Prediction of binary hard-sphere crystal structures

Abstract

We present a method based on a combination of a genetic algorithm and Monte Carlo simulations to predict close-packed crystal structures in hard-core systems. We employ this method to predict the binary crystal structures in a mixture of large and small hard spheres with various stoichiometries and diameter ratios between 0.4 and 0.84. In addition to known binary hard-sphere crystal structures similar to NaCl and AlB2, we predict additional crystal structures with the symmetry of CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se, and various structures for which an atomic analog was not found. In order to determine the crystal structures at infinite pressures, we calculate the maximum packing density as a function of size ratio for the crystal structures predicted by our GA using a simulated annealing approach.

Packing of Soft Asymmetric Dumbbells

“…Next is the NiAs-type, where the large spheres pack in an HCP lattice and the small ones again fill the octahedral holes, this time in form of an interpenetrating simple hexagonal lattice. Coexistence of NaCl/NiAs-type crystalline phases in the AB-type mixtures has been observed experimentally and theoretically also in [32,38]. The third crystal type is the FCC lattice of the large spheres, but no order for the small ones.…”

“…Interestingly, we find that for intermediate values of s (1.05 < s 2.4) the system remains fluid, implying that the hard limit has a crystallization gap in the size ratio space. These results are a bit surprising as a few papers dealing with the equilibrium properties of binary AB-type hard-sphere mixtures and hard dumbbells [31][32][33] report the stability of a variety of crystalline structures across a comparable range of size ratios. One would expect some of these structures to also nucleate from the fluids phase in our system, especially the ones predicted for hard dumbbells [33].…”

Hiding in Plain View: Colloidal Self-Assembly from Polydisperse Populations

“…One can reasonably expect that this phase is constituted by a mixture of nanoparticles with distinct mean diameters. Among the varied options [36], only one is of the compact hexagonal space group and contains 12 atoms per unit cell: the MgZn 2 Laves phase. Here, four Mg atoms sit on the four equivalent f Wyckoff positions, while eight Zn atoms are distributed on the six h and two a positions.…”

Predicting patchy particle crystals: Variable box shape simulations and evolutionary algorithms

“…Frequently in the past, the maximum packing fraction criterion has been used as it minimizes the Gibbs free energy at infinite pressure. [11][12][13] For finite pressures, the entropic term cannot be neglected and hence this criterion is not fully reliable. For instance, for binary hard-sphere mixtures, crystalline structures which are not the best packed ones exist as stable phases in the phase diagram.…”

“…For instance, for binary hard-sphere mixtures, crystalline structures which are not the best packed ones exist as stable phases in the phase diagram. 12 Recently, a method has been proposed to cope with hardparticle systems. 14 This approach is a statistical sampling method used as a search strategy for candidate crystals structures of given systems.…”