Influence of liquid bridge volume on the onset of oscillation in floating-zone convection .1. Experiments

The onset of oscillation in the floating zone convection driven by the gradient of surface tension was experimentally studied, and discussions were concentrated on the influence of liquid bridge volume on the onset of oscillation. Distributions of critical applied temperature difference and frequency depending on the volume of the liquid bridge were obtained, and there was a gap range of liquid volume which separated the curve of marginal stability into two parts for fixed rod diameter and aspect ratio. The results imply that the volume of the liquid bridge is a sensitive critical parameter for the onset of oscillation. The implication on the instability is also discussed in the present paper.

Influence of liquid bridge volume on the onset of oscillation in floating-zone convection .2. Numerical-simulation

The onset of oscillation in the floating zone convection driven by the gradient of surface tension was studied numerically for an unsteady and two-dimensional model, and studies were concentrated on the influence of liquid bridge volume on the onset of oscillation in comparison with the experimental results in the Paper I. The numerical results agree with the experimental ones presented in the previous paper, in which the distributions of critical applied temperature difference depending on the volume of liquid bridge and a gap range of liquid volume in marginal stability curve were obtained.

Effects of g-jitter on the critical marangoni number

A half floating zone is fixed on a vibrational deck, which supports a periodical applied acceleration to simulate the effect of g-jitter. This paper deals with the effects of g-jitter on the fluid fields and the critical Marangoni number, which describes the transition from a forced oscillation of thermocapillary convection into an instability oscillatory convection in a liquid bridge of half floating zone with top rod heated. The responses of g-jitter field on the temperature profiles and flow pattern in the liquid bridge were obtained experimentally. The results indicated that the critical Marangoni number decreases with the increasing of g-jitter effect and is slightly smaller for higher frequency of g-jitter with fixed strength of applied gravity.

Coupling of melting-solidification phase-change convection with floating-zone convection under microgravity

A finite element algorithm is used to analyze the process of floating zone crystal growth under microgravity. The effect of phase change convection coupled with surface tension convection is considered. The results show that the rate of crystal growth is very important. The single-crystal-melt interface is steeper than the feed-melt interface during the process of crystal growth. When the rate exceeds a critical value, the Marangoni vortex near the feed-melt interface will become so large that a secondary vortex will exist.

Two bifurcation processes for onset of oscillatory thermocapillary convection in a floating half zone

An overview on the onset of thermocapillary oscillatory convection in a floating half zone is provided, and it is a typical subject in the microgravity sciences related to the space materials science, especially the floating zone processing, and also to the microgravity fluid physics. The main interests are focused around the process for onset of oscillatory thermocapillary convection, which is known also as the bifurcation transition from quasi-steady convection to oscillatory convection. The onset of oscillation depends on a set of critical parameters, such as the Marangoni number, Prandtl number, geometrical parameters, and heat transfer parameters. Recent studies show that, there exists the bifurcation transition from steady and axial symmetric convection to the steady and axial non-symmetric convection before the onset of oscillation in cases of small Prandtl number fluids and in cases of larger Prandtl number fluids of fat liquid bridge with small aspect ratio. The transition process is a strong non-linear process because the velocity deviation has the same order of magnitude as that of an average flow after the onset of oscillation, and unsteady 3-D numerical simulation is suitable to do in depth analysis on strong non-linear process, and leads generally to a better comparison with the experimental results.

Floating zone convection

The microgravity research, as a branch of the advanced sciences and a spe- cialized field of high technology, has been made in China since the late 1980's. The research group investigating microgravity fluid physics consisted of our col- leagues and the authors in the Institute of Mechanics of the Chinese Academy of Sciences (CAS), and we pay special attention to the floating zone convection as our first research priority. Now, the research group has expanded and is a part of the National Microgravity Laboratory of the CAS, and the research fields have been extended to include more subjects related to microgravity science. Howev- er, the floating zone convection is still an important topic that greatly holds our research interests.

Period-doubling bifurcations of the thermocapillary convection in a floating half zone

This study experimentally explored the fine structures of the successive period-doubling bifurcations of the time-dependent thermocapillary convection in a floating half zone of 10 cSt silicone oil with the diameter d (0)=3.00 mm and the aspect ratio A=l/d (0)=0.72 in terrestrial conditions. The onset of time-dependent thermocapillary convection predominated in this experimental configuration and its subsequent evolution were experimentally detected through the local temperature measurements. The experimental results revealed a sequence of period-doubling bifurcations of the time-dependent thermocapillary convection, similar in some way to one of the routes to chaos for buoyant natural convection. The critical frequencies and the corresponding fractal frequencies were extracted through the real-time analysis of the frequency spectra by Fast-Fourier-Transformation (FFT). The projections of the trajectory onto the reconstructed phase-space were also provided. Furthermore, the experimentally predicted Feigenbaum constants were quite close to the theoretical asymptotic value of 4.669 [Feigenbaum M J. Phys Lett A, 1979, 74: 375-378].

Influence of Local Magnetic Fields on P-Doped Si Floating Zone Melting Crystal Growth in Microgravity

A two-dimensional axisymmetric numerical model is presented to study the influence of local magnetic fields on P-doped Si floating zone melting crystal growth in microgravity. The model is developed based on the finite difference method in a boundary-fitted curvilinear coordinate system. Extensive numerical simulations are carried out, and parameters studied include the curved growth interface shape and the magnetic field configurations. Computed results show that the local magnetic field is more effective in reducing the impurity concentration nonuniformity at the growth interface in comparison with the longitudinal magnetic field. Moreover, the curved growth interface causes more serious impurity concentration nonuniformity at the growth interface than the case with a planar growth interface.

Increasing Critical Sensitivity of the Load/Unload Response Ratio before Large Earthquakes with Identified Stress Acclumulation Pattern

The Load/Unload Response Ratio (LURR) method is proposed for short-to-intermediate-term earthquake prediction [Yin, X.C., Chen, X.Z., Song, Z.P., Yin, C., 1995. A New Approach to Earthquake Prediction — The Load/Unload Response Ratio (LURR) Theory, Pure Appl. Geophys., 145, 701–715]. This method is based on measuring the ratio between Benioff strains released during the time periods of loading and unloading, corresponding to the Coulomb Failure Stress change induced by Earth tides on optimally oriented faults. According to the method, the LURR time series usually climb to an anomalously high peak prior to occurrence of a large earthquake. Previous studies have indicated that the size of critical seismogenic region selected for LURR measurements has great influence on the evaluation of LURR. In this study, we replace the circular region usually adopted in LURR practice with an area within which the tectonic stress change would mostly affect the Coulomb stress on a potential seismogenic fault of a future event. The Coulomb stress change before a hypothetical earthquake is calculated based on a simple back-slip dislocation model of the event. This new algorithm, by combining the LURR method with our choice of identified area with increased Coulomb stress, is devised to improve the sensitivity of LURR to measure criticality of stress accumulation before a large earthquake. Retrospective tests of this algorithm on four large earthquakes occurred in California over the last two decades show remarkable enhancement of the LURR precursory anomalies. For some strong events of lesser magnitudes occurred in the same neighborhoods and during the same time periods, significant anomalies are found if circular areas are used, and are not found if increased Coulomb stress areas are used for LURR data selection. The unique feature of this algorithm may provide stronger constraints on forecasts of the size and location of future large events.

Analysis of strip electric saturation model of crack problem in piezoelectric materials

This paper presents a fully anisotropic analysis of strip electric saturation model proposed by Gao et al. (1997) (Gao, H.J., Zhang, T.Y., Tong, P., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids, 45, 491-510) for piezoelectric materials. The relationship between the size of the strip saturation zone ahead of a crack tip and the applied electric displacement field is established. It is revealed that the critical fracture stresses for a crack perpendicular to the poling axis is linearly decreased with the increase of the positive applied electric field and increases linearly with the increase of the negative applied electric field. For a crack parallel to the poring axis, the failure stress is not effected by the parallel applied electric field. In order to analyse the existed experimental results, the stress fields ahead of the tip of an elliptic notch in an infinite piezoelectric solid are calculated. The critical maximum stress criterion is adopted for determining the fracture stresses under different remote electric displacement fields. The present analysis indicates that the crack initiation and propagation from the tip of a sharp elliptic notch could be aided or impeded by an electric displacement field depending on the field direction. The fracture stress predicted by the present analysis is consistent with the experimental data given by Park and Sun (1995) (Park, S., Sun, C.T., 1995. Fracture criteria for piezoelectric materials. J. Am. Ceram. Soc 78, 1475-1480).

Effect of non-uniform magnetic field on crystal growth by floating-zone method in microgravity

The magnetic damping effect of the non-uniform magnetic field on the floating-zone crystal growth process in microgravity is studied by numerical simulation. The results show that the non-uniform magnetic field with designed configuration can effectively reduce the flow near the free surface and then in the melt zone. At the same time, the designed magnetic field can improve the impurity concentration non-uniformity along the solidification interface. The primary principles of the magnetic field configuration design are also discussed.

Experimental Evidence of Critical Sensitivity in Catastrophe

The paper presents an experimental study on critical sensitivity in rocks. Critical sensitivity means that the response of a system to external controlling variable may become significantly sensitive as the system approaches its catastrophic rupture point. It is found that the sensitivities measured by responses on three scales (sample scale, locally macroscopic scales and mesoscopic scale) display increase prior to catastrophic transition point. These experimental results do support the concept that critical sensitivity might be a common precursory feature of catastrophe. Furthermore, our previous theoretical model is extended to explore the fluctuations in critical sensitivity in the rock tests.

Tailoring of dendritic microstructure in solidification processing by crucible vibration

We analyzed the effects of both natural convection and forced flows on solid–liquid interface morphology during upward Bridgman solidification of metallic alloys. Experiments were carried out on Al–3.5wt% Ni alloy, for a cylindrical sample. The influence of natural convection induced by radial thermal gradient on solidified microstructure was first analyzed as a function of the pulling rate. Then, the influence of axial vibration on solidification microstructure was experimentally investigated by varying vibration parameters (frequency and amplitude). Experimental results demonstrated that vibrations could be used to either attenuate fluid flow in the melt and obtain a uniform dendritic pattern or to promote a fragmented dendritic microstructure. However, no marked effect was observed for cellular growth. This pointed out the critical role of the mushy zone in the interaction between fluid flow and solidification microstructure.

Mechanical effects of the self-organization of dislocations and related critical characteristics

The effects of the dislocation pattern formed due to the self-organization of the dislocations in crystals on the macroscopic hardening and dynamic internal friction (DIF) during deformation are studied. The classic dislocation models for the hardening and DIF corresponding to the homogeneous dislocation configuration are extended to the case for the non-homogeneous one. In addition, using the result of dislocation patterning deduced from the non-linear dlislocation dynamics model for single slip, the correlation between the dislocation pattern and hardening as well as DIF is obtained. It is shown that in the case of the tension with a constant strain rate, the bifurcation point of dislocation patterning corresponds to the turning point in the stress versus strain and DIF versus strain curves. This result along with the critical characteristics of the macroscopic behavior near the bifurcation point is microscopically and macroscopically in agreement with the experimental findings on mono-crystalline pure aluminum at temperatures around 0.5T(m). The present study suggests that measuring the DIF would be a sensitive and useful mechanical means in order to study the critical phenomenon of materials during deformation.

Effect of liquid bridge volume on the instability in small-Prandtl-number half zones

A perturbation method is used to examine the linear instability of thermocapillary convection in a liquid bridge of floating half-zone filled with a small Prandtl number fluid. The influence of liquid bridge volume on critical Marangoni number and flow features is analyzed. The neutral modes show that the instability is mainly caused by the bulk flow that is driven by the nonuniform thermocapillary forces acting on the free surface. The hydrodynamic instability is dominant in the case of small Prandtl number fluid and the first instability mode is a stationary bifurcation. The azimuthal wave number for the most dangerous mode depends on the liquid bridge volume, and is not always two as in the case of a cylindrical liquid bridge with aspect ratio near 0.6. Its value may be equal to unity when the liquid bridge is relatively slender.