Dimensionality and design of isotropic interactions that stabilize honeycomb, square, simple cubic, and diamond lattices

TL;DR

This study explores whether isotropic interactions designed for specific 2D lattices can also stabilize analogous 3D structures, revealing a transferability that simplifies designing materials with desired periodic arrangements.

Contribution

It demonstrates the transferability of isotropic potentials between 2D and 3D lattices, aiding the design of complex structures through simpler 2D optimization.

Findings

Isotropic potentials designed for 2D lattices also stabilize analogous 3D structures.

Transferability of interactions is robust across different potential forms.

Designing 3D structures can be simplified by targeting 2D analogs.

Abstract

We use inverse methods of statistical mechanics and computer simulations to investigate whether an isotropic interaction designed to stabilize a given two-dimensional (2D) lattice will also favor an analogous three-dimensional (3D) structure, and vice versa. Specifically, we determine the 3D ordered lattices favored by isotropic potentials optimized to exhibit stable 2D honeycomb (or square) periodic structures, as well as the 2D ordered structures favored by isotropic interactions designed to stabilize 3D diamond (or simple cubic) lattices. We find a remarkable `transferability' of isotropic potentials designed to stabilize analogous morphologies in 2D and 3D, irrespective of the exact interaction form, and we discuss the basis of this cross-dimensional behavior. Our results suggest that the discovery of interactions that drive assembly into certain 3D periodic structures of interest can be assisted by less computationally intensive optimizations targeting the analogous 2D lattices.