Natural crystals like quartz or salt are defined by sharp edges and perfectly flat faces, known as facets. These facets are the macroscopic manifestation of a highly ordered internal atomic structure. The question of whether crystals can possess curved surfaces explores the boundary between the theoretical ideal of a crystal and its real-world growth. While crystalline materials fundamentally prefer flatness, common growth conditions and certain structural exceptions introduce curvature. A crystal’s final shape is a dynamic balance between its intrinsic atomic arrangement and the environment in which it forms.
The Geometry of Ideal Crystals
The flat faces of a crystal are a direct consequence of its periodic, repeating atomic arrangement, which is the defining characteristic of a true crystal. This internal order is built from a repeating block, called the unit cell, which tiles three-dimensional space. When a crystal grows slowly under stable conditions, its final shape is governed by minimizing surface energy.
The energy required to form a new surface is not equal in all directions because the density of atoms differs on various crystallographic planes. Surfaces where atoms are tightly packed have a lower surface energy than those with a looser arrangement. The crystal naturally grows to expose the faces that require the least energy to maintain, which are the low-energy, densely packed planes.
The equilibrium shape of an ideal crystal, described by the Wulff construction, is a convex polyhedron bounded by low-energy facets. If a crystal formed a curved face, it would expose a mix of high-energy and low-energy atomic orientations. This mixture is thermodynamically unstable, meaning the crystal rearranges its atoms to form flat faces to achieve a lower overall energy state. This preference for minimizing surface energy is why flat facets are the defining feature of an ideal crystal.
How Growth Conditions Introduce Curvature
While the ideal crystal favors flat faces, real-world crystals often exhibit visible curvature, typically resulting from non-ideal growth conditions. The most common factor is a rapid growth rate, which is far from the slow, equilibrium state. When material is deposited too quickly, atoms do not have sufficient time to migrate and settle into the lowest-energy, flat-faced configuration.
Rapid deposition leads to kinetic instability at the growing surface, resulting in complex, curved morphologies like dendritic or skeletal growth. Dendrites are treelike or branchlike structures, and their curved surfaces are a direct consequence of rapid solidification. The presence of impurities or specialized additives in the growth solution can also alter the surface energy profile. Certain molecules can adsorb onto specific facets, blocking the deposition of new material and forcing the crystal to grow in other directions, which leads to a rounded, non-faceted appearance.
Curvature can also be introduced at a microscopic level due to internal structural flaws. A large number of internal defects, such as dislocations, create localized strain within the crystal lattice. This built-up strain can be relieved by slightly bending the surrounding planes, resulting in a gradual, overall curvature of the crystal body. Crystals grown on a curved substrate, such as colloidal particles forming on a spherical water droplet, are forced to adopt the curvature of the base. This constraint induces elastic stress, which is often relieved through the formation of ribbon-like, curved domains rather than compact, flat crystals.
Structural Exceptions: Quasicrystals and Non-Facets
Beyond the non-ideal growth of traditional materials, some solids are structurally distinct and inherently capable of forming non-flat surfaces. Quasicrystals represent a unique class of ordered solids that challenge the traditional definition of a crystal. Unlike standard crystals, quasicrystals possess long-range order but lack translational periodicity; their atomic pattern never exactly repeats.
This aperiodic but ordered structure allows quasicrystals to exhibit rotational symmetries—such as five-fold symmetry—that are forbidden in conventional crystals. The complex geometry of the quasicrystal unit, such as the rhombic triacontahedron, can result in shapes that are not simple polyhedra. Their growth can lead to more complex, sometimes rounded or star-like, overall shapes that deviate from the sharp edges of a periodic lattice.
Another exception involves materials that exhibit non-faceted growth because their surface energy is nearly isotropic, or equal in all directions. While rare in inorganic crystals, this occurs in certain organic crystals and colloidal assemblies. If the energy cost of forming any surface orientation is roughly the same, the crystal is no longer driven to expose only the low-energy facets. Instead, the equilibrium shape becomes more spherical or rounded, resulting in smooth, curved surfaces rather than sharp, flat faces. These non-faceted materials demonstrate that true curvature, unassociated with defects or rapid growth, is possible when the energetic constraints of a periodic lattice are either absent or uniform across all orientations.