Interface mechanics of 2D materials on metal substrates

Mitisha Surana, Tusher Ahmed, Nikhil Chandra Admal

Research output: Contribution to journalArticlepeer-review


The chemical vapor deposition (CVD) of graphene on metal substrate serves as a robust method to synthesize large graphene flakes. Therefore, understanding the thermodynamics and kinetics of graphene–metal interface is an important step towards synthesizing defect-free graphene during CVD. The focus of this paper is on the phenomenon of surface reconstruction of a metal substrate during the deposition of a 2D material. Key features of surface reconstruction include the formation of straight and pyramidal facets of size ∼300 nm in width and ∼15–80 nm in height. In addition, discontinuities in facet directions under a single graphene flake distributed over two grains highlight the strong crystallographic influence on surface reconstruction. In this paper, we present an atomistically informed continuum model of a graphene–metal interface in three dimensions. Graphene is modeled as an elastic surface that is in contact with a rigid metal substrate. Due to the weak van der Waals interaction between graphene and metal, the kinematics of the model incorporates sliding of graphene. However, since we assume that graphene is always in contact with the substrate, its normal displacement is mediated by surface diffusion of metal atoms. Based on evidence from recent molecular dynamics simulations and experiments, we model the graphene-covered-metal surface energy to include in-plane elasticity and bending energy of graphene, and an interaction energy that depends on the orientation of graphene relative to the substrate. We compare the predictions of our model with surface reconstructions observed during the CVD of graphene on forged thin film palladium polycrystals. As we continue to unravel the atomic scale mechanisms responsible for surface reconstruction during CVD, we expect the current continuum framework and its generalizations will serve to bridge the atomic- and the meso-scales.

Original languageEnglish (US)
Article number104831
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Jun 2022


  • A. surface diffusion
  • Anisotropic material
  • B. 2D material
  • C. finite elements
  • Microstructure

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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