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Research into a gas sensing material with excellent performance to detect or remove toxic phosgene (COCl

Based on thermodynamic data for related pure substances, the relations of (nCl/nH)Eq and (nCl/nH)o have been plotted in the Si–Cl–H system. The results show that the difference of (nSi/nCl)o and (nSi/nCl)Eq is the driving force for polycrystalline silicon chemical vapor deposition (CVD). SiHCl3 is preferred for polycrystalline silicon deposition to SiCl4. SiH2Cl2 would be even better, but it is not stable as a gas and hence it is less frequently used. Then, thermodynamic simulation of polycrystalline silicon CVD in the Si–H–Cl system has been investigated. The pressure has a negative effect on polycrystalline silicon yield. The optimum temperature is 1400 K, at which the kinetic rate of rate-determining step for the main reaction is large enough. The excess hydrogen is necessary for polycrystalline silicon CVD in the Si–Cl–H system. However, the silicon deposition rate increases then decreases with increasing H2 molar fraction. The optimum H2 molar fraction should be determined by considering thermodynamics and transport phenomena simultaneously. Finally, the optimum conditions have been obtained as 1400 K, about 0.1 MPa, and H2 to SiHCl3 ratio of 15, which are close to the limited reported values in the open literature. Under the optimum conditions, the silicon yield ratio is 34.82% against 20% reported in the open literature.

We perform numerical simulations to study effects of alternating current (AC) frequency on thermal stress evolution during the Joule heating process in a 48-rod Siemens reactor. The characteristics of temperature, current density, and stress distributions within the rods located in different rings are analyzed first. A Joule heating model using AC is then proposed for flexible power adjustment. The voltage-current curves are obtained from analysis of rod radius, location, and skin depth, as well as the properties of the polysilicon. The results indicate that, during the Joule heating process, large stresses typically occur in the central regions of the silicon rods. The highest stress occurs at the center of the silicon rods located in the outer ring when a standard power frequency of 50 Hz is utilized. The results further indicate that von Mises stress significantly decreases as AC frequency increases. Additionally, we propose a novel Joule heating method that is useful for producing larger high-purity polycrystalline silicon rods by considering both low frequency and high frequency power. Based on an analysis of energy consumption during the Joule heating process, we recommend optimized power supplies for the 48-rod Siemens reactor.

A parametric study was conducted for the cost reduction of polysilicon by decreasing the electrical energy loss of an existing Siemens reactor. In this work, a quartz ceramic lining was applied onto a reactor vessel, and the hot emitter mechanism was adopted to enhance the energy efficiency for the production of polycrystalline silicon. The effects of the geometrical and heat transfer parameters on the energy efficiency and productivity of the Siemens reactor were examined. Our results indicate that the ceramic lining behaved similarly to thermal insulators by restricting the heat transfer through the ceramic lining, causing the lining surface facing the heated polysilicon rod to emit thermal radiation, thus contributing to reactor’s energy efficiency. The results further demonstrated that the impact of the ceramic lining emissivity on the total radiated heat loss was very small. Furthermore, by addition of a quartz ceramic lining, there is a noteworthy reduction in the total electrical current, resulting in a smoother radial-dependent temperature and thermal stress distribution; thus, a higher deposition radius for the rods can be achieved. According to the energy efficiency analysis, the average energy consumption for the existing 24-rod Siemens reactor can be decreased from 55 kWh per kilograms polysilicon to approximately 36 kWh per kilograms polysilicon.

In the present work, a Joule heating model by direct current (DC) has been developed for the rods arranged in a 48-rod Siemens reactor (SMS-48). The combined effect of heat dissipation (radiation, convection and reaction energy) and heat conduction produced by Joule effect has been examined by application of the developed model, taking into account variations of the rod radius and wall emissivity. The influence of the rod location, rod radius and wall emissivity on temperature profile and voltage-current curves during the electric heating process have been studied. Furthermore, the thermal and electrical behavior of silicon rod arranged in the SMS-48 and SMS-24 has been compared with each other. The dimensionless parameter ( p ) has also been introduced to investigate the effect of the number of rods and their arrangement on energy consumption. The interesting results show that the temperature profile of the rod arranged in the inner ring within SMS-48 is flatter than that in the SMS-24. The curve of current increases and becomes lower for the inner ring and keeps a linear relation for the outer ring in a manufacturing process. The required current and voltage increase when the wall emissivity increases. Enlarging the reactor capacity and meanwhile decreasing the dimensionless parameter ( p ) is an effective method to decrease energy consumption.

The Maxwell’s field equations and Ohm’s Law were added to energy equation to account for the electromagnetic contributions to heat transfer phenomena within silicon rod arranged in an industrial Siemens reactor. Based on the combined effect of the heat dissipation (radiation, convection and reaction energy), a Joule heating model using alternating current (AC) has been developed. The analysis accounts for the rod radius, location, skin depth, as well as the properties of the polysilicon. The results indicate that high frequency current sources can generate an even temperature profile, and a higher deposition radius can be obtained. Alternating current, having a fixed or variable high frequency in the range of about 2.4 kHz to 500 kHz, is provided to concentrate at least 70% of the current in an annular region that is the outer 15% of a growing rod due to the skin effect. The voltage-current curves have been predicted based on the present model. Finally, a novel Joule heating method useful for producing the larger high-purity polycrystalline silicon rods by considering the low frequency power and the high frequency power is proposed. It is interesting that the average energy consumption ( AE ) can be decreased from 55 kWh/kg to about 44 kWh/kg as extending the maximum deposition radius from 7 cm to 10 cm by using a high-frequency current source.

This paper presents an electrical heating model using alternating current (AC) for the silicon rods located in a 24-rod Siemens reactor. In this model, the combined effects of heat dissipation (radiation, convection, and reaction energy), skin effect, and heat conduction owing to Joule effect are examined. The presence of the skin effect, which yields an important radial temperature profile controlled by the heat conduction equation for the rods, has been considered. The present model is validated using industrial current data, and it is observed that the numerical results are in good agreement with them. The influence of the location of the silicon rods, AC frequency, radius of rod, and wall emissivity on the temperature profile and current density has been studied through the application of the developed model. Tailoring the temperature profile of silicon rods and extending the maximum deposition radius has also been performed. Voltage-current curves, which are applied to generate the required heat during the manufacturing period, have also been studied using different AC frequencies and wall emissivities.

A parametric study of the flow field and mixing characteristics of a TiCl4 jet injected into an O2 crossflow in an oxidation reactor for titanium pigment production is numerically investigated. A three-dimensional computational fluid dynamics (CFD) simulation of the turbulent gas mixing model is performed. The effect of geometrical (reactor diameter, jet nozzle number n, jet nozzle diameter, jet nozzle spacing S) and flow parameters (momentum flux ratio J) on the penetration depth (h/R) and mixing quality of the gases is examined. The results are validated with available experimental data and a good agreement is obtained. We show that three stages: under-, optimum, and over-penetration, occur sequentially in the oxidation reactor with increasing J. The kidney-shaped structure, characteristic of a jet-in-crossflow is formed, which is blurred when the mixture of TiCl4 and O2 moves into the downstream fluid. The h/R value at a minimum temperature difference is 0.683 and 0.604 for n = 32 and 16, respectively, which are within industrial production data range of 0.56–0.72. The optimum range of S is between 3.25 and 7.35. h/R strongly depends on the only dimensionless parameter J/n2 expressed in terms of the geometrical and flow parameters via the relation: h/R = 0.7274 + 0.20228 ln (J/n2+0.04587). The TiCl4 concentration profile changes from a quasi-sine to quasi-cosine distribution with increasing J/n2. Both the mixing non-uniformity and the time to attain the optimum mixing quality of TiCl4 and O2 decrease first and then increase with increasing J/n2.

The vector diffraction of linearly polarized plane wave passing through a thin circular plate with a sub-wavelength radius is investigated by the finite element method. The transverse distribution and propagating evolution of the diffracted field with different intensity expressions are analyzed and compared. It shows that there are not only the component of the incident polarization, but also those of other two vertical directions in the near-field diffracted region. Regardless of the relationship between the wavelength and the radius of the circular plate, the diffracted field could evolve into a steady annular diffracted pattern, in which there is a central bright spot (so-called Poisson spot). There is an obvious difference of the diffracted properties between two intensity expressions from the square of electric field and the average magnitude of the Poynting vector as the propagation distance is very small, while they can be considered same with a large propagation distance (e.g. more than a wavelength).

In the Siemens reactor, all the energy is supplied by the heat generation on silicon rods which are heated up by the passage of current, the center of the rods will become hotter than the surface which is maintained ideally at 1373 K. Understanding the thermal and electrical behaviors of silicon rods in electric heating process is crucial for an optimal operation of the Siemens reactor. In the present paper, the electric heating model of silicon rod for the 24-rod Siemens reactor has been developed. In order to verify the present model valid, calculated results by application of the model were compared with industrial data. The results show that comparing to the industrial data obtained using a 24-rod Siemens reactor, the relative error of theoretical calculations are 7.32% and 9.41% for the rods located in the inner ring and outer ring, respectively. Based on the developed model, the influence of the location of silicon rods within Siemens reactor and reactor wall emissivity during electric heating process has been investigated. Interesting results show that the temperature gradient of silicon rods located in the outer ring is larger than the inner ones when the rods are heated up by direct current (DC). The temperature gradient within the rod becomes smaller and the required voltage and current decreases when the emissivity of the reactor wall surface decreases. Two interesting ways to reduce energy consumption can be deduced: increasing radius of the rod at the end of the process and decreasing the wall emissivity by wall surface treatment or/and selecting more appropriate materials.

The modified Siemens process, which is the major process of producing polycrystalline silicon through current technologies, is a high temperature, slow, semi-batch process and the product is expensive primarily due to the large energy consumption. Therefore, the zinc reduction process, which can produce solar-grade silicon in a cost effective manner, should be redeveloped for these conditions. The SiCl 2 generation ratio, which stands for the degree of the side reactions, can be decomposed to SiCl 4 and ZnCl 2 in gas phase zinc atmosphere in the exit where the temperature is very low. Therefore, the lower SiCl 2 generation ratio is profitable with lower power consumption. Based on the thermodynamic data for the related pure substances, the relations of the SiCl 2 generation ratio and pressure, temperature and the feed molar ratio n Z n / n SiCl 4 are investigated and the graphs thereof are plotted. And the diagrams of K p Θ – T at standard atmosphere pressure have been plotted to account for the influence of temperature on the SiCl 2 generation ratio. Furthermore, the diagram of K p Θ – T at different pressures have also been plotted to give an interpretation of the influence of pressure on the SiCl 2 generation ratio. The results show that SiCl 2 generation ratio increases with increasing temperature, and the higher pressure and excess gas phase zinc can restrict SiCl 2 generation ratio. Finally, suitable operational conditions in the practical process of polycrystalline silicon manufacture by gas phase zinc reduction of SiCl 4 have been established with 1200 K, 0.2 MPa and the feed molar ratio n Z n / n SiCl 4 of 4 at the entrance. Under these conditions, SiCl 2 generation ratio is very low, which indicates that the side reactions can be restricted and the energy consumption is reasonable.

The static and dynamic problems of Bernoulli–Euler beams are solved analytically on the basis of strain gradient elasticity theory due to Lam et al. The governing equations of equilibrium and all boundary conditions for static and dynamic analysis are obtained by a combination of the basic equations and a variational statement. Two boundary value problems for cantilever beams are solved and the size effects on the beam bending response and its natural frequencies are assessed for both cases. Two numerical examples of cantilever beams are presented respectively for static and dynamic analysis. It is found that beam deflections decrease and natural frequencies increase remarkably when the thickness of the beam becomes comparable to the material length scale parameter. The size effects are almost diminishing as the thickness of the beam is far greater than the material length scale parameter.

The dynamic problems of Bernoulli–Euler beams are solved analytically on the basis of modified couple stress theory. The governing equations of equilibrium, initial conditions and boundary conditions are obtained by a combination of the basic equations of modified couple stress theory and Hamilton’s principle. Two boundary value problems (one for simply supported beam and another for cantilever beam) are solved and the size effect on the beam’s natural frequencies for two kinds of boundary conditions are assessed. It is found that the natural frequencies of the beams predicted by the new model are size-dependent. The difference between the natural frequencies predicted by the newly established model and classical beam model is very significant when the ratio of characteristic sizes to internal material length scale parameter is approximately equal to one, but is diminishing with the increase of the ratio.

In the numerical methods of couple stress theory for elasticity, C 1 continuity on the shape functions is required, because the second-order derivatives of displacement appear in the variational equation. N. Sukumar constructed a C 1 natural neighbor interpolant by embedding Sibson’s interpolant in the Bernstein-Bezier surface representation of a cubic simplex and used it to solve the two-dimensional biharmonic problems of a circular plate under a biaxial state of stress. In this paper, all of the natural neighbors of the introduced point are determined based on the extended Delaunay triangulation which can be used to guarantee the uniqueness of the triangulation compared to traditional Delaunay triangulation, and the convex hull of the set of natural neighbors is defined to be the domain of the introduced point, so nodes outside of the domain have no influence on the introduced point. On account of the computational efficiency, the non-Sibson interpolant is calculated and introduced into a cubic Bernstein polynomials to obtain the Bernstein-Bezier basis function .According to the fact that the vertex Bezier ordinates are identical to the nodal function values, and the tangent Bezier ordinates and centre Bezier ordinates are related to the nodal gradient values, the relations between Bezier ordinates and the nodal function and gradient values are first presented, and the structure and computational algorithm are then outlined to construct the transformation matrix. When the construction of the transformation matrix is finished, a transformation matrix- Bernstein-Bezier basis function product is carried to compute the new C 1 natural neighbor interpolant and its derivatives. The new C 1 natural neighbor interpolant has quadratic completeness, interpolates to nodal function and nodal gradient values, and reduces to a cubic polynomial on the boundary of domain. The new C 1 natural element method based on Galerkin scheme is introduced to couple stress theory for elasticity to obtain the discrete form of governing equation. Numerical analyses of the method are presented, covering the influences of the couple stress on stress concentration of an infinite plate with central hole subjected to the uniaxial pull and biaxial pull respectively. Numerical results of typical problems show that when solving fourth-order elliptic problems such as those arising in couple stress theories, the C 1 natural neighbor interpolant based on the extended Delaunay triangulation is valid and feasible.