Table of contents

Electrical arcs and, more generally thermal plasmas, are widely used in many applications and the understanding or the improvement of the corresponding processes or systems, often requires precise modelling of the plasma. We present, here, a double approach to thermal plasma modelling, which combines the scientific procedure with an engineering point of view. First, we present the fundamental properties of thermal plasmas that are required in the models, followed by the basic equations and structures of the models. The third part is devoted to test cases, and its objectives are the study of some basic phenomena to show their influence on arc behaviour in simple configurations, and the validation of the models: we point out the roles of radiation, thermal conductivity and electrical conductivity for a stationary or transient wall-stabilized arc and we validate a three-dimensional model for a free-burning arc.

Sections 4–6 deal with several industrial configurations and the model is useful in each case for studying important phenomena or processes in greater detail. For transferred arcs, such as those used in metallurgy, the energy transfer from the arc to the anode, and the presence of metallic vapour and pumping gas are essential. For a non-transferred plasma torch used for plasma spraying, we illustrate the relevance of a three-dimensional model and we present the interaction of the plasma with powders. Problems related to high- and low-voltage circuit-breakers are then presented, and various typical mechanisms are modelled. Finally, several non-equilibrium models useful for quasi-thermal conditions are presented in detail, showing how they take into account the chemical kinetics and two-temperature plasmas occurring under particular conditions, such as decaying arcs or inductively coupled plasmas.

We have investigated the dielectric properties of Ti-doped K(Ta,Nb)O₃ films subjected to high temperature annealing. Titanium (+4) substitution on the Nb/Ta site introduces an acceptor state, thus reducing dielectric losses due to defect-related donor states. Using 3% Ti-doped targets, K(Ta,Nb)O₃ : Ti films were grown on MgO (001) crystals by pulsed-laser deposition. The films were annealed in oxygen at temperatures as high as 1000°C. A loss tangent of 0.002 at room temperature was observed for annealed Ti-doped K(Ta,Nb)O₃ thin films. A reduction in tunability was also seen. For these annealed films, the dielectric loss shows little temperature dependence, indicating a significant reduction in donor density due to defects.

We have studied the stability of RCo_5−xCu_x (R = Y, Sm) compounds with respect to phase separation. First principles density functional calculations imply that (i) decomposition into two phases having different x is energetically favourable and (ii) both the stable x values and the Cu atomic site preferences depend on the magnetic state of the alloys. Guided by this result, we studied the structure and magnetic properties of different Sm(Co,Cu)₅ and Sm(Co,Fe,Cu)₅ alloys. Separation into two chemically dissimilar Sm(Co,Cu)₅ phases is typical for the as-made Sm(Co,Cu)₅ alloys. We also observed in different alloys a universal correlation between the room-temperature coercivity and the magnetic state at the temperature of annealing. The coercivity increases significantly if annealed 100–140°C below the Curie temperature; in particular, for SmCo_2.25Fe_0.75Cu₂, the room-temperature coercivity increases from 12.3 to 37.3 kOe. The possibility of different magnetic state-dependent structure transformations is discussed. The experimental results do not support the spinodal decomposition theory, so we suggest that the coercivity increase might be caused by a change in preferred atomic site occupancies.

Superparamagnetic Fe₃O₄ nanocrystals were prepared by a chemical coprecipitation method with a thin thickness-adjustable silica layer coated on the surface by hydrolysis of tetraethyl orthosilicate. The silica-coated Fe₃O₄ nanocrystals were well dispersed and consisted of a 6–7 nm diameter magnetic core and a silica shell about 2 nm thick, according to transmission electron microscopy observations. Fourier transform infrared spectra revealed that amino (–NH₂) groups were successfully covalently bonded to the silica-coated Fe₃O₄ and then carboxyl (–COOH) groups were functionalized to the surface through the reaction of –NH₂ and glutaric anhydride. The synthesized nanocrystals have a cubic spinel structure as characterized by x-ray diffraction, electron diffraction and high-resolution transmission electron microscopy. Their magnetic properties were carefully investigated by a SQUID magnetometer. The results showed that the nanocrystals were superparamagnetic and the blocking temperature T_B shifted from 131 K down to 92 K after they were coated with a thin nonmagnetic layer, since this layer can effectively suppress the magnetic dipolar interaction between particles; the chemically inert silica layer can limit the outside environment effect on the Fe₃O₄ cores quite well due to the excellent magnetic reproducibility of the coated nanocrystals after ageing for 7 months at room temperature. In addition, the dependence of their high-field specific magnetization on temperature has a T² relationship. These functionalized silica-coated Fe₃O₄ superparamagnetic nanocrystals have great potential in biomagnetic applications.

The giant magneto-impedance (GMI) effect in nanocrystalline FeCuNbSiB multilayered films was investigated. The multilayered films were deposited by magnetron sputter equipment with an additional SiO₂ outer layer. The GMI ratio of multilayered films varied with the annealing temperature due to the changing orientation of the magnetic moments. The maximum GMI frequency of the nanocrystalline state was lower than that of the amorphous state, decreasing from 12.3 to 5.45 MHz. Ageing experiments were carried out for films with and without the insulator layer. It was seen that the GMI ratio of the multilayer film with a covered SiO₂ layer was preserved well even after ageing.

Thin films of Bi_3.25La_0.75Ti₃O₁₂ (BLT) and B-site substituted BLT by Zr, i.e. Bi_3.25La_0.75Ti_3−xZr_xO₁₂ (BLTZx, x = 0.20, 0.50, 0.75, 1.00 and 1.50) were fabricated on Pt/Ti/SiO₂/Si substrates by pulsed laser deposition. Structures and electrical characteristics of the polycrystalline films were studied as functions of Zr composition. Structures were investigated by x-ray diffraction, scanning electron microscopy and Raman spectroscopy. It is revealed that the Zr substitution does not destroy the layered structures of BLT but the Zr substitution tolerance is limited. With increasing Zr composition, generally, the octahedra-related vibration modes show a significant low-frequency shift. Compared with the well-known BLT films, the BLTZ0.20 films have larger remnant polarization (P_r), smaller coercive field (E_c) and better fatigue resistance. However, further increasing Zr composition leads to weakened ferroelectricity of the BLTZx films with decreased P_r and reduced fatigue resistance. The effects of Zr substitution on structures and ferroelectric properties of BLT and the correlation between structures and properties are discussed in detail.

The off-stoichiometric Heusler alloy Co₅₀Ni₂₀Ga₃₀ was synthesized by using the melt-spinning technique. The Co₅₀Ni₂₀Ga₃₀ ribbon exhibited a thermo-elastic martensitic transformation from cubic to a tetragonal structure at 270 K during cooling. The martensitic phase at lower temperature exhibited a high-saturated magnetization of 51.00 A m² kg⁻¹ and a high anisotropy field of more than 1 T. The material showed a recoverable two-way shape memory effect with a strain of 0.15% upon the martensitic transformation. The sample showed the maximum magnetostriction of about 97 ppm shrinkage for an applied magnetic field of 1.5 T at 200 K.

A small scale coupled Yb–silica and Tm–silica fibre laser system is described with output at 1.9 µm and with Q-switching using an acousto-optic modulator and also by mechanical optical modulation. The Yb-fibre laser pump source exhibited strong self-pulsation with high-intensity pulses due to stimulated Brillouin scattering. But regular Q-switched pulses were generated from the Tm-fibre laser with an energy of ∼2.4 µJ and duration (FWHM) of ∼280 ns for modulation frequencies of 1–20 kHz when using acousto-optic modulation. The main effects that limit the Q-switched pulse peak power are the onset of gain-switched pulsing during the low-Q state and strong pump excited state absorption.

The purpose of this paper is to propose and analyse a simplified model for plasma generation in air flows at atmospheric pressure. The starting point is a model previously proposed by Lowke (1992 J. Phys. D: Appl. Phys.25 202–10), enriched with a loss term which schematically takes into account the drag of the metastable and ionized species by the flow. An asymptotic analysis of this model confirmed by numerical simulations is proposed and shows that plasma generation is a two or three time scale process (depending on the electric field value). Eventually, the existence of the plasma over long time scales depends on the value of the flow velocity relative to a threshold value, which can be approximately computed analytically. A procedure for generating a plasma at atmospheric pressure in air at low energetic cost is also suggested.

Multipactor charts for parallel plate geometries have been computed using a program that numerically solves a phase equation for the crossing times rather than by detailed computation of electronic paths. Motion in three-dimensional is tracked and detailed models for secondary emission and elastic collisions with the walls are employed. The speed advantage of the method allows the dependence of multipactor prediction on surface properties and multipactor criteria, such as the number of electrons within a shower that are followed, to be assessed over a broad parameter range.

Threshold ionization mass spectrometry (TIMS) has been used to measure the excited molecular oxygen states O₂ (¹Δ_g) and during plasma-assisted chemical vapour deposition of tin oxide (SnO₂) thin films. The latter, composed of nanosized features, was deposited by feeding in a mixture of Ar, O₂ and tetramethyltin (Sn(CH₃)₄ or TMT) in a capacitively coupled RF discharge reactor. Langmuir probe measurements were performed along with TIMS to measure the electron temperature and density. The correlations between these two diagnostic methods have been investigated. The observed densities of O₂ (¹Δ_g) and in the γ mode of the discharge are maximum at a low electron temperature and high density. Furthermore, these results have been shown to be correlated to the trend of the electronic conductivity of the deposited SnO₂ thin films.

An atmospheric pressure plasma jet using radio-frequency (rf) (13.56 MHz) power is developed to produce a homogeneous glow discharge at low temperatures (between 50°C and 150°C on the inner electrode). Discharge parameters (power, voltage, current and the phase angle) are measured and the influence of the operating parameters on the discharge characteristics is investigated for a He/O₂ gas mixture. By varying the input power, a 'phase saturation' region and the 'arc failure' mode are identified. The optimized flow rate ratio between oxygen and helium is found to be 0.1/40 slpm in our experiment. At this ratio, a low power consumption and wide operational range for rf power (200 W) are obtained.

In this investigation three effects are included in a recently developed scale-dependent multi-asperity model of elastic contact and friction. First, a Weibull distribution of asperity heights is used, which allows the skew and kurtosis to be varied, but not independently of each other. Second, the effect of non-constant radii of curvature of the asperity summits, with the curvature varying with asperity height, is examined. Finally, the influence of noncontacting asperities on the normal force and hence on contact and friction is included. It is noted that the contact and friction model used (Adams et al 2003 ASME J. Tribol.125 700–8) includes the effects of adhesion and scale-dependent friction. It is demonstrated that positive/negative skew decreases/increases both the friction coefficient and its dependence on the normal load. The results also indicate that for radii of curvature that increase/decrease with height, the friction coefficient increases/decreases as does its dependence on load.

Nanostructured diamond was grown by microwave plasma chemical vapour deposition onto 2 mm diameter quartz spheres using a H₂/CH₄/N₂ feedgas mixture high in methane concentration (15% by volume). Deposition experiments were performed at low temperature (<425°C, below the temperature limit of the optical pyrometer used) as well as at high temperature (830°C). Nucleation and growth of nanostructured diamond was found to occur readily in both cases. In addition, it was found that pre-treatment scratching is not necessary for achieving high diamond nucleation/growth rates on quartz, although scratching did result in a more uniform and smooth surface morphology, especially for low temperature deposition. All films grown at low temperature resulted in higher diamond quality with less amorphous carbon and non-diamond components. Plasma reduction of the exposed silica surface to create oxygen-containing species near the substrate surface may explain the improved diamond quality and practical nucleation/growth rates at such low temperature.

Nanosized titanium dioxide (TiO₂) is synthesized by laser-induced pyrolysis using titanium isopropoxide as a liquid precursor. The specific surface area of as-produced nanopowders measured by the Brunauer–Emmett–Teller method (BET) varies from 84 to 110 m² g⁻¹. X-ray diffraction (XRD) and Raman scattering showed that the TiO₂ nanocrystals had an anatase structure. The grain size of the nanoparticles was estimated from scanning electron microscopy, XRD and BET measurements. The reflection spectra of nanocrystalline TiO₂ pressed pellets has been measured in the region between 80 and 1500 cm⁻¹ by Fourier transform infrared spectroscopy. To interpret the experimental results, a model based on a generalized Bruggeman effective medium approximation of a dielectric function has been proposed. It is based on the polycrystalline character of TiO₂ nanoparticles including island-structure and porosity of the nanopowders, along with the anatase single crystal dielectric functions. Thus, by comparing the results of calculated and experimental infrared (IR) spectra, the values of microscopic parameters of nanocrystalline powders can be deduced.

Analytical solutions for the acoustic wave equations obtained by temporal Fourier and spatial Laplace transformations directly provide a description of the motion of the crystal surface caused by the spatially distributed laser heating of a semi-infinite crystal. Evaluation of the acoustic field in the bulk of the material is not needed here. In general, all three acoustic modes are excited due to the laser-induced thermoelastic effect and contribute to each of the three components of the transient surface displacement. Numerical simulations of the surface displacement as a function of time and crystal surface orientation are performed with the use of the analytical formulae derived in the case of a hexagonal crystal, for which only two modes are excited. The formulae obtained make it possible to optimize the orientation of the surface of the crystal in order to improve the efficiency of the excitation of the in-plane motion of the surface.

The surface-area-difference (SAD) model is developed for the cohesive energy of metallic crystals by taking into account surface effects, and has been extended to predict the thermodynamic properties of metallic nanoparticles, nanowires and nanofilms with free and non-free surfaces (embedded in a matrix). It is found that the thermodynamic properties of metallic nanocrystals depend on the crystal size and the interface coherence, where the interface coherence determines the variation tendency (increasing or decreasing), and the size determines the magnitude of the variation. The present calculated results on the thermodynamic properties of metallic nanocrystals by the SAD model are consistent with the corresponding experimental values.

Current versus voltage (I versus V) and complex impedance, z^*(f) = z'(f) − iz''(f), measurements for polyaniline (PANI) films were carried out in samples with different doping levels and gold and/or aluminium as electrodes. The complex impedance of Au/PANI/Au presents the typical behaviour of a somewhat solid disordered material with negligible electrode influence. DC measurements confirm this evidence. However, some additional influence of the interface was observed to occur when Al was used as the electrode. A phenomenological model employing the Cole–Cole dielectric function for generating the conduction process is developed and the calculated z'(f) and z''(f) as functions of the polymer doping level and the bias polarization are found to be in good agreement with experimental data, thereby separating bulk and interface contributions to the complex impedance, as well as providing approximate values of the PANI–Al interface thickness and resistivity, around 10 nm and 10¹³ Ω cm, respectively.

Cold-worked and annealed copper powder are investigated in terms of realistic microstructural models based on the strain field model of dislocations and log-normal distribution of spherical crystallites. The dislocation type was observed to be either screw type or ⟨100⟩ type dipoles in cold-worked powder and edge type in annealed powder specimens, respectively. Dislocations are observed to be more correlated in the cold-worked state compared to the annealed state. Systematic differences exist in the mean square strain values for different crystallographic directions, indicating the importance of model-based approaches in analysing dislocation induced x-ray line broadening. For more correlated dislocation distribution model-based approaches should be adopted.

Broadband dielectric spectroscopy is applied to investigate the electrical properties of disordered perovskite-like ceramics in a wide temperature range. From the x-ray diffraction analysis it was found that the newly obtained (Na_0.75Bi_0.25) (Mn_0.25Nb_0.75)O₃ ceramics consist of two chemically different phases. The major perovskite one has an orthorhombic structure described by the Pbcm space group (No 57, in yxz setting). The minor phase shows an orthorhombic symmetry, all-face-centred lattice F, with the lattice parameters a = 10.797(4) Å, b = 7.601(3) Å and c = 7.691(3) Å. The electric modulus M^* formalism used in the analysis enabled us to distinguish and separate the relaxation processes, dominated by marked conductivity in the ε^*(ω) representation. In the ceramics studied, the relaxation times are thermally activated and the dipole process has a clearly non-Debye behaviour. The relaxation process described with the use of the activation energy of approximately 0.4 eV and the characteristic relaxation time, τ₀ = 1 × 10⁻¹¹ s, was found to be related to oxygen vacancies. The low frequency relaxation shows Debye behaviour with a slightly lower activation energy and a longer characteristic time.

We report the ultraviolet laser-induced absorption spectra and refractive index changes in bismuth-based silicate glass. A positive maximum refractive index change of 6 × 10⁻⁴ has been observed in bismuth-based silicate glass upon exposure to a pulsed 248 nm KrF excimer laser. It is also seen that the changes in the absorbance and refractive index are strongly dependent on glass melting conditions.

The structural, dielectric and piezoelectric properties of xPMS–(1 − x)PZT ceramics were investigated as a function of Pb(Mn_1/3Sb_2/3)O₃ (PMS) content by x-ray diffraction, scanning electron microscopy, and dielectric and piezoelectric spectroscopy techniques. All the Pb(Mn_1/3Sb_2/3)O₃–PbZrO₃–PbTiO₃ (PMS–PZT) samples exhibit a single phase of perovskite structure with tetragonal symmetry. Dielectric studies revealed that the phase transition temperature (T_c) is suppressed with increasing PMS content. For PMS–PZT samples with 0.08 ⩽ x ⩽ 0.15, the maximum dielectric constant decreases as the measurement frequencies increase and the permittivity maximum temperature (T_m) is shifted towards higher temperatures as well, which indicates that dielectric relaxor behaviour was observed, while for x = 0.02 and 0.05, there is no shift in T_m, which implies normal ferroelectric behaviour. The samples with a composition of x = 0.05 exhibit excellent dielectric and piezoelectric properties (ε_r = 1540, d₃₃ = 360 pC N⁻¹, K_p = 0.58, tan δ = 0.45%, Q_m = 1210) and, therefore, should be ideal candidates for high-power applications, such as in piezoelectric transformers.

An examination of an active waveplate device using a one-dimensional model, giving numerical and analytical results, is presented. The model calculates the director and twist configuration by minimizing the free energy of the system with simple homeotropic boundary conditions.

The effect of varying the in-plane electric field in both magnitude and direction is examined, and it is shown that the twist through the cell is constant in time as the field is rotated. As the electric field is rotated, the director field lags behind by an angle which increases as the frequency of the electric field rotation increases. When this angle reaches approximately π/4 the director field no longer follows the electric field in a uniform way. Using mathematical analysis it is shown that the conditions on which the director profile will fail to follow the rotating electric field depend on the frequency of electric field rotation, the magnitude of the electric field, the dielectric anisotropy and the viscosity of the liquid crystal.

The potential for synchrotron–laser pump–probe luminescence measurements to provide a direct link between the chemical/structural properties of light emitting wide band-gap solids and optically active electronic trapping states is evaluated. Initial results are presented that demonstrate the various excitation and relaxation processes involved, whereby the synchrotron pump provides the chemical/structural information, and the laser probes both radiative and non-radiative electronic trapping states. The examples described here demonstrate that the laser probe may quench, be neutral, or enhance the synchrotron-pumped luminescence of the wide band-gap materials boron nitride, SiO₂ and Na_0.7Ca_0.3Al_1.3Si_2.7O₈, respectively. Consideration is given to the potential of the method to provide a general route to the analysis of single components in heterogeneous systems.

The varistor system SnO₂·CuO· Ta₂O₅ with different Ta₂O₅ dopants sintered at 1300°C for 80 min was investigated. It is found that Ta₂O₅ significantly affects the grain size and the electrical properties. The average grain size decreases from 6.8 to 1.9 µm with an increase in Ta₂O₅ concentration from 0.05 to 1.00 mol%. The sample with 0.05 mol% Ta₂O₅ has the best nonlinear electrical property and the highest nonlinear coefficient (α = 37.9) and the sample with 0.50 mol% Ta₂O₅ possesses the highest densification (98.7% of the theoretical density) among all the samples. The reason for the nonlinearity of SnO₂ ceramics is explained.