Relaxation and Formation Energy of Vacancies in Metals

Abstract

An expression for the vacancy formation energy in metals is obtained taking into account the associated lattice distortions. For the purpose of finding the electrostatic energy Ewald's method was generalized specially for a lattice with a vacancy. Equations are found for the calculation of the displacements around the vacancy.HonyqeHo BbipameHHe AJIH a~e p r m i 0 6 p a 3 0 s a~~n BaKaHcm B MeTame c yqeTobi BOBHMK~IOIIIHX acKameHui pemeTm. j J n~ Haxomaemirr a n e~~p o c~a~w i e c~o z t a~e p -~H M MeTon, 3 s a n b~a 0 6 0 6~1 e~ AJIH cnysaH pemeTm c BaKaHcHeii. HonyseHbI ypaB-HeHHH &Ill3 HaXOmAeHHR CTaTE19eCKMX CMeUIeHMfi B O K P Y r BaKaHCKMH.

Self‐Interstitials in Normal Metals

“…Minimizing the relaxation energy and following the calculations performed in [2] and [lo] we obtain for the relaxation energy an iteration series, the first two terms of which can be represented as…”

“…where R t ) is the radius vector of an ion of a regular lattice and cn is its displacement from the site. Expanding the structure factor (4) in a series up to second order in the displacement (see [ 2 ] ) it is possible to single out from ( 5 ) the part independent of lattice relaxation. Subtracting from this N E , and adding corrections to Do) and E@) dependent on the electronic density change (first two terms in (7)) we obtain the structural part of the interstitial formation energy For the calculation of the relaxation part of the energy we expand the displacements in terms of normal coordinates of the lattice in the first Brillouin zone.…”

“…Subtracting from this N E , and adding corrections to Do) and E@) dependent on the electronic density change (first two terms in (7)) we obtain the structural part of the interstitial formation energy For the calculation of the relaxation part of the energy we expand the displacements in terms of normal coordinates of the lattice in the first Brillouin zone. Minimizing the relaxation energy and following the calculations performed in [2] and [lo] we obtain for the relaxation energy an iteration series, the first two terms of which can be represented as…”