Showing papers by "Solid State Physics Laboratory published in 1988"

Theory of fractal growth

Abstract: In the past few years a great deal of activity has been devoted to the study of fractal structures [3] in relation to physical phenomena [4,5]. The prototype fractal growth model is based on a combination of the Laplace equation and a stochastic field. The first model of this class to be formulated was Diffusion Limited Aggregation (DLA) [6]. A few years later the more general Dielectric Breakdown Model (DBM) [7] was introduced. This model used the relation between the random walk and potential theory and made clear that growth could also occur “from inside”. In addition to their intrinsic theoretical interest, these models are now believed to capture the essential features necessary to describe pattern formation in seemingly different phenomena like electrochemical deposition, deudritic growth, dielectric breakdown, viscous fingering in fluids, fracture propagation and others [4,5].

Theory of Laplacian fractals: diffusion limited aggregation and dielectric breakdown model

Abstract: We describe a new theoretical approach that clarifies the origin of fractal structures in irreversible growth models based on the Laplace equation and a stochastic field. This new theory provides a systematic method for the calculation of the fractal dimension D and of the multifractal spectrum of the growth probability (ƒ(α)). A detailed application to the dielectric breakdown model and diffusion limited aggregation in two dimensions is presented. Our approach exploits the scale invariance of the Laplace equation that implies that the structure is self-similar both under growth and scale transformation. This allows one to introduce a Fixed Scale Transformation (instead of coarse graining as in the renormalization group theory) that defines a functional equation for the fixed point of the distribution of basic diagrams used in the coarse graining process. For the calculation of the matrix elements of this transformation one has to consider an infinite, but rapidly convergent, number of processes that occurs outside a considered diagram.

From physical dielectric-breakdown to the stochastic fractal model

Abstract: We show how the stochastic growth model we have formulated for dielectric breakdown is related to microscopic mechanisms. Beginning with gas discharges we focus on the origin of the stochastic features and the dependence of growth probability on the local electric field. For dielectric breakdown in solid insulators we argue that quenched disorder does not appreciably modify the patterns which appear in the gaseous case.

New insights into the structure of b2o3 glass

Abstract: The results of structural investigations of various types of B 2 O 3 glass with different thermal histories are presented. The density and the glass transition temperature T g depend on the cooling rate at which the glass is quenched. For quickly quenched glass (cooling rate 10 3 K/s) the density is 1.79 g/cm 3 and T g is 278°C whereas these values for slowly quenched glass (cooling rate 4 × 10 −3 K/s) are respectively 1.83 g/cm 3 and 298° C. X-ray diffraction and Molecular Dynamics simulations show that the structure of vitreous B 2 O 3 can be explained by a model of randomly connected BO 3 triangles. The slower the glass is quenched, the more the BOB angles of adjacent BO 3 units approach 120°. We have found no tendency of neighbouring BO 3 triangles to form equiplanar complexes if the cooling rate decreases and therefore we have found no evidence for the existence of boroxol rings. The combination of the results of density measurements and X-ray diffraction studies indicates that for the slowly quenched glass the oxygen tend to be out of the plane of adjacent BO 3 triangles. This results in a more densely packed glass structure for slowly quenched B 2 O 3 glass.

Structural and dynamical properties of some lithium borate glasses

Abstract: Structural and dynamical properties of some lithium borate glasses have been investigated by means of X-ray diffraction studies and molecular dynamics (MD) calculations. The structure of lithium borate glasses appears to consist of randomly connected planar BO3 triangles and BO4 units. A comparison of the slowly quenched glasses (studied by X-ray diffraction) and fastly quenched glasses (studied by MD simulations) leads to the conclusion that a small quench rate leads to a preponderance for the B-O-B angles of adjacent BO3 triangles to 120°. The frequency spectra of B-O vibrations in the MD simulations agree qualitatively with infrared transmission spectra.

Effect of hole-induced shakedown in the auger spectrum of lanthanum

Abstract: It is shown from the ${M}_{4}$,5${\mathrm{N}}_{4}$,5X (X=${O}_{1}$,${O}_{2}$,3,${N}_{6}$,7) Auger emissions of La metal, ${\mathrm{La}}_{2}$${\mathrm{O}}_{3}$, and ${\mathrm{LaF}}_{3}$ that the 4f hole pulled down below the Fermi level by the 3d core hole in La metal is significantly populated before Auger decays take place. This extra relaxation mechanism by the ${N}_{4}$,5VV Auger process from conduction electrons gives important contribution to the intensity of the ${M}_{4}$,5${\mathrm{N}}_{4}$,5${\mathrm{N}}_{6}$,7 Auger emission. The amount of this contribution can be calculated by existing theories on the shakeup or shakedown satellites on the La 3d core-level x-ray photoemission spectra (XPS) of these La compounds, and the results are found to be consistent with our experimental data. The criterion for the importance of this hole-induced shakedown process in the initial state of Auger spectra is determined, and the implications of this finding on other spectroscopies are discussed.

Optical absorption of ZnGa2Se

Abstract: Single crystals of ${\mathrm{ZnGa}}_{2}$${\mathrm{Se}}_{4}$:${\mathrm{Co}}^{2+}$ were grown by the chemical transport reaction method. The optical absorption of single crystals was investigated in the temperature range 20\char21{}300 K. The optical-absorption peaks due to the transition $^{4}\mathrm{A}_{2}$${(}^{4}$F)${\ensuremath{\rightarrow}}^{4}$${\mathrm{T}}_{1}$${(}^{4}$P), $^{4}\mathrm{A}_{2}$${(}^{4}$F)${\ensuremath{\rightarrow}}^{4}$${\mathrm{T}}_{1}$${(}^{4}$F), and $^{4}\mathrm{A}_{2}$${(}^{4}$F)${\ensuremath{\rightarrow}}^{4}$${\mathrm{T}}_{2}$${(}^{4}$F) of the ${\mathrm{Co}}^{2+}$ ion that has entered the substitutional tetrahedral sites appeared at 12 830, 6221, and 4000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ at 289 K. The crystal-field parameter and the Racah parameter were given by Dq=400 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and B=469 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, respectively. The transition $^{4}\mathrm{A}_{2}$${(}^{4}$F)${\ensuremath{\rightarrow}}^{4}$${\mathrm{T}}_{1}$${(}^{4}$P) split into a triplet state by first-order spin-orbit\char21{}coupling effects in the temperature range 55\char21{}289 K, and the ${\ensuremath{\Gamma}}_{8}$+${\ensuremath{\Gamma}}_{7}$ level split into ${\ensuremath{\Gamma}}_{8}$ and ${\ensuremath{\Gamma}}_{7}$ levels by second-order spin-orbit\char21{}coupling effects of ${\mathrm{Co}}^{2+}$ ions in the low-temperature range below 55 K. The spin-orbit\char21{}coupling parameter was found to be \ensuremath{\lambda}=-363 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.

X-ray diffraction measurements on liquid iodine and some dilute mixtures of KI in I2

Abstract: Using X-ray diffraction we have determined the structure factor of pure iodine and of a number of dilute mixtures of KI in I2. We show that these liquids exhibit short-range orientational order, adjacent molecules being orient- ed more or less parallel. The intramolecular bond length in pure liquid iodine is 2·70±0·01 A, intermediate between the bond lengths of gaseous and solid iodine. Upon addition of KI the bond length increases, while the distances to atoms in the second and third shell decrease. These effects are related to recent high-pressure diffraction measurements on solid iodine.

The mixed alkali effect in some borate glasses

Abstract: The ionic conductivity of glasses of the type γ B 2 O 2 ·( x Cs 2 O·(1− x )Li 2 O) have been investigated by means of ionic thermo currents (ITC) and dielectric loss measurements. The conductivity shows a pronounced mixed alkali (MA) effect, where the conductivity of pure Li borate glass is higher than that of pure Cs borate glass with the same alkali content. It is shown that the MA effect can be explained very well with the weak electrolyte theory, provided that a short range dipole-induced dipole interaction between alkali ions is assumed.

X-ray reflectivity of classical smectic-A liquid crystals

Abstract: Using X-ray reflectivity smectic layering is investigated on both sides of a classical monolayer smectic-A to nematic phase transition in a polar NCS substituted compound. At the surface, only monolayering is observed; there is no breaking of up-down symmetry. This contrasts with the situation of a smectic-A1 phase in a polar CN substituted compound, where bilayering occurs at the surface. Consequences for molecular models of smectic-A phases are discussed Etude de la stratification en couches d'un cristal liquide polaire NCS lorsqu'il passe d'une phase nematique a une structure smectique A classique en monocouches. Etude de la surface du materiau par mesure de la reflectivite des rayons X

Low-frequency Raman spectroscopy of alkali-borate glasses

Abstract: Low-frequency Raman spectra of glasses of the types (B 2 O 3 ) 1− x (Li 2 O) x , (B 2 O 3 ) 1− x (Rb 2 O) x and (B 2 O 3 ) 1 − x − y (Li 2 O) x -(Li 2 Cl 2 ) y are presented. The temperature-reduced spectra show a peak at 50 cm −1 and a peak at about 130 cm −1 . The peak at 50 cm −1 appears to be a common property of oxide glasses and arises because the limited structural correlation length of the glass network causes a non-zero maximum of the frequency-dependent Raman coupling coefficient. The 130 cm −1 band can be attributed to librational modes of BO 3 and BO 4 units. For v-B 2 O 3 , a structural correlation length equal to the size of a pair of BO 3 triangles is found. Addition of alkali oxide leads to a decrease of this correlation length. The extra oxygens are mostly incorporated in BO 4 units but larger ions such as Rb + will also enhance the number of non-bridging oxygens. Addition of LiCl does not produce major changes in the Raman spectra and consequently does not change the ratio of the numbers of BO 3 and BO 4 units. The Cl − ions are incorporated in interstitial vacancies of the network, which leads to an expansion of the B-O network structure.

Fractals in Physics: Introductory Concepts

Abstract: Having treated lasers, nonlinear optics, and electron and phonon instabilities at some length in previous chapters, we now return in more detail to the concept of fractals introduced in Chapter 1.

Concentration fluctuations in molten Li0.62Na0.38

Abstract: Inelastic neutron scattering spectra of molten 7Li0.62Na0.38 have been measured using the IN6 time of flight spectrometer at the Institut Laue-Langevin. The composition is close to the critical composition and has been chosen such that coherent scattering is only from Scc(Q, ω). Measurements have been made at temperatures between 725 and 571 K and the critical temperature for phase separation determined to be 576 ± 2 K. The inverse correlation length for concentration fluctuations κ < 0.1 A-1 and consequently only very slight evidence of critical narrowing of the quasi-elastic peak is observed in the range 0.3 < Q < 2 A-1 covered. No changes in the inelastic scattering spectrum are observed other than a change in intensity consistent with the change in temperature. The results are therefore in accord with those expected for a well-behaved system at the critical point for phase separation with long-range concentration fluctuations. The critical indices are found to be η < 0.04, ν ≅ 0.5 and γ ≅ 1.

Transitions and relaxations in amorphous polymers

Abstract: Etude par TSC, DSC, relaxation mecanique de polystyrenes atactiques non-orientes et orientes biaxialement et de copolymeres styrene/acrylate de butyle statistiques et sequences prepares differemment

Correlations in multifractals

Abstract: We present an analysis of the implicit assumptions that lie at the basis of the scaling relations for fractal measures proposed by CATES et. al. [1]. Furthermore,the scaling relations which have been shown to hold for trivial multifractals like the generalized Cantor set [2] are tested numerically for critical wave functions of an incommensurate system.

A Laplacian Walk for the Travelling Salesman

Abstract: The problem of Hamiltonian cycles is considered on the Voronoi lattice formed by N random points uniformly distributed over the unit square by using techniques borrowed from kinetic growth models. It is shown that for Laplacian random walks with appropriate boundary conditions and special growth rules one obtains nonintersecting tours covering all points of the lattice. These walks form a subset of all possible tours of the travelling salesman problem (TSP), which is well known as the canonical example of an ?-complete optimization problem. Used as a heuristic methods for the TSP, the Laplacian walk method leads to tour lengths which are comparable to Opt(2) tours.

Growth and spectroscopic characterisation of Neodymium Aluminium Barium Borate using floating zone apparatus

Abstract: Transparent Neodymium Aluminium Barium Borate (NABB) rods, 60 mm long and 5 mm in diameter, have been grown using a Floating Zone (FZ) apparatus. The preparation of sintered feed rods and growth conditions are presented. The vibrational spectra (IR and Raman) of the rods were compared with those of Neodymium Aluminium Borate (NAB) crystals grown from flux. The spectra confirmed the presence of BO3 network which had been identified to have more advantages when compared to the silicates. The absorption and the fluorescence spectra obtained for the sample demonstrates its efficiency for use as a laser material.

Screening effects on the quadrupole splitting in amorphous Fe-Zr alloys

Abstract: The screening by the conduction electrons changes the local symmetry of the charge distribution as experienced by a local /sup 57/Fe probe nucleus. As a consequence the quadrupole splitting in an amorphous alloy cannot be used as a characteristic feature of the structure for identification. The concentration dependence of the quadrupole splitting in amorphous Fe-Zr alloys can be understood by assuming a transition in the electronic structure, without the assumption of a structural transition. Further evidence for such a transition has been found in the literature.

Cooperation of antiferromagnetic interactions and phonons in La2−x/Ba,Sr/xCuO4−δ

Abstract: This paper discuss a pairing mechanism relevant to LaCuO based high T c superconductors. The underlying theoretical model is nearly-half-filled two-dimensional Hubbard hamiltonian with some electron-phonon interactions. It is shown that the hopping energy is much reduced by the coupling between electrons and localized phonons but the kinetic exchange interaction is not reduced. The cooperation of antiferromagnetic interactions and polaron effects makes the singlet hole pair a stable bound state.