Charge Balance Equations Research Articles

Numerical Simulation Study for the Effect of the Strength and the Direction of a Static Magnetic Field on the Transient Double-Diffusive Flow in Liquid Phase during an Alloy Solidification

A numerical simulation study has been carried out to examine the effect of a static magnetic field on the solidification process of an alloy. A mathematical model, based on the continuum model, was developed for the computation of a transient double-diffusive fluid flow under Lorentz body force. The model includes conservation of mass and momentum, heat, species and electrical charge balance equations. The simulation domain was selected as a cavity filled with a metallic alloy and differentially heated, which may be taken as a Bridgman model domain used in the crystal growth process. The solution is carried out by using a Finite Volume Method. Study of the direction and the intensity of the applied magnetic field effects on stabilizing the double diffusive flow field were also carried out. Simulation results indicate that the use of a static, magnetic field in this growth setup is effective in suppressing natural convection in the solution.

Thermodynamic Research of Leaching Copper Oxide Materials with Ammonia-ammonium Chloride-water Solution

The solubilities of copper hydroxide Cu(OH)2, copper oxide CuO, atacamite Cu(OH)1.5Cl0.5, malachite Cu2(OH)2CO3 and chessylite Cu3(OH)2(CO3)2 in an ammonia-ammonium chloride-water solution were calculated using an exponential computation method based on both mass balance and charge balance equations. The range of stability of each solid phase was also established. A group of experiments were designed to validate the veracity of the results of the thermodynamic calculation.

Exact determination of electrical properties of wurtzite Al1−xInxN/(AlN)/GaN heterostructures (0.07 ≤ x ≤ 0.21) by means of a detailed charge balance equation

This paper discusses the determination of key electrical parameters of AlInN/(AlN)/GaN heterostructures from capacitance–voltage (CV) measurements. These heterostructures gained recently importance since they allow for high electron mobility transistor (HEMT) devices with several remarkable records: densities of the 2D electron gas (2DEG) of 2.6 × 1013 cm−2 for lattice-matched (LM) heterostructures and barrier thickness of 14 nm, beyond 2 A/mm saturation currents, above 100 GHz operation for heterostructures grown on Si (111) with gate length of 0.1 µm. Despite these striking experimental results, a consistent determination of the most important electrical parameters, namely polarization sheet charge density, surface potential, and dielectric constant of the alloy are still missing. By setting up the correct charge balance equation, these parameters can unambiguously be determined. For instance, in the case of nearly LM Al0.85In0.15N these parameters amount to σAl0.85In0.15N/GaN ~ 3.7 × 1017 m−2, eΦS ~ 3 eV and ɛAl0.85In0.15N ~11.2, for the charge density, the surface barrier potential, and the dielectric constant, respectively.

Chemical Equilibria of Nickel Chloride in HCl Solution at 25˚C

Chemical equilbria of nickel chloride in HCl solution at <TEX>$25\;{^{\circ}C}$</TEX> were analyzed by considering chemical equilibria, mass and charge balance equations. The activity coefficients of solutes were calculated by using Bromley equation. The necessary thermodynamic properties, such as the equilibrium constant for the formation of Ni<TEX>$Cl^+$</TEX> at zero ionic strength and interaction parameter, were evaluated by applying Bromley equation to the stability constant data reported in the literature. It was found that most nickel exists as <TEX>$Ni^{2+}$</TEX> in HCl solution up to 5 molality HCl. The pH values of Ni<TEX>$Cl_2-HCl-H_2O$</TEX> system at <TEX>$25\;{^{\circ}C}$</TEX> calculated in this study agreed well with the pH values measured by employing pH meter.

Highly charged cloud particles in the atmosphere of Venus

The accumulation of charges on cloud particles by the charge transfer of ions and attachment of electrons in the atmosphere of Venus is investigated in the present work. Three cloud layers between 45 and 70 km exist in the atmosphere of Venus. Ions and electrons are produced by the interaction of galactic cosmic rays with the neutral molecules. Ion to particle and electron to particle attachment coefficients are calculated. The charge balance equations include ion‐ion recombination, ion‐electron recombination, electron attachment to neutrals, electron detachment from negative ions, and attachment of electron and charge transfer from ions to particles. It is found that the ion concentrations are reduced by a maximum of a factor of 5 by charging of the particles, while the earlier studies showed a maximum reduction of about an order of magnitude due to the differences in the surface area of the particles. A similar result is observed in the calculation of electrical conductivity. Both monodisperse and polydisperse distribution of particles are considered. The conductivity was reduced by a factor of 3 when using the monodisperse distribution of particles, while the maximum reduction observed was a factor of 2 when using the polydisperse distribution. This result implies that the monodisperse particle distribution overestimates the effect of particles on the atmospheric conductivity. The ratio of negative to positive charges is found to be very large in the middle and upper cloud layers. The low abundance of the aerosols and high conductivity of the atmosphere appear to rule out lightning activity in the 40 to 70 km altitude region.

Role of deep-level centers in compensated semi-insulating GaAs

Requirements are defined for GaAs materials intended for solid-state detectors of ionizing radiation. A model is proposed to ascertain the role of deep-level centers in compensated semi-insulating GaAs. The model consists of transport equations and a charge-balance equation describing carrier transitions in a multi-level system. Its numerical analysis is performed to ascertain the relationship to be satisfied by dopant concentrations.

Nonlinear two-phase equilibrium model for the binding of arsenic anions to cationic micelles

The binding of arsenic ions to cationic cetylpyridinium chloride (CPC) micelles has been investigated using the semiequilibrium dialysis (SED) technique. In SED experiments, it has been shown that CPC micelles are very effective in binding arsenic ions in the retentate. At the studied pH (pH 8), the unbound and bound arsenic exists primarily as divalent anions (HAsO 4 2−) while CPC molecules exist as monovalent cations. Therefore, arsenic ions are bound electrostatically to the cationic micelle. The resultant colloid is large enough not to pass through the dialysis membrane, producing a rejection greater than 99.59%. The concentration of the unbound arsenic anions passing through the dialysis membrane is practically the same as the permeate concentration of these species in the analogous micellar-enhanced ultrafiltration (MEUF) experiments. Therefore, a nonlinear equilibrium model which combines thermodynamic relations, charge balance equations, and material balance equations with the Oosawa two-phase polyelectrolyte theory has been developed to correlate the binding of arsenic to CPC micelles in SED and MEUF. It was shown that the equilibrium model successfully accounts for the experimental data in both SED and MEUF in the absence and presence of monovalent (HCO 3 1−) and divalent co-ions (HPO 4 2−). Because of their small sizes (less than 10 nm), micelles should retain their equilibrium shapes in the presence of hydrodynamic shear typically attained in most dynamic processes. Therefore, the equilibrium model can be used to predict separation efficiencies in other ultrafiltration units such as in crossflow ultrafiltration processes.

Dust charging and electrical conductivity in the day and nighttime atmosphere of Mars

Understanding aerosol charging and atmospheric conductivity are necessary in describing the global electric circuit, the aerosol coagulation rate, aerosol‐cloud interaction and their subsequent affect on the climate. The importance of aerosol charging for the conductivity variations of the lower Martian atmosphere during both day and night is calculated. Galactic cosmic rays are the dominant ionizing agent in the lower atmosphere, producing molecular ions and ion clusters. During the nighttime these ion clusters get attached to the aerosols and charging occurs. Solar UV photons are an additional ionizing agent during the day‐time. Only solar photons of energy less than 6 eV reach the surface of Mars as those with energies greater than 6 eV are absorbed by atmospheric molecules before they reach the lower atmosphere. Those photons which do reach the lower atmosphere ionize the aerosols as the ionization potential of most of the aerosols is less than 6 eV and produce electrons. Aerosols become charged by the attachment of ions and electrons during the day‐time. The ion‐aerosol and electron‐aerosol attachment coefficients, as well as the ion‐ion and ion‐electron recombination rates are calculated. The charge distribution of aerosols is obtained by the simultaneous solution of the ion‐aerosol charge balance equations. Both the steady state and time dependent concentration of charged aerosols are calculated. More than 60% of the ions and 95% of the electrons get attached to the aerosols. There are more negatively charged aerosols in steady state due to the presence of highly mobile electrons during the day‐time. The presence of electrons increases the conductivity during the day time. The day‐time results are compared with the nighttime results.

Calculating pH in pig manure taking into account ionic strength

Models such as the Anaerobic Digestion Model No. 1 (ADM1) assume that pH can be calculated directly from the concentration of hydrogen ions. However because pH is, by definition, the negative logarithm of the hydrogen ion activity, and thus pH measurements represent hydrogen ion activities, this approach may lead to a bias between measured and predicted pH values. Implementing ionic strength effects into the charge balance equation and the calculation of pH is a theoretical improvement to this. In this study a model, implementing a procedure for calculating pH, was developed to analyse the effect of ionic strength on pH in a pig manure. By adding KCl to samples of pig manure, experimental results could be analysed with help from the model. A modified form of the Davies equation was found to give the most accurate prediction of pH in the pig manure studied in this paper with changing ionic strength.

Rapid Throughput Screening of Apparent KSP values for Weakly Basic Drugs Using 96-Well Format

A rapid-throughput screening assay was developed to estimate the salt solubility parameter, KSP, with a minimal quantity of drug. This assay allows for early evaluation of salt limited solubility with a large number of counter-ions and biologically promising drug leads. Drugs dissolved (typically 10 mM) in DMSO are robotically distributed to a 96-well plate. DMSO is evaporated, and drugs are equilibrated with various acids at different concentrations (typically <1 M) to yield final total drug concentrations around 2.5 mM. The plate is checked for precipitation. Filtrates from only those precipitated wells were subjected to rapid gradient HPLC analysis. An iterative procedure is employed to calculate all species concentrations based on mass and charge balance equations. The apparent KSP values assuming 1:1 stoichiometry are determined from counter-ion and ionized drug activities. A correlation coefficient >0.975 for eight drugs totaling 16 salts is reported. Intra-day and inter-day reproducibility was <10%. Conventional apparent KSP measurements were translated to 96-well format for increased throughput and minimal drug consumption (typically 10 mg) to evaluate at least eight different counter-ions. Although the current protocol estimates KSP from 10−3 to 10−7 M, the dynamic range of the assay could be expanded by adjusting drug and counter-ion concentrations.

Surface science opportunities in the electronic structure of ZnO (A perspective on the article, “Quantitative analysis of surface donors in ZnO”, by D.C. Look)

ZnO is a wide-gap oxide semiconductor of considerable current interest for electronics, optoelectronics, and, possibly, semiconductor spintronics. Through selective electronic doping, ZnO can be a transparent conducting oxide [1], a UV light emitter [2,3], and, when alloyed with a few to several atomic percent of Co, Mn or other transition metals with unpaired d electrons, is squarely at the center of controversy in the field of high-Tc ferromagnetic semiconductors [4]. Despite this range of interests, fundamental aspects of electronic doping in ZnO remain poorly understood. For instance, theoretical calculations suggest that H at either interstitial or substitutional sites is responsible for the persistent n-type conductivity that frustrates efforts to achieve p-type behavior, an essential requirement for the fabrication of pn light emitting diodes and hole-mediated ferromagnetic coupling of Mn dopants [5,6]. Yet, experimental studies do not in general align with this prediction. Another interesting aspect of n-type conduction in ZnO is the appearance of a near-surface conducting channel that appears to be present in bulk crystals [7,8]. Although it has been a few years since the original observation of this phenomenon was described, detailed understanding is lacking. In this paper, David Look presents a transport study aimed at gaining insightmore » into the phenomenon of near-surface conductivity in bulk ZnO. All samples investigated were unintentionally n-type, as is typical. The measured Hall data were interpreted using a two-layer conduction model based on standard charge balance equations. Look fit the temperature dependence of the electron mobility and carrier concentration and extracted the thicknesses of the surface conducting layer, which dominates at lower temperatures, for bulk crystals synthesized by different methods and marketed by different companies. By making reasonable assumptions about the surface acceptor density, the lower limit of the surface conducting layer thickness was extracted from the transport data. From a surface science perspective, two aspects of the investigation are of particular interest: (i) the donor concentration was enhanced by annealing in forming gas, which is 5% H2, and, (ii) despite relatively weak variation in the sheet carrier concentration, the surface conducting layer thickness (dsurf) varied from as large as 28 nm to as small as 1.5 nm, depending on the method of preparation and supplier. The ongoing exploration of this phenomenon begs for the kind of experiments that practitioners of surface, interface and thin-film science can readily conduct. In bulk crystals, is H doping really the cause? Answering this question represents a major challenge because the donor concentration is in the 1017-1018 cm-3 range. Determining the donor identity in this concentration range is a major experimental hurdle. How does dsurf depend on crystallographic orientation? How does the phenomenon depend on the extent of band bending? Does persistent photoconductivity come into play? Can the effect be modified by band bending modification via surface photovoltage effects? All of the above questions pertain to epitaxial films as well, but other questions also arise. How do the film thickness and strain state affect dsurf? Can the surface conduction effect be enhanced by judicious design and growth of quantum well structures made from ZnO, MgxZn1-xO, and/or CdxZn1-xO? Answering these and other questions that arise will expand our understanding of this fascinating and potentially important material, as well as pave the way for device applications.« less

Variation of plasma parameters on boundary conditions in an inductively coupled plasma source for hyperthermal neutral beam generation

The variations of plasma parameters on the boundary conditions, especially potential, of plasmas were measured in an inductively coupled plasma source developed to generate a hyperthermal neutral beam. Hyperthermal neutrals can be produced by Auger neutralization when ions with low energy are neutralized by impinging on a metal surface called a reflector. However, the reflector is a significant source of ion drain when it is biased to a negative potential. The plasma potential can be negative with respect to the grounded chamber potential while the reflector is negatively biased, but other plasma parameters, namely density and temperature, are not sensitive to the reflector bias. If the electron loss current into the chamber wall is governed by the space charge limited current law, sustainment of the plasma with a negative potential can be explained in terms of the charge balance equations for quasineutrality.

Compensation mechanism in high purity semi-insulating 4H-SiC

A study of deep levels in high purity semi-insulating 4H-SiC has been made using temperature dependent Hall effect (TDH), thermal and optical admittance spectroscopies, and secondary ion mass spectrometry (SIMS). Thermal activation energies from TDH varied from a low of 0.55eV to a high of 1.65eV. All samples studied showed n-type conduction with the Fermi level in the upper half of the band gap. Fits of the TDH data to different charge balance equations and comparison of the fitting results with SIMS measurements indicated that the deep levels are acceptorlike even though they are in the upper half of the band gap. Carrier concentration measurements indicated that the deep levels are present in concentrations in the low 1015cm−3 range, while SIMS results demonstrate nitrogen and boron concentrations in the low to mid-1015-cm−3 range. The results suggest that compensation in this material is a complex process involving multiple deep levels.

Numerical predictions of aerosol charging and electrical conductivity of the lower atmosphere of Mars

The charging of aerosols and the conductivity of the lower, night time atmosphere of Mars are calculated. The charge distribution of aerosols was obtained by the simultaneous solution of the ion‐aerosol charge balance equations. Galactic cosmic rays are the dominant ionizing process in the night time lower atmosphere producing molecular ions and ion clusters. The ion production rates for different solar activities are considered. The ion‐ion recombination rates and the ion‐aerosols attachment coefficients are calculated for altitudes from 0 to 70 km. Both the steady state and time dependent concentration of charged aerosols are calculated. The conductivity produced by ion‐attachment of aerosols was found to decrease by a factor of five yielding a value of about 4 × 10−12 Ohm−1 m−1 close to the surface. The effect on the conductivity of the temperature vs. altitude and the aerosol density are also estimated.

GaN-based heterostructures: electric–static equilibrium and boundary conditions

In the GaN-based heterostructures, this paper reports that the strong electric fields induced by polarization effects at the structure boundaries complicate the electric–static equilibrium and the boundary conditions. The basic requirements of electric–static equilibrium for the heterostructure systems are discussed first, and it is deduced that in the application of the coupled Schrodinger–Poisson model to the heterostructures of electric–static equilibrium state, zero external electric field guarantees the overall electric neutrality, and there is no need to introduce the charge balance equation. Then the relation between the screening of the polar charges in GaN-based heterostructures and the possible boundary conditions of the Poisson equation is analysed, it is shown that the various boundary conditions are equivalent to each other, and the surface charge, which can be used in studying the screening of the polar charges, can be precisely solved even if only the conduction band energy is correctly known at the surface. Finally, through the calculations on an AlGaN/GaN heterostructure with typical structure parameters by the coupled Schrodinger–Poisson model under the various boundary conditions, the correctness of the above analyses are validated.

Use of the bromley equation for the analysis of ionic equilibria in mixed ferric and ferrous chloride solutions at 25 °C

The ionic equilibria in the mixed ferric and ferrous chloride solution were analyzed by considering the complex formation reactions as well as the mass and charge balance equations. The activity coefficients of the ions were calculated using the Bromley equation. The equilibrium constants for the formation of ferrous complexes were determined from the reported thermodynamic data. The interaction parameters of the ferric species were estimated from the reported values of FeCl3 in an HCl solution. By applying the ionic equilibria, the speciation of the ferric and ferrous species with the composition was obtained. The predicted pH values of the FeCl3-FeCl2-HCl-H2O system agreed well with the measured values at 25 °C in the ionic strength range of up to 9.34 m.

Numerical modeling of crystal growth under strong magnetic fields: An application to the travelling heater method

The article presents a 3-D numerical simulation study for the growth of single crystal semiconductors under strong magnetic fields. In such high fields, the magnetic body force components, which also depend on the flow velocity components present numerical challenges particularly in terms of convergence of iterations. To remedy such difficulties, a novel numerical approach was introduced in an in-house 3-D finite volume-based computer code. As an application, the Travelling Heater Method (THM) was selected for the growth of CdTe crystals under a static vertical magnetic field. The governing equations of the model, which also include the electric charge balance equation in terms of the induced electric potential and the applied magnetic field intensity, are solved numerically. Evolution of the growth interface is simulated with the help of a moving grid algorithm in a block-structured finite-volume code. The convergence rate of iterations is significantly improved by treating a part of the magnetic body force terms implicitly in the iteration loop. Consequently, the magnetic field as high as 15.0 kG did not lead to any convergence problems. Simulation results are presented for the flow, concentration, temperature, and electric potential fields in the liquid solution. Results show that, in spite of the initially assumed-axisymmetric boundary conditions, three-dimensional transport structures develop as soon as the growth process begins. Application of the magnetic field suppresses convection in the solution, and the magnitude of the maximum flow velocity decreases monotonically with the increasing magnetic field intensity.

On the significance of the surface states in isolated Al xGa 1− xN/GaN heterostructures

The significance of the surface states in isolated Al x Ga 1− x N/GaN heterostructures is investigated. A model based on a self-consistent solution of the Schrödinger, Poisson and charge balance equations is presented. The singular value decomposition is used to calculate the eigenstates of the real non-symmetric matrix which is obtained when a non-uniform mesh is used. The discontinuity of the spontaneous and piezoelectric polarization at the interface is taken into account. The results obtained for the 2DEG density and the surface potential agree well with theoretical and experimental data already published.

Mathematical Modeling of a Cs(I) – Sr(II) – Bentonite – Magnetite Sorption System, Simulating the Processes Taking Place in a Deep Geological Repository

The derivation of mathematical models of systems consisting of Cs(I) or Sr(II) and of bentonite (B), magnetite (M) or their mixtures (B+M) are described. The paper deals especially with modeling of the protonation and sorption processes occurring on the functional groups of the solid phase, namely on so called edge sites and layer sites. The two types of sites have different properties and, as a result, three types of Surface Complexation Models (SCM) are used for edge sites, viz. two electrostatic SCMs: the Constant Capacitance Model (CCM) and the Diffusion Double Layer Model (DLM), and one without electrostatic correction: the Chemical Model (CEM). The processes taking place on the layer sites are described by means of the Ion Exchange Model (IExM). In the course of modeling, the speciation of the given metal in the liquid (aqueous) phase has to be taken into account. In principle, the model of protonation or sorption processes is based on the reactions occurring in the aqueous phase and on the surface of the solid phase, and comprises not only the equations of the equilibrium constants of the individual reactions, but also the mass and charge balance equations. The algorithm of the numerical solution is compatible with FAMULUS 3.5 (a Czech software product quite extensively used at Czech universities in the last decade, the bookcase codes of which are utilized).

Chemical Equilibria in a Mixed Solution of Nickel and Cobalt Chloride

Ionic equilibria in the mixed solution of nickel and cobalt chloride were analyzed by considering the complex formation reactions, the mass and charge balance equations. The activity coefficients of solutes and water activity were calculated by using Bromley equation. Cobalt ion has a strong tendency to form various complexes with chloride ion, such as CoCl3− and CoCl42−, while NiCl+ was the only complex formed between nickel and chloride ion. Distribution of nickel and cobalt species with the compositions and pH values of the solution was obtained from the analysis of ionic equilibria in the mixed chloride solutions. The predicted pH values for NiCl2-CoCl2-HCl-NaOH-H2O system agreed well with those measured at 298 K up to ionic strength of 9.53 mol/kg.