Thermodynamic behavior of binary mixtures of hard spheres: Semianalytical solutions on a Husimi lattice built with cubes

Abstract: We study binary mixtures of hard particles, which exclude up to their $k$th nearest neighbors ($k$NN) on the simple cubic lattice and have activities $z_k$. In the first model analyzed, point particles (0NN) are mixed with 1NN ones. The grand-canonical solution of this model on a Husimi lattice built with cubes unveils a phase diagram with a fluid and a solid phase separated by a continuous and a discontinuous transition line which meet at a tricritical point. A density anomaly, characterized by minima in isobaric curves of the total density of particles against $z_0$ (or $z_1$), is also observed in this system. Overall, this scenario is identical to the one previously found for this model when defined on the square lattice. The second model investigated consists of the mixture of 1NN particles with 2NN ones. In this case, a very rich phase behavior is found in its Husimi lattice solution, with two solid phases - one associated with the ordering of 1NN particles ($S1$) and the other with the ordering of 2NN ones ($S2$) -, beyond the fluid ($F$) phase. While the transitions between $F$-$S2$ and $S1$-$S2$ phases are always discontinuous, the $F$-$S1$ transition is continuous (discontinuous) for small (large) $z_2$. The critical and coexistence $F$-$S1$ lines meet at a tricritical point. Moreover, the coexistence $F$-$S1$, $F$-$S2$ and $S1$-$S2$ lines meet at a triple point. Density anomalies are absent in this case.