Changes in the vibrational energies and interatomic spacings upon the formation of vacancies in the volumes and in the cores of crystallite-conjugation regions of polycrystalline transition metals with cubic lattices

The changes in the vibrational energies and the signs of changes in the interatomic spacings upon the formation of vacancies in the bulk of metal and in the cores of the crystallite-conjugation regions (CCR) in polycrystalline transition metals with bcc and fcc lattices have been determined. The vibrational energy increases upon the formation of a vacancy in the bulk of metal because of a positive “relaxation” contribution to the change in the force constant of the atoms surrounding a vacancy. Positive “relaxation” contributions to the changes in the force constants and, correspondingly, an increase in the vibrational energy of the atoms surrounding a vacancy arise also upon the formation of “split” vacancies (S vacancies) in the cores of CCRs of polycrystalline transition metals with a face-centered cubic lattice. The positive “relaxation” contributions to the changes of the force constant of atoms in the region of localization of S vacancies are caused by a decrease in the interatomic spacings upon their formation, just as upon the formation of conventional vacancies in the bulk of metals. The vibrational energy of the nearest environment of the vacancies that are formed in the CCR cores in the polycrystalline d transition metals with a bcc lattice decreases because of a negative “relaxation” contribution to the change in the force constants. The cores of the high-angle CCRs in polycrystalline d transition metals with a bcc lattice are characterized by a negative internal pressure. Therefore, vacancies with positive relaxation volumes νBCC > 0 are formed in them, causing an increase in the interatomic distances in the nearest environment of such vacancies.