Structural origins of thermal expansion behavior in 2D materials

Two-dimensional (2D) materials exhibit diverse thermal expansion behavior—with coefficients spanning a broad range from negative to positive values—fundamentally challenging our understanding of thermal expansion mechanisms and creating critical uncertainties in thermal stress prediction for next-generation devices. Despite numerous experimental measurements, the fundamental structural mechanisms underlying this remarkable variability remains elusive. Here, we resolve this longstanding puzzle through systematical molecular dynamics simulations of four representative 2D materials: h BN, PbTe, graphene, and MoS₂. Our simulations reveal that thermal expansion behavior is governed by the interplay between the intrinsic chemical bond thermal expansion and out-of-plane structural flexibility. This interplay enables 2D materials to achieve thermal expansion coefficients ranging from -15.0 × 10⁻⁶ K⁻¹ to +52.4 × 10⁻⁶ K⁻¹. Crucially, we demonstrate that thickness and lateral size effects arise exclusively through modulation of out-of-plane deformation freedom, while substrate interactions operate via a dual pathway that simultaneously constrains structural flexibility and modifies intrinsic bond behavior. Our findings culminate in a universal scaling relationship between area-specific bending rigidity and thermal expansion coefficients, providing the first predictive framework for 2D material thermal behavior. © 2026 Acta Materialia Inc.