Using density functionals from fundamental measure theory, phase diagrams and crystal-fluid surface tensions in additive and nonadditive (Asakura-Oosawa model) two-dimensional binary hard-disk mixtures are determined for the whole range of size ratios $q=\text{small}\text{diameter/large}\text{diameter}$, assuming random disorder (lattice points or interstitial occupied by large or small disks at random) in the crystal phase. The fluid-crystal transitions are first order due to the assumption of a periodic unit cell in the density-functional calculations. Qualitatively, the shape of the phase diagrams is similar to the case of three-dimensional hard-sphere mixtures. For the nonadditive case, a broadening of the fluid-crystal coexistence region is found for small $q$, whereas for large $q$ a vapor-fluid transition intervenes. In the additive case, we find a sequence of spindle-type, azeotropic, and eutectic phase diagrams upon lowering $q$ from 1 to 0.6. The transition from azeotropic to eutectic is different from the three-dimensional case. Surface tensions in general become smaller (up to a factor 2) upon addition of a second species and they are rather small. The minimization of the functionals proceeds without restrictions and optimized graphics card routines are used.

• Received 16 May 2018

DOI:https://doi.org/10.1103/PhysRevE.98.012608