Non-Lyapunov Type Stability in a Model of the Dewetted Bridgman Crystal Growth Under Zero Gravity Conditions

A numerical model has been developed based on a mass conservation level set algorithm considering a wall adhesion to predict the surface motion for a single and double dam break problems. The simulation for the single dam break shows that the wall adhesion force can be introduced through contact angle by modifying the level set function on the boundary in the level set method, and the magnitude of the contact angle has an effect on the moving location of the leading front of water–gas system. Moreover, the simulation for the double dam break presents clearly the processes of coalescence and break up of the free surface.     

Self-similarity in the kinetic growth regime of a crystal in a phase-separating medium

An analysis is made of a simple model of the kinetic growth regime of a crystal possessing cubic symmetry in a phase-separating medium. Impurity diffusion is neglected. It is shown that in this approximation the crystal growth is self-similar. A cellular automaton model is used to represent the successive stages of structural modification as the impurity concentration increases. Pis’ma Zh. Tekh. Fiz. 25, 71–77 (October 26, 1999)     

Fatigue strength of a single crystal in the gigacycle regime

The objective of this work is to investigate the fatigue behavior of a single crystal nickel-based superalloy in the gigacycle regime. Testing from 10⁶ to 10⁹ cycles at 593 °C was performed using an ultrasonic fatigue system operating at 20 kHz. Multiple tests were performed at stresses near the fatigue limit to determine the variability in fatigue life in this regime. Endurance limit results were compared to similar data generated on conventional servohydraulic test systems to determine if there are any frequency effects. Scanning electron microscopy was then used to determine the initiation sites and the failure mechanisms. Initial results indicate little or no frequency effect on the fatigue strength or failure mechanisms of PWA 1484 at 593 °C.     

Crystal growth of KCl in a reactive atmosphere II: The crystal growth technique

The crystal growth technique employed in the growth of large single crystals of KCl while the material is undergoing reactive-atmosphere processing is described in detail.     

Thermal boundary layers over a wedge with uniform suction or injection in forced flow

Summary The behavior of incompressible laminar boundary layers in forced flow over a wedge with uniform suction or injection was theoretically investigated. The boundary layer equations along a wedge are transformed into non-similar partial differential ones, and the ordinary differential equations were obtained by means of the difference-differential method. The solutions of the resulting equations are expressed in a form of integral equations which are in turn solved by iterative numerical quadratures. The numerical results are given for the velocity distribution, temperature distribution and the coefficient of skin friction and heat transfer for various values of suction/injection parameter.     

Numerical simulation of dendritic crystal growth in a channel

A quasi-stationary mathematical model of dendritic growth from an undercooled melt in a channel is considered. This is based on the integral representation formula of the problem which assumes that the crystals grow steadily so that the temperature field satisfies a convection-diffusion equation in the moving frame of reference. Numerically, the above phenomenon is very unstable and any small perturbation in the interface shape may give rise to the growth of an artificial (numerical) branch in the dendrite. Although important advances have been made in the numerical simulation of this process in the last decade, more stable numerical schemes are required in order to understand, in detail, the dynamics of pattern formation. The proposed numerical approach is based on a BEM formulation where cubic B-splines are used to represent the contour geometry, as a result of the requirement of C²-continuity for the evaluation of the surface curvature. A standard quadratic interpolation is used for the densities within each boundary element, with an appropriate smoothing scheme to avoid the zig-zag instability which develops at the interface after a large number of time steps. The results obtained with the proposed numerical formulation are compared with experimental, theoretical and other numerical results.     

Non-Darcian effects on forced convection heat transfer over a flat plate in a highly porous medium

Summary The effects of inertia forces and the distance from the leading edge of the plate on the velocity and temperature fields as well as on the skin friction and heat transfer coefficients in the boundary layer flow over a semi-infinite flat plate embedded in a saturated porous medium of high porosity are studied. It is shown that the inertia forces have a significant influence on the flow characteristics in this problem.     

Nucleation and crystal growth in a fly ash derived glass

The devitrification behaviour of a fly ash derived glass, examined by differential thermal analysis (DTA), X-ray diffraction and scanning electron microscopy (SEM), is reported and discussed. The crystallized phases were identified as mullite (3Al₂O₃·2SiO₂) and anorthite (CaO·Al₂O₃·2SiO₂). Kinetic parameters for nucleation and crystal growth were estimated from the DTA curves. The temperature of maximum nucleation rate was 790°C and the activation energy for crystal growth E=370 kJ mol^–1. The crystal morphology was investigated by SEM and the crystal shape found to be consistent with the morphological index n calculated by DTA. The glass-ceramic obtained from a previously nucleated glass showed a fine-grained texture.     

Biomimetic coatings on titanium: a crystal growth study of octacalcium phosphate

The biomimetic approach allows the coating of metal implants with different calcium-phosphate (Ca-P) phases. Films elaborated at physiological conditions exhibited structures closely resembling those of bone mineral. For instance, octacalcium phosphate (OCP, Ca₈(HPO₄)₂(PO₄)₄ · 5H₂O) crystals have been deposited on titanium through a two-step procedure. After cleaning and etching, Ti6Al4V plates were immersed for 24 h into a simulated body fluid (SBF1). A thin amorphous carbonated Ca-P layer precipitated on the metal substrate. Secondly, these thinly Ca-P coated titanium substrates were immersed for 48 h into another simulated body fluid (SBF2). The thin amorphous carbonated Ca-P layer induced the fast precipitation of a second Ca-P layer of 55 m in thickness composed of OCP crystals. The measurements of Ca and P concentrations versus soaking time in SBF2 showed that the carbonated Ca-P layer partially dissolved before the deposition of the OCP coating. X-ray diffraction (XRD) revealed that OCP crystals grew epitaxially on the substrate. OCP is known to be one of the precursors during the bone mineralization process, thereby, this new generation of biomimetic coatings are promising for orthopedic surgery. © 2001 Kluwer Academic Publishers     

Simulation studies of the hydrodynamics in high-temperature solutions for crystal growth. V. Shape of the crystal/liquid interface in the presence of simultaneous free and forced convections

The formation conditions of a concave, convex or flat crystal/liquid interface in the presence of simultaneous free and forced convections have been investigated using model liquids. Simultaneous free and forced convections with both the same and opposite flow directions have been considered. The interface shape was found to depend on the direction and rate of the resultant convection flow under the crystal. The formation conditions of a flat interface for liquids having kinematic viscosities of 0.001·10^?3 – 0.5·10^?3 m²/s and for crystal diameters of 10, 15 and 20 mm, respectively, have been established. These conditions have been compared with the optimum conditions found experimentally by other authors for the growth of several kinds of crystals from high-temperature solutions by the TSSG method and from melts by the Czochralski method. The comparison has shown that the model proposed describes well the real processes.     

Formation of a crystallization courtyard in eutectic systems and crystal growth

The so-called crystallization courtyard is investigated that forms in processes of mass crystallization around the Ge and Si crystals and their solid solutions (Ge+Si) during cooling of hypereutectic alloys in the Ge-Al, Si-Al, and (Ge+Si)-Al eutectic systems. For the first time, data on the composition and microhardness of this crystallization courtyard are given and its role is shown as a stopper of cracking in an Al-(Ge,Si) system during rapid cooling after the heating system is turned off. For the first time, it is suggested that a crystallization courtyard forms in all hypereutectic systems (including every system in which the amount of the taken solvent does not correspond to the eutectic point).     

Spectral Fraunhofer regime: time-to-frequency conversion by the action of a single time lens on an optical pulse

We analyze a new regime in the interaction between an optical pulse and a time lens (spectral Fraunhofer regime), where the input pulse amplitude is mapped from the time domain into the frequency domain (time-to-frequency conversion). Here we derive in detail the conditions for achieving time-to-frequency conversion with a single time lens (i.e., for entering the spectral Fraunhofer regime) as well as the expressions governing this operation. Our theoretical findings are demonstrated both numerically and experimentally. A comparative study between the proposed single-time-lens configuration and the conventional dispersion + time-lens configuration for time-to-frequency conversion is also conducted. Time-to-frequency conversion with a single time lens can be used for applications similar to those previously proposed for the conventional time-to-frequency converters, e.g., high-resolution measurement of fast optical temporal waveforms. Moreover, our results also indicate that the spectral Fraunhofer regime provides additional capabilities for controlling and processing optical pulses.     

Programming of crystal diameter in Czochralski growth by a cooling plot: Application to InSb

It is shown, that under thermal “stiffness” conditions, the dimensions of a crystal grown by the Czochralski method may be programmed by a cooling plot. The cooling plot is calculated from the measured longitudinal and radial thermal gradients, involving also the melt-to-solid densities ratio. Utilization of the principle could save the need for sophisticated expensive automatic diameter control systems. In the present work the principle was successfully applied to the growing of InSb single crystals of diameters around 2cm.     

Coupled heat and mass transfer in mixed convection over a VHF/VMF wedge in porous media: The entire regime

Summary The development of flow and heat transfer of a viscous electrically conducting fluid in the stagnation point region of a three-dimensional body with an applied magnetic field is studied when the external stream is set into an impulsive motion from rest and at the same time the surface temperature is suddenly raised from that of the surrounding fluid. This analysis includes both short time solution (Rayleigh-type of solution) and the steady-state solution as time tends to infinity (Falkner-Skan type of solution). The unsteady three-dimensional boundary layer equations represented by a system of parabolic partial differential equations are solved numerically using an implicit finite-difference scheme. For certain particular cases analytical solutions are obtained. In the absence of the magnetic field, the reverse flow occurs in the transverse component of the velocity in a certain portion of the saddle-point region (–1c<–0.4, wherec=b/a is the ratio of the velocity gradients in they- andx-directions at the edge of the boundary layer). The magnetic field delays or prevents the reverse flow. The surface shear stresses in the principal and transverse directions and the surface heat transfer increase with the magnetic field both in nodal point (0c1) and saddle point (–1c<0) regions. For a fixed magnetic field, the surface shear stress inx-direction and the surface heat transfer increase with time in nodal and saddle point regions, but the surface shear stress in the transverse direction increases with time for 0<c1 and decreases with increasing time for –1c<0.     

Body-force-driven multiplicity and stability of combined free and forced convection in rotating curved ducts: Coriolis force

 A numerical study is made on the fully developed bifurcation structure and stability of forced convection in a rotating curved duct of square cross-section. Solution structure is determined as variation of a parameter that indicates the effect of rotation (Coriolis-force-driven multiplicity). Three solutions for the flows in a stationary curved duct obtained in the work of Yang and Wang [1] are used as initial solutions of continuation calculations to unfold the solution branches. Twenty-one solution branches are found comparing with five obtained by Selmi and Nandakumar [2]. Dynamic responses of the multiple solutions to finite random disturbances are examined by the direct transient computation. Results show that characteristics of physically realizable fully developed flows changes significantly with variation of effect of rotation. Fourteen sub-ranges are identified according to characteristics of physically realizable solutions. As rotation effect changes, possible physically realizable fully-developed flows can be stable steady 2-cell state, stable multi-cell state, temporal periodic oscillation between symmetric/asymmetric 2-cell/4-cell flows, temporal oscillation with intermittency, temporal chaotic oscillation and temporal oscillation with pseudo intermittency. Among these possible physically realizable fully developed flows, stable multi-cell state and stable steady 2-cell state exist as dual stable. And oscillation with pseudo intermittency is a new phenomenon. In addition to the temporal oscillation with intermittency, sudden shift from stationary stable solution to temporal chaotic oscillation is identified to be another way of onset of chaos. Received: 20 December 2001 / Accepted: 5 August 2002 The financial support from the Research Grants Council of Hong Kong (RGC, Project No: HKU7086/00 E), the CRCG and the Outstanding Young Researcher Award of the University of Hong Kong to LW is gratefully acknowledged.