Phase-field-crystal (PFC) modeling has emerged as a computationally efficient tool to address crystal growth phenomena on atomistic length and diffusive time scales. We use a two-dimensional phase-field-crystal model for a binary system based on Elder et al. [Phys. Rev. B 75, 064107 (2007)] to study critical nuclei and their liquid-solid phase boundaries, in particular the nucleus size dependence of the liquid-solid interface tension as well as of the nucleation barrier. Critical nuclei are stabilized in finite systems of various sizes, however, the extracted interface tension as function of the nucleus radius r is independent of system size. We suggest a phenomenological expression to describe the dependence of the extracted interface tension on the nucleus radius r for the liquid-solid system. Moreover, the numerical PFC results show that this dependency can not be fully described by the nonclassical Tolman formula.