Total Energy Calculations for Structural Phase Transformations

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Abstract
The structural integrity and physical properties of crys talline solids are frequently limited or enhanced by the occurrence of phase transformations. Martensitic trans formations 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 close- packed 9R structure in sodium metal are described. The minimum energy coordinate or configuration path be tween 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 calcu lational methods used to solve the Schrödinger equa tion include pseudopotentials, fast Fourier transforms, efficient matrix diagonalization, and supercells with many atoms.