Atomistic calculations of defects in ionic solids-their development and their significance

Methods which have been developed and employed for the calculation of point defects in ionic crystals are described. These methods involve a detailed Hartree-Fock-like treatment by way of angular-momentum-dependent exchange potentials of the ions within an inner region ${\ensuremath{\tau}}_{1}$ centered about the defect. In the outer region ${\ensuremath{\tau}}_{2}$, composed of the rest of the crystal, the ions are treated in two different approximations, the most successful of which involves an effective-mass formalism. Polarization effects are included by expressions of the form resulting from the work of Toyozawa, Haken, and Schottky. Although the main purpose of the paper is to describe the methods, applications are made to the calculation of the electronic energy levels in the optical absorption of the $F$ center in KCl and NaCl. Good agreement with experiment is found only if polarization effects, which are important even in the ground state, are included. Additional applications will be given in subsequent papers.

The energy, the elastic dipole tensor and the entropy of point defects in ionic crystals are usually calculated by the Mott-Littleton approach, which treats a single defect in an infinite crystal. The authors suggest that there may be advantages, particularly for the dipole tensor and the entropy, in performing the calculations in periodically repeating geometry. They examine how this 'supercell' method can be used for the energy and the dipole tensor, paying attention to the problem that for charged defects the repeating unit carries a net charge, so that the Coulomb energy is divergent. They test the supercell method on a number of both charged and uncharged defects, and show that the results for the energy and dipole tensor are in close agreement with those obtained by the conventional approach.

Excitation of Plasmons and Interband Transitions by Electrons. By H. Raether. (Berlin, Heidelberg, New York: Springer-Verlag, 1980.) [Pp. 192+subject index.] Price DM 59, – –/US $32.50 hardback. Physics of Superionic Conductors. Edited by M. B. Salamon. (Berlin, Heidelberg, New York: Springer-Verlag, 1979.) [Pp. xii+248+subject index.] Price DM 59, – –/US $32.50 hardback. Electronic and Vibrational Properties of Point Defects in Ionic Crystals. By Y. Farces and M. P. Fontana. (Amsterdam: North Holland, 1979.) [Pp. xix+247+author and subject index.] Price Dfl. 100.00/US $48.75 hardback. Defects and Diffusion in Solids. An Introduction. By S. Mrowec. (Amsterdam, Oxford, New York: Elsevier, 1980.) [Pp. 464+subject index.] Price Dfl. 170.00/US $83.00 hardback. Fluctuation Phenomena. Edited by E. W. Montroll and J. L. Lebowitz. (Amsterdam: North-Holland, 1979.) [Pp. 340+author and subject index.] Price Dfl. 120.00/US $58.50 hardback. Crystal Growth: A Tutorial Approach. Edited by W. Bardsley, D. T. J. Hurle and J. B. Mullin. (Amsterdam: North-Holland, 1979.) [Pp. vi+401+subject index.] Price Dfl. 110.00/US $53.75 hardback. Liquid Crystals. By S. Chandrasekhar. (Cambridge University Press, 1980.) [Pp. x+336+subject index.] Price £8.95 paperback. Light Scattering in Solids. Edited by J. L. Birman, H. Z. Cummins and K. K. Rebane. (New York: Plenum Press, 1979.) [Pp. xxi+523+author and subject index.] Price US $55.00 hardback (camera-ready typescript). Electrostatics 1979. Edited by J. Lowell. (London, Bristol: The Institute of Physics, 1979.) [Pp. 349+author index.] Price £32.00 hardback. Auger Electron Spectroscopy Reference Manual. By G. E. Mcguire. (New York: Plenum Press, 1979.) [Pp. ix+129.] Price US $39.50 paperback. Laser Handbook, Volume 3. Edited by M. L. Stitch. (Amsterdam: North-Holland, 1979.) [Pp. ix+846+author and subject index.] Price Dfl. 250.00/ US $122.00 hardback.

Various mechanisms for the formation of point defects in ionic crystals are considered. Their probable importance as a function of the energy of the ionizing radiation and the temperature at which the irradiation takes place is discussed. Complex centers formed from aggregates of simple point defects are reviewed and their occurrence is considered in terms of the expected spatial distribution of the point defects. The effect of high-energy X-rays and protons on the ionic conductivity is dis- cussed in terms of a new interpretation of the conductivity curve as a function of temperature, and it is suggested that radiation-enhanced diffusion may be important in explaining the experimental data.

The subsurface electric potential in oriented single crystals of silver chloride has been directly mapped out by a technique based on the equilibrium distribution of a very small concentration of a charged radiotracer. The potential was found to vary with depth according to the Gouy-Chapman solution of Poisson's equation, with screening lengths in the range 10\char21{}20 nm. The surfaces were all negative, relative to the deep interior, by 0.10\char21{}0.30 V, depending on temperature and surface orientation. The present results on the subsurface potential difference can be employed to resolve the Frenkel-pair formation enthalpy and entropy, as determined from transport measurements, into the formation enthalpies and entropies of the individual point defects comprising the pair. For the silver chloride (110) surface, for example, ${G}_{v}$=0.74 eV and ${G}_{i}$=0.37 eV at 150 \ifmmode^\circ\else\textdegree\fi{}C; the best values obtained to date for ${H}_{v}$, ${H}_{i}$, ${S}_{v}$, and ${S}_{i}$, are 0.77 eV, 0.70 eV, 0.79k, and 9.0k, respectively.

The electrostatic potential which arises from a lattice array of point ions is computed in terms of a Taylor's series expansion for small distances from a lattice site. This expansion gives the change in electrostatic energy when an ion moves in the background of a perfect point ion lattice potential. The Taylor's series coefficients for terms up to fourth order in the ion displacement are evaluated for the NaCl and CaF2 lattice structures.

Any deviation from a perfect periodic lattice or structure in a crystal is an imperfection. There are three main types of imperfections, point, line and plane imperfections1, of which we shall deal only with the point defects in this chapter. The point imperfections encountered in ionic solids are: (i) chemical impurities (ii) vacant lattice sites and (iii) interstitial ions. Real crystals are always imperfect in some respect. In thermal equilibrium in an otherwise perfect crystal a certain number of lattice vacancies or interstitials are always present, because the entropy is increased by the presence of disorder in the structure and at a finite temperature, the equilibrium condition of a crystal happens to be a state of minimum free energy.

The Stark effect of localized electronic centres is reviewed by using a few selected examples of impurity centres or simple defects. Important information on the symmetry of centres and on the position of energy levels is obtained through the electric-field-induced absorption changes. Typical results are summarized for the Stark effect on the zerophonon lines and on the broad absorption band of point defects in ionic crystals and of impurities in semiconductors.

The authors present and describe a new embedded-cluster approach for calculating both the electronic and the spatial structure of point defects in ionic crystals with self-consistent incorporation of the polarisation effects into the eigenvalue spectrum and the total energy of a crystal. For the first time both the electronic structure and the ionic displacements within a large cluster containing a defect are obtained in the framework of the same calculating scheme. It permits one to describe correctly back-coupling between redistribution of the electron density in a defective region and polarisation of the rest of the crystal outside the cluster, which can play a vital role for the study of small polaron effects. Making use of a 45-atom cluster with 175 electrons and the semi-empirical INDO method, the authors have simulated the impurity-induced trapping of a hole in the (Li)0 centre in an MgO crystal. The calculations do not use a priori assumptions and do confirm that one-centre localisation of a hole in the ground state is energetically favourable. They show that polarisation energies can differ considerably for the ground and charge-transfer excited states of the defect. It is also demonstrated that the generally accepted model of the O- hole polaron is oversimplified: a considerable charge redistribution between Li+ and another O- along the (100) direction takes place.

Investigation of the electronic structure of point defects in ionic crystals by the cluster scattered wave method with the self-consistent calculation of the lattice distortion and long-range polarization

Atomic transport phenomena in the glow discharge source during the analysis of powders—I. Investigation of model specimens

At each stage of human development, new technical capabilities appear that allow obtaining new, more complete and reliable experimental results. When considering the state of a solid, both experimental data and theoretical interpretation of the results obtained are equally important. A comprehensive, complex consideration of the processes occurring can give a relatively objective idea of the state of matter. In this monograph, theoretical calculations are carried out from the standpoint of molecular-kinetic theory. Molecular-kinetic theory allows us to clarify the main characteristic features of such phenomena in alloys as atomic ordering, atomic diffusion, solubility of atoms in alloys, decomposition of alloys, plastic deformation of metals, heat capacity of alloys, etc. Metal-hydrogen systems are interesting both from a scientific and from an applied point of view. The extreme simplicity of the electronic structure, the small mass and the geometric size of hydrogen atoms make the “metal – hydrogen” systems exceptionally interesting for studying a wide range of problems of modern solid-state physical chemistry. The high mobility of hydrogen in metals makes these systems unique in terms of diffusion, atomic transport phenomena during phase transformations. The studies described in the fifth section of this monograph are significantly ahead of modern technological progress. The results of these studies will be relevant when interplanetary and interstellar flights become commonplace. It is currently known that important components of outer space are substances in the plasma state. This is mainly atomic hydrogen. Therefore, it is very important to know the behavior of structural materials that make up the skin of aircraft (titanium-based alloys and others), and to study the processes that occur when they interact with plasma flows. Thus, the material presented in this section is of exceptional importance for structural materials that can be used in outer space.

The technique of synchrotron white beam topographic imaging in grazing Bragg-Laue geometries has been developed at the Stony Brook synchrotron topography station (beamline X-19C) at the National Synchrotron Light Source. This technique enables both general quality characterization and imaging of defects in subsurface regions of thickness which can range from hundreds of angstroms to hundreds of micrometers as determined by the effective penetration depth of the x rays. This penetration depth, which is shown in most cases to be determined by the kinematical theory of x-ray diffraction, can be conveniently varied in a controlled manner by simple manipulation of the diffraction geometry, thereby enabling a depth profiling of the defect content. The fundamentals of the technique are described, and its advantages and disadvantages compared to existing techniques are discussed. Brief examples of the application of the technique in the characterization of defects in both single crystals and heteroepitaxial systems are given, and the general applicability of the technique is discussed.

The general failure of theory to account for the observed electrical and thermal resistivities associated with dislocations is reviewed in the light of the resonance scattering previously shown to be a characteristic property of linear defects in crystals. Expressions for the scattering width and density of states near a resonance are obtained, and the magnitude of the resonance scattering is shown to be consistent with the observed electrical resistivity of dislocations in a number of metals. Observed stacking-fault electrical resistivities are consistent with the absence of resonance scattering; such scattering is not expected to occur for plane defects. The resonance-scattering mechanism is shown to be capable of accounting for the magnitude of the dislocation thermal resistivity in ionic crystals, and also, possibly, for the much smaller effect in metals. The observed temperature dependence of the thermal resistivity in ionic crystals is rather difficult to explain in terms of resonance scattering, although it would probably be expecting too much for the simple treatment given here to deal adequately with this point. The generally encouraging results would appear to justify the expenditure of more effort, both experimentally and theoretically, on these problems.

Positrons localize in trapped states at a variety of defect sites in solids, from which they subsequently annihilate with unique observable characteristics. As such, the positron is a valuable probe for the study of these defects. Positron annihilation spectroscopy (PAS) has made significant contributions in recent years to the determination of atomic defect properties in metals and alloys, and in molecular solids as well. It has also been used extensively in the monitoring and characterization of vacancy-like microstructure development, as occurs during post-irradiation annealing. The characterization of defects using PAS is selectively reviewed and some possibilities for using the positron as a localized probe of the atomic and electronic structure of atomic defects and their aggregates are discussed.