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By using a Cahn-Hoffman $\boldsymbol{\xi}$-vector formulation, we propose asharp-interface approach for solving solid-state dewetting problems in twodimensions. First, based on the thermodynamic variation and smooth vector-fieldperturbation method, we rigorously derive a sharp-interface model with weaklyanisotropic surface energies, and this model describes the interface evolutionwhich occurs through surface diffusion flow and contact line migration. Second,a parametric finite element method in terms of the $\boldsymbol{\xi}$-vectorformulation is proposed for numerically solving the sharp-interface model. Byperforming numerical simulations, we examine several specific evolutionprocesses for solid-state dewetting of thin films, e.g., the evolution of smallislands, pinch-off of large islands and power-law retraction dynamics ofsemi-infinite step films, and these simulation results are highly consistentwith experimental observations. Finally, we also include the strong surfaceenergy anisotropy into the sharp-interface model and design its correspondingnumerical scheme via the $\boldsymbol{\xi}$-vector formulation.

Sharp-interface approach for simulating solid-state dewetting in two dimensions: a Cahn-Hoffman $\boldsymbol{\xi}$-vector formulation