Total energy calculations for structural phase transformations

The structural integrity and physical properties of crystalline solids are frequently limited or enhanced by the occurrence of phase transformations. Martensitic transformations involve the collective displacement of atoms from one ordered state to another. Modern methods to determine the microscopic electronic changes as the atoms move are now accurate enough to evaluate the very small energy differences involved. Extensive first principles calculations for the prototypical martensitic transformation from body-centered cubic (bcc) to closepacked 9R structure in sodium metal are described. The minimum energy coordinate or configuration path between the bcc and 9R structures is determined as well as paths to other competing close-packed structures. The energy barriers and important anharmonic interactions are identified and general conclusions drawn. The calculational methods used to solve the Schrodinger equation include pseudopotentials, fast Fourier transforms, efficient matrix diagnonalization, and supercells with many atoms