Point Defects In Ionic Crystals Research Articles

Recommendations for calculating the characteristics of thermal creep of mixed uranium–plutonium oxide fuel when analyzing fuel-element serviceability

Recommendations for calculating the characteristics of thermal creep of mixed uranium‐plutonium oxide fuel when analyzing the serviceability of fuel elements are developed on the basis of a physical model of deformation. The deformation processes in the model include diffusion and diffusion-controlled motion of dislocations. It is shown on the basis of an analysis of the thermodynamics of point defects in ionic crystals that the diffusion of ions in the cationic sublattice is controlled by the vacancy and displacement mechanisms and the coefficient of diffusion depends on the temperature and the oxygen coefficient. The model takes account of the effect of temperature, stress, fuel density, plutonium content, grain size, and oxygen coefficient on the creep rate. The application of physical ideas to obtain computational relations made it possible to improve by more than a factor of 10 the agreement between the calculations and the experimental data as compared with the previously used empirical relations to describe the characteristics of creep. The use of mixed uranium‐plutonium oxide fuel in the fuel elements in power reactors is a necessary condition for adopting a closed fuel cycle and expanding the raw materials resources of nuclear power. Adding to the knowledge base on the properties of mixed fuel is a necessary and important problem for designing fuel elements to be used in power reactors. Recommendations for calculating the characteristics of thermal creep of uranium dioxide are presented in [1]. The objective of the present work is to obtain relations for calculating the characteristics of thermal creep of mixed uranium‐plutonium oxide fuel. Analysis of the experimental data on the thermal creep of mixed fuel has shown that the creep rate is a linear function of the stress for σ≤ 30‐40 MPa. A power law with exponent 4‐5 is observed at high stress levels. The creep rate at low stress is inversely proportional to the squared grain size. Therefore, just as in uranium dioxide [1], the creep rate ξ can be represented in the following form with accuracy to verification coefficients in a wide range of stresses:

Recommendations for calculating the thermal creep properties of uranium dioxide when analyzing fuel-element serviceability

Recommendations for calculating the thermal creep properties of uranium dioxide for fuel element serviceability analysis programs are developed on the basis of a physical model. The deformation processes in the model include diffusion and diffusion-controlled motion of dislocations. It is shown on the basis of the analysis of the thermodynamics of point defects in ionic crystals that the diffusion of ions is controlled by a vacancy mechanism and that the diffusion coefficient depends on the temperature and oxygen coefficient. The model includes the influence of temperature, stress, fuel density, grain size, and oxygen ratio on the creep rate. The relations obtained in the this work have made it possible to improve by approximately a factor of 10 the agreement between the calculations and experimental data as compared with the empirical relation used previously to describe the characteristics of creep.

Ground- and excited-state properties ofM-center oxygen vacancy aggregates in the bulk and surface of MgO

Aggregates of oxygen vacancies (F centers) represent a particular form of point defects in ionic crystals. In this study we have considered the combination of two oxygen vacancies, the M center, in the bulk and on the surface of MgO by means of cluster model calculations. Both neutral and charged forms of the defect M and ${M}^{+}$ have been taken into account. The ground state of the M center is characterized by the presence of two doubly occupied impurity levels in the gap of the material; in ${M}^{+}$ centers the highest level is singly occupied. For the ground-state properties we used a gradient corrected density functional theory approach. The dipole-allowed singlet-to-singlet and doublet-to-doublet electronic transitions have been determined by means of explicitly correlated multireference second-order perturbation theory calculations. These have been compared with optical transitions determined with the time-dependent density functional theory formalism. The results show that bulk M and ${M}^{+}$ centers give rise to intense absorptions at about 4.4 and 4.0 eV, respectively. Another less intense transition at 1.3 eV has also been found for the ${M}^{+}$ center. On the surface the transitions occur at 1.6 eV ${(M}^{+})$ and 2 eV (M). The results are compared with recently reported electron energy loss spectroscopy spectra on MgO thin films.

The mechanism of interaction of dislocations with point defects in ioniccrystals

A mechanism of interaction of dislocations with point defects is suggestedon the basis of a study of deformation-stimulated luminescence (DL)from irradiated KCl. DL is considered to be a result of destruction ofhole colour centres by dislocations. The centres destroyed by dislocationsare responsible for irradiation-induced strengthening of alkali halides.

Effect of a weak magnetic field on the state of structural defects and the plasticity of ionic crystals

The aim of this work is to examine the influence of a weak (on the energy scale) magnetic field on the state of dislocations and point defects in ionic crystals. It is found that complex point defects existing in a metastable state are sensitive to a magnetic field B∼1 T. The contributions are identified, and the kinetics of various types of reactions within the structural defects and between them leading to plastification of the crystals in a magnetic field are determined. The effect of light on the sensitivity of the point defects to a magnetic field is described, and the spectral characteristics of this effect are determined. A resonant effect of the combined action of a weak constant magnetic field and a high-frequency magnetic field on the dislocation mobility is found to occur when these fields satisfy the conditions of electron paramagnetic resonance.

Dislocations used to probe the defect state of an ionic crystal lattice excited by a pulsed magnetic field

This paper presents the results of an investigation into the effect of a pulsed magnetic field on the state of linear and point defects in ionic crystals. For different amplitudes (1–7 T) and pulse lengths (3×10−5 to 102 s) of the pulsed field the kinetics of the transformation of defects into a new state and their relaxation after the field is turned off are studied in the temperature range 77–400 K. It is found that the relaxation of the states of point defects is mainly through recombination, and the change of state of the dislocations and of the point defects contribute nonadditively to the change in the dislocation mobility. The exposure of the crystal to a magnetic field leads to an increase in the dislocation mobility when the sample is mechanically stressed and to a decrease in the dislocation displacement with a second field pulse.

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

Abstract This paper describes the calculations of the electronic structures of the F-center in NaCl, pure anion vacancy. F+ and F-centers in MgO by the embedded cluster method. This work is an alternative approach relative to the ICECAP method within which the embedded cluster model based on Johnson's Scattered Wave method is combined with the Mott-Littleton method. The main features of the model are: self-interaction correction of single-particle energies in the case of perfect crystals and point defects whose states are in the band gap of a perfect crystal: Mott-Littleton method modification allowing for the description of the defect wave function in the analytical form: construction of the cluster one-electron potential when describing the rest of the crystal in shell model terms.

Role of induced quadrupoles in the simulation of intrinsic point defects in AgCl and NaCl.

The paper presents a detailed formulation of the energetics of point defects in ionic crystals that takes into account the quadrupolar deformation of the ions surrounding the defect within a polarizable-point-ion picture. The dipolar polarizabilities are modeled to represent correctly the static dielectric response of the crystal. Consideration of the axial symmetry of the electric-field-gradient tensor, the residual site symmetries in the defect crystal, and the symmetry of the quadrupolar-polarizability tensor leads to a cylindrical symmetry for the induced quadrupoles for both the vacancy and interstitial type of defects. These quadrupoles give rise to an additional polarization contribution to the defect formation besides affecting the dipolar energy. Computer codes have been developed based on this model and results are presented for vacancies and interstitials in AgCl and NaCl and discussed in detail. The calculations use a two-body central-force potential with well-represented van der Waals interactions. It is found that there is a substantial contribution from the quadrupoles to the defect enthalpy. The investigations reveal the comparative importance of accurate modeling of the polarization features vis \`a vis subtle refinements in the interionic potential.

An Extended Polarizable Point Ion Model for Schottky Defects

AbstractThe polarizable point ion model for Schottky defects is extended to include the effects of induced quadrupoles in region 1. Schottky defects in AgCl are studied using this model. It is found that it is important to include induced quadrupole moments in any theoretical treatment of charged point defects in ionic crystals. Quadrupolar deformations make sizable contribution to the defect energy which ranged from −0.2 to −0.4 eV in the case of the cation vacancy over the range of anion quadrupole polarizabilities studied. The work further points to the relative significance of chlorine ions in respect of the quadrupole distortions.

The volume of formation of point defects in ionic crystals

Abstract In this Letter we report calculated values of the volume of formation of Schottky defects in ionic crystals using a three-body-force shell model which includes the effects of charge transfer arising from electron shell overlap. It is shown that the volume-derivative method suggested by Gillan (1981) can reproduce the experimental data reasonably well when a suitable interionic potential is used.

Multipole Theory of the Polarization of Solids by Point Defects. IV. Electronic and Spatial Structure of Single Electronic and Hole Centers and Their Pairs in LiF, KCl Crystals

AbstractA method proposed previously for calculating the electronic and spatial structure of neutral and charged point defects in ionic crystals with self‐consistent incorporation of the polarization effects into the eigenvalue spectrum is applied to the calculation of characteristics of concrete single electronic (F2, F, F) and hole (H, Vk, V2) centers and their pairs ({F, Vk}, {F, H}) in LiF, KCl crystals. The necessity of self‐consistent evaluation of polarization, as well as the dependence of calculation results on approximations used in simulating uncompensated charge density in defective region are discussed. Approximations based on point and non‐point polarizable charges (simulators) are compared. The electronic structure of defects is calculated on the basis of the INDO semiempirical method.

Individual formation parameters of charged point defects in ionic crystals: Silver chloride.

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.

Quantum-chemical simulation of impurity-induced trapping of a hole: (Li)0centre in MgO

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.

Dielectric Huang scattering from point defects in ionic crystals

Abstract We discuss the intensity of the scattering of X-rays or neutrons from point defects in ionic crystals. It is well known that the long-range elastic distortion field surrounding a defect causes the intensity to diverge as the scattering wave-vector approaches a reciprocal lattice vector, an effect known as Huang scattering. We show that the dielectric polarization field surrounding a defect with a net charge in an ionic crystal gives rise to a divergence of the same kind and we derive a formula for the intensity, which includes this dielectric contribution. Published experimental analyses of Huang scattering in ionic crystals have not taken account of this contribution, and may need to be reconsidered.

The calculation of free energies of point defects in ionic crystals

We discuss the calculation of defect enthalpies, entropies and volumes within the quasi-harmonic approximation. A general program for calculating defect entropies at constant volume (SHEOL) is described. It is shown that the defect entropy at constant volume cannot be used as an approximation for the defect entropy at constant pressure and that the volume dependence of the defect entropy cannot be ignored in calculating volumes of formation and migration. The use of Vineyard's theory is discussed and a simple method given for correcting it when the energy surface near the saddle point is grossly anharmonic in one direction. The problem of the correct specification of interionic potentials at finite temperature is considered and a general method suggested for solving it.

The energy and elastic dipole tensor of defects in ionic crystals calculated by the supercell method

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.

The Formation Energy of Point Defects in Ionic Crystals

Simple calculations have been made of the formation energy of different types of defect centres such as those formed by hexavalent uranium introduced into lithium fluoride in an oxygen atmosphere. The Coulomb energies are compared for different configurations of the same defects. The method of calculation is described and results quoted for configurations including, in addition to oxygen ions, (a) a uranium ion and a divalent positive ion, (b) a uranium ion and a negative-ion vacancy and (c) two uranium ions.

The elastic dipole tensor for point defects in ionic crystals

The author discusses the problem of calculating the elastic dipole tensor G for point defects in ionic crystals. It is shown that the relation between G and the derivative with respect to bulk strain of the defect formation energy Delta E provides a natural and practical means of calculating G. This relation may be exploited either by computing Delta E for a series of values of strain and extracting the derivative numerically, or by making use of an explicit expression for G in terms of the relaxed ionic positions. The method of calculation is illustrated for some colour centres for which experimental values of G are available: the H, Vk and O2- centres in alkali halides and the V- centre in MgO. He obtains satisfactory agreement with experiment for the H and O2- centres, but rather poor agreement of the Vk and V- centres. He discusses what may be learnt from the comparison between theory and experiment for G and suggests that further compositions of this kind may contribute to the improvement of atomistic models for point defects in ionic crystals.

Electronic and vibrational properties of point defects in ionic crystalsby Y. Farge and M. P. Fontana

<i>Electronic and vibrational properties of point defects in ionic crystals</i>by Y. Farge and M. P. Fontana

Defects in Crystalline Solids Vol 11 – Electronic and Vibrational Properties of Point Defects in Ionic Crystals

Y Farge and M P Fontana 1979 Amsterdam: North-Holland xix + 271 pp price $48.75 This is the English version of a book that was first published in French in 1974. The authors have rearranged the original material, and brought it up to date in some places where fundamental advances have been made.