It is conjectured that crystal nets may minimize entropy in the following sense. Suppose one is given an ensemble of uniformly discrete Euclidean graphs that fill space, with vertices representing atoms or molecular building blocks and with edges representing bonds or ligands, extending through all space to represent a solid. For some restrictions, there may be a unique Euclidean graph that minimizes a reasonably defined energy function, and the conjecture is that that Euclidean graph may necessarily be periodic. This question is still open, but some researchers observe crystal nets of high symmetry tending to predominate observed Euclidean graphs derived from some classes of materials.
Historically, crystals were developed by experimentation, currently formalized as combinatorial chemistry, but one contemporary desideratum is the synthesis of materials designed in advance, and one proposal is to design crystals (the designs being crystal nets, perhaps represented as one unit cell of a crystal net) and then synthesize them from the design. This effort, in what Omar Yaghi described as reticular chemistry is proceeding on several fronts, from the theoretical to synthesizing highly porous crystals.
One of the primary issues in annealing crystals is controlling the constituents, which can be difficult if the constituents are individual atoms, e.g., in zeolites, which are typically porous crystals primarily of silicon and oxygen and occasional impurities. Synthesis of a specific zeolite de novo from a novel crystal net design remains one of the major goals of contemporary research. There are similar efforts in sulfides and phosphates.
Control is more tractable if the constituents are molecular building blocks, i.e., stable molecules that can be readily induced to assemble in accordance with geometric restrictions. Typically, while there may be many species of constituents, there are two main classes: somewhat compact and often polyhedral secondary building units (SBUs), and linking or bridging building units. A popular class of examples are the Metal-Organic Frameworks (MOFs), in which (classically) the secondary building units are metal ions or clusters of ions and the linking building units are organic ligands. These SBUs and ligands are relatively controllable, and some new crystals have been synthesized using designs of novel nets. An organic variant are the Covalent Organic Frameworks (COFs), in which the SBUs might (but not necessarily) be themselves organic. The greater control over the SBUs and ligands can be seen in the fact that while no novel zeolites have been synthesized per design, several MOFs have been synthesized from crystal nets designed for zeolite synthesis, such as Zeolite-like Metal-Organic Frameworks (Z-MOFs) and zeolitic imidazolate framework (ZIFs).