Radiative Heat Transfer in a Resistance Heated Floating Zone Furnace: A Numerical Study with FIDAPTM

This paper presents a numerical study of radiative heat transfer in a floating zone (FZ) furnace which was performed by using the commercial finite element program FIDAP^TM. This resistance furnace should provide a temperature higher than the melting temperature of silicon (i.e. T_max ≈ 1500 °C) and a variable temperature gradient at the liquid/solid interface (≥ 25 K/cm). Due to the high working temperatures, heat radiation plays the dominant role for the heat transfer in the furnace. For this reason, the quality of view factors used in the wall‐to‐wall model was carefully inspected with energy‐balance checks. A numerical model with two control parameters is applied to study the influence of material and geometrical parameters on the temperature field. In addition, this model allows us to estimate the internal thermal conditions which were used as thermal boundary conditions for partial 3D simulations. The influences of an optical lens system on the radial symmetry of the temperature field were examined with these partial 3D simulations. Furthermore, we used the inverse modeling method to achieve maximum possible temperature gradients at the liquid/solid interface according to the limitation of maximum available power and the maximum stable height of a melt zone.     

Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 2: rotating seed

In this paper, the role of seed rotation on the characteristics of the two‐dimensional temperature and flow field in the oxide Czochralski crystal growth system has been studied numerically for the seeding process. Based on the finite element method, a set of two‐dimensional quasi‐steady state numerical simulations were carried out to analyze the seed‐melt interface shape and heat transfer mechanism in a Czochralski furnace with different seed rotation rates: ω_seed = 5‐30 rpm. The results presented here demonstrate the important role played by the seed rotation for influencing the shape of the seed‐melt interface during the seeding process. The seed‐melt interface shape is quite sensitive to the convective heat transfer in the melt and gaseous domain. When the local flow close to the seed‐melt interface is formed mainly due to the natural convection and the Marangoni effect, the interface becomes convex towards the melt. When the local flow under the seed‐melt interface is of forced convection flow type (seed rotation), the interface becomes more concave towards the melt as the seed rotation rate (ω_seed) is increased. A linear variation of the interface deflection with respect to the seed rotation rate has been found, too. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

3D simulation of the effects of growth parameters on the growth of sapphire crystals using heat exchanger method

3D simulations using the commercial CFDRC and FIDAP code, which are based on finite element techniques, were performed to investigate the effects of anisotropic conductivity on the convexity of the melt–crystal interface and the hot spots of sapphire crystal in a heat‐exchanger‐method crystal growth system. The convection boundary conditions of both the energy input to the crucible by the radiation as well as convection inside the furnace and the energy output through the heat exchanger are modeled. The cross‐sectional flow pattern and the shape of the melt–crystal interface are confirmed by comparing the 3‐D modeling results with previous 2D simulation results. In the 3D model, the “hot spots” in the corners of the crucible are donut shaped, and the shape changes with the value of the conductivity of anisotropic crystal. The outline of the crystal becomes more convex as the conductivity in the z direction (k_sz) increases. The outline of melt–crystal interface is elliptical when the anisotropic conductivity is moving in the radial direction (k_sx and k_sy). The portion at the outline touching the bottom of the crucible is smaller than the maximum outline of the crystal, meaning that the shape at the “hot spot”, changes with the value of the conductivities of anisotropic crystal. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparative analysis of the heat transfer processes during growth of Bi<Subscript>12</Subscript>GeO<Subscript>20</Subscript> and Bi<Subscript>4</Subscript>Ge<Subscript>3</Subscript>O<Subscript>12</Subscript> crystals by the low-thermal-gradient Czochralski technique

The heat transfer processes occurring in the solid and liquid phases during growth of Bi₁₂GeO₂₀ and Bi₄Ge₃O₁₂ crystals by the low-thermal gradient Czochralski method are analyzed and compared. It is experimentally found that, under similar growth conditions, the deflection of the crystallization front for the Bi₁₂GeO₂₀ crystal is considerably smaller than the deflection of the crystallization front for the Bi₄Ge₃O₁₂ crystal and the faceting of the former front is observed at the earlier stage of pulling. The results of the numerical simulation demonstrate that the different behavior of the crystallization fronts is associated with the difference between the coefficients of thermal absorption in the crystals.     

Global heat loss and thermal stress analysis in Czochralski crystal growth

Based on our invention of an energy‐efficient Czochalski crystal growth furnace, a 2D‐axisymmetric numerical simulation model of LiNbO₃ crystal growth is developed. The heat transfer, melt and gas flow, radiation and the interface deflection have been examined. Heat losses in the furnace and the insulator, as well as the heating power and thermal stress distribution at three stages of crystal growth are calculated in detail. It is found that a large proportion of heat dissipates through the water‐cooling system, and at the steel shell of the furnace, gas convection heat transfer is the major cooling mechanism. Less heat dissipation by radiation and more heat flux by gas convection to the crystal sidewall results in a larger concentrated thermal stress, which may induce large crystal cracks in the growth process. The simulation results of heating power are in coincidence with the actual power of our furnace, which verifies the feasibility of our model. The detailed information with respect to the device obtained from simulation can help to optimize the energy‐saving design and growth process.     

Optimization of thermal environment during crystal growth of large‐sized Nd:YAG by Temperature Gradient Technique

A finite‐element model is employed to analysis the thermal environments in Temperature Gradient Technique (TGT) furnace during the growth of large‐sized Nd:YAG crystal. The obtained results show that when the crucible is located at the lower position inside of the heater, a flatter solid‐liquid interface is established, which makes it easier to obtain the core‐free Nd:YAG crystal. Meanwhile, the lower crucible position can induce higher axial temperature gradient, which is beneficial to the release of latent heat. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal expansion and structural properties of (CuAlTe2)1–x(CuAlSe2)x solid solutions

Investigations of the thermal expansion of (CuAlTe₂)_1–x(CuAlSe₂)_x solid solutions in the temperature range from 100 to 800 K have been carried out for the first time. It has been demonstrated that the thermal expansion coefficient α_L grows considerably in the temperature range from 100 to 300 K, whereas the temperature dependence above 300 K is rather weak. The isotherms of composition dependence of the thermal expansion coefficient α_L for 100, 293, 500 and 800 K were constructed, and it was found that linear relations could express them. The Debye temperatures θ_D , the average mean‐square dynamic displacements , the average root‐mean‐square amplitudes of thermal vibration RMS , the anion position parameter u using S. C. Abrahams & J. L. Bernstein (u_AB ) and J. E. Jaffe & A. Zunger (u_JZ ) models were calculated. The composition dependence of microhardness H using the phenomenological theory was also calculated, and it was discovered that this dependence has a non‐linear character with a maximum of 383 kg/mm² at x=0.67. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis and the crystal and molecular structures of (H3L · Cl)[CoCl4] and H2L[CuBr4] (L is 2,4,6-Tri(N,N-dimethylamino)methylphenol)

The complex compounds (H₃ L · Cl)[CoCl₄] (I) and H₂ L[CuBr₄] (II), where L is 2,4,6-tri(N,N-dimethylamino)methylphenol, were isolated in the crystalline state and studied by X-ray diffraction. The organic cations were found to be outer-sphere ligands. All three nitrogen atoms of the tertiary amino groups are protonated. In compound I, the H₃ L ³⁺ cation exists as the cis tautomer. In compound II, the H₂ L ²⁺ dication exists as the trans isomer. In the crystal structure, the dications are arranged in layers via hydrogen bonds.     

Interaction between a dislocation and monovalent anion in various alkali halide crystals

It was investigated from (L₀/L)² versus ϕ₀ curve that the Friedel relation between the effective stress and the average length of dislocation segments, L, is appropriate for the interaction between a dislocation and the monovalent anion in various alkali halides single crystals (NaCl: Br^‐, NaBr: Cl^‐ or I^‐, KCl: Br^‐or I^‐, and RbCl: Br^‐ or I^‐). Here, L₀ represents the average spacing of monovalent anions on a slip plane and ϕ₀ is the bending angle at which the dislocation breaks away from the anion at the temperature of 0 K. This is because the anions are the weak obstacles such as impede the dislocation at ϕ₀ above about 150 degrees, where the Friedel relation agrees with the Fleischer one (L₀² = L²(π–ϕ₀)/2). Furthermore, the values of (L /L₀) were found to be within 4.05 to 5.87 for the crystals. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global simulation of a Czochralski furnace for silicon crystal growth against the assumed thermophysical properties

In order to understand the effects of the thermophysical properties of the melt on the transport phenomena in the Czochralski (Cz) furnace for the single crystal growth of silicon, a set of global analyses of momentum, heat and mass transfer in small Cz furnace (crucible diameter: 7.2 cm, crystal diameter: 3.5 cm, operated in a 10 Torr argon flow environment) was carried out using the finite‐element method. The global analysis assumed a pseudosteady axisymmetric state with laminar flow. The results show that different thermophysical properties will bring different variations of the heater power, the deflection of the melt/crystal interface, the axial temperature gradient in the crystal on the center of the melt/crystal interface and the average oxygen concentration along the melt/crystal interface. The application of the axial magnetic field is insensitive to this effect. This analysis reveals the importance of the determination of the thermophysical property in numerical simulation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystal structure of complexes of bivalent Co,Ni, and Cd with anions of benzoic and 2-(acetylamino)-5-nitrobenzoic acids

The structure of three complexes of bivalent metals (cobalt, nickel, and cadmium) with anions of benzoic (HL ¹) and 2-(acetylamino)-5-nitrobenzoic (HL ²) acids, namely, [Co₂¹ (H₂O)₂(μ-C₄H₄N₂)] _n (I), [NiL²(H₂O)₅]L² · 2H₂O (II), and [Cd(μ-L ²)₂(H₂O)₂] _n · 2nH₂O (III), is determined. In chainlike structure I, cobalt atoms are connected by bridging pyrazine molecules; structure II contains isolated complexes. In structure III, centrosymmetric (CdOCO)₂ cycles and polymeric ribbons are formed due to the coordination of the carboxylate group of the L ² ligand to two cadmium atoms.     

Lyotropic Mesophase Behaviour of n-C16H33EO3 - Evidence for Two “V2” Phases

Abstract

Nonionic surfactants of the alkyl polyoxyethylene ether variety commonly form hexagonal (H₁) or lamellar (L_α) lyotropic mesophases with water¹. Less well-known is the frequent occurrence of I₁ or V₁ cubic mesophases.? No reports exist to date of the occurrence of reversed phases with these materials. While the surfactants are known to form several solid complexes with water, their melting points are below those of the anhydrous surfactants². In an optical microscope study of the liquid crystals formed by water penetration into n-hexadecyl trioxyethylene glycol ether (C₁₆EO₃) we have observed a solid complex with a melting point above that of the pure surfactant. We also observe a cubic region which we classify as a reversed structure (V₂). Moreover, the occurrence of a refractive index discontinuity within this region strongly suggests that two different phases are present. The cubic region coexists with water for part of the temperature range over which it occurs. When water droplets form within the cubic region on heating, they adopt angular shapes which suggest that a single, long-range structure exists, rather than a “powder” orientation of domains.     

Syntheses,structures, and electrochemistry of a dinuclear compound and a mononuclear–mononuclear cocrystalline compound of uranyl(VI)

Syntheses, structures, and electrochemistry of a dialkoxo‐bridged diuranyl(VI) compound [(UO₂)₂(L¹)₂(dimethylformamide)₂] ( 1 ) and a mononuclear–mononuclear cocrystalline compound [(UO₂)(L²)(H₂O)⊂(H₂O)]·[(UO₂)(L²)(H₂O)] ( 2 ) derived from Schiff base ligands are reported (H₂L¹ = Schiff base ligand obtained on condensation of 3‐ethoxysalicylaldehyde with 2‐aminoethanol; H₂L² = N,N ′‐o ‐phenylenebis(3‐ethoxysalicylaldimine)). The compounds 1 and 2 crystallize in the space groups P 2₁/c and P 1, respectively. Compound 1 is a dialkoxo‐bridged dinuclear compound of uranium(VI) containing two deprotonated ligands, [L]^2–, two dimethylformamide (dmf) molecules and two UO₂²⁺ centers. Three C–H···O type hydrogen bonds involving one uranyl oxygen, two dmf hydrogens, and the imine hydrogen link the dinuclear units into a two‐dimensional network. Compound 2 is a cocrystal of two mononuclear units, [(UO₂)(L²)(H₂O)⊂(H₂O)] (unit 1) and [(UO₂)(L²)(H₂O)] (unit 2). In unit 1, the non‐coordinated water molecule forms hydrogen bonds with oxygens of phenoxo, ethoxy, and coordinated water molecules resulting in the formation of an inclusion product. The overall supramolecular structure of compound 2 is one‐dimensional and consists of interlinked self‐assembled dimeric unit of unit 1 and unit 2. Cyclic voltammetric measurements reveal that the uranium(VI) center in [(UO₂)₂(L¹)₂(dimethylformamide)₂] ( 1 ) is reduced quasireversibly at E_1/2 = –773 mV with ΔE_P = 121 mV, while the metal center in [(UO₂)(L²)(H₂O)⊂(H₂O)]·[(UO₂)(L²)(H₂O)] ( 2 ) is reduced reversibly with E_1/2 = –765 mV with ΔE_P = 68 mV. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis and crystal structure of a silver(I) complex with dithioether ligand

The reaction of the dithioether ligand, 2,3-bis(5-methyl-1,3,4-thiadiazole-2-thiomethyl) quinoxaline (L) with AgBF₄, leads to the formation of a novel complex {[AgL](BF₄)}_∞ 1, which has been characterized by single-crystal X-ray diffraction analysis: monoclinic, space group C2/c, with a = 20.316(7) ?, b = 12.401(4) ?, c = 18.039(6) ?, β = 108.404(6)° and V = 4312(3) ?³. The crystal structure of the complex consists of 1D {[AgL]⁺}_∞ cation chain and BF₄ ⁻ anions. In 1, the coordination geometry of Ag^I center can be best described as trigonal planar coordinated by three N from two distinct L ligands. The ligand is polydentate with one end adopting a bidentate conformation to chelate an Ag^I atom and the other end monodentate to bridge another Ag^I resulting in an infinite chain along b axis. There exist Ag⋯N weak coordination, π–π stacking and F⋯S weak interactions in the complex, and these weak interactions link the 1D complex into 3D supramolecular structure and further stabilize the crystal structure in the solid state.     

Determination of mechanical, electrical and thermal properties of the Sn―Bi―Zn ternary alloy

The development of lead-free solders has emerged as one of the key issues in the electronics packaging industries. Sn―Zn―Bi eutectic alloy has been considered as one of the lead-free solder materials that can replace the toxic Pb―Sn eutectic solder without increasing soldering temperature. This study investigates the effect of temperature gradient and growth rate on the mechanical, electrical and thermal properties of the Sn―Zn―Bi eutectic alloy. Sn-23 wt.% Bi-5 wt.% Zn alloy was directionally solidified upward with different growth rates (V = 8.3-478.6 μm/s) at a constant temperature gradient (G = 3.99 K/mm) and with different temperature gradients (G = 1.78-3.99 K/mm) at a constant growth rate (V = 8.3 μm/s) in the Bridgman-type growth apparatus. The microhardness (HV), tensile stress (σ_t) and compressive stress (σ_c) were measured from directionally solidified samples. The dependency of the HV, σ_t and σ_c for directionally solidified Sn-23 wt.% Bi-5 wt.% Zn alloy on the solidification parameters (G, V) were investigated and the relationships between them were obtained by using regression analysis. According to present results, HV, σ_t and σ_c of directionally solidified Sn-23 wt.% Bi-5 wt.% Zn alloy increase with increasing G and V. Variations of electrical resistivity (ρ) for cast samples with the temperature in the range of 300-420 K were also measured by using a standard dc four-point probe technique. The enthalpy of fusion (ΔH) and specific heat (C_p) for same alloy was also determined by means of differential scanning calorimeter (DSC) from heating trace during the transformation from eutectic liquid to eutectic solid.     

Numerical and analytical modelling of the MHD buoyancy-driven flow in a Bridgman crystal growth configuration

We present analytical and numerical models of magnetohydrodynamic(MHD) buoyancy-driven flow within the liquid pool of a horizontal Bridgman crystal growth furnace, under the influence of a uniform vertical magnetic field B₀. A horizontal differentially heated cylinder, whose aspect ratio (radius to length) is small enough for a fully developed regime to be established in the central core, is considered. With Hartmann layers remaining electrically inactive, a modified Rayleigh number Ra_G, which is the ration of the ordinary Rayleigh number to the square of the Hartmann number, is found to control the MHD reorganisation of the flow. This modified Rayleigh number is a measure of the importance of thermal convection relative to diffusion if velocity is estimated from the balance between the torques of buoyancy and the Laplace force. When Ra_G is much smaller than unity (quasi-diffusive regime), an analytical modelling of the flow, based on a power series of Ra_G, demonstrates that this balance requires secondary vortices within vertical mid-planes of the cylinder, both within the core flow and near the end walls. A 3-D numerical calculation of the flow provides evidence of the transition from a convective MHD flow (when Ra_G is still of the order of unity) to the quasi-diffusive flow, analytically studied. Indeed, this transition takes the form of a rather complex 3-D MHD organisation of the flow which is due to the nonuniformity of the axial temperature gradient along the cylinder.     

Supramolecular organization of the crystal structure of <Emphasis Type="Italic">cis</Emphasis>-bis(thiosemicarbazide)palladium(II) <Emphasis Type="Italic">ortho</Emphasis>-hydrophthalate

This paper reports on the synthesis of a new palladium(II) thiosemicarbazide complex of the composition [Pd(HL)₂](HPht)₂ · 4H₂O(I) (where HL is N(1)H₂-N(2)H-C(3)(=S)-N(4)H₂ and HPht ⁻ is a monoanion of ortho-phthalic acid) and the results of an investigation of its structure. It has been demonstrated that two organic ligands are bidentately coordinated in the neutral form through a set of N and S donor atoms, which are located in the cis position with respect to the central metal atom. Three independent water molecules are joined by hydrogen bonds into the centrosymmetric associate {H₂O}₆. In the crystal, thiosemi-carbazide cationic complexes of palladium(II), monophthalate anions, and water molecules are self-organized into a supramolecular system with the formation of a three-dimensional structure based on ionic and hydrogen bonds.     

Melting and Crystallization Processes of EBBA I. Thermal Analysis

Melting and crystallization processes of EBBA (N-p-Ethoxybenzylidene-p'-butylaniline) have been studied by the method of thermal analysis and measurement of light transmittance. When the sample is cooled down from the nematic phase at a rapid cooling rate, solid phase (solid S) is formed directly. Solid S contains two solid modifications (solid S₁ and solid S₂. By heating the solid S, some amount of Solid S₁ is transformed into the nematic phase through the process of (melting of solid S₁ → crystallization to solid S₂ → melting of solid S₂). After the melting of solid S₁, some liquid crystalline state appears transiently. Solid S₁ is stabilized by the heat treatment at low temperature. The quantity of solid S₁ in solid S increases with the heat treatment time and/or with cooling at a low temperature.     

Synthesis and the crystal and molecular structures of 4-(piperidyl-1)-2-phenylpyrido[2,3- a ]anthraquinone-7,12 Mono- and dibromohydrates (H L )Br · 3H2O and (H2 L )Br2 · 3H2O

4-(Piperidyl-1)-2-phenylpyrido[2,3-a]anthraquinone-7,12 monobromohydrate (HL)Br · 3H₂O (I) and 4-(piperidyl-1)-2-phenylpyrido[2,3-a]anthraquinone-7,12 dibromohydrate (H₂ L)Br₂ · 3H₂O (II) are isolated in the crystalline state. The crystal structures of compounds I and II are determined using X-ray diffraction. It is established that the protonation of 4-(piperidyl-1)-2-phenylpyrido[2,3-a]anthraquinone-7,12 proceeds primarily through the pyridine atom at pH 2–3. The attachment of the second proton occurs through the piperidine nitrogen atom at pH ∼ 1. Original Russian Text ? O.V. Kovalchukova, A.I. Stash, V.K. Belsky, S.B. Strashnova, B.E. Zaĭtsev, M.A. Ryabov, 2009, published in Kristallografiya, 2009, Vol. 54, No. 1, pp. 72–76.