelines. The findings show that SSL breakdown pressures can surpass the intrinsic strengths of the contacting materials, underscoring exceptional robustness. Future research should precisely determine P_cr for graphite/graphite at higher pressures, systematically study the roles of temperature, sliding speed, environment (oxidation/adsorbates), and extend materials screening and device demonstrations leveraging pressure-tunable SSL states.

• The maximum experimental pressure for graphite/graphite was limited to ~9.45 GPa by the loading system; the actual P_cr for pristine graphite/graphite was not reached or precisely determined.
• Non-self-mated experiments involved tungsten tips with surface oxidation (WO3), potentially influencing P_cr; bare W/graphite behavior was inferred from DFT rather than experiment.
• Tests were conducted under ambient conditions at a single sliding speed (10 µm/s); effects of temperature, humidity, and higher/lower speeds on P_cr and wear activation were not systematically explored.
• Contact geometry approximates a single smooth contact; while roughness was minimal, real-world multi-asperity effects were not addressed.
• Hydrostatic versus indentation loading conditions differ; comparisons to graphite-to-diamond transition pressures are qualitative.
• Pre-cleaning reduces but may not eliminate confined contaminants; their residual effects were assumed minimal based on friction behavior.