Stability of LS and LS2 crystal structures in binary mixtures of hard and charged spheres

Abstract

We study by computer simulations the stability of various crystal structures in a binary mixture of large and small spheres interacting either with a hard sphere or a screened-Coulomb potential. In the case of hard-core systems, we consider structures that have atomic prototypes CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se and the Laves phases (MgCu2, MgNi2, and MgZn2) as well as a structure with space group symmetry 74. By utilizing Monte Carlo simulations to calculate Gibbs free energies, we determine composition versus pressure and constant volume phase diagrams for diameter ratios of q=0.74, 0.76, 0.8, 0.82, 0.84, and 0.85 for the small and large spheres. For diameter ratios 0.76 < or = q < or = 0.84, we find the Laves phases to be stable with respect to the other crystal structures that we considered and the fluid mixture. By extrapolating to the thermodynamic limit, we show that the MgZn2 structure is the most stable one of the Laves structures. We also calculate phase diagrams for equally and oppositely charged spheres for size ratio of 0.73 taking into consideration the Laves phases and CsCl. In the case of equally charged spheres, we find a pocket of stable Laves phases, while in the case of oppositely charged spheres, Laves phases are found to be metastable with respect to the CsCl and fluid phases.

Entropy-Driven Formation of Binary Semiconductor-Nanocrystal Superlattices

“…Solvent evapora- 20 The same conclusion holds for a size ratio γ of 0.75. Using this combination of PbSe and CdSe NCs, we have also performed solvent evaporation experiments at temperatures below 70°C.…”

“…e γ e 0.61, AlB 2 is stable; [17][18][19] for 0.54 e γ e 0.625, NaZn 13 is stable; 18,19 and for 0.76 e γ e 0.84 it was recently established that the Laves phases (MgZn 2 , MgCu 2 , MgNi 2 ) are stable, 20 although their maximum filling fraction is lower than that of the fcc lattice. Note that between 0.63 e γ e 0.75 there are no known stable binary hard-sphere crystal structures.…”

“…[16][17][18][19][20][21] It has been shown that the crystallization of a binary mixture of micrometer-sized colloidal hard spheres is driven only by an increase in entropy. 16,19,21 In the case of monolayerstabilized NCs in a good organic solvent, the effective interaction consists to a first approximation of van der Waals attraction between the cores and steric repulsion between the stabilizing ligand molecules.…”

“…The self-assembled crystal structures on the TEM grids are compared with the phase diagrams as determined from free energy calculations using the Frenkel-Ladd Einstein thermodynamic integration in computer simulations for binary mixtures of hard spheres. [17][18][19][20] Using this method, the freeenergy can be determined exactly and accounts for all entropic contributions. From the available theoretical predictions, the following conclusions can be drawn (Supporting Information, Section II): apart from the single-component fcc phases, for 0.414 e γ e 0.45, NaCl is stable; 17 for 0.45…”

Crystal-structure prediction via the Floppy-Box Monte Carlo algorithm: Method and application to hard (non)convex particles

“…This is particularly relevant, since densest-packed candidate crystal structure need not be thermodynamically stable at all pressures for which the system crystallizes. 28,51,66,67,95 It is important to realize that there are strong finite-size effects for the prediction of candidates at finite pressure. The pressure P at which we perform the FBMC simulations only sets a range from which we sample crystal structures.…”