Nanometric flow and earthquake instability

The study addresses how nanocrystalline fault rocks—commonly found in principal slip zones—control fault stability and earthquake nucleation. Fault zones localize deformation into high- and low-strain domains, enabling weakening mechanisms such as thermal pressurization and shear heating, and driving microstructural transformations (comminution, reactions, phase transitions, melting) that can create nanocrystalline to amorphous materials. Despite their ubiquity and suspected weakness, the rheology of these nanocrystalline materials is poorly constrained; existing models rely on microstructural inferences or extrapolations from microcrystalline flow laws that may not apply due to size-dependent properties. A key challenge is isolating the intrinsic rheology of nanomaterials from experimental signals dominated by coarser-grained material in low-velocity tests or confounded by transient heating in high-velocity experiments. The authors produce bulk nanomaterials via high-energy ball milling and test them under controlled pressure-temperature conditions representative of the base of the seismogenic zone to directly determine their flow law and implications for earthquake instability.

Prior work shows that deformation localizes in faults and enables weakening via thermal pressurization and shear heating. High local work promotes comminution, metamorphic reactions, microstructural and phase transformations, and melting, which can weaken rocks and generate nano- to amorphous materials in nature and experiments. Existing rheological models for nanocrystalline fault rocks often extrapolate from microcrystalline materials, despite evidence that nanomaterials have distinct surface-dominated properties. Nanocrystalline fault rocks commonly form compact, low-porosity zones with 1–10s of nm grains or 100s of nm aggregates, sometimes in an amorphous matrix. Diffusion can be competitive at conditions where cataclasis often dominates due to short diffusion distances and disordered lattices. Evidence suggests nanocrystalline rocks are weaker and can deform at low temperatures, but the responsible processes are debated. Experimental challenges include dominance of coarse grains in low-velocity tests and temperature transients in high-velocity tests, complicating attribution of weakening to nanomaterial formation versus heating. Related studies document velocity weakening in some gouges, formation of amorphous materials and nanosilica, superplastic nanofibrous slip zones, and deep-earthquake analog mechanisms involving phase transitions and shear heating. However, a direct, bulk rheology for granitoid nanomaterials under controlled seismogenic conditions has been lacking.

Starting materials: Verzasca gneiss powder (≤200 µm) comprising ~37% quartz, 33% plagioclase, 28% K-feldspar, ~2% micas; XRF: 77 wt% SiO2, 13.3 wt% Al2O3, 4.63 wt% K2O, 3.16 wt% Na2O, ≤1 wt% others. Nanomaterial production: planetary ball milling in deionized water with 0.1 mm zirconia balls for 12 minutes total (2 min milling intervals with ~20 min cooling), temperature buffered ≤100 °C; dried at 110 °C >48 h. Particle size distribution of starting nanomaterial: 0.01–1 µm, median ~0.1 µm (noting clustering). SEM-BSE shows thorough mixing and cohesive, uniform material. Sample assembly: ~0.1 g nanogouge placed between alumina forcing blocks pre-cut at 45°, sealed in 0.2 mm gold jacket (annealed at 900 °C for malleability). Alumina pistons transmit load; graphite furnace provides heat. NaCl confining medium; K-type thermocouple adjacent to sample via alumina ring for direct temperature measurement. Copper discs conduct current to furnace. Assembly uses WC plug and pyrophyllite base; lead piece on top transmits pressure. Apparatus: Griggs-type solid-medium deformation apparatus providing confining pressure via σ3 piston into salt sleeves and differential stress via σ1 piston. External load cell and pressure transducers measure force and pressure. Temperature controlled via PID to thermocouple. Experimental conditions and procedures: Confining pressure P = 500 MPa; temperatures T = 200, 300, 500 °C. Pressurization in 100 MPa/100 °C increments; deformation; then quenching/depressurization (quench at 300 °C/min to 30 °C; σ1 reversed to keep σ1−σ3 ≤100 MPa). Two boundary conditions: (1) constant displacement rate experiments with σ1 pump driven at ~10⁻³ mm s⁻¹; (2) load-stepping experiments: after contact, load held at successive steps until steady creep achieved. Data recorded at 1 Hz. Data processing: Corrections for rig stiffness (−0.0061 mm/kN), total friction-related forces (empirical friction correction 1.31 kN/mm), and area reduction with shear displacement. Shear strain computed from piston displacement decomposed into thinning and simple shear, assuming constant thinning rate; initial shear zone thickness from an undeformed/pressurized sample. Conversion to equivalent stress σ=2τ and equivalent strain rate ε̇=γ̇/2. Microstructural characterization: Thin sections analyzed by polarized light microscopy and SEM-BSE (Zeiss Merlin) for compositional contrast and microstructures; TEM (FIB foils) for grain size, grain shape, selected area electron diffraction (SAED) to assess crystallinity and CPO; image analysis for grain size distributions and SPO. Flow law estimation: ε̇ = A σⁿ exp(−Q/RT). Stress exponent n determined from log ε̇–log σ slope in load-stepping experiments at 300 and 500 °C; activation energy Q from Arrhenius plot of log(ε̇/σⁿ) vs 1/T using constant-displacement-rate experiments at multiple T; A from intercept. Sensitivity of n and Q to friction correction assessed. Shear heating calculations: Steady-state temperature rise estimated by solving −∇·(k∇T)=Q̇/ρCp with 1D finite differences, ambient temperature boundary conditions, heat source centered in shear zone. Parameters: ρ=2800 kg/m³, Cp=1000 J/kg/K, k=2.5 W/m/K; principal slip zone thickness d from 10 µm to 10 cm; boundary shear velocity v from 10⁻¹³ to 10¹ m/s; γ̇=v/d; equivalent stress from experimental flow law; contours of σ after accounting for shear heating plotted.

• Nanocrystalline granitoid fault rocks are intrinsically much weaker than microcrystalline counterparts under identical P–T–rate conditions, with about an order of magnitude lower apparent viscosity and ~1 GPa lower shear strength in comparisons (Fig. 1a,b).
• At 300 °C, microcrystalline gouge (≤200 µm) exhibits an abrupt stress drop (stick–slip style failure), while the nanocrystalline material creeps stably without loss of strength at the same conditions.
• Both grain sizes weaken with increasing temperature: maximum shear stress τ, apparent viscosity η=τ/γ̇, and friction coefficient μ=τ/σn decrease from 200 to 500 °C.
• Nanocrystalline material shows strain hardening after yield at 200–300 °C, with reduced hardening at higher T; both nanocrystalline and microcrystalline materials approach steady-state flow at 500 °C.
• Load-stepping experiments yield a near-linear stress–strain rate relation with stress exponent n = 1.3 ± 0.4 (300–500 °C), consistent with diffusion creep dominance.
• Activation energy estimated from constant-displacement-rate experiments: Q = 16,000 ± 14,000 J/mol (for n ≈ 1.3), significantly lower than typical microcrystalline diffusion creep values, consistent with high surface-to-volume ratios in nanomaterials.
• Experimental flow law for granitoid nanometric fault rocks: ε̇ = 3.69×10⁻⁶ σ¹·³ exp(−16000/RT) (σ in MPa; ε̇ in s⁻¹; R=8.314 J/mol/K; Q in J/mol). Predicted strain rates match measured rates in validation cases.
• Shear heating is ineffective at producing velocity weakening due to low Q; extremely high equivalent stresses (tens of GPa) would be required for modest temperature increases at plausible conditions.
• Microstructures: At 200–300 °C, pervasive R1 and R2 Riedel shear fractures and kink bands, with optical anisotropy and evidence of dilatancy. At 500 °C, fractures are scarce (mostly unloading), optical anisotropy increases, and SEM/TEM show compact, porosity-free material with flow features (smeared domains), implying volume-conserving viscous flow. TEM grain size mean ≈46 nm; silicates rounded (b/a≈0.9) with no strong SPO, micas with strong SPO (b/a≈0.4); SAED indicates crystalline nanograins without strong CPO.
• Despite intrinsic rate-strengthening rheology, instability and abrupt failure can occur in initially microcrystalline gouge once sufficient nanocrystalline material (≈10–20 vol%) forms and interconnects to provide a kinematically favorable weak network.
• The weak nanolayers allow high strain rates at low stresses (e.g., at 300 °C, ε̇ ~10⁻⁴ s⁻¹ at ≤100 MPa), highlighting extreme weakness near the base of the seismogenic zone.

The experiments isolate the intrinsic rheology of nanocrystalline fault rocks and demonstrate that they are exceptionally weak and predominantly deform by diffusion creep with n ≈ 1.3 and very low activation energy. As a result, these materials are strongly rate strengthening and only weakly temperature sensitive, making classic velocity-weakening friction an unlikely mechanism for instability within nanocrystalline zones. Shear heating cannot readily induce sufficient weakening due to the low Q; realistic fault-zone stresses would not generate large temperature rises. Nevertheless, abrupt failure is observed in microcrystalline gouges once nanocrystalline patches produced by comminution grow and coalesce. The proposed mechanism is that the intrinsic low viscosity of the nanocrystalline material provides a percolating, kinematically favorable weak plane on which displacement can accelerate at roughly the same stress without requiring significant temperature increase. This instability differs from traditional frictional instabilities and aligns with mechanisms invoked for deep earthquakes (e.g., phase transformations, viscoelastic shear heating, cavitation), where a weak, rate-strengthening layer enables shear failure of the surrounding stronger rock. Thus, nanometric flow may enable earthquake nucleation in the crust, particularly near the brittle–viscous transition where many large earthquakes initiate.

This study provides a direct experimental determination of the rheology of nanocrystalline granitoid fault rocks under seismogenic P–T conditions. The materials exhibit linear to near-linear viscous behavior (n ≈ 1.3) with a very low activation energy (Q ≈ 16 kJ/mol) and are an order of magnitude weaker than microcrystalline counterparts. A calibrated flow law quantifies their extreme weakness and temperature insensitivity. Although the nanomaterial is rate strengthening, earthquake-like instability can arise when nanocrystalline layers, produced within initially coarser gouges, coalesce into a percolating, kinematically favorable weak network, enabling rapid slip without significant thermal weakening. This mechanism is distinct from classic frictional velocity weakening and suggests a broader framework for earthquake nucleation involving weak, rate-strengthening inclusions. Future research could quantify the percolation threshold and evolution of nanocrystalline volume with work and temperature, assess the effects of mineralogy, fluids, and aging on rheology, and further bridge laboratory flow laws to natural fault-zone conditions and slip histories.

• Determination of activation energy from constant-displacement-rate experiments is not fully rigorous because steady-state stress was not always achieved at lower temperatures, and Q depends on the assumed n.
• Mechanical data require corrections (rig stiffness, friction, contact area changes); the total friction correction is empirically estimated and not precisely measured, introducing uncertainty in σ and hence in n and Q. Sensitivity tests indicate n ~0.9–1.4 and Q ~10–16 kJ/mol across plausible friction corrections.
• Conversion of piston displacement into shear strain assumes constant thinning rate and idealized geometry, contributing uncertainty at higher strains.
• Nanomaterials may age/react even at room conditions; although one batch and consistent behavior were used, some uncertainty in starting material properties remains.
• Shear heating calculations adopt simplified steady-state, 1D geometry and constant thermal properties; real faults have transient, heterogeneous conditions and variable thicknesses.
• Extrapolation from laboratory strain rates, thicknesses, and compositions to natural faults involves scale and material uncertainties, including the evolving volume fraction of nanomaterial during slip.