The widely used Amonton’s law, which describes the common observation that dry friction between two surfaces is proportional to the normal load, has yet to be explicitly derived since its discovery from Leonardo da Vinci era. Here, Amonton’s law is explicitly extrapolated as the friction coefficient $\mu =\mathrm{\Delta }{F}_{\mathrm{N}}/\left(k\mathrm{\Delta }x\right)$ via concise perturbation theory analysis of the frictional energy landscape parametrized by the load. This reveals that Amonton’s law may arise from the competition between the normal stiffness (k) and the interfacial normal force fluctuation during sliding (ΔF_N/Δx). The predicted friction coefficient is quantitatively validated through both atomic force microscopy (AFM) experiments and atomistic simulations of frictional systems ranging from bulk to layered materials. Unlike the traditional framework of recondite rough contact theory, this study concisely extrapolates Amonton’s law and friction coefficient and traces their microscopic origins to the inherent mechanical properties, thereby enabling their rational design.

The atomic edge structure of graphene governs its unique electronic properties with applications in nanoscale electronics and optoelectronics. To fully realize its potential, it is critical to develop a precision etching process producing graphene edges along desired directions. Here, we present a novel approach utilizing scanning probe lithography (SPL) facilitated by a mechanochemical atomic attrition process. This technique enables the fabrication of nanopatterns in single-layer graphene from graphene edges, precisely along the crystallographic orientation of zigzag (ZZ) and armchair (AC) edges, without inducing mechanical damage to the surrounding area. Density functional theory (DFT) calculations revealed that the dissociation of C‒C bonds by the SPL probe is mediated by the formation of interfacial bridge bonds between the graphene edge and the reactive silica surface. This SPL-based mechanochemical etching method enables the construction of various nanodevice structures with specific edge orientations, which allows the exploitation of their electronic properties.