C.W. Lan

Heat transfer, fluid flow and interface shapes in floating-zone crystal growth

Abstract Computer simulation was carried out to study heat transfer and fluid flow in the melt zone in floating-zone crystal growth. A high Prandtl-number material, i.e., NaNO 3 , and a low Prandtl-number material, i.e., Si, were considered. The unknown shapes of the melt/gas, melt/crystal and melt/feed interfaces were calculated for each of the following three cases: (1) conduction, (2) natural convection and (3) thermocapillary and natural convections. The effects of the growth rate, gravity and feed/crystal diameter ratio were demonstrated. It was observed that in both NaNO 3 and Si thermocapillary convection dominates over natural convection, at least for the conditions examined in the present study. This thermocapillary convection tends to reduce the stability of the melt zone, increase the convexity of the melt/crystal interface and reduce the maximum surface temperature. The effect of thermocapillary convection is significantly more pronounced in NaNO 3 than in Si, even though thermocapillary convection in Si is far stronger. The dynamic effect of convection on the shape of the melt/gas interface is very small.

Optical and microhardness studies of KDP crystals grown from aqueous solutions with organic additives

Non-linear optical (NLO) materials have acquired new significance with the advent of a large number of devices utilising solid-state laser sources. From this technological point of view, potassium dihydrogen phosphate (KDP) having superior non-linear optical properties has been exploited for variety of applications. KDP crystals were grown from aqueous solutions added with organic additives by the slow cooling method for obtaining better non-linear properties. The influence of the organic additives on the optical and mechanical properties has been studied. It has been observed that the addition of organic additives improves the mechanical strength of the crystal. It is also observed that the addition of organic additives improves the optical transmission percentage of the crystal.

Adaptive phase field simulation of non-isothermal free dendritic growth of a binary alloy

Efficient adaptive phase field simulation is carried out for a free dendritic growth in a nickel/copper system. The adaptive nature of the present scheme allows the simulation to be performed in an extremely large domain for thermal boundary layer, while keeping fine mesh for the diffusive interface. For isothermal cases, our calculated results agree reasonably well with those of Warren and Boettinger [Acta. Metall. Mater. 43 (1995) 689]. For non-isothermal growth, our results also agree well with those by Loginova et al. [Acta. Mater. Mater. 49 (2001) 573] for using a small domain. However, the domain size used in the previous calculations was too small for heat conduction, so that the calculated results are domain dependent and the dendrite could not grow freely. By choosing an extremely large domain, we have obtained a truly free growth simulation for the first time for a non-isothermal dendrite. The effect of supercooling is also illustrated and discussed.

Effects of rotation on heat transfer, fluid flow and interfaces in normal gravity floating-zone crystal growth

Abstract Computer simulation was conducted to study heat transfer and fluid flow in normal gravity floating-zone crystal growth of NaNO 3 with: (1) fast feed/crystal counterrotation and (2) fast single rotation of the feed or crystal. Natural convection, thermocapillary convection and forced convection were considered. The shapes of the melt/gas, melt/crystal and melt/feed interfaces were calculated and compared with those observed during crystal growth. The effects of key operating parameters were discussed, including the mode and speed of rotation, growth rate, heat input and growth direction.

Studies on the growth and characterization of p-hydroxyacetophenone single crystals

Good-quality single crystals of organic p-hydroxyacetophenone have been grown by slow evaporation solution growth technique at 37°C using methanol as solvent. The grown crystals have been characterized by Raman studies, FT-IR, X-ray powder diffraction and thermal analyses. The mechanical properties of the grown crystals have been studied using Vickers micro-hardness tester.

Three-dimensional convection and solute segregation in vertical Bridgman crystal growth

Abstract Perfect axisymmetry is difficult to achieve in the vertical Bridgman crystal growth. Nonaxisymmetry is, to a certain degree, always present in a real crystal growth configuration. To study how fluid flow and solute fields in the process are affected by slight deviations from axisymmetry, a three-dimensional finite-volume/Newton method is developed. Pseudosteady-state heat and mass transfer, fluid flow, and the growth front are solved simultaneously. The calculated results for axisymmetric cases are compared with those by two-dimensional finite volume and finite element methods, and they are in excellent agreement. Calculated results also show that three-dimensional flow and solute fields are easily induced by imperfect axisymmetry. A slightly tilted ampoule or a small temperature gradient in the azimuthal direction could break axisymmetry and dramatically affect flow patterns and solute segregation.

Thermocapillary flow and melt/solid interfaces in floating-zone crystal growth under microgravity

Abstract Computer simulation of steady-state axisymmetrical heat transfer and fluid flow was conducted to study thermocapillary flow and melt/solid interfaces in floating-zone crystal growth under microgravity. The effects of key variables on the extent of thermocapillary flow in the melt zone, the shapes of the melt/solid interfaces and the length of the melt zone were discussed. These variables are: (1) the temperature coefficient of surface tension (or the Marangoni number), (2) the pulling speed (or the Peclet number), (3) the feed rod radius, (4) the ambient temperature distribution, (5) the heat transfer coefficient (or the Biot number), and (6) the thermal diffusivity of the material (or the Prandtl number).

A finite volume method for solute segregation in directional solidification and comparison with a finite element method

Abstract A finite volume method is presented for the calculation of solute transport in directional solidification. Gallium and silicon doped germanium growth in the vertical Bridgman process are used as examples. The method is based on the stream function/vorticity formulation of the Navier-Stokes equation, energy and mass equations, and their associated boundary conditions in generalized curvilinear coordinates. Fluid flow, heat and mass transfer and the growth interface are solved simultaneously by Newtons method with a nearly quadratic convergence. A consistent implementation of solute boundary conditions, which is crucial to the global conservation of solute, is used. Calculated results are compared with those obtained from the Galerkin finite element method for various process conditions, and they are in excellent agreement. With the present approach, the global conservation of solute is preserved, even with a coarse mesh, and is not affected by meshes and convection. However, fine meshes are required for the finite element method to achieve an acceptable global accuracy for the cases with stronger convection. Multiple steady states of double-diffusive convection and constitutional supercooling in the non-dilute solution are also illustrated.

Effects of ampoule rotation on vertical zone-melting crystal growth : steady rotation versus accelerated crucible rotation technique (ACRT)

Computer simulation is performed to illustrate the significance of ampoule rotation on the flows, interface shapes, and the growth rate in vertical zone-melting (VZM) crystal growth. For the growth of a 2 cm GaAs crystal in a quartz ampoule, simulation results show that even low-speed ampoule rotation can significantly affect the flows and further the growth interface. The concave growth front due to buoyancy convection can be inverted easily to a convex one by steady ampoule rotation. The accelerated crucible rotation technique (ACRT) also has a similar effect on the growth interface, but less effective. In addition, severe periodic growth and remelting is induced by ACRT, and it is enhanced significantly by natural convection.

Effects of internal radiation on heat flow and facet formation in Bridgman growth of YAG crystals

Internal radiation, in the crystal and the melt, is investigated using the P1-approximation for the Bridgman growth of YAG crystals. Its effects on the interface shape and facet formation are illustrated through three-dimensional simulation. The P1-approximation is first validated by a one-dimensional solution. Further comparison for axisymmetric cases with the rigorous calculations by Brandon and Derby [J. Crystal Growth 121 (1992) 473] is performed for opaque melt, and reasonable agreement is obtained for optical distance being <1 cm. The no-slip Rosseland model also gives a reasonable prediction in the interface shape; however, interface position and facet size are over predicted due to the poor approximation in the thermal gradients at the interface. Furthermore, melt transparency introduces radiation heating from the hot zone to the interface. Accordingly, the interface concavity is reduced with the increasing optical distance of the melt.