On equilibrium states and dust charging in dusty plasmas

The dust-charge variation process is revisited, accounting for the background density variation associated with electron capture and release by the dust grains. It appears possible to maintain overall charge neutrality in the plasma without any external particle source or sink. It is shown that if the dust charge and density are sufficiently high, the effect of the background electron density variation on dust-charge relaxation is important. The equilibrium dust charge and its rate of variation are obtained for dusty plasmas subject to strong UV irradiation. The latter releases photoelectrons from the dust surface and can significantly affect the equilibrium dust charge, its variation rate, as well as the overall charge neutrality in the plasma.

Equilibrium and relaxation of particulate charge in fluorocarbon plasmas

Charging of micron-size particulates, often appearing in fluorocarbon plasma etching experiments, is considered. It is shown that in inductively coupled and microwave slot-excited plasmas of C4F8 and Ar gas mixtures, the equilibrium particle charge and charge relaxation processes are controlled by a combination of microscopic electron, atomic (Ar+ and F+), and molecular ion (CF+ 3, CF+ 2, and CF+) currents. The impact of molecular ion currents on the particulate charging and charge relaxation processes is analyzed. It is revealed that in low-power (<0.5 kW) microwave slot-excited plasmas, the impact of the combined molecular ion current to the total positive microscopic current on the particle can be as high as 40%. The particulate charge relaxation rate in fluorocarbon plasmas appears to exceed 108 s-1, which is almost one order of magnitude higher than that from purely argon plasmas. This can be attributed to the impact of positive currents of fluorocarbon molecular ions, as well as to the electron density fluctuations with particle charge, associated with electron capture and release by the particulates.

Extremely non-equilibrium synthesis of luminescent zinc oxide nanoparticles through energetic ion condensation in a dense plasma focus device

Luminescent ZnO nanoparticles have been synthesized on silicon and quartz substrates under extremely non-equilibrium conditions of energetic ion condensation during the post-focus phase in a dense plasma focus (DPF) device. Ar+, O+, Zn+ and ZnO+ ions are generated as a result of interaction of hot and dense argon plasma focus with the surfaces of ZnO pellets placed at the anode. It is found that the sizes, structural and photoluminescence (PL) properties of the ZnO nanoparticles appear to be quite different on Si(1 0 0) and quartz substrates. The results of x-ray diffractometry and atomic force microscopy show that the ZnO nanoparticles are crystalline and range in size from 5-7 nm on Si(1 0 0) substrates to 10-38 nm on quartz substrates. Room-temperature PL studies reveal strong peaks related to excitonic bands and defects for the ZnO nanoparticles deposited on Si (1 0 0), whereas the excitonic bands are not excited in the quartz substrate case. Raman studies indicate the presence of E2 (high) mode for ZnO nanoparticles deposited on Si(1 0 0).

Rapid, low-temperature synthesis of nc-Si in high-density, non-equilibrium plasmas : enabling nanocrystallinity at very low hydrogen dilution

Nanocrystalline silicon thin films were deposited on single-crystal silicon and glass substrates simultaneously by inductively coupled plasma-assisted chemical vapor deposition from the reactive silane reactant gas diluted with hydrogen at a substrate temperature of 200 °C. The effect of hydrogen dilution ratio X (X is defined as the flow rate ratio of hydrogen to silane gas), ranging from 1 to 20, on the structural and optical properties of the deposited films, is extensively investigated by Raman spectroscopy, X-ray diffraction, Fourier transform infrared absorption spectroscopy, UV/VIS spectroscopy, and scanning electron microscopy. Our experimental results reveal that, with the increase of the hydrogen dilution ratio X, the deposition rate Rd and hydrogen content CH are reduced while the crystalline fraction Fc, mean grain size δ and optical bandgap ETauc are increased. In comparison with other plasma enhanced chemical vapor deposition methods of nanocrystalline silicon films where a very high hydrogen dilution ratio X is routinely required (e.g. X > 16), we have achieved nanocrystalline silicon films at a very low hydrogen dilution ratio of 1, featuring a high deposition rate of 1.57 nm/s, a high crystalline fraction of 67.1%, a very low hydrogen content of 4.4 at.%, an optical bandgap of 1.89 eV, and an almost vertically aligned columnar structure with a mean grain size of approximately 19 nm. We have also shown that a sufficient amount of atomic hydrogen on the growth surface essential for the formation of nanocrystalline silicon is obtained through highly-effective dissociation of silane and hydrogen molecules in the high-density inductively coupled plasmas. © 2009 The Royal Society of Chemistry.

Parameters and equilibrium profiles for large-area surface-wave sustained plasmas

The equilibrium profiles of the plasma parameters of large-area if discharges in a finite-length metal-shielded dielectric cylinder are computed using a two-dimensional fluid code. The rf power is coupled to the plasma through edge-localized surface waves traveling in the azimuthal direction along the plasma edge. It is shown that self-consistent accounting for axial plasma diffusion and radial nonuniformity of the electron temperature can explain the frequently reported deviations of experimentally measured radial density profiles from that of the conventional linear diffusion models. The simulation results are in a good agreement with existing experimental data obtained from surface-wave sustained large-diameter plasmas. © 2002 The American Physical Society.

Low-pressure diffusion equilibrium of electronegative complex plasmas

A model for electronegative plasmas containing charged dust or colloidal grains was used. Numerical solutions based on the model demonstrate how a low-pressure diffusion equilibrium of the complex electronegative plasma system is dynamically sustained through plasma particle sources.

kmth price sealed-bid auctions with general independent values and equilibrium linear mark-ups

A generalised bidding model is developed to calculate a bidder’s expected profit and auctioners expected revenue/payment for both a General Independent Value and Independent Private Value (IPV) kmth price sealed-bid auction (where the mth bidder wins at the kth bid payment) using a linear (affine) mark-up function. The Common Value (CV) assumption, and highbid and lowbid symmetric and asymmetric First Price Auctions and Second Price Auctions are included as special cases. The optimal n bidder symmetric analytical results are then provided for the uniform IPV and CV models in equilibrium. Final comments concern implications, the assumptions involved and prospects for further research.

Exploration of the fundamental equilibrium behaviour of calcium exchange with weak acid cation resins

This study evaluated the complexity of calcium ion exchange with sodium exchanged weak acid cation resin (DOW MAC-3). Exchange equilibria recorded for a range of different solution normalities revealed profiles which were represented by conventional “L” or “H” type isotherms at low values of equilibrium concentration (Ce) of calcium ions, plus a superimposed region of increasing calcium uptake was observed at high Ce values. The loading of calcium ions was determined to be ca. 53.5 to 58.7 g/kg of resin when modelling only the sorption curve created at low Ce values,which exhibited a well-defined plateau. The calculated calcium ion loading capacity for DOWMAC-3 resin appeared to correlate with the manufacturer's recommendation. The phenomenon of super equivalent ion exchange (SEIX) was observed when the “driving force” for the exchange process was increased in excess of 2.25 mmol calcium ions per gram of resin in the starting solution. This latter event was explained in terms of displacement of sodium ions from sodium hydroxide solution which remained in the resin bead following the initial conversion of the as supplied “H+” exchanged resin sites to the “Na+” version required for softening studies. Evidence for hydrolysis of a small fraction of the sites on the sodium exchanged resin surface was noted. The importance of carefully choosing experimental parameters was discussed especially in relation to application of the Langmuir–Vageler expression. This latter model which compared the ratio of the initial calcium ion concentration in solution to resin mass, versus final equilibrium loading of the calcium ions on the resin; was discovered to be an excellent means of identifying the progress of the calcium–sodium ion exchange process. Moreover, the Langmuir–Vageler model facilitated standardization of various calcium–sodium ion exchange experiments which allowed systematic experimental design.

Equilibrium and column studies of iron exchange with strong acid cation resin

The exchange of iron species from iron (III) chloride solutions with a strong acid cation resin has been investigated in relation to a variety of water and wastewater applications. A detailed equilibrium isotherm analysis was conducted wherein models such as Langmuir Vageler, Competitive Langmuir, Freundlich, Temkin, Dubinin Astakhov, Sips and Brouers-Sotolongo were applied to the experimental data. An important conclusion was that both the bottle-point method and solution normality used to generate the ion exchange equilibrium information influenced which sorption model fitted the isotherm profiles optimally. Invariably, the calculated value for the maximum loading of iron on strong acid cation resin was substantially higher than the value of 47.1 g/kg of resin which would occur if one Fe3+ ion exchanged for three “H+” sites on the resin surface. Consequently, it was suggested that above pH 1, various iron complexes sorbed to the resin in a manner which required less than 3 sites per iron moiety. Column trials suggested that the iron loading was 86.6 g/kg of resin when 1342 mg/L Fe (III) ions in water were flowed at 31.7 bed volumes per hour. Regeneration with 5 to 10 % HCl solutions reclaimed approximately 90 % of exchange sites.

The equilibrium geometry and electronic structure of Bi nanolines on clean and hydrogenated Si(001) surfaces

The equilibrium geometry, electronic structure and energetic stability of Bi nanolines on clean and hydrogenated Si(001) surfaces have been examined by means of ab initio total energy calculations and scanning tunnelling microscopy. For the Bi nanolines on a clean Si surface the two most plausible structural models, the Miki or M model (Miki et al 1999 Phys. Rev. B 59 14868) and the Haiku or H model (Owen et al 2002 Phys. Rev. Lett. 88 226104), have been examined in detail. The results of the total energy calculations support the stability of the H model over the M model, in agreement with previous theoretical results. For Bi nanolines on the hydrogenated Si(001) surface, we find that an atomic configuration derived from the H model is also more stable than an atomic configuration derived from the M model. However, the energetically less stable (M) model exhibits better agreement with experimental measurements for equilibrium geometry. The electronic structures of the H and M models are very similar. Both models exhibit a semiconducting character, with the highest occupied Bi-derived bands lying at ~0.5 eV below the valence band maximum. Simulated and experimental STM images confirm that at a low negative bias the Bi lines exhibit an 'antiwire' property for both structural models.

The nature of non-equilibrium solidification of undercooled Agsingle bondCu alloys in contact with primary copper dendrites

Liquids of silver-copper alloys with near eutectic compositions embedded in a copper matrix were undercooled. The structural and microstructural investigations of these alloys solidified from undercooled temperature indicated the absence of both the eutectic reaction and diffusionless transformation below the equal free energy curve (T0). Instead the liquid maintained local equilibrium with the copper dendrites continuously until it intersected the extended solidus of the silver rich solid solution.

Equilibrium studies of ammonium exchange with Australian natural zeolites

This paper is concerned with the study of the equilibrium exchange of ammonium ions with two natural zeolite samples sourced in Australia from Castle Mountain Zeolites and Zeolite Australia. A range of sorption models including Langmuir Vageler, Competitive Langmuir, Freundlich, Temkin, Dubinin Astakhov and Brouers–Sotolongo were applied in order to gain an insight as to the exchange process. In contrast to most previous studies, non-linear regression was used in all instances to determine the best fit of the experimental data. Castle Mountain natural zeolite was found to exhibit higher ammonium capacity than Zeolite Australia material when in the freshly received state, and this behavior was related to the greater amount of sodium ions present relative to calcium ions on the zeolite exchange sites. The zeolite capacity for ammonium ions was also found to be dependent on the solution normality, with 35–60% increase inuptake noted when increasing the ammonium concentration from 250 to 1000 mg/L. The optimal fit ofthe equilibrium data was achieved by the Freundlich expression as confirmed by use of Akaikes Information Criteria. It was emphasized that the bottle-point method chosen influenced the isotherm profile in several ways, and could lead to misleading interpretation of experiments, especially if the constant zeolite mass approach was followed. Pre-treatment of natural zeolite with acid and subsequently sodium hydroxide promoted the uptake of ammonium species by at least 90%. This paper highlighted the factors which should be taken into account when investigating ammonium ion exchange with natural zeolites.

Non-equilibrium trapping in Al---In system

The comparative trapping efficiency of indium in aluminium solid solution during vapour deposition and rapid solidification at room temperature was evaluated by studying the nature of the decomposition of the metastable solid solution. A spinodal decomposition was observed in the case of rapid solidification while vapour deposited foils decompose by a nucleation and growth type of process. From this we conclude that rapid solidification effects a more efficient non-equilibrium trapping of indium in aluminium solid solution compared to vapour deposition at room temperature.

Turbulence measurements in an equilibrium axisymmetric wall jet

This paper reports measurements of turbulent quantities in an axisymmetric wall jet subjected to an adverse pressure gradient in a conical diffuser, in such a way that a suitably defined pressure-gradient parameter is everywhere small. Self-similarity is observed in the mean velocity profile, as well as the profiles of many turbulent quantities at sufficiently large distances from the injection slot. Autocorrelation measurements indicate that, in the region of turbulent production, the time scale of ν fluctuations is very much smaller than the time scale of u fluctuations. Based on the data on these time scales, a possible model is proposed for the Reynolds stress. One-dimensional energy spectra are obtained for the u, v and w components at several points in the wall jet. It is found that self-similarity is exhibited by the one-dimensional wavenumber spectrum of $\overline{q^2}(=\overline{u^2}+\overline{v^2}+\overline{w^2})$, if the half-width of the wall jet and the local mean velocity are used for forming the non-dimensional wavenumber. Both the autocorrelation curves and the spectra indicate the existence of periodicity in the flow. The rate of dissipation of turbulent energy is estimated from the $\overline{q^2}$ spectra, using a slightly modified version of a previously suggested method.