Vacancy-stabilized crystalline order in hard cubes

Abstract

We examine the effect of vacancies on the phase behavior and structure of systems consisting of hard cubes using event-driven molecular dynamics and Monte Carlo simulations. We find a firstorder phase transition between a fluid and a simple cubic crystal phase that is stabilized by a surprisingly large number of vacancies, reaching a net vacancy concentration of approximately 6.4% near bulk coexistence. Remarkably, we find that vacancies increase the positional order in the system. Finally, we show that the vacancies are delocalized and therefore hard to detect.hard polyhedra | colloids | free energy T he free energy of crystal phases is generally minimized by a finite fraction of point defects like vacancies and interstitials. However, the equilibrium number of such defects in most colloidal and atomic/molecular crystals with a single constituent is extremely low. Exemplarily, for the face-centered cubic crystal of hard spheres, one of the few colloidal systems where the vacancy and interstitial fractions have been calculated, the fraction of vacancies and interstitials is on the order of 10 −4 and 10 −8 , respectively, near coexistence (1). As such, neither the vacancies nor the interstitials strongly affect the phase behavior, and so most studies of crystals ignore the effect of these defects. Nevertheless, vacancies and interstitials have a significant effect on the dynamics in an otherwise perfect crystal, as the main mechanism for particle diffusion is hopping of particles from filled to empty sites or between interstitial sites.In this paper, we examine a system of hard cubes where, as we will demonstrate, one cannot ignore the presence of vacancies. Arguably, a cube is one of the simplest nonspherical shapes and the archetype of a space-filling polyhedron. Surprisingly, despite the simplicity of this system, we find that the stable ordered phase is strongly affected by the presence of vacancies, so much that vacancies actually increase the positional order and change the melting point. Remarkably, the fraction of vacancies in this system is more than two orders of magnitude higher than that of hard spheres or any other known typical, experimentally realizable, single-component atomic or colloidal system, reaching 6.4% near coexistence. Additionally, while purely hard (not rounded) colloidal cubes are yet to be realized, colloidal cubes with various interactions are now a reality (2-7), and it is likely that hard cubes will be realized in the future.Here, we use Monte Carlo (MC) and event-driven molecular dynamics (EDMD) (8) simulations to examine in detail the effect of vacancies on the equilibrium phase behavior of hard cubes. The model we study consists of N perfectly sharp hard cubes with edge length σ in a volume V . Aside from hard-core interactions that prevent configurations of overlapping cubes, the particles do not interact. In both types of simulation (MC and EDMD), overlaps are detected using an algorithm based on the separating axis theorem (e.g., ref. 9). More information on the EDMD impleme...

Phase Diagram and Structural Diversity of a Family of Truncated Cubes: Degenerate Close-Packed Structures and Vacancy-Rich States

“…In accordance with the observations of Ref. [36], we find that f def ð Þ ¼ f def ð0Þ þ f 1 represents the data accurately, suggesting weak interactions between vacancies. Here, f def ð0Þ is the free energy of a system with no vacancies and f 1 > 0 is the free-energy cost to create a single vacancy.…”

“…The vacancies are delocalized along rows in the crystal lattice, in accordance with the results of Ref. [36], since the particles can easily move with respect to each other and fill up the vacated space.…”

“…This is an unexpected result, since the particle shape varies smoothly from that of a cube to that of an octahedron by truncation. Moreover, we find that the equilibrium concentration of vacancies, which is already unusually high for a simple-cubic phase of cubes [36], increases at a fixed packing fraction upon increasing the level of truncation. In this Letter, we identify and describe in detail the different phases that we obtained, as well as the nature of the phase transitions between these phases.…”

“…For instance, liquid-crystal, plastic-crystal, vacancy-rich simple-cubic, and quasicrystalline mesophases are stabilized by entropy alone under non-closepacked conditions of hard anisotropic particle systems [30][31][32][33][34]36,37]. Predicting the phase behavior from the shape of the building blocks alone is therefore a major challenge in materials science and is crucial for the design of new functional materials.…”

“…To determine the equilibrium vacancy concentration, we calculated the free energy (per particle per k B T) fð Þ as a function of for s ¼ 0:05, s ¼ 0:15, and s ¼ 0:25, at packing fraction ¼ 0:56 using the method as described in Ref. [36]. Surprisingly, Fig.…”