In the world of creation, natural materials may be found in various phases with distinct properties. As a traditional example, carbon is found in two natural phases, the first one is diamond which is a very hard and transparent material, while the second phase is graphite which is a layered dark material. The large abundance of graphite (coal) in nature shows the more thermodynamic stability of this phase of carbon, and therefore diamond is recognized as a metastable phase of carbon that can form under certain conditions (deep in the earth: high pressures). Nowadays, new metastable phases of carbon such as carbon nanotubes, fullerene, and graphene are produced by modern experimental techniques, each of which has interesting characteristics useful for diverse technologies. The discovery of new metastable phases of a substance provides the opportunity to achieve novel properties and thus new applications. A very efficient theoretical scheme to search for new phases of a material is the evolutionary algorithm [1], which is inspired by the natural genetic evolution theory. In this algorithm, first, a set of different structural phases is produced for a certain material, which is called the first generation. Then the energy of these phases is calculated and compared to select a subset of the preferred (more stable) phases. Next, by applying genetic operators to the preferred phases of the first generation, a desired number of new phases are produced to collect the second generation of the candidate phases of the target material. In the same way, the evolution of generations continues and the third, fourth, ... generations are produced until the coincidence of the preferred phases of two consecutive generations. In this case, the genetic algorithm is converged and thus stopped.
Another application of structure search covers the investigation of materials in extreme thermodynamic conditions. Our knowledge of the natural phases of a material is limited to our scientific observations in conventional conditions, while in some cases, such as the inner layers of the Earth, there are extreme thermodynamic conditions (very high pressures) that may lead to the formation of new phases of materials. Experimental investigation of materials in such thermodynamic conditions is very expensive and in some cases impossible, and therefore, structure search algorithms are very suitable tools for theoretical investigation of the phase of a material in extreme thermodynamic conditions.
[1] Oganov, Artem R., Andriy O. Lyakhov, and Mario Valle. "How Evolutionary Crystal Structure Prediction Works and Why." Accounts of chemical research 44.3 (2011): 227-237.