Crystallization of binary melt with a periodically varying rate

The time dependence of the crystallization rate at crystal pulling to the cold zone with a velocity that has a sinusoidal component has been investigated within a one-dimensional time-dependent model of solidification of a diluted binary melt by the net method. It is shown that the regularities that were obtained previously by the analytical method for pulling rates with small oscillations are repeated in many respects when considering oscillations of larger amplitudes. At significant oscillation amplitudes, the time-averaged values of impurity concentration at the interface for the stationary and vibrational crystallization modes may differ by several dozen percent.     

Peculiarities of the initial transient process of binary melt crystallization

The time dependence of the crystallization rate V(t) in the transient process that occurs during crystal pulling into a cold zone at a constant rate W has been investigated within the one-dimensional time-dependent model of binary melt solidification using numerical and analytical approaches. It is shown that the character of the dependence V(t) in this process is mainly determined by the parameter B _w = V _c /W, where V _c is the crystallization rate at which the constitutional supercooling zone is formed in the melt. At B _w ≥ 1, the function V(t) monotonically approaches its steady-state value W, while at B _w < 1 V(t) is generally nonmonotonic. The nonmonotonic character of V(t) can manifest itself both as aperiodic damping and in the form of damping oscillations. At B _w ∼ 0.1, the vibrational amplitude of the crystallization rate in the initial transient process may reach several tens of a percent of W.     

On the dependence of the surface tension at the crystal-melt interface on the impurity concentration

The stationary task of impurity diffusion in a melt has been solved within a two-dimensional crystallization model in a second-order approximation with respect to the amplitude of deviation from a smooth crystallization front. The dependence of the surface tension Γ at the interface on the impurity concentration C is taken into account in the form Γ = Γ₀ + ζ _d C, where Γ₀ and ζ _d are constants. The variational method is used to obtain the condition for the transition from a smooth crystallization front to a cellular one. It is shown that calculated cell sizes are in agreement with the experimental data in the literature only when the parameter ζ _d ≠ 0. For binary systems with distribution coefficients k < 1 and k > 1, ζ _d should be positive and negative, respectively.

     

Investigations on the structural perfection of bridgman-grown PbTe single crystals

It is reported on the possibility of improving the structural perfection by the Bridgman method, shown with the example of the influence on the low-angle grain boundary substructures in PbTe arranged in growth direction. In the employed crystal growth apparatus temperature gradients from 15 to 100°C/cm and solidification rates from 0.33 to 4.2 mm/hr could be achieved. The low-angle grain boundary substructure was characterized by X-ray-topographic and etch investigations on (100)-orientated ingots. The thermal conditions during the growth affect the structural perfection decisively. An axial spot dependence of etch pit density and substructure abundance was observed. By reducing the cooling rate during growth — expressed by the product of temperature gradient G and solidification rate V — it is possible to obtain more perfect PbTe-crystals. It seems that the diameter l of the substructure cells which was lying between 0.5 and 2 mm, is related to the cooling rate G · V by the functional coherency l ≈ 1/√G · V. The choice of different initial melt combinations up to 1 at.% Te-surplus exerted no influence on the abundance of the low-angle grain boundaries. The in literature suggested connection of low-angle grain boundary substructure with phenomena resulting from a constitutional supercooling could not be established.     

Simplified version of calculation of the composition distribution along a single crystal of a binary solid solution obtained by pulling from a feeding melt

The possibility of obtaining single crystals of binary solid solutions exhibiting strong segregation upon crystallization by pulling from a feeding melt with the use of a crucible shaped as a truncated cone and a feeding ingot of complex shape is shown. The composition distribution along the crystal length is found by solving the continuity equation for the second component flux under certain initial and boundary conditions. It is shown that single crystals can be obtained in which the second-component concentration in the stationary mode exceeds the corresponding value in the feeding ingot. The method developed is applied to Ge-Si solid solutions.     

Evaporation induced diameter control in fiber crystal growth by micro‐pulling‐down technique: Bi4Ge3O12

Diameter self‐control was established in Bi₄Ge₃O₁₂ fiber crystal growth by micro‐pulling‐down technique. In accordance with Bi₂O₃‐GeO₂ phase diagram, the diameter was controlled due to compensation of solidification with evaporation of volatile Bi₂O₃ self‐flux charged into the crucible with excess. The crucibles had capillary channels of 310 or 650 μm in outer diameter. The crystals up to 400 mm long and 50‐300 μm in diameter were grown at pulling‐down rates of 0.04‐1.00 mm/min. The melt composition and the pulling rate were generally only two parameters determining solidification rate. As a result, crystals with uniform (± 10%) diameter and aspect ratio up to 10⁴ were produced without automation of the process. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fluctuation mechanism of normal crystal growth during solidification of binary metallic melts

A recently published theory on the solidification of a one-component melt has been extended to the more complex case of binary systems. The theory is based on the model of a two-phase transitional zone existing between the crystalline phase and the melt. The concentration of solid state atoms within each mono-atomic layer of the transitional zone are assumed to fluctuate due to thermal fluctuations. A crystal growth law has been derived expressing the crystallization velocity in terms of probability functions describing these concentrations fluctuations. When certain restricting conditions concerning the atomic interaction energies within the transitional zone and the distribution of the atoms among the solid and liquid phases at supercooling are fulfilled the crystal growth law attains a simple form predicting for small supercoolings a growth rate proportional to supercooling (linear growth law), roughly proportional to physical parameter θ_AA, and with a weak dependence on another parameter Δ.     

Haze in sapphire crystals grown by SAPMAC method

Haze defect in SAPMAC method grown sapphire crystal was studied in detail. It is shown that haze is composed by a large number of CO₂ bubbles, and haze always appears in the axis region of the crystal since the bubbles formed in front of the crystallization surface are most always draged to the convection rolls in front of the central part of the crystallizaiton surface by melt and then engulfed by the rolls. Moreover, the effects of pulling rate on the formation of haze were analyzed and means for restraining haze was suggested. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystallizaton Characteristics of the Alternating Tetrafluoroethylene-Ethylene Copolymer

The alternating tetrafluoroethylene-ethylene (TFE-E) copolymer has been studied with respect to its crystallization by using differential scanning calorimetry and optical microscopy. The value of the specific surface energy σ at the melt/crystal interface is calculated to be about 2 · 10⁻³ J/m². The nucleating activity Φ of TiO₂ particles introduced into TFE-E copolymer is estimated to be approximately 0.9. The temperature dependence of the nucleation rate and of the linear growth velocity are constructed in the whole region from the melting temperature T_m to the vitrification temperature T_g. The minimum cooling rate for the formation of a crystal-free TFE-E copolymer glass is calculated and its value amounts to 10⁴ K · min⁻¹.     

Effect of supersaturation on the crystallization of phenylbutazone polymorphs

The article describes the effect of degree of supersaturation, σ, on the crystallization of specific polymorphs of phenylbutazone from its methanolic solution at 20 °C. At low initial supersaturation, σ ≤ 2.0, the fraction of the metastable α polymorph in the crystallized product exceeds that of the δ polymorph, while at σ ≥ 5.0, the fraction of the stable δ polymorph increases in the crystallized product. The results are explained by the effect of supersaturation on the relative rates of nucleation and crystal growth of the polymorphs. Furthermore, the mechanism of nucleation and crystal growth also change with supersaturation. Supersaturated methanolic solutions of phenylbutazone exhibit a critical temperature at which the nucleation rates of the polymorphs decrease drastically. This effect is partly explained by the decreased mobility of phenylbutazone molecules at lower temperatures. Nucleation is most rapid when the crystallization temperature is close to the transition temperature, T_t(α ⟷ δ), between the polymorphs, α and δ. The nucleation rate decreases as the temperature difference between T_t(α ⟷ δ) and the crystallization temperature increases. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Verteilungskoeffizienten und Konzentrationsanreicherungen an der Phasengrenzfläche bei ebenem und zellularem Erstarren von Zinn-Zink-Legierungen

The experimental results of KRUMNACKER on the effective distribution coefficient k_eff and the concentration-profil at the solidification interface were examined. On the basis of this examination and some new calculations the depencence of the segregation coefficient on the solidification rate R and on the concentration C₀ is studied in the cases of planar and cellular solidification. — In the case of planar interface the dependence of k_eff on the solidification rate is that of the Burton-Prim-Slichter-theorie. The interface distribution coefficient is not a function of R, or C₀. Thus, the result od BRICE , basing on the same experiments, is not correct. It is impossible, to improve the model of BRICE by these values. — In the case of cellular growth the distribution depends on the diffusion in the diffusion layer at the interface and on the segregation in the grooves of the cells. Under the applied experimental conditions of a large diffusion-boundary-layer the diffusion determines the dependence of k_eff on the solidification rate also under the condition of cellular growth.     

Nature of large-scale oscillations in oxygen concentration along the growth axis in Czochralski-grown silicon crystals

Oxygen distribution in a Si crystal (100 mm in diameter) has been studied by the absorption method in the range of the absorption band of interstitial oxygen, λ = 5.81 μm. Large-scale fluctuations (～1 cm) of the oxygen concentration (N ₀) along the growth axis were determined. Depending on the melt height, the regions of the chaotic and quasiperiodic changes were established, as well as the region of the constant N ₀ value, and their relation to turbulent, quasiperiodic, and stationary modes of melt convection in crystallization. The values of the critical Rayleigh number for the melt transition from stationary to quasiperiodic (3 × 10³) and from quasiperiodic to turbulent (1.7 × 10⁴) convection modes are determined for growth of silicon crystals by the Czochralski method. The dominating modes of N ₀ concentration oscillations at two incommensurable frequencies, f ₁ = 1.3 × 10^?3 and f ₂ = 6 × 10^?4 Hz, are assumed to be related to the oscillatory transfer of oxygen from the walls of the quartz crucible to the crystallization front and restructurization of the convective flow pattern of the melt in the course of crystal growth.     

“Crystallization E.M.F.” Investigation in the lithium niobate pulling process from the melt

E.M.F. in the lithium niobate crystal-melt system as a function of pulling and rotation rates, crystal diameter and orientation was determined. Total E.M.F. is a sum of thermo-E.M.F. and “crystallization E.M.F.” Δφ. The logarithmic approximation Δφ = Δφ₀ In (1 + /v₀), where v is a growth rate, Δφ₀ = 3.9 mV, v₀ = 1.9 mm/h is adequate. The Δφ magnitude is independent within the experimental error on the rotation rate and crystal orientation, whereas it is slightly increasing along with the diameter increase. Some existing models of electric phenomena accompanying crystal growth are discussed and a new model based on charge carrier injection into solid during growth is proposed.     

Mechanisms of Interaction of Molybdenum and Tungsten Polyoxide with Aluminum Oxide Melt under Reducing Conditions

The main chemical reactions between Mo and W polyoxides and Al₂O₃ melt in a controlled Ar + H₂ atmosphere (T = 2400 K, P = 1 bar) during sapphire growth by horizontal directional solidification have been investigated. Under these thermodynamic conditions, the melt and products of its dissociative evaporation may actively react with the tungsten heater and molybdenum thermal screens of the crystallization system. It is shown that the polyoxides formed during evaporation do not directly interact with the melt; this interaction occurs only with participation of reagents exhibiting pronounced reducing properties (Al, H₂, H, WO, Al₂O, AlH, AlH₂, AlH₃). It is established that most of processes occur with participation of aluminum hydrides. A particular role of Mo(W) dioxide–W(Mo) polyoxide functional pairs in the interaction with the melt is determined.

     

Crystallization process on amorphous GeTeSb samples near to eutectic point Ge15Te85

One of most important properties of some tellurium-based chalcogenide glasses is the optical and electrical switching between two states: the glass and the crystalline state. The understanding in these systems of the glass to crystal transition and its transformation kinetics is essential for their application in non-volatile memories. GeTeSb and GeTe amorphous samples of compositions close to the eutectic point Ge₁₅Te₈₅ were obtained by rapid solidification from the liquid state employing melt spinning technique. The glass forming ability of this system, for this cooling technique, is restricted to a small composition range nearby the binary eutectic. The crystallization kinetics of the samples was studied by means of differential scanning calorimetry (DSC) under both isothermal and continuous heating regimes. The quenched samples and the crystallization products have been characterized by X-ray diffraction with Cu(Kα) radiation. The crystallization temperature, activation energy, crystallization enthalpy and the dependence of these properties on concentration are reported. The crystallization study of Ge₁₅Te₈₅ glasses shows: a primary crystallization of Te superimposed with a secondary crystallization of GeTe. The addition of Sb (5 at.%) to the eutectic point Ge₁₅Te₈₅ modifies this behavior: the crystallization of Ge₁₃Sb₅Te₈₂ glasses consists on the crystallization of Te and Ge₂Sb₂Te_5. The crystallization of the ternary glasses was modeled.     

Direct melt crystal growth of isotactic polybutene‐1 trigonal phase

The morphology, crystalline structure and crystal growth kinetics of melt‐crystallized thin isotactic polybutene‐1 films have been studied with transmission electron microscopy, electron diffraction and optical microscopy. It is demonstrated that a bypass of tetragonal phase crystallization and direct melt crystal growth of the trigonal phase can be achieved via self‐seeding at atmospheric pressure using solution‐grown trigonal crystals as nuclei. Electron microscopy and optical microscopy observations show that melt‐crystallized isotactic polybutene‐1 single crystals of the trigonal phase have rounded or hexagonal morphologies around 75°C. The growth rate of trigonal crystals in the melt has been obtained by in‐situ optical microscopy. The growth rate of trigonal crystals in the melt is 1/100 and 1/1000 that of tetragonal crystals in the melt around 70 and 90°C, respectively. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nd:YVO4 crystal growth by Czochralski technique with a submerged plate

This paper is to investigate the growth of Nd:YVO₄ (yttrium vanadate) crystal by the modified Czochralski technique with a submerged plate. Numerical studies are performed to examine melt convection and heat transfer during Nd:YVO₄ growth. The attention is paid to study the effects of initial elevation of the submerged plate, crystal diameter, and melt level on melt inclusions. It is found that the increase in crystal rotation rate and crystal diameter, and the decrease in melt level will increase the axial temperature gradient at the edge and in the center of the crystal, and change the interface shape from convex to flat. The experiments are also carried out to confirm the feasibility of the proposed new technique for controlling melt inclusions in Nd:YVO₄ crystal growth.     

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.     

Investigation of the possibility of obtaining homogeneous Ga<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>In<Subscript>x</Subscript>Sb crystals under weak flow conditions

The possibility of growing macrohomogeneous Ga_{1 ? x}In_xSb crystals with x = 0.2 was studied using the axial heating process close to the melt/crystal interface. The grown ingots were analyzed by a JSM-5300 scanning electron microscope and the experimental results were compared with the results of numerical simulation. It was shown that, as a whole, the mathematical model adequately describes the processes of the steady-state heat and mass transfer. It was found that, at the crystallization of Ga_{1 ? x}In_xSb by the axial heating process under conditions of weak laminar flows, longitudinal homogeneity is observed when a dead zone is formed in the melt and that the crystallization regime is similar to diffusion. It was shown that the composition of the grown crystals strongly depends on the structure of a melt flow and its dynamics.