Efficient Method for Predicting Crystal Structures at Finite Temperature: Variable Box Shape Simulations

We present an efficient and robust method based on Monte Carlo simulations for predicting crystal structures at finite temperature. We apply this method, which is surprisingly easy to implement, to a variety of systems, demonstrating its effectiveness for hard, attractive, and anisotropic interactions, binary mixtures, semi-long-range soft interactions, and truly long-range interactions where the truly long-range interactions are treated using Ewald sums. In the case of binary hard-sphere mixtures, star polymers, and binary Lennard-Jones mixtures, the crystal structures predicted by this algorithm are consistent with literature, providing confidence in the method. Finally, we predict new crystal structures for hard asymmetric dumbbell particles, bowl-like particles and hard oblate cylinders and present the phase diagram for the oblate cylinders based on full free energy calculations.

Figure 1

(a) and (b) correspond, respectively, to the $xy$ and $xz$ faces of the $AB$ crystal structure from Space Group 166 found in the set of predicted phases for size ratios 0.4–0.6. (c) and (d) correspond to the $xy$ and $xz$ phases of the ${\mathrm{AlB}}_2$ crystal structure. Note that the planes made by the small particles in both structures correspond to 2D honeycomb planes, while the large colloids sit on a hexagonal lattice.

Figure 2

Cartoon and predicted crystal structures for hard bowls.

Figure 3

Phase diagram of hard oblate spherocylinders in the packing fraction ($\varphi$) versus dimensionless thickness ($L/D$) representation (d), where the diameter $D$ and thickness $L$ are depicted in (a). The state points in the dark gray area are inaccessible since they lie above the maximum close packing line. $X_{\mathrm{aligned}}$ and $X_{\mathrm{tilted}}$, denote the aligned and tilted crystal structures as shown in (b) and (c), “iso,” “nem,” and “col” are the isotropic, nematic, and the columnar phase, respectively. The lines are a guide to the eye. The coexistence packing fractions of the nematic and the columnar phase for $L/D=0$ are from Ref. 24.