Nonstoichiometry in steps on AB crystals (I). General aspects,including bulk imperfections

Starting with a quasichemical treatment, simple model calculations are given for the equilibrium composition in surface steps containing A and B kinks, the amount and ratio of which is varied by changing the adjacent gas composition. In connection with deviations from step stoichiometry, the total amount of kinks increases strongly. A nearest neighbour approximation has been applied to the attachment of A or B atoms at kinks from the gas phase, and also from the bulk by formation of vacancies V_A or V_B. These processes can be formulated separately for the two elements, taking into account the effective formation of bulk atoms of the other kind (B_B or B_A).     

Synthesis of stereoregular poly(alkyl malolactonates)

Optically pure methyl, ethyl, isopropyl, and benzyl (R)-malolactonate were prepared from (S)-(-)-malic acid and were polymerized in the bulk with tetraethylammonium benzoate as the initiator to yield high-molecular-weight, crystalline polymers. The optical purity of methyl and benzyl malolactonate was determined by ¹H NMR spectroscopy of the β-lactone complexed with a chiral europium shift reagent. Enantiomeric excesses of 100% were found (the experimental error was 3%). Optically active poly(β-malic acid) was obtained from optically active poly[benzyl (S)-malate] by catalytic hydrogenolysis of the pendent benzyl esters. Ethyl and benzyl (R)-malolactonate were also copolymerized, and the benzyl esters of the resulting copolymer were converted into carboxylic acid units by hydrogenolysis.     

The microscopic visualisation of the sonocrystallisation of ice using a novel ultrasonic cold stage

This work reports dynamic video images of the influence of ultrasonic cavitation on the sonocrystallisation of ice at a microscopic level. This has been achieved through the construction of a unique ultrasonic system for an optical microscope. The system consists of (1). an ultrasonic cold stage, (2). a temperature control system, and (3). a microscope and imaging setup. This allows the temperature of a sample to be systematically controlled while it is subjected to simultaneous excitation with alternating pressures in the ultrasonic frequency range. Both the amplitude of excitation and the frequency can be varied. Experiments on ice crystals in pure water and sucrose solutions were conducted. Three distinct phenomena were observed. Firstly, there is a tendency for cavitation bubbles to form at the grain boundaries between ice crystals. Secondly, there is a progressive melting of ice by cavitation bubbles which appear to eat their way into the ice phase. Thirdly, the dendritic ice structures may fragment under the influence of ultrasound, thus increasing the number of nuclei which may subsequently grow (secondary nucleation). These observations form the basis of a significantly enhanced understanding and exploitation of the sonocrystallisation of ice.     

Pressure enhancement of the giant magnetocaloric effect in Tb5Si2Ge2

Effects of temperature and pressure on magnetic, elastic, structural, and thermal properties of Tb5Si2Ge2 have been studied by means of macroscopic (thermal expansion and magnetization) and microscopic (neutron powder diffraction) techniques. We present evidence that the high-temperature second-order ferromagnetic transition can be coupled with the low-temperature first-order structural phase change into a single first-order magnetic-crystallographic transformation at and above a tricritical point in the vicinity of 8.6 kbar. This pressure-induced coupling has a remarkable effect on the magnetocaloric effect, transforming Tb5Si2Ge2 from an ordinary into a giant magnetocaloric effect material.     

Coupled whispering gallery modes in a multilayer-coated microsphere

Whispering gallery modes in a microsphere coated with three layers of high, low, and high refractive indices (RIs) are considered. Coastal modes and inland modes, centered on the outer and inner high-RI layers, exist as different radial modes. At right values of RI and thickness of the three layers, an inland mode and a coastal mode couple to produce a radial distribution of the photonic field that resembles bonding and antibonding orbitals. The coupling occurs across a layer of the middle low-RI layer, much thicker than the wavelength of light. The coupling is analyzed in a quantum-mechanical analog of a one-dimensional particle in a double-well potential.     

Flow field analysis by large-area interrogation in particle image velocimetry

The evaluation of flow records obtained by particle image velocimetry (PIV) employs the interrogation of certain regions in the flow image. Basic relations are derived for the case that the velocity is not constant within the region of interrogation. The influence of a distribution of velocities on the Young's fringe system and its Fourier transform, the autocorrelation of the flow record, are discussed. The considerations show that there is an easy access to statistical parameters of the flow by carrying out large-field interrogation. The autocorrelation function will reproduce the probability density function of the velocity, and there is no need for a large number of time-consuming small-area interrogations. Furthermore, the effects of velocity variations in ordinary fringe analysis are discussed. Examples are given from synthetic PIV records and measurements in a wind tunnel.     

BEC transition temperature of a dilute homogeneous imperfect Bose gas

The leading-order effect of interactions on a homogeneous Bose gas is theoretically predicted to shift the critical temperature by an amount DeltaT(c) approximately equal to ca(sc)n(1/3)T(0) from the ideal gas result T(0), where a(sc) is the scattering length, n is the density, and c is a pure number. There have been several different theoretical estimates for c. We claim to settle the issue by measuring the numerical coefficient in a lattice simulation of O(2) straight phi(4) field theory in three dimensions-an effective theory which, as observed previously in the literature, can be systematically matched to the dilute Bose gas problem to reproduce nonuniversal quantities such as the critical temperature. We find c = 1.32+/-0.02.     

Deterministic version of Wigner's semicircle law for the distribution of matrix eigenvalues

It is proved that Wigner's semicircle law for the distribution of eigenvalues of random matrices, which is important in the statistical theory of energy levels of heavy nuclei, possesses the following completely deterministic version. Let A_n=(a_ij), 1?i, ?n, be the nth section of an infinite Hermitian matrix, {λ⁽ⁿ⁾}_1?k?n its eigenvalues, and {u_k⁽ⁿ⁾}_1?k?n the corresponding (orthonormalized column) eigenvectors. Let $\text{v}{}^1{}_{\mathrm{n}}\text{=(a}{}_{\mathrm{n1}}\text{,a}{}_{\mathrm{n2}}\text{,?,a}{}_{\mathrm{n,n?1}}\text{)}$, put

$\text{X}{}_{\mathrm{n}}\text{(t)=[n(n-1)]}{}^{\mathrm{<mtext>-1</mtext><mtext>2</mtext>}}\text{∑}\text{k=1}\text{[(n-1)t]}\text{|v}{}_{\mathrm{n}}{}^1\text{u}{}_{\mathrm{f}}{}^{\mathrm{(n-1)}}\text{|}{}^2\text{,}\text{0?t?1}$

(bookeeping function for the length of the projections of the new row v¹_n of A_n onto the eigenvectors of the preceding matrix A_n?1), and let finally

$\text{F}{}_{\mathrm{n}}\text{(x)=n}{}^{-1}\text{(}\text{number of}\text{λ}{}_{\mathrm{k}}{}^{\mathrm{(n)}}\text{?x}\text{n}\text{,1?k?n)}$

(empirical distribution function of the eigenvalues of $\text{A}{}_{\mathrm{n}}\text{n}$. Suppose (i) $\text{lim}{}_{\mathrm{n}}\text{a}{}_{\mathrm{nn}}\text{n}\text{=0}$, (ii) lim_nX_n(t)=Ct(0<C<∞,0?t?1). Then

$\text{F}{}_{\mathrm{n}}\text{?W(·,C)}\text{(n→∞)}$

,where W is absolutely continuous with (semicircle) density

$\text{w(x,C)=}\text{(2Cπ)}{}^{-1}\text{(4C-x}{}^2{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{for}\text{|x|?2}\text{C}\text{0}\text{for}\text{|x|?2}\text{C}$

     

Lithium nickel oxide Li(Ni0.75Al0.17Co0.08)O2 as cathode material for lithium ion batteries

Al- and Co-substituted lithium nickel oxide of the nominal composition Li(Ni_0.75Al_0.17Co_0.08)O₂ was synthesised by a coprecipitation technique and by several solid state routes. Rietveld analysis of XRD profiles and galvanostatic cycling in glass cells were performed for structural and electrochemical characterisation. Depending on the reactivity of the respective precursor, there is in each case a minimal synthesis temperature, at which a single phase of the R layered structure could be obtained. The coprecipitation technique and solid state routes using pre-substituted nickel hydroxide are suitable for the synthesis of single phase Al- and Co-substituted lithium nickel oxide, even at rather low synthesis temperatures. The electrochemical performance of lithium nickel oxide Li(Ni_0.75Al_0.17Co_0.08)O₂ synthesised in air is poor due to an enhanced lithium nickel disorder. Synthesis in oxygen atmosphere seems to be required. Paper presented at the 6th Euroconference on Solid State Ionics, Cetraro, Calabria, Italy, Sept. 12–19, 1999.