Binary cluster crystals formed by ultrasoft particles: Classical density functional theory

We provide evidence of the existence of cluster crystals formed by a binary mixture of ultrasoft, cluster-forming particles, interacting via a "generalized exponential model of index 4." In an effort to reduce the high dimensionality of the parameter space of a general binary mixture (and keeping the computational costs within a reasonable range), we have investigated a binary, size-symmetric, equimolar mixture of these particles: here, the like-particle interactions are identical, while the cross interaction between particles is scaled by a factor ζ, a parameter that plays a pivotal role in our investigations. Applying classical density functional-DFT-(with a mean-field format and a spherically symmetric Gaussian shape for the density profiles), we identify via an unbiased, unrestricted optimization of the functional with respect to the parameters of the density profile and among "all possible lattice structures," two ordered cluster crystal phases, a BCC-type and a tetragonal lattice; for the latter one, we recover-as ζ → 1-the FCC lattice that has already emerged in the phase diagram of the one component, cluster-forming systems. The degree of elongation of the tetragonal lattice is induced by ζ and the density. The phase diagram provides evidence that the BCC phase is able to form stable cluster crystals in a wedge-shaped area in the temperature (T) vs density (ρ) plane up to a threshold value ζth, beyond which only the tetragonal lattice remains as the only ordered cluster crystal. A thorough discussion of the characteristic parameters of the system-such as the occupancy of the clusters or the width of the density profile-as we vary the external parameters T, ρ, and ζ provides a comprehensive and exhaustive insight into the properties of this remarkable phase. A brief account is given to ongoing computer simulations, which provide a stringent assessment of the simplifying assumptions that were imposed by the DFT approach.