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We have calculated the lattice distortion produced by a single vacancy in Na, K, Rb, and Cs. The calculations have been carried out using the technique of lattice statics, which is based on the Fourier transformation of the direct-space equilibrium equations, making consistent use of discrete lattice theory. Three distinct types of potential have been used to describe the interactions between the host atoms. The first of these applies only to sodium, and contains an ion-electron-ion term derived from the measured phonon dispersion curves. The second applies only to potassium, and has been similarly obtained. The third is based on a model pseudopotential and applies to all four metals. Comparison has been made between our displacements due to a single vacancy in Na, using the first of these potentials, and analogous results obtained by a semidiscrete method in which only the atoms in the first five shells are allowed to relax. The agreement is reasonable for atoms in the first two neighbor shells about the vacancy, but poor for atoms farther away. The calculated displacements have been used to calculate the dilatations and relaxation energies associated with single vacancies in alkali metals. There is a large discrepancy between the magnitudes of these quantities calculated using the first Na potential and those obtained using the second Na potential, and a similar discrepancy exists between the two sets of K results. We have also used the method of lattice statics to determine the strain-field interaction energies between several types of vacancy pairs in these metals. In every case we find the next-nearest-neighbor configuration to be the most stable, whereas in the nearest-neighbor configuration, the two vacancies repel one another. The magnitudes of these binding energies depend strongly on which model potential is used.

We have calculated the lattice distortion produced by a body-centered interstitial Cu atom in a Cu host lattice. The calculations have been carried out consistently on the basis of discrete lattice theory, using the technique of lattice statics which is based on the Fourier transformation of the direct-space equilibrium equations. The force constants for the perfect lattice have been taken from measured phonon-dispersion curves, and we have used Huntington's Born-Mayer potential to describe the interaction between the interstitial atom and the atoms of the host lattice. The comparison of our results with those obtained by earlier workers, using semidiscrete matching techniques in which a continuum displacement solution is matched to the displacements of a few close neighbors of the defect, indicates that this latter technique is very unreliable. Similarly, the activation volumes estimated by semidiscrete techniques are also unreliable. We have also used the technique of lattice statics to calculate the strain-field interaction between two body-centered interstitial Cu atoms as a function of their separation. As in the case of the displacement fields, we have made these calculations for two different models which differ in the input elastic constants. For what we believe to be the most realistic of our models, we find a repulsive energy of 0.40 eV for two nearest-neighbor interstitials and a repulsive interaction of 0.0975 eV between two second-neighbor interstitials, For the same model, the calculated formation volume per interstitial is 1.12 atomic volumes.

We have carried out molecular-dynamics simulations on BaXF 4 compounds, where X is Mg, Mn, or Zn. Ab initio potentials, with no adjustable parameters, were used to obtain short-range interactions between ion pairs. We found a polar ground-state structure which is in agreement with the A2 1 am space group reported experimentally. We were able to reverse polarization in BaMgF 4 at high temperatures, using large fields, but were unable to reverse polarization in the other compounds. The second-order phase transition in the Mn compound at 250 K was reproduced. We believe this to be the first extension of molecular dynamics to materials consisting of chains of F octahedra. We have carried out molecular-dynamics simulations on BaXF, compounds, where X is Mg, Mn, or Zn. Ab initio potentials, with no adjustable parameters, were used to obtain short-range interactions between ion pairs. We found a polar ground-state structure which is in agreement with the A2,am space group reported experimentally. We were able to reverse polarization in BaMgF, at high temperatures, using large fields, but were unable to reverse polarization in the other compounds. The second-order phase transition in the Mn compound at 250 K was reproduced. We believe this to be the first extension of molecular dynamics to materials consisting of chains of F octahedra. ©1994 The American Physical Society