▎ 摘　　要

Graphyne (GY), a two-dimensional (2D) allotrope of carbon with mixed sp/sp(2) hybridization, is predicted to exist in many stable phases and has recently received great attention. However, it is energetically less stable than graphene and remains difficult to be synthesized in experiment to date. In this report, the possible environments for synthesis of graphyne on Ru(0001), Rh(111), and Pd(111) substrates are investigated by considering three typical phases of GY (alpha, beta and gamma). Their structures, interactions with metal substrates, as well as thermodynamic stability are calculated using first-principles calculations. The chemical potential phase diagram of GYs and graphene on metal substrates is constructed. For all these substrates, the alpha phase of GY can form in the carbon-poor environment, while formation of graphene dominates in the carbon-rich condition.