Crystal structures of metals are often treated as dense packing of atomic spheres. Face-centered cubic and hexagonal close-packed structures are favored in many metals. Long-period-stacking structures such as 9$R$ are sometimes formed. However, nonclose packed structures such as body centered cubic and $\omega$ are formed depending upon chemistry and process conditions. Even in metallic elements, it is a priori unknown how such close/nonclose packed structures are formed and what are their interrelationships. In the present study we show a simple algorithm for automated searching of the phase-transition pathway based upon first-principles calculations, which is applied to systematically pursue the evolution of crystal structures. Following the present algorithm, dynamical stability and interrelationships of different structures generated from a simple cubic structure are revealed for seven metallic elements. Effects of pressure are examined as well. The powerfulness of the automated method to investigate the nature of the phase transition and to predict as-yet-unknown metastable structures is demonstrated.

• Received 14 February 2013

DOI:https://doi.org/10.1103/PhysRevB.87.184104