Breathing Shell Research Articles

Inelastic scattering of He from LiF(001) surface: Theoretical analysis of time-of-flight spectra

The recent time-of-flight spectra of 4He scattered from LiF(100) surface measured by Brusdeylins, Doak and Toennies are theoretically analyzed in the framework of the hard corrugated surface approximation and of the breathing shell model for surface dynamics. The observed structures are shown to be associated with Rayleigh waves close to the zone boundary, and with other features of the surface-projected phonon density.

Inelastic scattering of He from LiF(001) surface: Theoretical analysis of time-of-flight spectra

The recent time-of-flight spectra of 4He scattered from LiF(100) surface measured by Brusdeylins, Doak and Toennies are theoretically analyzed in the framework of the hard corrugated surface approximation and of the breathing shell model for surface dynamics. The observed structures are shown to be associated with Rayleigh waves close to the zone boundary, and with other features of the surface-projected phonon density.

A Comparative Study of Dynamical Behaviour of Ionic Lattices

AbstractA critical study of all the three extensions of the shell model i.e. the breathing shell model (BSM), the deformable shell model (DSM), and the three‐body force shell model (TSM) is further carried out for cesium chloride type ionic crystals on the similar pattern as reported earlier. These models are applied to study comparatively the dynamical behaviour of cesium chloride (CsCI) and thallous bromide (TIBr). The results so obtained, again confirm the superiority of TSM over DSM and BSM, not only in explaining the phonon dispersion curves but also for interpreting the infrared (IR) and Raman spectral peaks and Debye temperature variations.

X-Ray Absorption Study of Mixed-Valent TmSe

The ${L}_{\mathrm{III}}$ x-ray absorption edge of Tm in TmSe yields a temperature-independent valence of 2.58\ifmmode\pm\else\textpm\fi{}0.07. The thermal damping of the extended x-ray absorption fine structure of TmSe is nearly identical to that of ErSe. This indicates very weak coupling of breathing shell charge fluctuations of the Tm ions to the phonons and very little static disorder of the lattice.

X-Ray Absorption Study of Mixed-Valence TmSe

The ${L}_{\mathrm{III}}$ x-ray absorption edge of Tm in TmSe yields a temperature-independent valence of 2.58\ifmmode\pm\else\textpm\fi{}0.07. The thermal damping of the extended x-ray absorption fine structure of TmSe is nearly identical to that of ErSe. This indicates very weak coupling of breathing shell charge fluctuations of the Tm ions to the phonons and very little static disorder of the lattice.

X-Ray Absorption Study of Mixed-Valence TmSe

The ${L}_{\mathrm{III}}$ x-ray absorption edge of Tm in TmSe yields a temperature-independent valence of 2.58\ifmmode\pm\else\textpm\fi{}0.07. The thermal damping of the extended x-ray absorption fine structure of TmSe is nearly identical to that of ErSe. This indicates very weak coupling of breathing shell charge fluctuations of the Tm ions to the phonons and very little static disorder of the lattice.

Theory of Raman Scattering in Various Magnetic Phases of Eu-Chalcogenides

The spin assisted phonon Raman scattering in EuS, EuSe and EuTe is Studied, based on the Raman Polarizability whose spin-phonon dependence originates from the cross effect of the 4 f spin-orbit interaction and the exciton-phonon interction. The phonon dispersions are calculated on the basis of the breathing shell model. The scattering spectrum consists of two parts: One part is a broad line assisted by the spin fluctuations. Most contribution for it comes from LO-phonon, but in EuTe TO-, LA- and TA-phonon contributions also become considerably large. The other part is the sharp line induced by the staggered magnetization. The result of calculation explains the observed results, such as the line shape, and its temperature and magnetic field dependence.

The Core Structure of an Edge Dislocation in NaCl

AbstractA theoretical study is carried out to determine the core structure of (a/2) < 110 > {110} edge dislocations in NaCl and to investigate whether the dislocations dissociate. The calculations show that they do not. This result is opposite to the predictions of Fontaine and Haasen and the conclusions of Belzner and Granzer. The results are generated with the same point‐ion model (PIM) potential employed by Belzner and Granzer, plus a breathing shell model (BSM) potential due to Corish, Parker, and Jacobs. Core properties such as the stable symmetry type, the strain energy, and the Peierls stress are determined. Both potentials produce an approximately sinusoidally shaped Peierls barrier with a periodicity of one Burgers vector. The PIM and BSM potentials yield Peierls stresses of 80 and 17.3 MPa, respectively. Comparison of these results with low‐temperature flow stress data suggests that the BSM result is consistent with the experimental data whereas the PIM result is not.

Erratum: Calculation of strain and polarization fields at the surface of MgO crystals. Breathing shell model

Erratum: Calculation of strain and polarization fields at the surface of MgO crystals. Breathing shell model

A Critical Study of Dynamical Properties of Ionic Crystals

AbstractThe basic differences among the three most popular extensions of the shell model i. e. the breathing shell model (BSM), the deformable shell model (DSM), and the three‐body force shell model (TSM) are sought out by applying their nearest‐neighbour versions to some representative rocksalt type ionic crystals. The phonon dispersion curves are determined by each model for each of the crystals and compared with the experimental phonons which forms perhaps the best test for this purpose. The same number (eight) of parameters of each model are determined by using the same set of input data. The results and degrees of agreement obtained in each case show clearly the superiority of the “charge‐transfer mechanism” for representing the deformations of electron shells, used in the TSM, over the “breathing” and “deformation mechanism” used in the BSM and DSM, respectively, for the same purpose. The study also shows that the TSM, DSM, and BSM form a series of descending order according to their relative degrees of agreement, obtained in explaining the lattice dynamical behaviour of these crystals.

Phonon frequencies in off‐symmetry directions of NaCl determined by neutron inelastic scattering

AbstractPhonon frequencies in NaCl at 80 K have been determined using neutron inelastic scattering. 72 off‐symmetry phonons are measured, both in the symmetry plane (110) and in the off‐symmetry plane (301). The experimental frequencies are compared to earlier breathing shell model calculations and found to be in excellent agreement.

Calculation of strain and polarization fields at the surface of MgO crystals. Breathing shell model

The strain and polarization fields associated with an (001) surface of MgO have been calculated within the lattice statics approximation. A central force shell model was used to describe the interionic potential, and isotropic shell deformation effects are included to account for the Cauchy breakdown in MgO. This breathing shell model has already excelled in describing the phonon spectrum of MgO. It is found that there are strong distortions in the first ten layers of the slab in addition to a small bulk contraction. The bulk contraction, a consequence of the shell breathing, contributes a term to the surface energy which is independent of the slab thickness.

Theory of Raman scattering in magnetically ordered phases of EuSe and EuTe

The first order Raman scattering in various phases of EuSe and EuTe was theoretically studied. The Raman lines which depend on spin structures are caused via the spin-dependent polarizabilities. The phonon dispersion relations of the crystals were calculated on the breathing shell model. The Stokes shifts and intensities of the Raman lines, and their polarization selection rules obtained from the present theory are in good agreement with experiments.

Atomistic breathing shell model calculations of dislocation core configurations in ionic crystals

Abstract A study was undertaken to improve upon a previous rigid boundary atomistic calculation of the core properties of a/2〈110〉{110} edge dislocations in MgO. A flexible boundary method (Flex-II) based on linear elasticity theory and recently developed by Hoagland, Hirth and Gehlen (1976) was used to provide a more accurate determination of the boundary between the atomistic and the elasto-atomic regions. A central-force breathing shell model due to Sangster (1973) was used to take account of many-body effects in the interaction between ions. This marks the first application of the breathing shell model to the calculation of dislocation core configurations in ionic crystals. Within this model two potentials were used. One is due to Sangster (1973), the other is our previously developed Model 1 potential. The results obtained using the above potentials are analysed in terms of the stability of the dislocation symmetry type, the core displacement field, the volume of expansion and the total strain energy...

The Green function approach to the surface lattice dynamics of ionic crystals

The Green function approach to the surface dynamics of semiinfinite lattices is developed in detail and shown to be applicable to crystals with long-range interionic potentials. Such applicability stands on the use of an effective short range perturbation, uniquely defined by the imposition of the translational and rotational invariance conditions for the stress-free semiinfinite crystal. Numerical calculations of the surface dispersion curves and of the surface projected phonon densities of NaCl, LiF and NaI, based on the breathing shell model, are reported and discussed.

Zero and First Sound in NaF and RbI

AbstractZero and first sound as well as the transition region are investigated theoretically in RbI and NaF. The temperature dependence of the first sound, zero sound, and isothermal elastic constants is calculated on the basis of a breathing shell model for the harmonic lattice dynamics and anharmonic parameters from microscopic Grüneisen constants. The theoretical results are compared with ultrasonic data and inelastic neutron scattering results. Own recent neutron experiments in RbI are concerned with the zero sound region at room temperature while the NaF experiments cover also parts of the transition region between first and zero sound at various temperatures between 295 and 700 K. It is shown that the dispersion of sound is satisfactorily described by use of an averaged thermal phonon lifetime. In NaF for each temperature first sound elastic constants and averaged phonon lifetimes are deduced from an analysis of the experimental data.

The effect of second and fourth nearest neighbours on impurity induced Raman scattering

The E g component of Raman scattering from KBr: Tl and KCl:Tl at 75°K is calculated and fitted to experimental data. The calcualtion is based on a Breathing Shell Model the parameters of which are determined by best fit to neutron scattering data. Three scattering models are compared. (1) With polarizability change produced by nearest neighbours (nn) only. In this case no fitting parameters are necessary. (2) With nn and 2nd nn. Where, two fitting parameters are needed. (3) With nn and 4th nn. Here, only one parameter is needed. Comparison of the different theoretical results for the scattering spectra shows, (a) that the inclusion of 2nd or 4th nn greatly improve the fit between theory and experiment; (b) that the polarizability parameters associated with 2nd nn and 4th nn are close in magnitude to that due to nn, and (c) that the inclusion of 2nd nn improves the high energy end of the spectrum but distorts the low energy end, whereas the inclusion of 4th nn only somewhat distorts the low energy end but the fit at the high energy end is less satisfactory. It is concluded that additional experiments may be necessary to decide which of the last two models is more appropriate.

Shell and breathing shell model calculations for defect formation energies and volumes in magnesium oxide

The authors have calculated defect energies for MgO using both a simple central-force shell model and the central-force breathing shell model proposed by Sangster (1973). Such an extension is required to account for the large Cauchy violation C44>>C12 found for this material. A critical comparison has been made of various techniques used in such calculations and studied the effect of including the many-body force in an effective two-body interaction. The results are rather insensitive to the model and method of calculation as long as the model reproduces the dielectric behaviour of MgO correctly. The calculated Schottky energies are so large (7.4-7.9 eV) that no intrinsic diffusion could be observed.

Three body interaction in breathing shell model

It is shown that the dominant contribution of the breathing degree of freedom of the electron charge cloud is an effective three body interaction and an attractive two body interaction in addition to the usual overlap interaction. The explicit forms for these interactions are obtained and it is found that the form of the three body interaction is identical to that given in the deformable shell model (DSM).

Anharmonic temperature dependences of the reststrahlen frequencies and the dielectric properties of potassium halides

The anharmonic temperature dependence of the reststrahlen frequency and the complex frequency-dependent index of refraction are calculated for KBr, KCl, and KI. Starting with harmonic phonons obtained from the breathing shell model (BSM) with input parameters appropriate to the crystal at 0 K, volume-dependent quasiharmonic phonons were calculated at different temperatures. These quasiharmonic phonons were then used to compute the self-energies of the zone-center TO modes, from which the frequency-dependent dielectric functions as well as the reststrahlen frequencies were obtained. The anharmonic force-constant parameters, assumed to be derivable from a central potential and restricted to nearest neighbors, were obtained by a fit of the measured coefficient of linear expansion and the "bare harmonic" reststrahlen frequency extrapolated from experiment. The calculated dielectric properties and the temperature dependence of the reststrahlen frequencies are in good agreement with experiment. As an alternative procedure for obtaining the anharmonic parameters a Born-Mayer potential was employed, but the results so obtained are in poor agreement with experiment. Different computional methods are studied and discussed.