Lattice dynamics studies of grain boundary structures: I. Method and application to stability

The method of lattice dynamics has been applied to an atomistic model of a grain boundary with emphasis on its utility in examining structural instability. A 36.9° 001] coincidence symmetrical tilt boundary was used with a Morse pairwise potential. Several structures derived by a static relaxation procedure were studied. Stable structures are characterized by a vibrational spectrum consisting of real frequencies only, while one of the statically relaxed structures yielded a pair of imaginary frequencies and therefore was unstable. A comparison of the lattice dynamics method with other methods for testing stability of a defect configuration is given.