The phase behavior of hard superballs is examined using molecular dynamics
within a deformable periodic simulation box. A superball's interior is defined
by the inequality ∣x∣2q+∣y∣2q+∣z∣2q≤1, which provides a
versatile family of convex particles (q≥0.5) with cube-like and
octahedron-like shapes as well as concave particles (q<0.5) with
octahedron-like shapes. Here, we consider the convex case with a deformation
parameter q between the sphere point (q = 1) and the cube (q = 1). We find that
the asphericity plays a significant role in the extent of cubatic ordering of
both the liquid and crystal phases. Calculation of the first few virial
coefficients shows that superballs that are visually similar to cubes can have
low-density equations of state closer to spheres than to cubes. Dense liquids
of superballs display cubatic orientational order that extends over several
particle lengths only for large q. Along the ordered, high-density equation of
state, superballs with 1 < q < 3 exhibit clear evidence of a phase transition
from a crystal state to a state with reduced long-ranged orientational order
upon the reduction of density. For q≥3, long-ranged orientational order
persists until the melting transition. The width of coexistence region between
the liquid and ordered, high-density phase decreases with q up to q = 4.0. The
structures of the high-density phases are examined using certain order
parameters, distribution functions, and orientational correlation functions. We
also find that a fixed simulation cell induces artificial phase transitions
that are out of equilibrium. Current fabrication techniques allow for the
synthesis of colloidal superballs, and thus the phase behavior of such systems
can be investigated experimentally.Comment: 33 pages, 14 figure