Average Impurity Concentration Research Articles

New approach to predict impurity concentration in high-purity antimony metal prepared by vacuum distillation

Previous studies have shown that there is a significant difference in impurity concentration in the distillate, resulting in an unclear average impurity concentration in the distilled product. To address this issue, a variation model of impurity average concentration in the distillate was developed based on the mass conservation of the solute during the vacuum distillation process. Five continuous distillation experiments of crude antimony (Sb) metal were carried out to obtain the variation regularity of impurity average concentration in the distillate, and two verification experiments of vacuum distillation were conducted to verify the model. The research results showed that, the concentration of As impurity in residue decreases exponentially as the distillation proceeds, whereas the concentration of Bi impurity increases exponentially; there are the increasing and decreasing concentration gradients of As and Bi impurities in the distillate along with the decreasing condensing temperature, respectively; the average concentrations of As and Bi impurities in the distillate present the linearly decreasing and exponentially increasing tendency, respectively; the calculated values of As and Bi impurities average concentrations in the distillate are in good agreement with the values of two verification experiments, confirming the efficacy of the model.

Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Starting from the hamiltonian for the Heisenberg ferromagnet which comprise randomly distributed nonmagnetic ions as impurities in a Bravais lattice, we express the spin operators by means of the Dyson–Maleev transformation in terms of the Bose operators of the second quantization. Then by using methods of quantum statistical field theory, we derive the partition function and the free energy for the system. We adopt the Matsubara thermal perturbation method to a portion of the hamiltonian which describes the interaction between magnons and the stationary field of nonmagnetic ions. Upon averaging over all possible distributions of impurities, we express the free energy of the system as a function of the mean impurity concentration. Subsequently, we set up the double-time single particle Green function at temperature T in the momentum space in terms of magnon operators and derive the equation of motion for the Green function through the Heisenberg equation of motion and then solve the resulting equation. From this, we calculate the self-energy and then the spectral density function for the system. We apply the formalism to the case of the simple cubic lattice and compute the density of states, the spectral density function and the lifetime of the magnons as a function of energy for several values of the mean concentration of nonmagnetic ions in the ferromagnetic lattice. We calculate the magnon energy spectrum as a function of the average impurity concentration fraction c, which shows that for low lying states, the excitation energy increases continuously with c in the studied range 0.1≤c≤0.7. We also use the spectral density function to compute some thermodynamical quantities through the magnon occupation number. We have obtained closed form expressions for the configurationally averaged physical quantities of interest in a unified fashion as functions of the mean concentration of nonmagnetic impurities c to any order of c applicable below a critical percolation concentration cp. The quantities of interest comprise the thermodynamic potential (free energy), the spin-wave self-energy and the spectral density function from which other quantities can be derived.

Захват примеси в разбавленном растворе: фазово-полевое моделирование затвердевания

Based on numerical simulation of the nonstationary process of directional solidification of a weak solution flat–front within locally the non–equilibrium phase–field model study of the process of redistribution of the impurity in the vicinity of the diffuse boundary between the liquid and solid phases. As a result of numerical modeling, profiles of the average impurity concentration near the interface are obtained. From the obtained profiles of the average concentration, the distribution of concentrations in the solid and liquid phases at different speeds of the front movement is determined using the phase field. The constructed graphs of the dependence of the distribution coefficient on the velocity are compared with the data for the hyperbolic model of continuous growth and previously performed calculations in the quasi–stationary approximation. The influence of the model parameters on the type of dependence of the distribution coefficient on the front velocity and on the distribution profile of the concentration inside the diffuse interface is studied.

Calculation of high-temperature sublimation refining in relation to the degree of sublimation for a material consisting of separate parts

This paper considers high-temperature sublimation of a two-component material consisting of parts differing in size. A sublimation equation is used to calculate the average impurity concentration in the condensate as a function of the degree of sublimation. The results demonstrate that the sublimation refining of a multipart material can be both more effective and less effective than the sublimation of a material in the form of a single block, depending on process and material parameters, but the difference between the purity levels achieved is not very large.

Zone recrystallization modeling and optimization based on the concept of average impurity concentration in the ingot portion being refined

We present a mathematical model and results of computational experiments aimed at investigating multipass zone refining kinetics based on the concept of average impurity concentration in the ingot portion being refined and demonstrate that ultrapurification of an ingot at a small molten zone length has an induction period. Using stepwise optimization of zone recrystallization with a molten zone length varying from pass to pass, we find a zone length control function that minimizes the number of zone passes needed to ensure a given purity level.

The Solution of Semi-empirical Equation of Turbulent Diffusion in Problems of Polluting Impurity Transfer by Gauss Approach

The analysis of the solution of the semi-empirical solution of turbulent diffusion in problems of polluting impurity transfer is carried out by Gauss approach. It is assumed that there is a certain occupied industrial point, which has one or several sources of the pollution, the arrangement of which is determined by coordinates x, y, z. For calculation of average impurity concentration from a point source the solution of semi-empirical equation by Gaussian function of impurity distribution, obtained by a method of Green's function was used. Furthermore, the normalization of the key parameters of the problem is carried out and the initial data are defined. By means of the obtained equation, the model of quantity assessment of the aerosol polluting substances arriving from a source with final and continuous duration of action is made. Thus, the considered computational and analytical model of methodology of assessing the concentration of polluting substances is applicable for applied problems of operational control of the condition of industrial region. Proposed model can be adapted to the air pollution monitoring robotic system.

О конвективной устойчивости коллоидной суспензии в ячейке Хеле–Шоу

The article is devoted to the influence of sedimentation and thermal diffusion on threshold of convective instability of a suspension in the Hele-Shaw cell heated from below. Impurity distribution adjustment in colloid in a state of mechanical equilibrium is not uniform, due to the gravitational separation of the mixture. In the channels with the height much less than the sedimentation length, concentration gradient is almost constant. In this case, the ratio of the average impurity concentration to the sedimentation length determines the instability threshold. Mathematical model that describes the convective motion of the colloid, has been based on the Boussinesq approximation. The solution of the linearized system of equations has been performed using the Galerkin method with a large number of basic functions. During research, neutral instability curves are obtained for different values of the Boltzmann number. The influence of gravity stratification on the structure of near-threshold flows has been established. The dependence of the threshold of convective instability and the wave number are determined as a function of parameters of the problem, such as the Boltzmann number and the parameter of thermal diffusion. Received 31 .10.20 16; accepted 05 . 12 .20 16

Grain boundary segregations in nanocrystalline alloys

The dependence of grain boundary segregations and alloy composition in the bulk of the grain on the grain size was considered. At moderate temperatures, there is a critical grain size for which the integrated degree of alloy decomposition reaches its maximum; this size increases as the average (over the sample) impurity concentration decreases. In complex alloys, the type of the component that segregates on the boundaries depends on the grain size. For segregation kinetics, an approximate analytical solution was obtained based on the assumption that the grain boundary is an ideal drain for the impurity. The equilibrium grain size exists below the critical temperature and its temperature dependence is nonmonotonic in the general case. A segregation mechanism of stabilization of nonequilibrium grain boundaries in nanocrystalline alloys obtained by severe plastic deformation was suggested.

Purification of Refined Metallurgical-grade Silicon up to Solar Grade Silicon by Extraction

AbstractThe paper studies the theoretical analysis of silicon purification process using the method of extraction from solid phase in fine-dyspersated condition. Axial profile impurity concentration in silicon particles, time dynamics of average impurity concentration at various purification conditions (temperature, particle size, impurity concentration in extractant) are obtained by numerical simulation. The requirements to a particle size and temperature condition when practically important purification efficiency is reached, are determined. The design of an industrial-scale plant is shown schematically.

Modeling and calculation of slurry-chemistry effects on chemical–mechanical planarization with a grooved pad

During chemical–mechanical planarization (CMP), a rotating wafer is pressed against a rotating pad, while a slurry is dragged into the pad–wafer interface. Here, taking into account the dependence of local material removal rate (MRR) on the slurry’s chemical activity, the effects of pad groove geometry and various other process parameters on the spatial average and non-uniformity of MRR are examined. Technically, the slurry flow is calculated by following an existing approach that integrates two-dimensional fluid-film lubrication theory and contact-mechanics models. A slurry impurity transport equation is then used to calculate the impurity concentration that determines the slurry’s chemical activity and hence the local MRR. The numerical results obtained here indicate that the presence of pad grooves generally decreases the average slurry impurity concentration, and increases the average contact stress on the pad–wafer interface. However, as a grooved pad has less contact area for effective interaction with the wafer surface, the average MRR may or may not be increased, depending upon the specific setting of process parameters. Meanwhile, it appears that the retaining ring generally used to keep the wafer in place also plays an important part in reducing the MRR non-uniformity.

Determination of the band offset and the characteristic interdiffusion length in quantum-well lasers using a capacitance–voltage technique

In this work, a capacitance–voltage (C–V) technique, based on a combination of measured and simulated C–V characteristics, was applied to characterize In0.35Ga0.65As/GaAs multiquantum-well laser structures at room temperature. A theoretical model, including the self-consistent solution of Poisson and Schrödinger equations, was developed to simulate the C–V characteristics and the carrier concentration profiles. Measured C–V carrier concentration profiles were used to obtain the average impurity concentration in active regions. The comparison between experimental and simulated results was used to determine the conduction band offset, yielding ΔEc/ΔEg≈0.8. In the case of samples with postgrowth quantum-well intermixing, this technique was applied to extract the characteristic interdiffusion length.

General approach to the calculation of the average impurity concentration fields in the atmosphere

General approach to the calculation of the average impurity concentration fields in the atmosphere

Effect of Polishing on Time Dependence of Average Substitutional Impurity Concentration in Dissociative and Kick-Out Mechanisms

From the standpoint of experimentally distinguishing the dissociative mechanism from the kick-out mechanism, the time dependence of the substitutional impurity concentration in the diffusion is useful. In a dislocation-free sample, the reaction of point defects with sample surfaces is the limiting process, and the impurity concentration may depend on distance from the surface. In the experiment, the surface is polished before the concentration measurement. Therefore it is important to know the effect of amount of polishing on the time dependence of the average substitutional impurity concentration. In this paper, the effects for both in-diffusion and annealing processes are calculated. It is concluded that, when a dislocation-free sample is used, the effect is strong for both in-diffusion and annealing processes in terms of the dissociative mechanism and for the annealing process in terms of the kick-out mechanism.

Stoichiometry and impurity concentration in synthetically grown iron pyrite crystals and their constituents

The iron to sulfur ratio in different synthetic iron pyrite samples, prepared as powders and crystals, was measured by means of ICP-AES (Inductively Coupled Plasma with Atomic Emission Spectrometry). A remarkably high sulfur deficiency in single crystals grown by chemical vapor transport has been established which leads to the gross formula FeS2−xfor 0.24<x< 0.13. In addition, the doping concentration of zinc was determined for intentionally doped pyrite single crystals by this method. A maximum doping concentration of about 2000 mg/kg has been found. By ICP-MS (Inductively Coupled Plasma with Mass Spectrometry) the trace element concentration from lithium to uranium was simultaneously measured for iron pentacarbonyl, which was used as the starting material for the iron pyrite synthesis, both synthesized pyrite crystals and powders. The impurity concentrations of the single crystal samples are correlated to impurities of the starting materials and to the method of production. Common impurities, analysed in all pyrite samples, were sodium and phosphorus, which occur in a concentration up to 940 and 230 Μg/g respectively. Depending on the growth technique, impurity concentrations were found to range from 280 Μg/g for bromine to 2000 and 9000 Μg/g for zinc and lead, respectively. Up to 70000 Μg/g tellurium were found in samples grown in tellurium melts. The average impurity concentration of all other elements analysed amounted to 7 Μg/g. Since the carbonyl-iron precursor was found to be of high purity the contamination of the crystals is attributed to impurities arising from the preparation process (Na), from the used sulfur (P), from the transport agent (Br, PbCl2, Te) and the quartz container material (Si, O). The advantage of the ICP-methods is the direct employment of the samples after a dissolution process without further preparation steps.

Conditional averaging of the equations of flow in random composite porous media

The problem of conditional averaging of the transport equations is solved for a neutral impurity in a composite medium with random porosity and impurity diffusion tensor. An unclosed system of conditionally averaged equations is constructed and closed using the globally averaged equations. The average impurity concentration fields for the individual phases of the composite medium and the phase-continuum interaction characteristics are calculated.

Impurity scavenging by foreign phase in heterogeneous CuInS 2

The average impurity concentration of chemical vapor transported (CVT) and vapor liquid solid (VLS) grown CuInS 2 has been determined by spark source mass spectrometry (SSMS). Transition metal impurities range between 10 17 atoms cm −3 (Ti, V, Cr, Co, Ni, Zn) and (3–5)×10 18 atoms cm −3 (Mn, Fe). On heterogeneous VLS grown samples, the Fe content of the CuInS 2 host material and of foreign incorporated phases has been compared by inductive coupled plasma spectrometry (ICP). The foreign phases, particularly In spheres, show a drastically increased impurity content. The results are discussed assuming impurity scavenging by metallic In.

Mixing of two gases one of which is expelled from a cylindrical space by the other

The flow structure and impurity distribution in an axisymmetric cylindrical space is obtained from the system of equations of convective heat and mass transfer in the Boussinesq approximation for different variants of the gas inflow and outflow conditions. The variation of the average impurity concentration in the space investigated, obtained as a result of numerical calculations, is compared with two limiting cases of expulsion of the contaminated gas: the “gas piston” case and total mixing. The dependence of the velocity and impurity concentration fields on the regime parameters (Reynolds, Grashof, and Schmidt numbers, velocity profiles at the gas inlet and outlet) and the geometric and design parameters (elongation of cylinder, inflow and outflow geometry) is investigated numerically.

Electrical properties of ion‐implanted poly(p‐phenylene sulfide)

AbstractIon implantation of impurities into thin films of poly(p‐phenylene sulfide) (PPS) is found to increase the conductivity of the material by up to 12 orders of magnitude. The increase is stable under exposure to ambient conditions, in contrast to the instability of the conductivity increases in PPS produced by chemical doping with AsF5. PPS films 0.1–0.2 μm thick are spin cast from solution onto interdigitated electrodes patterned on an oxidized silicon substrate. The room‐temperature interelectrode resistance is measured as a function of implantation fluence. An estimate of film conductivity is obtained from this resistance with a simple model for the electrode and film geometry. A first experiment yielded similar conductivity increases for implantation of either arsenic or krypton. At a fluence of 1 × 1016cm−;2, which corresponds to an average impurity concentration of 2.5 × 1021cm−3, the conductivity reaches an apparently saturated value of 1.5 × 10−5 (Ω cm)−1. Infrared spectra of the films before and after implantation suggest that crosslinking may be present in the implanted films, and Auger studies show stoichiometric changes throughout the implanted layer. These results suggest that the observed conductivity changes are the result of molecular rearrangements produced by the implantation rather than the result of specific chemical doping. Specific chemical doping may, however, explain the results of a second experiment in which implantation of bromine resulted in substantially larger conductivities found to increase at an approximate linear rate from a value of 1.0 × 10−4 (Ω cm)−1 at a fluence of 1 × 1016 cm−2 to a value of 4.0 × 10−4 (Ω cm)−1 at a fluence of 3.16 × 1016 cm−2.

On the equilibrium distribution of the impurity atoms in real crystals

This work discusses the equilibrium distribution of impurity atoms among different sinks and the matrix of a real crystal. A simple formula, interpolating the McLean formula is obtained. Impurity segregation in crystals, containing two types of sinks (e.g. grain boundaries and dislocations) is investigated. Impurity concentration on a weakly- binding sink (grain boundary) as a function of the temperature, T, may be represented by a curve, the shape of which depends on the ratio of the average impurity concentration and the relative volume of a strongly-binding sink (dislocation) and on the ratio of the binding energies of an impurity atom on different sinks. There are four possible shapes of the curve. Three of them are not monotonic and show a maximum at T=Tmax. One of these three also exhibits a minimum at T=Tmin < Tmax. This may be used to diminish the content of a “harmful” impurity on the grain boundaries.

Critical temperature of niobium and tantalum films

A method for depositing thin, superconductive films of Nb and Ta by electron beam evaporation is presented, and the critical temperature of these films is discussed as a function of deposition conditions. Gettering, increasing the ratio of impinging vapor atoms to residual gas atoms, and raising the substrate temperature during deposition gives films with a lower impurity content and higher critical temperature. The resistance ratio of a film and its x-ray lattice parameter are taken as measures of its average impurity concentration. Critical temperatures above 9°K are measured for Nb films of resistance ratio of 3 or higher, and critical temperatures above 4.2°K are measured for Ta films of resistance ratio of 5 or higher.