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Full-Text Articles in Physics
Schottky Defects In Alkali Halides, Paul D. Schulze, John R. Hardy
Schottky Defects In Alkali Halides, Paul D. Schulze, John R. Hardy
John R. Hardy Papers
The method of lattice statics and the deformation-dipole model have been applied to Schottky defects in ionic crystals in approximations higher than zero order. For an isolated vacancy, all host-lattice-ion potential energy functions for short-ranged repulsive and Coulomb-defect forces were expanded to terms quadratic in the displacements and dipole moments, and the resulting forces were allowed to act on the first and/or second neighbors to the vacancy. The zero-order Coulomb force was allowed to act on the remainder of the host-lattice ions past first and/or second neighbors. The vacancy and Schottky-pair-formation energies in the 12 Na, K, Rb halides have …
Application Of The Method Of Lattice Statics To Vacancies In Aluminum, Larry Boyer, John R. Hardy
Application Of The Method Of Lattice Statics To Vacancies In Aluminum, Larry Boyer, John R. Hardy
John R. Hardy Papers
In this paper the method of lattice statics is applied to the calculation of the atomic displacements about a vacancy in aluminum using a fifth-neighbor force-constant model for the dynamical matrix and the vacancy-host lattice interaction. The strain-field interaction energy between two vacancies is similarly calculated. The main object of this work is to demonstrate the important modifications of earlier results, obtained for a first- and second-neighbor force-constant model, when one uses the fifth-neighbor model designed to give a significantly better fit to the measured phonon dispersion curves. In particular it is demonstrated that the displacements about the vacancy continue …
Calculation Of Point-Defect Energies And Displacements In Alkali Halides Using The Lattice-Statics Method, Arnold Karo, John Hardy
Calculation Of Point-Defect Energies And Displacements In Alkali Halides Using The Lattice-Statics Method, Arnold Karo, John Hardy
John R. Hardy Papers
The method of lattice statics, in the zero-order approximation, is used to evaluate the Schottky-pair formation energies and the displacement fields about positive- and negative-ion vacancies for all alkali halide crystals with rock-salt structures. The deformation-dipole model, used extensively in earlier work on the lattice dynamics of these crystals, is employed to describe the host lattice. Long-range Coulomb interactions are included explicitly, and short-range repulsive interactions are described by a simple Born-Mayer potential. Comparison is made with earlier Mott-Littleton-type calculations and very satisfactory agreement is found. Comparison with available experimental values is somewhat less satisfactory, particularly regarding the lithium salts; …
Calculations Of The Intensity Of X-Ray Diffuse Scattering Produced By Point Defects In Cubic Metals, John W. Flocken, John Hardy
Calculations Of The Intensity Of X-Ray Diffuse Scattering Produced By Point Defects In Cubic Metals, John W. Flocken, John Hardy
John R. Hardy Papers
We have calculated isointensity profiles for the diffuse x-ray scattering associated with certain types of defects in Cu, Al, Na, K, Li, and a theoretical model lattice. These profiles were computed for high-symmetry planes very close to reciprocal-lattice points of the (S, 0,0), (S,S,0), and (S,S,S) type. Both cubic and double-force defects were treated. The calculations were done using a technique presented by Kanzaki for the theoretical model lattice. Kanzaki's general conclusion that cubic defects produce leminiscate profiles and that double-force defects produce ellipsoidal profiles is confirmed for all the material studied. Our profiles for the model lattice agree with …
Asymptotic Lattice Displacements About Point Defects In Cubic Metals, John W. Flocken, John R. Hardy
Asymptotic Lattice Displacements About Point Defects In Cubic Metals, John W. Flocken, John R. Hardy
John R. Hardy Papers
We have calculated the asymptotic displacements (a) about a single vacancy in Al, Na, K, and Li, (b) about a single interstitial Cu atom in a Cu host lattice, and (c) about a unit single double force along a (100) direction in A1 and Cu. These calculations were made using the asymptotic equations of the method of lattice statics which, in its full form, is based on the Fourier transformation of the direct-space force equations between the detect and the host atoms in a large "supercell" of the lattice. Results were also obtained for each of the defect types in …
Lattice Dynamics Of Naf, Arnold Karo, John R. Hardy
Lattice Dynamics Of Naf, Arnold Karo, John R. Hardy
John R. Hardy Papers
The results of an extended calculation of the normal modes of the NaF lattice are presented. Three models have been considered : a "rigid-ion" (RI) model, a "deformation-dipole" model with central F--F- short- range interactions (DDNNN), and a “deformation-dipole" model including both central F--F- interactions and a noncentral component in the first-neighbor, short-range interactions [DDNNN(NC)]. For each of these models we have derived frequency spectra for both 300 and 0°K input parameters, the associated dispersion curves for symmetry directions, Debye characteristic temperatures ΘD, moment functions ωD(n), and the …
Lattice Dynamics And Second-Order Raman Spectrum Of Naf, John R. Hardy, A. M. Karo, I. W. Morrison, C. T. Sennett, J. P. Russell
Lattice Dynamics And Second-Order Raman Spectrum Of Naf, John R. Hardy, A. M. Karo, I. W. Morrison, C. T. Sennett, J. P. Russell
John R. Hardy Papers
The second-order Raman spectrum of NaF has been measured using an argon laser source. For a light beam incident along the [010] direction, polarized along the [001] direction, and viewed along the [100] direction, the scattered radiation is almost completely polarized. It is shown theoretically that it is possible to account for the polarization and the detailed shape of the observed spectrum within the experimental resolution using a Raman polarizability tensor whose second derivatives with respect to nuclear displacements depend only on the positions of first neighbors in the crystal, provided one uses the phonon frequencies derived from a deformation …
Application Of The Method Of Lattice Statics To Vacancies In Na, K, Rb, And Cs, John W. Flocken, John R. Hardy
Application Of The Method Of Lattice Statics To Vacancies In Na, K, Rb, And Cs, John W. Flocken, John R. Hardy
John R. Hardy Papers
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 …
Application Of The Method Of Lattice Statics To Interstitial Cu Atoms In Cu, John Flocken, John Hardy
Application Of The Method Of Lattice Statics To Interstitial Cu Atoms In Cu, John Flocken, John Hardy
John R. Hardy Papers
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 …
Infrared Absorption Properties Of Lih, Lid Mixed Crystals, Sitaram S. Jaswal, John R. Hardy
Infrared Absorption Properties Of Lih, Lid Mixed Crystals, Sitaram S. Jaswal, John R. Hardy
John R. Hardy Papers
The normal modes of pure LiH and LiD, required in impurity mode calculations, have been computed on the basis of the deformation-dipole model. Neutron-scattering results of Verble, Warren, and Yarnell for Li7D, along with some other experimental quantities, have been used to determine the various parameters involved. It is found that the frequency spectrum of LiH has a gap and that a substitutional D- ion produces a local mode in this gap whose frequency has been computed, together with its amplitude at the impurity. The infrared absorption frequency associated with this local mode and its integrated absorption …
Lattice Dynamics And Second-Order Raman Spectrum Of Csf, John R. Hardy, Arnold Karo
Lattice Dynamics And Second-Order Raman Spectrum Of Csf, John R. Hardy, Arnold Karo
John R. Hardy Papers
Results are presented for a precise calculation, based on the deformation dipole model with short-range repulsive interactions between second-neighbor negative ions, of the normal-mode frequency distribution of CsF. The extreme properties of this crystal are reflected in the unusual appearance of the distribution. From these results, we can also predict the form of the second-order Raman spectrum of CsF for two alternative assumptions regarding the Raman polarizability tensor. Both spectra are unusual in that they consist almost entirely of very sharp, clearly separated lines. Furthermore, the spectra corresponding to these two assumptions are very different and should be easily distinguishable …
Room-Temperature Second-Order Raman Spectra Of Csc1, Csbr, And Csi, A. M. Karo, John R. Hardy
Room-Temperature Second-Order Raman Spectra Of Csc1, Csbr, And Csi, A. M. Karo, John R. Hardy
John R. Hardy Papers
The room-temperature Raman spectra of CsC1, CsBr, and CsI have been computed from a simple, combined density-of-states approximation. Calculations have been made for four different model potential functions and compared with experiment in the cases of CsBr and CsI. In this way it is found that one of the variations, called the DD(-) model, is the most satisfactory. The agreement with the observed spectra is surprisingly close when one considers that no allowance has been made for variations in the elements of the Raman polarizability tensor.
Lattice Dynamics And Specific-Heat Data For Rocksalt-Structure Alkali Halides, Arnold Karo, John R. Hardy
Lattice Dynamics And Specific-Heat Data For Rocksalt-Structure Alkali Halides, Arnold Karo, John R. Hardy
John R. Hardy Papers
Vibrational distribution functions are derived for a number of rocksalt-structure alkali halides using a more refined treatment of the interionic forces than that provided by regarding them as rigid point charges. The dipole moment at any given ion site is calculated taking into account the contribution from the deformation of the electron distribution resulting from both polarization and overlap repulsion between nearest neighbors. In this way the dipole-dipole part of the Coulomb interaction is treated self-consistently.
Both room temperature and 0°K input parameters are used, and the derived specific-heat data are compared with experimental results. The over-all agreement with experiment …