The displacements and polarization caused by point defects in ionic crystals

Hardy, J. R.; Lidiard, A. B.

doi:10.1080/14786436708220930

Cited by 44 publications

(4 citation statements)

References 18 publications

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“…In other words, the value of ∆E is computed as the difference in formation energies between strained and unstrained environments. Two prominent methods of computing the dipole tensor are available in the literature, namely, the Kanzaki Hardy forces method 36,37 , and Gillan's strain derivative relation 38,39 . The latter method is used in this paper because (a) it has been shown to be the more accurate of the two 38 , and (b) it is applicable to complex defects (such as interstitial clusters), a situation where the Kanzaki Hardy forces method might not be easily applicable due to the difficulty in unambiguously deciding which atoms are part of the defect, and which atoms are part of the environment.…”

Section: B Dipole Tensor Computationmentioning

confidence: 99%

Method to account for arbitrary strains in kinetic Monte Carlo simulations

et al. 2013

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We present a method for efficiently recomputing rates in a kinetic Monte Carlo simulation when the existing rate catalog is modified by the presence of a strain field. We use the concept of the dipole tensor to estimate the changes in the kinetic barriers that comprise the catalog, thereby obviating the need for recomputing it from scratch. The underlying assumptions in the method are that linear elasticity is valid, and that the topology of the underlying potential energy surface (and consequently, the fundamental structure of the rate catalog) is not changed by the strain field. As a simple test case, we apply the method to a single vacancy in zirconium diffusing in the strain field of a dislocation, and discuss the consequences of the assumptions on simulating more complex materials.

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Section: B Dipole Tensor Computationmentioning

confidence: 99%

Method to account for arbitrary strains in kinetic Monte Carlo simulations

et al. 2013

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“…This change in energy due to external strain can be described, to first order, by the elastic dipole tensor. [45][46][47]53,54 The change in energy is given by…”

Section: Dipole Tensor Formalismmentioning

confidence: 99%

Impact of homogeneous strain on uranium vacancy diffusion in uranium dioxide

et al. 2015

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We present a detailed mechanism of, and the effect of homogeneous strains on, the migration of uranium vacancies in UO2. Vacancy migration pathways and barriers are identified using density functional theory (DFT) and the effect of uniform strain fields are accounted for using the dipole tensor approach. We report complex migration pathways and non-cubic symmetry associated with the uranium vacancy in UO2 and show that these complexities need to be carefully accounted for to predict the correct diffusion behavior of uranium vacancies. We show that under homogeneous strain fields, only the dipole tensor of the saddle with respect to the minimum is required to correctly predict the change in the energy barrier between the strained and the unstrained case. Diffusivities are computed using kinetic Monte Carlo (KMC) simulations for both neutral and fully charged state of uranium single and di-vacancies. We calculate the effect of strain on migration barriers in the temperature range 800 -1800 K for both vacancy types. Homogeneous strains as small as 2% have a considerable effect on diffusivity of both single and di-vacancies of uranium, with the effect of strain being more pronounced for single vacancies than di-vacancies. In contrast, the response of a given defect to strain is less sensitive to changes in the charge state of the defect. Further, strain leads to anisotropies in the mobility of the vacancy and the degree of anisotropy is very sensitive to the nature of the applied strain field for strain of equal magnitude. Our results suggest that the influence of strain on vacancy diffusivity will be significantly greater when single vacancies dominate the defect structure, such as sintering, while the effects will be much less substantial under irradiation conditions where di-vacancies dominate.

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“…He also finds that the polarizability of the lattice ions leads to different displacements of ionic cores and shells (in the language of the shell model, see Sect. 27) (HARDY, 1962a;HARDY and LIDIARD, 1967), the difference being the larger the more polarizable the ions. Page's results for some ionic shells along a (100) direction are given in Fig.…”

Section: Substituting Into H a One Has (S=o)mentioning

confidence: 98%

Vibrational Infrared and Raman Spectra of Non-Metals

Bilz¹,

Strauch²,

Wehner³

1984

Light and Matter Id / Licht Und Materie Id

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The vibrational properties of crystals determine the photon infrared absorption, inelastic neutron scattering and, to a large extent, inelastic photon scattering by phonons, i.e., Raman scattering. The interpretation of infrared and Raman spectra requires, therefore, an understanding of the basic features of lattice dynamics. The quantum theory of solids describes the crystal properties in terms of elementary excitations and their mutual interactions. Dynamic properties are represented by phonons (lattice vibrations) and their interactions mainly with other phonons (anharmonicity), electrons (electron-phonon coupling), and photons (interaction with radiation). This characterizes the scope of the article. Its emphasis is on the interrelation between theory and experiment, i.e., on the microscopic or model interpretation of experimental spectra.Work on infrared absorption and Raman scattering of non-metallic solids was summarized twenty years ago in two review articles in this Encyclopedia by LECOMTE (1958) and by MIZUSHIMA (1958). Since then, many important new experimental data have become available, thanks to very refined techniques for measuring spectra of pure and imperfect single crystals. Furthermore, the theory of the interactions of phonons and photons has been much improved, stimulated by the remarkable development of the theory of lattice vibrations and the mathematical techniques of many-body physics.In this article we describe the dispersion and absorption of infrared radiation and Raman scattering in non-metallic crystals, both perfect and containing point defects. At present, quantitative calculations are usually restricted to diatomic crystals, especially those with simple structures such as the alkali halides or germanium and its homologues, since our knowledge of lattice vibrations is still rather poor for polyatomic and low-symmetry crystals. The theory of lattice vibrations, as reviewed by COCHRAN and COWLEY (1967) in Vol. XXV /2a of this Encyclopedia, constitutes the background and the natural starting point for our investigations. There are other recent reviews by LUDWIG (1967), COCHRAN (1971), MARADUDIN et al. (1971), SINHA (1973), and several articles in: HORTON and MARADUDIN (eds., 1974). A summary of the developments during the last few years is given in Chap. B.An important part of the theory of lattice vibrations is the construction of models. A good example is the so-called shell model for phonons (see Sect. 4) which describes the adiabatic linear electron-ion interaction in terms of localized charges and coupling constants. This provides a natural explanation of some long-range ion-ion forces in insulators in terms of induced dipole forces. Anharmonic extensions of this shell model and its modifications seem very desirable, and first attempts in this direction are discussed.Models can often give a qualitatively and sometimes quantitatively correct description of certain processes in terms of a few parameters. They provide, therefore, an orientation for microscopic approaches. Furthermo...

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The displacements and polarization caused by point defects in ionic crystals

Cited by 44 publications

References 18 publications

Method to account for arbitrary strains in kinetic Monte Carlo simulations

Method to account for arbitrary strains in kinetic Monte Carlo simulations

Impact of homogeneous strain on uranium vacancy diffusion in uranium dioxide

Vibrational Infrared and Raman Spectra of Non-Metals

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