Superior directional thermal conductivity and stiffness in rectangular γ-graphyne revealed by neuroevolution machine-learning potentials

Graphynes have emerged as promising carbon allotropes for next-generation nanoelectronics and thermoelectric devices due to their unique combination of porous frameworks, tunable bandgaps, and unconventional thermal transport. In this work we comprehensively investigate the thermal, vibrational, and mechanical properties of hexagonal ( γ -GY) and rectangular (r γ -GY) graphynes by developing an accurate and efficient machine-learning interatomic potential trained via an active learning framework. The developed neuroevolution potential closely captures the potential energy surfaces of both structures, showing excellent agreement with reference first-principles calculations. Molecular dynamics simulations driven by this potential reveal a remarkable directional anisotropy in the rectangular phase. Notably, the zigzag direction exhibits a significantly enhanced thermal performance compared to both its armchair direction and the hexagonal counterpart. This superior thermal conductivity is accompanied by higher lattice stiffness, higher phonon group velocities, and a substantially larger contribution from long-wavelength phonons with extended effective mean free paths. Spectral and modal decompositions reveal the dominance of low-frequency modes, where in-plane branches dominate the zigzag direction of both structures, whereas out-of-plane modes slightly surpass in-plane thermal channels along the rectangular armchair axis. These findings provide insights into how lattice topology and acetylenic groups influence phonon transport, contributing to a better understanding of directional thermal transport in graphyne-based nanostructures. • Neuroevolution potentials are developed for hexagonal and rectangular γ -graphynes. • Strong thermal and mechanical anisotropy is observed in r γ -graphyne. • The rectangular phase has superior thermal conductivity along the zigzag direction. • Thermal conductivity anisotropy correlates with lattice mechanical anisotropy.