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Computer calculations for vacancies in alkali halides with NaCl structure
Author(s) -
Scholz A. H.
Publication year - 1968
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.19680250127
Subject(s) - vacancy defect , coulomb , ion , dipole , alkali metal , lattice (music) , ionic bonding , lattice constant , crystal (programming language) , physics , lattice energy , condensed matter physics , atomic physics , crystal structure , chemistry , crystallography , quantum mechanics , diffraction , electron , acoustics , computer science , programming language
In calculations of the energies of point defects in ionic crystals one conventionally divides the crystal into two regions. Region I contains the defect and a number of its neighbours and all relaxations in region I are handled explicitly. Region II is the rest of the crystal and assumed analytical solutions are used here. All previous calculations have used a rather small region I. A computer method presented in a previous article [12] has been significantly improved and permits the treatment of a large region I containing 256 ions around the vacancy. In particular the polarization energy U Pol was handled much more accurately than before, the electric fields E P and E Dip in region I due to monopoles and dipoles of the ions being the relevant quantities. Since the lattice around the vacancy has full cubic point symmetry we expand E P and E Dip in power series of the displacements σ and dipoles m , and the associated coefficients of such series were evaluated numerically. The Coulomb energy U Coul was treated in a similar way. Hence we obtained suitable and very fast computer programmes for the lattice energy of region I. The evaluated 4733 constant coefficients are included in these programmes. Following Boswarva and Lidiard the effect of region II had to be taken into account; also the interaction of ions in region I with those in region II was estimated. Several numerical results for the vacancy calculations are described.