Theorists Found a Way of Predicting the Shapes of Crystals Lacking Symmetry

The shape of a crystal is defined by its underlying chemistry, a feature that eventually dictates its final form from the most fundamental of aspects. However, when a crystal lacks symmetry, the surface energies of its facets are unknown, complicating any theoretical prediction of its structure.

But researchers from Rice University have found a way of predicting how crystals will take shape based on their underlying chemistry even when they lack symmetry by assigning arbitrary surface energies or, in the case of 2D materials, edges.

Theorists Found a Way of Predicting the Shapes of Crystals Lacking Symmetry Pixabay/cocoparisienne

Predicting Crystal Shapes

The method described in the study, titled "Defining Shapes of Two-dimensional Crystals With Undefinable Edge Energies" published in Nature Computational Science, shows that using what are known as auxiliary edge energies can bring predictions back in line with the Wulff construction, a geometrical recipe that has been used for over 100 years to know how crystals formed in their shapes.

Lead author Boris Yakobson, an alumnus of Luqing Wang, along with colleagues at Rice's George R. Brown School of Engineering provides methods that use any integers for the right-hand components in the equations while still delivering the correct unique shape-solution, as per SciTech Daily.

Yakobson said the issue of crystal shapes is compelling. But academics have been attempting and failing to compute surface energy for asymmetrical crystals for years. The team discovered that they were going down a rabbit hole, but understood that there should be a method to figure it out just as nature has found a solution through a gazillion atomic motions.

Yakobson stated that the new work was driven by the current surge in interest in 2D materials. He explained that they had a 'eureka' moment after switching from geometrical to algebraic reasoning and included closure equations with arbitrary parameters.

After running it all through the computer, they saw a well-defined form emerge. Wang highlighted that the hard part was convincing their viewers that edge energy is undefinable but there is a solution.

Significance of Predicting Crystal Shapes

The findings might be useful to researchers who build crystals from the bottom up for catalytic, light-emitting, sensing, magnetic, and plasmonic applications, particularly when the morphologies and active edges are critical.

Natural crystals have the luxury of geological time. According to Science Daily, they build their shapes by "relentlessly executing a trial-and-error experiment" as they seek equilibrium or the lowest energy of all their constituent atoms.

However, they must rely on the energies of outward-facing atoms because computational and theoretical techniques cannot cope with billions of atoms at once. That is sufficient for numerous crystals with equal facets or edges.

Almost all of the atoms in 2D materials are "outward-facing," and when their edges are all symmetrical, completing a Wulff construction is straightforward after computing the edge energies using density functional theory.

However, Yakobson noted that the estimated average energy is worthless when all of the edges deviate or are assymetrical. He said that nature has the answer to shape crystals regardless of what it knows or does not know about surface energies. The challenge now is to mimic it with theory.