Measurement of physical properties of DyScO3 melt

Rare earth scandate crystals ReScO₃ (Re=La, Ce, Pr, Nd, Sm, Eu, Gd, Tb and Dy) can be grown from the melt at temperatures of about 2100 °C. The needs of thermal insulation of the whole system are very high in order to reach the melting point and to control the thermal gradients which are required by the Czochralski (Cz) method. The consequence is that in‐vivo system observations are practically almost impossible or very hard to perform. Therefore numerical investigations using a mathematical model of the real system can be very helpful. However, numerical models need some physical properties of the considered real system (e.g. density, viscosity, thermal expansion coefficients, thermal conductivity). Most material properties of high melting oxides are not referenced in the literature or they are incomplete and inaccurate. Because the accuracy of qualitative and quantitative results of numerical simulations depend on the used physical properties, we performed corresponding measurements in an adapted Cz configuration at a temperature around the melting point of DyScO₃ (2060 °C). The results are presented and discussed in this work. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimization of thermal conditions during crystal growth in a multi‐zone resistance furnace

The thermal condition is one the of most important control parameters for crystal growth. In this paper we present an effective numerical method in detail for optimizing thermal conditions in multi‐zone crystal growth facilities, especially for crystal growth by the float zone (FZ) technique. A furnace function Ω is introduced to integrate the character of a growth furnace into a linear equation system. The desired power distribution can be therefore approached by solving the linear equation system iteratively. An expert systemlike algorithm has been developed in order to obtain a more suitable solution for practical applications. This method was used to investigate thermal parameters for experiments of SiGe/GeSi single crystal growth by the FZ technique. It is an individual program which can be combined with any commercial finite element/finite volume (FE/FV) program such as FIDAP^TM.     

An analysis of dielectric relaxation using the fractional master equation of the stochastic Ising model

In this paper, we begin introducing some basic definitions and mathematical preliminaries of the fractional calculus theory. By using the fractional calculus technique (that is, calculus of derivatives and integrals of any arbitrary real or complex order) a solution of the fractional master equation derived from the stochastic Ising model of Glauber has been obtained and the result is applied to an analysis of the dielectric relaxation processes. From the solution of the equation, the Cole-Cole dispersion relation, KWW (Kohlrausch-William-Watts) equation and algebraic decay relaxation functions are obtained easily. Then these functions are compared with Bozdemir's earlier analysis of the stochastic Ising model.     

Crystal growth,morphology, spectrographic characterization and thermal properties of 4,5‐bis(benzoylthio)‐1,3‐dithiole‐2‐thione

Single crystals of 4,5‐bis(benzoylthio)‐1,3‐dithiole‐2‐thione (BBDT), were grown from methylene chloride and the growth morphology was deduced by the Bravais–Friedel Donnay–Harker (BFDH) model. The grown crystals were characterized by optical absorption, infrared, Raman and X‐ray powder diffraction spectroscopy. The thermal behavior of BBDT has been investigated by means of thermogravimetric analysis and differential thermal analysis measurements in air. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of the Transport Processes in Bridgman grown Gallium Antimonide

In this work the thermal, velocity and species fields in the melt during the crystal growth by the vertical Bridgman method, has been studied. The simulations were focused on the special case of GaSb, which is a semiconductor of high technological importance. The simulations have been carried out both in 2 and 3‐D. In both cases the momentum (Navier‐Stockes), energy and mass transport equations were solved. The wall‐to‐wall radiation has also been included. In the two‐dimensional case an axisymmetric global model was developed taking into account the different elements present inside the real Bridgman growth system. In order to study the transport processes in the whole system during a complete growth process, the time dependence has also been considered. In the three‐dimensional case, the mathematical domain is restricted to the melt. These simulations were developed in order to study the influence of the ampoule tilting on the dopant distribution in the melt.     

Optical studies on ZnO films prepared by sol‐gel method

A standard sol‐gel method was used to deposit ZnO thin films of suitable thickness on glass substrate.The optical characteristics of the visible to infrared range on thermal stress were critically observed. Morphological signature of the films was detected by X‐ray diffraction (XRD) and the crystallite size determined by Scherrer method from XRD data were consistent with grain size estimated from spectroscopic data through Meulenkamp equation. The optical band gap value from the transmission spectrum was found to corroborate with the existing works. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diffusion induced segregation in the case of the ternary system sphalerite,chalcopyrite and cubanite

A mathematical model for describing natural and experimental diffusion induced segregation (DIS) in the case of a (Zn,Fe)S single crystal with three coexisting phases is derived. As main result, a new and quite general segregation principle for ternary systems is discovered where one phase has a flat free energy density and serves as catalyst for the segregation of the other two phases. The model includes also a stochastic noise term to represent fluctuations of the copper concentration. Numerical simulations in 2‐d underline the physical significance of the model and allow to make quantitative predictions. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The influence of substrate temperature on the growth of sexiphenyl on mica(001)

Sexiphenyl thin films were grown by Hot Wall Epitaxy on air‐cleaved mica (001) surfaces at substrate temperatures between 293 K and 440 K. For the entire temperature range, organic thin films show nano‐needle like morphology. The nano‐needles grown at low substrate temperature (293 K) are shortest, and their growth is accompanied by a simultaneous formation of flat islands which disturbs the growth of nano‐needles. On the contrary, unusually long nano‐needles with typical lengths up to the mm range evolve during the growth at a substrate temperature close to the material's thermal desorption temperature at about 440 K. X‐ray diffraction reveals two different crystalline orientations for nano‐needles in the entire temperature range. At low substrate temperatures dominantly the (11 ) plane of the β‐phase is formed parallel to the mica (001) surface. At elevated temperatures another strong texture becomes dominant which is close to the (11 ) crystal orientation. In contrast to this, crystallites with the preferred orientation (001) parallel to the surface of the substrate are formed at low substrate temperature (293 K). This crystal orientation can be associated with flat islands observed in the early growth stage. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kinetical study of the nonstoichiometric vapour growth process in the system ZnSe:I2

We have studied the growth of ZnSe crystals by chemical transport in a closed system in nonstoichiometric conditions, and we have deduced that the interface kinetics is the phenomenon limiting the growth process. The effect on the growth process of the deviation from stoichiometry of the II‐VI compound was investigated using a mathematical model that involves indirect data computed from directly obtained experimental values. The experimental crystallization rate was compared with the maximum value of the transport flux calculated using the Arizumi‐Nishinaga model. The influence of the stoichiometry of the source material and of the variations in the growth parameters (supercooling, geometrical dimension, specific loading of the ampoule and iodine concentration) on the ZnSe crystal growth process has also been studied. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dendritic grain growth simulation in weld molten pool based on CA‐FD model

The finite difference model is coupled with a cellular automaton (CA) model to simulate dendrite growth in TIG (tungsten inert‐gas) weld molten pool of nickel‐based alloys. Based on the macro finite difference computation of the thermal field of the whole weldment, the micro CA model is used to simulate grain formation process in 2‐dimension area within weld molten pool. The results illustrate that the complicated thermal field and solute field can lead to complex grain morphologies in weld molten pool. The primary dendrite spacing changes during welding solidification process and the final primary dendrite spacing is decided by the thermal field, solute field and other parameters. And it is indicated that the grain boundary segregation has important relationship with welding speed. The grain boundary segregations become more severe as the welding speed increases when the other parameters are kept unchanged. (© 2007 WILEY ‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Complex boron redistribution kinetics in strongly doped polycrystalline‐silicon/nitrogen‐doped‐silicon thin bi‐layers

We have investigated the complex behaviour of boron (B) redistribution process via silicon thin bi‐layers interface. It concerns the instantaneous kinetics of B transfer, trapping, clustering and segregation during the thermal B activation annealing. The used silicon bi‐layers have been obtained by low pressure chemical vapor deposition (LPCVD) method at 480 °C, by using in‐situ nitrogen‐doped‐silicon (NiDoS) layer and strongly B doped polycrystalline‐silicon (P⁺) layer. To avoid long‐range B redistributions, thermal annealing was carried out at relatively low‐temperatures (600 °C and 700 °C) for various times ranging between 30 min and 2 h. To investigate the experimental secondary ion mass spectroscopy (SIMS) doping profiles, a redistribution model well adapted to the particular structure of two thin layers and to the effects of strong‐concentrations has been established. The good adjustment of the simulated profiles with the experimental SIMS profiles allowed a fundamental understanding about the instantaneous physical phenomena giving and disturbing the complex B redistribution profiles‐shoulders. The increasing kinetics of the B peak concentration near the bi‐layers interface is well reproduced by the established model.     

Three‐dimensional numerical investigation of the effects of an open window on the convective heat transfer of an oxide Czochralski system

A three‐dimensional numerical analysis was carried out for a real Czochralski crystal growth furnace containing only gas and without any melt and crystal in order to investigate the effects of a small observation window on the temperature and flow field of the system. For this approach, the induction heating equations, the Navier‐Stokes equation with Boussinesq approximation, the continuity and energy equations have been solved in cylindrical coordinates using the finite element method. It has been found that the flow and thermal fields in the system are obviously three‐dimensional and non‐axisymmetric. The gas enters the system through the window is directed towards the opposite side wall where it is divided into two parts of vertical direction as well as expands in horizontal direction. Consequently, there is a spiral gas flow in the crucible and afterheater which rotates upwards in azimuthal direction along the walls. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of Kinetic Parameters of Bi2Se3 Thin Films by Computation

Bi₂Se₃ thin films are prepared by thermal evaporation method onto well‐cleaned glass substrates. From the XRD analysis, the film is found to be amorphous in nature. Thermal analysis of Bi₂Se₃ sample scraped off from the glass substrate is performed using the technique differential scanning calorimetry (DSC) at different heating rates. Kissinger method is used to analysis these constant heating rate spectra and the activation energy 'E_a′ corresponding to the phase transformation is calculated through the examination of the DSC peak temperature shift induced by variation of the heating rate. An analytical equation with three kinetic parameters (activation energy (E_a), transformation order (n) and the frequency factor (v)) is derived from the Johnson‐Mehl‐Avrami (JMA) theory to describe the constant heating rate DSC spectra. Using the activation energy from Kissinger plot, theoretical constant heating rate DSC traces are generated for arbitrary values of 'v' and 'n' using the analytical equation. Finally, theoretically generated DSC spectra is compared with that of the experimental one and the unknown values 'v' and 'n' are determined.     

Photoacoustic studies on the thermal properties of the NLO compound: L‐alaninium maleate

Studies on thermal and optical properties are very essential for a nonlinear optical material. Photoacoustics (PA) is a recently developed non‐destructive testing (NDT) tool for studying such properties. L‐Alaninium maleate (C₃H₈NO₂⁺·C₄H₃O₄^‐), an organic non‐linear optical (NLO) material was synthesized using submerged seed solution method and was characterized by single crystal X‐ray diffraction (XRD) and density. PA technique was used to determine the thermal parameters of LAM crystals. Moreover, possible phase transition analysis was conducted to ascertain the thermal stability. Scanning electron microscopic (SEM) studies were also carried out and crystal‐packing features discussed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical investigation of induction heating and heat transfer in a SiC growth system

A global simulation model is applied for a silicon carbide growth system heated by induction coils. A finite‐volume method (FVM) and a global model are applied to solve the equations for electromagnetic field, conductive and radiative heat transfer. The growth rate is predicted by Hertz‐Knudsen equation and one‐dimensional mass transfer equation. Further, simulations for five different coil positions are carried out to investigate the effects of coil position on temperature distribution in the furnace. The numerical results reveal that the variation of temperature in the radial direction along the substrate surface and the temperature difference between the powder and substrate are greatly affected by the coil position. The predicted growth rate along the substrate surface for five coil positions is also studied. Finally, a reasonable range of coil positions maintaining a balance between large‐diameter crystal, high growth rate, temperature limitation of material and lower electrical power consumption is obtained. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hydrophobic and thermal insulation properties of silica aerogel/epoxy composite

Silica aerogel/epoxy composite was prepared by dry mixing hydrophobic aerogels with epoxy powders and heat pressing method. The composite materials show a serviceability temperature up to 250 °C with low thermal conductivity (0.11–0.044 W/m k) and hydrophobic property (water contact angle of 117–140°). Transmission electron microscope photos proved that part of silica aerogels nanopores had been immersed by epoxy. Based on this phenomenon, an immersion model was build up to study the effect of immersion on the thermal insulation and hydrophobic properties. In addition a thermal conductivity prediction equation of aerogel/polymer system was obtained and confirmed by comparing the experimental data.     

Experimental investigation of phase transitions exhibited by symmetric liquid crystal dimers

As a part of our systematic study of phase transitions in liquid crystal dimers we report here the variation of density across the phase transitions Isotropic – Smectic A and Smectic A – Smectic F exhibited by the Schiff base liquid crystal dimeric compounds of α,ω‐bis(4‐alkylanilinebenzylidene‐4′‐oxy)alkane (m.OnO.m) homologous series. The compounds studied are 6.O5O.6 and 6.O6O.6. The compound 6.O5O.6 exhibits only Smectic A phase, whereas the compound 6.O6O.6 exhibits Smectic A and Smectic F phases. The density jumps and peak in thermal expansion coefficient at the transitions confirm the first order nature of the transitions with a smaller density jumps compared to the monomeric liquid crystals. The calculated pressure dependance of the transition temperatures using Clauasius‐ Clapeyron equation is also reported. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The numerical simulation of heat and mass transfer during growth of a binary system by the travelling heater method

The influence of convection and heat and mass transfer on the shape and position of melt/solid interfaces and on radial composition segregation is analysed numerically for the travelling heater method growth of a binary alloy in a vertical transparent ampoule. Results are presented for crystal and melt with thermophysical properties similar to Cd_xHg_1−xTe with the assumption that the pseudobinary CdTe-HgTe phase diagram is true. The two-dimensional axisymmetric heat transfer equation, hydrodynamical equation and convective diffusion equation are included in the mathematical model. The rates of crystal growth and dissolution are supposed to be proportional to the compositional supercooling in the melt near the interfaces. It is shown for the conditions when convection is absent that the interfaces are asymmetrically positioned respectively to the heater centre line. Intensive convection makes their position more symmetrical but the length of the liquid zone greater. The flow pattern in the melt appears to be greatly influenced by solutal gravitational convection. The nonlinear dependence of the melt density on the temperature and composition are used in the model. The cases when speed of the heater is antiparallel (stable density stratification) or parallel (unstable stratification) to the vector of gravitational acceleration are considered.     

Effect of the seed crystallographic orientation on AlN bulk crystal growth by PVT method

The growth of AlN crystals by PVT method was investigated using TaC crucible in the temperature range of 2250‐2350 °C. AlN boules with 30 mm in diameter were successfully grown on the crucible lid by self‐seeded growth. The AlN boules consist of the spontaneously nucleated AlN single crystal grains with the {1010} natural crystalline face. The fast growth rate of more than 1 mm/h was achieved. AlN crystals grown on (11 0)‐, (10 0)‐, and (0001)‐face AlN seeds were investigated. Different experimental phenomena have been observed under particular condition. The crystal grown on (11 0)‐face seed has different natural crystalline face from the seed. For the crystal grown on (10 0) or (0001) seed, the crystal natural crystalline face is same as the crystallographic orientation of the seed. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Isothermal liquid phase epitaxy of A 3 B 5 compounds under excessive vapor pressure of the B 5 component

A mathematical model has been developed of isothermal epitaxial growth of A³B⁵ films on the A³B⁵ substrates from flux by creating the excessive pressure of diatomic vapors of the B ⁵ component. The model is based on the diffusion equation with the nonlinear boundary condition at the evaporation surface and the thirdkind condition at the crystallization surface. The problem is solved numerically on a computer.