Table of contents

Volume 29

Number 1, 14 January 1996

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APPLIED MAGNETISM AND MAGNETIC MATERIALS

1

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Based upon the density matrix formulations of nonlinear optical susceptibility, optical phase conjugation via stimulated Brillouin scattering (OPC-SPS) in the presence of a moderately high magnetostatic field is studied in centrosymmetric semiconducting crystals under a parabolic approximation. The magnetostatic field B has a twofold contribution to the coherent radiation - semiconductor interaction through the formation of discrete Landau levels and the sharpening of the density-of-states. Numerical estimations made for an InSb sample at low temperature irradiated by a 5.5 to 6.0 m CO laser reveal enhancement in the value of Brillouin susceptibility in the presence of the magnetostatic field B. This in turn lowers the threshold intensity required for the onset of OPC-SBS. A considerably high reflectivity is obtained when B is increased from 1 to 4.02 T. For experimental observation of OPC-SBS as described in the paper, it may be stressed that the polarization of the laser should be properly determined so that the crystal is effectively centrosymmetric.

8

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Microstructural changes induced by hydrogen ion implantation in haematite () have been investigated by transmission electron microscopy. It has been found that the hydrogen ion implantation causes the haematite magnetite () reduction at room temperature. From electron diffraction patterns after the hydrogen implantation, the following orientation relationship was found to exist between haematite and magnetite: . Since these results agree with those in previous studies, microstructural changes during the reduction were obtained by using the implantation technique. The reduction mechanism of magnetite from haematite is discussed in terms of the experimental results on crystallographic relationships.

14

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The temperature- and magnetic-field-dependences of the resistance in giant magnetoresistance (GMR) (LCMO) thin films have been studied. It is found that the magnetoresistance ratio can be expressed as near the ferromagnetic transition temperature when H<3 T. The temperature-dependence of is determined by A(T) and the exponent below 60 K and above 80 K. Under certain conditions, this kind of power-law magnetic-field-dependence of in LCMO thin film is similar to that in metallic magnetic multilayer or grain-type GMR thin films.

20

An explanation for the magnetization anomalies recently measured in Y - B - Cu - O and single crystals is provided. This explanation considers the impact of the disordered state and percolation effects in these materials. The scaling behaviour of the low-field minimum in the magnatization curves () as a function of the oxygen deficiency parameter () is deduced. In addition, the temperature-dependence of the secondary peak observed in magnetization curves of single crystals was found to be consistent with the experimental measurements. The model takes into account the random nature of the defect distribution in the two-dimensional planes and the percolation effects due to grain size distributions.

25

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The effects of sintering temperature on density, microhardness and Barkhausen jumps of and were investigated. The density and microhardness increase with sintering temperature. The microhardness of is much lower than that of . The increase in sintering temperature causes a decrease in Barkhausen jumps in and an increase in Barkhausen jumps in .

29

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Granular Co - Ag and NiFe - Ag thin films were prepared by magnetron sputtering with low-energy (0 - 500 eV) ion radiation assisted deposition. For sputter-only films the giant magnetoresistance (GMR) ratio varied with composition, with a peak occurring at about 35 at.% magnetic component. The ion beam was found to increase the GMR slightly with increasing energy and then progressively decrease it. There was an accompanying decrease in film thickness and Ag concentration as the ion beam preferentially sputtered the Ag. TEM has revealed sputtered films to contain ordered 10 - 20 nm spherical particles whilst the ion-beam-assisted films were made up of a network of particles clustered into channels.

FUNDAMENTAL AREAS OF PHENOMENOLOGY (INCLUDING APPLICATIONS)

34

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Laser imaging set-ups permit characterization of the vectorial nature of the optical wave which is transmitted by a medium or reflected by a target, from polarimetric formalisms such as Jones or Stokes - Mueller calculi. When the Mueller matrix of targets (or media) is experimentally determined, information about the polarizing and depolarizing properties can be obtained from a Mueller - Jones matrix, which operation requires knowledge of the experimental uncertainties in the elements of . We will discuss the possibility of a polar decomposition of the extracted Mueller - Jones matrix. We then obtain the product of a Hermitian matrix and a unitary matrix, which can be associated with it, for a polarization transformer, with an elliptical partial polarizer and a pure elliptical retarder respectively. Classification of a target is deduced from its polarimetric characteristics (depolarization, polarizing and retardation properties). Experimental Mueller matrices of polarization transformers (media or targets) are provided and analysed by this method in order to characterize the physical behaviour of these optical systems with respect to polarization phenomena.

39

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Error contour charts have been generated comparing scattered intensities calculated using the RGD and the single-wave and two-wave WKB approximations against Mie theory in the range of real refractive index from 1 to 1.5 and of size parameter from 0 to 20. It is demonstrated that the two-wave WKB method is superior to the others. Nonetheless its range of applicability is very limited, especially at scattering angles larger than .}

43

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The upper limit of a self-sustained discharge-pumped ArF laser was studied by numerical modelling. It was shown that kinetic processes alone serve to limit the specific laser energy to a value of 20 J . Optimization of laser performance was performed by varying the gas mixture. Possible ways of increasing specific laser energy and efficiency are discussed.

50

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A single-mode frequency stable helium neon laser operating on the 543 nm neon transition was used to probe an electrical discharge in helium neon mixtures. Values for the optical gain at this wavelength were obtained. A comparison with the widely documented behaviour of the 633 nm transition, which shares the same upper state as the 543 nm transition, shows a marked difference in the variation of the optical gain with discharge pressure. This is shown to occur due to the differing behaviour of the lower laser state population densities with pressure. It is proposed that this could be due to the resonance peak in the electron excitation cross section from the ground state to the 2 level. Variation of gain with discharge current is also presented.

57

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Q-switched low-pressure lasers allow both the production of maximum laser pulse power and high average laser power at high pulse repetition rates. A Q-switched laser oscillator amplifier system consisting of a DC discharged, wavelength tunable and diffusion cooled oscillator and a microwave excited amplifier is described. By mechanical Q-switching of the oscillator laser pulses with a pulse repetition rate of 4 - 200 kHz and beam quality can be produced. After the amplification the peak power reaches 0.9 MW at a pulse repetition rate of 10 kHz and 0.2 MW at a 100 kHz repetition rate. The pulse duration (FWHM) is about 0.2 s. The maximum average power of 7 kW in the Q-switched mode reaches nearly the maximum cw laser power of 10 kW (with beam quality). The laser pulse duration can be shortened by the combination of cavity dumping and electro-optical Q-switching. This pulsed operation leads to laser pulses with 35 ns pulse duration and 1.9 MW maximum power at a pulse repetition rate of 10 kHz and an average laser power of 0.8 kW. The self-oscillation of the oscillator amplifier system can be suppressed by an optical shutter between oscillator and amplifier. The laser beam power can be calculated by a six-temperature model including rotational relaxation, intramode and intermode vibrational energy exchange.

68

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We describe the application of a tunable differential interferometer to the characterization of pulsed gas valves, operating in the low-pressure regime ( Torr). The spatial profile of the pressure in the gas jet has been studied for piezoelectric and electromagnetic valves in various experimental conditions, for both Ne and Ar gases. Moreover the time response of the valves has been investigated by using, for the first time to our knowledge, the third harmonic generation process. The number of third harmonic photons has been determined as a function of the delay time between a Nd:YAG pump laser pulse and the opening time of the valve, thus allowing the determination of the jet temporal profile. The time dependence of the local pressure in the jet has been studied for various gas pulse durations.

76

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Field-induced periodic domain reversal has been achieved in a 0.5 mm thick, c-cut sample with Al electrodes by optimizing fabrication conditions. The quality of the sample has been tested by measuring the efficiency of second harmonic blue light generation and its tuning behaviour.

80

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We propose a finite-time thermodynamics model for an Otto thermal cycle. Our model considers global losses in a simplified way lumped into a friction-like term, and takes into account the departure from an endoreversible regime through a parameter (R) arising from the Clausius inequality. Our numerical results suggest that the cycle's power output and efficiency are very sensitive to that parameter. We find that R is the ratio of the constant-volume heat capacities of the reactants and products in the combustion reaction occurring inside the working fluid. Our results have implications in the search for new fuels for internal combustion engines.

84

An analytical solution for the singular problem of two dimensional flow for the impulsively started, translating and expanding, heated circular cylinder is obtained. This solution has been related to the complex problem of heat transfer to the three dimensional steady flow over a slender body of revolution at high angle of attack. The energy equation has been solved using the method of matched asymptotic expansion to second order. The solution for the temperature field has been obtained. The effect of the expanding surface on heat transfer has been investigated. The relation between the local Nusselt number over the cylinder surface and the progress of the Nusselt number with time, which is related to the third dimension, is explored.

FLUIDS, PLASMAS AND ELECTRIC DISCHARGES

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A new plasma maser scheme, the ion-channel electron cyclotron maser (ICECM) is investigated, and the electromagnetic instability in the ICECM is studied. Using three-dimensional perturbation theory, the dispersion relation of the ICECM is derived in this paper. Analysis finds that three typical regions of electromagnetic instability exist in the ICECM after considering the influence of the plasma wave, and some potential physical mechanisms for the instability are identified. In the Compton regime, an approximate calculation example for the instability growth rate is given. As a high-power short-wavelength electromagnetic radiation source, some evident advantages of ICECM in comparison with other electron cyclotron masers are shown.

95

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The evolution of a low-voltage electric arc is studied with a matrix of microcoils which behaves like a magnetic camera. The arc is assimilated to a series of straight segments. The shape that it assumes in the electrode gap as well as re-striking phenomena are analysed. The influence of insulating and conducting obstacles is stressed.

99

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Langmuir probe measurements are a useful tool to evaluate the influence of plasma parameters on the mechanical properties of sputtered thin films. Ti - N is deposited by unbalanced magnetron sputtering at room temperature. The plasma parameters are determined by a cylindrical Langmuir probe. The deposition parameters are correlated to the plasma characteristics through the determination of the electron mean free path. The ion density is calculated according to the collisional Zakrzewski and Kopiczynski correction to the Laframboise model extended to a two-component gas. In order to evaluate the ion bombardment per condensing atom, the chemical composition and the density of the deposited thin films are determined by accurate electron probe microanalysis. The calculations show how the action of ion - atom collisions on ion collection by the probe affects the evaluation of the ion bombardment.

105

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We have investigated the motion of electrons in a new, high voltage segmented hollow cathode discharge, which is known to be an efficient pumping source for charge-transfer excited UV metal ion lasers. We have studied the spatial distribution of ion production, electron energy distributions, statistics of electron avalanches, the fraction of oscillating electrons, and the distribution of the fast electrons' current on the anode surface in a helium discharge having four electrode segments. We have found that the ion production is strongly peaked in the centre of the discharge due to the focusing cathode geometry. The effect of magnetic field on the characteristics of the discharge was also studied. With increasing magnetic field the peak of the spatial distribution of ionization was split into two regions of high ionization rate. Furthermore, due to the magnetic field, at fixed discharge current the number of high-energy electrons absorbed on the anode increased considerably, and a higher number of primary electrons were absorbed by the anode without making any ionization. At constant discharge voltage the fraction of oscillating electrons was found to decrease, due to the applied longitudinal magnetic field. The magnetic field dependence of the spatial distribution of ion production, the energy distribution of electrons absorbed by the anode and the fraction of oscillating electrons at different discharge conditions were also studied in a discharge having six electrode segments.

115

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The detailed radial structure of the electron kinetics in the positive column of cylindrical DC glow discharges is investigated to reveal the microscopic nature of the electron confinement by the radial space charge potential and the distinctly non-local properties of the kinetics. Therefore, a method has been developed to solve the relevant inhomogeneous kinetic equation including the radial electric field action and to determine the isotropic and anisotropic parts of the electron velocity distribution function. This allows one to determine the radial dependence of all important macroscopic quantities from the velocity distribution. Furthermore, the strict solution of the inhomogeneous equation can be used to inspect the validity of the so-called `non-local approach', which is a simpler kinetic model. The method is applied to a real neon glow discharge. Significant radial dependences of the isotropic distribution and, in particular, of the radial and axial anisotropic distributions were found with large consequences for the non-local behaviour of the electron particle and energy balance.

121

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A one-dimensional model of the non-equilibrium plasma region adjacent to an electric arc cathode is developed. The collisionless space-charge zone (sheath) and the hydrodynamically described ionization zone (pre-sheath) are connected to a unified model. In the pre-sheath, ionization, diffusion and decoupling of electron and heavy-particle temperature are considered. The voltage drop in the space-charge zone is computed self-consistently including thermionic electron emission at the cathode surface. This unified model yields the overall cathode potential drop (cathode fall), the extent of the non-equilibrium region and the net energy flux towards the cathode surface. In this paper, the model is applied to an argon arc plasma at atmospheric pressure with a thoriated tungsten cathode, as is typically used for welding of stainless steel materials.

CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES

129

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The results of calculations on the optical properties of zone plates at grazing incidence angles are presented. In terms of the diffraction theory, the diffraction integrals for the Fresnel zone geometries are shown to be similar at normal and grazing incidence angles in the Fresnel approximation. One-dimensional and two-dimensional cases are discussed.

133

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Phase objects are readily imaged through Fresnel diffraction in the hard x-ray beams of third-generation synchrotron radiation sources such as the ESRF, due essentially to the very small angular size of the source. Phase objects can lead to spurious contrast in x-ray diffraction images (topographs) of crystals. It is shown that this contrast can be eliminated through random phase plates, which provide an effective way of tailoring the angular size of the source. The possibilities of this very simple technique for imaging phase objects in the hard x-ray range are explored experimentally and discussed. They appear very promising, as shown in particular by the example of a piece of human vertebra, and could be extended to phase tomography.

147

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This paper describes a simple finite-difference method to simulate and Lamb wave modes in plane metal sheets. The simulation is used to predict time-domain histories of field displacements vertical to the sheet at groups of points on the sheet. The time - space data so obtained are transformed by two-dimensional FFT to yield frequency - wavenumber representations for comparison with the Lamb mode dispersion waves. An experimental rig is developed for transmission and reception of Lamb waves in sheet metal, with adjustable transducer positions on the Lamb wave axis. The rig enables two-dimensional time - space, and by transformation, frequency - wavenumber, data to be obtained experimentally. An electronic system to provide appropriate band-limited signals for single-mode Lamb wave excitation is outlined and used in conjunction with the physical rig. Experimental results show good agreement with simulation.

156

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Ionic transport properties and battery discharge studies on the fast ion conducting quenched mixed glass system x[0.75AgI:0.25AgCl]: (1 - x)[] are reported, where in molar wt %. The conventional host AgI has been replaced by an alternative compound: `a quenched [0.75AgI:0.25AgCl] mixed system'. The compositional ratio, for x = 0.75, exhibited the optimum conductivity, at C. Samples of the optimum conducting composition were prepared from the melt at two different cooling rates, namely about and about , referred to as quenched and annealed compositions respectively. The conductivity increase in the quenched composition has been attributed to the introduction of amorphousness due to rapid quenching. The structural and thermal analyses were carried out on material of the optimum composition. Various ionic transport parameters such as electrical conductivity (), transference number (), ionic mobility () and drift velocity () were measured as a function of temperature. The discharge characteristic of the solid state batteries fabricated, using the optimum conducting composition as electrolyte, were studied under different load conditions and some important cell parameters were computed from the discharge profile.

163

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A numerical method has been developed to account for the micro-meniscus effect of an ultra-thin liquid film on the static friction of rough surface contact. The classical meniscus theory of a single-sphere contact was modified to include the effect of multiple asperity contacts with a pre-existing ultra-thin liquid film during the contact of two rough surfaces. The effect of micro-meniscus formation was considered in terms of elastic - plastic deformation of rough surfaces under applied load, roughness parameters, thickness of liquid film and meniscus height. In the numerical model, elastic - plastic dry contact of rough surfaces is first analysed. In the next step, a liquid film of known mean thickness is introduced over the deformed rough surfaces. Wetted areas are determined by selecting the areas where asperities of both contacting surfaces touch the liquid. The total projected meniscus area is determined by selecting those area islands of cross cut area at a given mean meniscus height which overlap the wetted area. The meniscus force is then calculated using the meniscus equation derived from first principles of the micro-meniscus theory. Two parameters, meniscus height and liquid film thickness, are required for the analysis, which can be obtained for a given relative humidity. However, for a given liquid-film thickness, meniscus height is a function of liquid-film thickness and needs to be estimated. The present numerical method was applied to data-processing magnetic rigid disk drives to analyse the static friction during contact in the presence of an ultra-thin liquid film on one of the surfaces. Trends in numerical predictions correlate well with the measured effect of liquid films on the static friction. The analysis reveals some new insights into the `stiction' problems of disk drives.

179

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In this paper we present a complex admittance analysis of three electrode systems when exposed to aqueous KCl solutions: uncoated gold, gold/alkyl mercaptan and gold/alkyl mercaptan/22-tricosenoic acid Langmuir - Blodgett film. For each arrangement, the experimental data were fitted to the theoretical responses of equivalent electrical networks of capacitors and resistors. For the first two electrodes, a simple model consisting of an electrolyte resistance in series with the Gouy - Chapman diffuse layer capacitance described the experimental data well. For the third system, incorporating the high-impedance bilayer of 22-tricosenoic acid, a more complex equivalent circuit was needed. The physical interpretation of its components is discussed. In all cases universal capacitors with a power-law frequency response had to be used to model the real systems accurately.

185

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This paper analyses theoretically the `crossed field' scheme for acoustic excitation of an acoustic superlattice. The electrical admittance is deduced by the use of Green functions. A configuration with an electromechanical coupling coefficient as high as 0.76 is found.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC AND OPTICAL PROPERTIES

188

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Anomalous photovoltage in polycrystalline thin films has been studied. The effect is described as a combined effect of mainly p - junctions at the grain boundaries and surface band bending apart from other factors. A new method has been developed to enhance the photovoltage by placing a fine mesh in front of the substrate during the film deposition. This enhancement of photovoltage is explained with the help of a trap-induced space-charge model.

195

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Polyparaphenylene has been synthesized by a range of chemical methods and the products are studied for their electrical and electronic properties. It is shown that the properties of the polymer are sensitive to the method of synthesis.

205

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Thermoluminescence (TL) - fluence response characteristics for peaks 5, 7, 8 and 9 in LiF:Mg,Ti (TLD-100; Harshaw/Bicron) were measured for 5 MeV alpha particles, in both `non-parallel' and `near-parallel' geometries,and for 1 MeV alpha particles in `near-parallel' geometry. The onset of supralinearity in the non-parallel configuration is always at a significantly lower fluence (by approximately a factor of five) than in the nearly parallel configuration. This dependence of the onset of supralinearity on the vector properties of the alpha particle radiation field is interpreted as `proof positive' of the dominant importance of track interaction effects in the linear/supralinear behaviour of the glow peaks of TLD-100. A mathematical expression for the linear/supralinear behaviour for heavy charged particles in near-parallel geometry has been developed and fitted to the TL - fluence response curves. The model incorporates both possibilities of electron and hole diffusion in the glow curve heating stage as well as the contribution to the supralinearity of all the participating nearest-neighbour track interactions. The model is capable of yielding excellent fits to the experimental data; the inclusion of hole diffusion and retrapping is preferred to predict the very abrupt transition from linear to supralinear behaviour for the high-temperature peaks.

218

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This work reports a study of the spatial distribution of atoms evaporated under vacuum and its influence on the thickness distribution of metallic films achieved by this technique. Its goal is to justify the law which has been introduced in an empirical way to explain the thickness distribution obtained when the evaporation rates are high. Taking into account a collision region just above the vapour source, it is possible to determine a new distribution of vapour atom velocities which is no longer a Maxwell form. The spatial distribution of the vapour beam was deduced and then it was fitted experimentally. The comparison between this new distribution function and that deduced from the law leads to a relation able to determine the constant n. This relation shows that the constant n tends to a limiting value when the evaporation rate increases, whatever the metal evaporated. These results were verified when the thickness distribution models were compared with these obtained experimentally for three different metals (Ti, Cu and Al).

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

225

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In order to control laser treatments, precise knowledge of the radiation - surface coupling is required. For this purpose, a numerical identification of the absorption coefficient was achieved from thermal cycles measurements and computations. Variations of the coupling during the laser treatment were studied both in the case of the hardening of pre-coated steel (XC 55: 0.55% C, 0.18% Cr with graphite and manganese phosphate coatings) and in the case of the solid state nitriding of titanium alloys (TA6V).

233

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Applications of high-frequency dielectric measurements (300 kHz to 3 GHz) to the non-destructive examination (NDE) of composite structures are discussed. Preliminary data indicate that the method, previously used for aluminium bonded structures, can be applied to bonded carbon fibre composite structures. Water ingress into the bond structure was observed to influence both the time- and the frequency-domain data. Comparison of exposed and dry joints demonstrated that a good correlation exists between changes with time in the dielectric properties of the composites and the extend of water uptake in the matrix. Parallel gravimetric measurements were also performed. Diffusion of water into the composite structures is discussed in terms of various models. This paper demonstrates that this NDE method may be used for assessment of the water content in the matrix and has general applicability to the study of carbon-reinforced matrix materials.

240

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Auger electron spectroscopy has been applied to determine the near-surface composition of thin A/B/A heterostructures. General equations are established in terms of inelastic mean free path ratios for presumed layer growth conditions, for an analyser geometry which can be specified in terms of a sample tilt angle and ranges of take-off angles . Use of a controlled glancing incidence, in conjunction with RHEED, gives high surface sensitivity. Applications to the technically interesting systems Si/Ge/Si(100) and Fe/Ag/Fe(110) are given; comparison with experiment is used to infer the growth morphology, extent of surface segregation and interdiffusion.

246

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A model of a hybrid solar converter proposed by Goetzberger et al was used to optimize the overall efficiency of the combined system in two different situations. Firstly, the original semi-empirical models for the solar cell and the thermal engine were used. Secondly, more general theoretical models were proposed for each of the two components of the combined converter. The theoretical model of the solar cell produces results in good agreement with the simple empirical model when the ideal cell with no reflection losses is considered. Both the theoretical model and the empirical model of the thermal engine give similar results in the range of temperatures allowed for the proper usage of a solar cell. Reasonable low optimum temperatures could be reached by using materials with a band gap of less than 2 eV. Some ways of improving the hybrid solar converter model proposed by Goetzberger et al are discussed at the end of the paper.

253

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A theoretical treatment, based on the Devonshire theory of ferroelectrics, is presented to describe the storage of electrostatic energy in ferroelectric and paraelectric materials at very high field strengths. In all cases, optimal energy density is achieved by using compositions with Curie temperatures well below the operating temperature. The theory is applied to barium - strontium titanate ceramics and optimal compositions are deduced for energy storage at given working fields. The theory is supported by experimental data showing energy densities up to 8 J at 100 kV .

259

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Recent neurobiophysics experiments based on synchrotron spectromicroscopy indicated that aluminium is selectively accumulated by GABAergic neurons and glial cells rather than by granule cells. Does a similar cell specificity occur in the accumulation of other metals? We provide experimental evidence to the contrary: cobalt is found in granule cells at least with equal probability as in glial cells and GABAergic neurons. This result also confirms that neurobiophysics studies based on surface physics techniques have reached a stage of maturity.

RAPID COMMUNICATIONS

263

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Using a Ludwieg tube wind tunnel, first evidence is obtained of a vanishing triple correlation in supersonic compressible turbulent flow. The results take advantage of a new technique for very high frequency direct estimation velocimetry from density measurements through laser induced fluorescence and seem to confirm early theoretical predictions of Tsugé and Sagara.

267

A dynamical model based on simplified dynamical plasma equations is described and used to simulate radiation-stimulated electromagnetic emissions (SEE) of plasmas. Simulated SEE spectra not only verify linear theory, but also reveal effects of density perturbation caused by ponderomotive force of high-frequency transverse plasma waves and anomalous absorption on SEE.

271

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The nonequilibrium process of mechanical alloying was used to prepare nanocrystalline powder. The crystallization of the -type structure in mechanically alloyed Sm - Fe(Ga) - C material begins at about C. The single phase structure can be obtained after homogenization for one hour at temperatures between C and C. The coercivity increases to a maximum value of about 1.5 T after annealing at a temperature of C. The nearly square shape of the demagnetization curve suggests a very homogeneous microstructure of the highly coercive powder. By hot pressing, a fully dense magnet was successfully obtained with a density of 7.6 g and a coercivity of 1.5 T. No texture could be observed after a 75% hot deformation at C.

274

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A model has been developed that describes the propagation of the transient sheath which forms inside a cylindrical target immersed in a plasma for inner surface implantation. Following this model, a differential equation and its integrated solution are obtained for the sheath-edge position as a function of time. This result can be used to predict the final sheath extent during each pulse for inner surface implantation of a cylindrical target.