Congruent phase behavior of a binary compound crystal of colloidal spheres and dimpled cubes

Abstract

Monte Carlo simulations were performed to study the phase behavior of equimolar mixtures of spheres and cubes having selective inter-species affinity. Such a selectivity was designed to promote the formation of the substitutionally ordered NaCl compound, the "C* phase,"and to be driven not only by energetic bonds but also by entropic bonds generated by dimples on the cube facets. Nestling of the spheres in the cube indentations can promote negative nonadditive mixing and increase the C* phase packing entropy. The focus is on congruent phase behavior wherein the C* phase directly melts into, and can be conveniently accessed from, the disordered state. A specialized thermodynamic integration scheme was used to trace the coexisting curves for varying the values of the interspecies contact energy, ϵ*, the relative indentation size, λ, and the sphere-to-cube size ratio, ζ. By starting from a known coexistence point with ϵ* > 0 and λ = 0 (no indentation), it is found that increasing λ (at fixed ϵ* and ζ) reduces the free-energy and pressure of the C* phase at coexistence, indicative of stronger entropic bonding. Remarkably, it is demonstrated that a purely athermal C* phase (i.e., with ϵ* = 0) can be formed for λ ≥ 0.7 and suitable choices of ζ. A metric of nonadditive (excess) volume of mixing is also suggested as an approximate predictor of athermal C* phase stability. The principles used to engineer selective entropic bonds and compounds with congruent melting are expected to be applicable to other particle shapes and crystalline phases.