A new thermal assembly design for the directional solidification of transparent alloys

A modified design of the thermal assembly is presented for the directional solidification of transparent alloys that eliminates the radial temperature gradient and minimizes the curvature of the interface. An additional booster heater is designed, and the position of the heater is shown to be critical in obtaining a flat interface. A full-scale numerical calculation, carried out for succinonitrile-0.5 wt% Salol, shows that the interface concavity can be reduced gradually by placing the booster heater just above the cold end and by adjusting the temperature of the booster heater while keeping the hot and cold zone temperatures fixed. Experimental measurements of temperatures at the wall and at the center have been carried out systematically by using two calibrated thermocouples, and the observed thermal profiles have been shown to strongly support the numerical prediction. When a macroscopically flat interface is obtained, it is shown that columnar growth away from the ampoule wall can be observed and photographed. The effects of thermal gradient and the temperature setting of the booster heater on the planarity of the interface are discussed.     

Simulation of the cell to plane front transition during directional solidification at high velocity

Using the alloy phase-field method with a frozen temperature approximation, interface morphology and solute segregation patterns during directional solidification are examined near the high velocity (absolute stability) condition for planar growth. The dynamics of the breakdown of initially planar interfaces into cellular structures are shown. At sufficiently high solidification speed, a planar interface is reestablished after breakdown during the initial transient. The cell spacings, depths, tip temperatures, tip radii, and concentration patterns are determined as a function of solidification velocity. The presence of solute trapping is manifest in the variation of the degree of solute partitioning across the interfacial region with interface speed.     

Mono-crystalline growth in directional solidification of silicon with different orientation and splitting of seed crystals

This work presents the results of a systematic study of mono- and poly-crystalline grain growth in directional solidification of silicon using different kinds of seed crystals. The seed orientation was varied between 〈100〉, 〈111〉 and 〈110〉. In some experiments the seeds were split into several seed pieces. The results show that the growth of misoriented grains at the crystal periphery as well as in the gaps between split seeds depends strongly on the crystallographic orientation of the seeds. It is shown that this problem can be minimized if certain seed orientations and combinations are chosen. Generally the 〈100〉 seed orientation turns out to be most difficult with respect to mono-crystalline growth. Heterogeneous nucleation originating from the crucible walls seems to be a minor problem.     

Oscillatory instability and minimum undercooling criterion in directional solidification

We show in this paper that, when small Peclet number effects are taken into account, steady state deep cells which satisfy the minimum undercooling criterion never undergo an oscillatory instability. However, if the stability criterion for the oscillatory mode found in this limit is extended to Peclet number of order unity, deep cells may become unstable if:

a criterion which can be directly tested on the existing experimental data. Here Δ is the tip undercooling, U the interface velocity, K the partition coefficient and v the control parameter, ratio between thermal and diffusive lengths.     

Modeling of directional solidification in 2D and 3D cases

A method of numerical solution of the directional solidification problem for sharp interfaces is developed. The cellular-structure development is analyzed by calculating the concentration fields and consecutive profiles of the solid-liquid interface. The anisotropy of growth rate and surface tension is taken into account. The wavelength ranges in which distortions develop are determined and the dependences of the rate of increase in the distortion amplitude on the wavelength are found. The results obtained for the 2D and 3D cases are compared with the known experimental and calculated data.     

Influence of thermal stabilization on the solute concentration of the melt in directional solidification

Experiments on Al–25 at%Ni peritectic alloy consisting of melting followed by thermal stabilization ranging from 0 to 2 h were carried out in a Bridgman-type furnace. Temperature distribution, microstructure evolution and solute concentration in the mushy zone are characterized. An analytical model is proposed to evaluate the Ni concentration of the melt after thermal stabilization. Effect of temperature gradient and volume fraction of liquid phase in the mushy zone on the Ni concentration of the melt is discussed. The steady state Ni concentration of the melt is inappropriately below the initial Ni concentration of the sample. The deviation increases with decreasing temperature gradient. Finally, the influence of thermal stabilization on the solute concentration of the melt is discussed based on a comparison of Al–Ni peritectic alloys with Al–Ni hyper-eutectic alloys and Al–Cu hypo-eutectic alloys.     

Effects of surface tension anisotropy on interfacial instability in directional solidification

Effects of surface tension anisotropy on the planar interfacial stability are studied with asymptotic analysis method in both the solidification from undercooled pure melts and the unidirectional solidification of binary alloys. The asymptotic approach developed by Xu is adopted to study the interfacial stability here, which is different from that used by other investigators previously in their works. A simple linear analysis result is obtained, i.e., the surface tension anisotropy may compete to determine interfacial stability near some critical conditions in unidirectional solidification of binary alloys. The exsitstence of the surface tension anisotropy enlarges the instability region of disturbed wave number. And the threshold of instability is strongly affected by surface tension anisotropy, especially at high pulling velocity or high temperature gradient. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Grain refinement in the solidification of undercooled Ni–Pd alloys

Two bulk Ni–Pd alloys Ni₇₅Pd₂₅ and Ni_54.8Pd_45.2 have been undercooled beyond their hypercooling limits. As undercooling increases, two grain refinements, occurring at low and high undercooling, respectively, were observed in the solidification of both alloys, even though the equilibrium crystallization temperature range of the latter is only 5 K. Reaching of the hypercooling limit did not change the microstructural morphology abruptly, and dendritic substructure could still be found in the refined grains. Such experimental results cannot be interpreted satisfactorily by the theory that the break-up of dendrites during solidification is dominated by capillary force. It is proposed that the grain refinement at low undercooling results from the remelting associated with chemical superheating, but that at high undercooling is due to the post-solidification recrystallization.     

Structural evolution in the solidification process of Cu–Sn alloys

The liquid structures in the solidification process of the Cu_100−xSn_x (x = 10, 20, 30, 40) alloys were investigated by X-ray diffraction method. The results show that the Cu₃Sn and quasi Cu₃Sn structures exist in the Cu–Sn liquids. Which arouses an obvious structure change indicated by the correlation radius r_c at about 900 °C. In addition, the structure change induced by the liquid–solid transition at about 30–40 °C below the liquidus is also observed.     

Investigations of phase relations and eutectic directional solidification on the NiAl-V join

The NiAl-V join was investigated out to 45 at % vanaduim and the two-phase nature of the alloys formed indicates that a true binary exist with a eutectic at 40 ± 2% vanadium. The eutectic temperature was determined by optical methods to be 1350°C (1360°C was indicated by DTA). Directional solidification of the NiAl-V eutectic composition produced a structure which is lamellar, with interlamellar sapcing of λ = 4.2 μm at a solidification rate R = 1.5 cm/h.     

The effect of gravity modulation on solutal convection during directional solidification

During directional solidification of a binary alloy at constant velocity, thermosolutal convection may occur due to the temperature and solute gradients associated with the solidification process. For vertical growth in an ideal furnace (lacking horizontal gradients) a quiescent state is possible. For a range of processing conditions, the thermal Rayleigh number is sufficiently small that the stabilizing role of the thermal field during growth vertically upwards may be neglected, and only solutal convection need be considered. The effect of a time-periodic vertical gravitational acceleration (or equivalently vibration) on the onset of solutal convection is calculated based on linear stability using Floquet theory. We find that a stable base state can be destabilized due to modulation, while an unstable state can be stabilized. The flow and solute disturbance fields show both synchronous and subharmonic temporal response to the driving sinusoidal modulation.     

Morphological instability due to double diffusive convection in directional solidification: the pit formation

Deep interface depression or “pit formation”, as a result of solute accumulation, due to double-diffusive convection in the directional solidification of succinonitrile (SCN) containing ethanol in an ampoule is investigated by a fully nonlinear numerical simulation. The calculated results are consistent with previous observations (Schaefer and Coriell, Metal. Trans. 15A (1984) 2109), and the instability margin falls between the convective and morphological boundaries at a low growth rate. For a high growth rate, the global interface depression becomes deep due to significant release of the heat of fusion; in this case, the critical concentration can be lower than the convective value. Near the instability margin, the pit forms at the center of the interface and is soon followed by constitutional supercooling. Also, the pit shape is affected significantly by the convective solute transport and thus the flow structures. Such pit formation, results from the nonlinear coupling of double-diffusive convection and the interface deformation, and although differs from the traditional mechanisms, it could be an important route to interface breakdown.     

Capabilities of X-ray topography for studying interfacial instabilities during directional solidification

X-ray topography is very sensitive to segregation inhomogeneities. It is shown that the related contrasts can be used for revealing, over large distances, different features of the instabilities of the growth interface. Additional information can be obtained from orientation contrast. The capabilities of the method are illustrated on In doped GaAs.     

Influence of furnace design on the thermal stress during directional solidification of multicrystalline silicon

Directional solidification is one of the most popular techniques for massive production of multicrystalline silicon (mc-Si). Dislocation is one of the major defects that significantly affect the photovoltaic performance. For the analysis and optimization of stress-induced dislocation, a computational tool has been developed to investigate thermal stress distribution during directional solidification process of multicrystalline silicon. Temperature distribution in the furnace, S/L interface shape and melt flow are simulated. Parametric studies are further conducted to evaluate the effect of furnace design on the interface shape and on the maximum von Mises stress in the growing ingot. To consider the effects of the crucible geometry qualitatively, three-dimensional modeling of the thermal stress is performed with or without the constraint of the crucible. The regions of dislocation multiplication are evaluated by comparing von Mises stress to critical resolved shear stress (CRSS). The results imply that the dislocation in the growing ingot can be reduced by optimizing the design of the directional solidification furnace.     

The influence of crystalline anisotropy on the evolution of the crystallization front during directional solidification

The evolution of the crystallization front of transparent crystals of succinonitrile and pivalic acid in the course of directional solidification in the field of a temperature gradient (Bridgman method) is investigated experimentally. The influence of crystalline anisotropy is examined using single crystals of different orientations. Bulk (cylindrical) and planar single crystals of the materials under investigation are studied and compared for the first time. It is established that the crystallographic direction of growth plays an important role and determines the structure of the crystallization front at different stages of its evolution. New manifestations of the dynamic effects responsible for the development of the nonstationary periodic structure are revealed.     

Phenomenon of the maximum inhomogeneity in solidification of alloys from the peritectic-eutectic phase systems

An application of the Scheil equation with the purpose to: 1 describe the maximum dendritic microsegregation phenomenon, i.e. amount of the solid solution in function of the initial composition of alloys from the Ag Sb phase system, 2 determine the nature of the maximum microsegregation in the Ag–30 Sb and Ag–10 Sb alloys is presented. A new relation, supplementary to the Scheil equation is proposed.     

Efficient adaptive phase field simulation of directional solidification of a binary alloy

Efficient adaptive phase field simulation based on a finite volume method is carried out to study the morphological development during directional solidification of a nickel/copper alloy. The adaptive nature of the method allows the calculation to cover different length scales for the interface, solute diffusion, and heat conduction. With the frozen temperature approximation, our calculated results are in reasonable agreement with previous ones (J. Crystal Growth 200 (1999) 583). However, the use of a much larger domain allows us to perform simulation at low speed near the onset of constitutional supercooling, where both solutal boundary layer and cell wavelength are large. For the same domain size, the calculated results without using the frozen temperature approximation remain about the same, even though the release of latent heat lowers the steady interface position and the thermal gradient in the melt side.     

Structural properties and evolution in the solidification process of Cu–Ag alloys

The atomic structures of liquid Cu–Ag alloys (Cu₈₀Ag₂₀, Cu₆₀Ag₄₀, Cu₄₀Ag₆₀ and Cu₂₀Ag₈₀) have been investigated in the solidification process by means of X-ray diffraction. The results show that the liquid structures of Cu–Ag alloys, which are micro-homogeneous and similar with their solid state, display quite stable changes on a large-scale range indicated by the correlation radius r_c, although the short-range order structures change obviously around their liquidus (liquid–solid transformation). This is different from the results of the In₃₀Sn₇₀ alloy we previously reported, which shows an abrupt structure changes around its liquidus. In addition, the Gaussian peaks decomposition of the radial distribution functions (RDF(r)) was also performed to shed light on the element distribution and structure evolution in the whole solidification process especially around the liquidus.     

An enhanced cooling design in directional solidification for high quality multi-crystalline solar silicon

An enhanced cooling design for nucleation was proposed for directional solidification based on the enhanced heat transfer through gas flow, and the effects of initial cooling conditions during directional solidification on the quality of multi-crystalline silicon for solar cells were studied. The properties of the grown grains under different initial cooling conditions were measured. The grain size, grain orientations, and the percentage of twin boundaries, as well as minority lifetime and defect density, were affected significantly by the initial cooling. The implementation of this design to a commercial furnace was also discussed, and promising results were obtained.     

Growth defects in a PZNT93/7 crystal prepared by directional solidification

Novel relaxor ferroelectric crystal 0.93Pb(Zn_1/3Nb_2/3)O₃‐0.07PbTiO₃ (PZNT93/7) with dimensions about Ø40× 70 mm³ was obtained by directional solidification technique. The growth defects of the crystal were investigated. Rocking curve analysis revealed the crystalline quality of PZNT93/7 crystal was not perfect and the FWHM value was measured to be about 0.7°. Some pits and oxide particles in micro‐size were formed in the crystal due to the growth conditions. A series of growth steps parallel to (001) face were observed which were attributed to the growth behavior. Moreover, it was found the average chemical composition of the crystal was deviated slightly to the stoichiometric value of PZNT93/7. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)