Radial segregation induced by natural convection and melt/solid interface shape in vertical bridgman growth

Chang, Chao‐Kai; Brown, Robert A.

doi:10.1016/0022-0248(83)90225-7

Cited by 229 publications

(60 citation statements)

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“…With [17]. As already discussed in [21], the calculations show that, for sufficiently low driving forces, relation (5b) applies with Gr defined from the radius of the sample and the maximum radial temperature difference and K N 30.…”

mentioning

confidence: 71%

“…A number of results have already been obtained by this way [13][14][15][16][17][18]. However, as more and more complex problems are considered, some specific limitations of a purely numerical analysis appear.…”

mentioning

confidence: 99%

“…The solutions of (17), (29) and (30) Finally, the present paper shows that scaling analysis can be usefully associated to experimental, analytical and numerical work in the study of convective phenomena in crystal growth.…”

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confidence: 99%

“…Chang and Brown [17] Witt [19] and Favier [22,32] where L is the melt depth (which for the sake of simplicity is presently considered equal to the crystal radius : L H), and u(xf) is given by (17).…”

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confidence: 99%

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Scaling analysis of convective solute transport and segregation in Bridgman crystal growth from the doped melt

Camel

Favier

1986

J. Phys. France

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Scaling analysis of convective solute transport and segregation in Bridgman crystal growth from the doped melt

Camel

Favier

1986

J. Phys. France

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“…There are many papers dealing with the Bridgman problem itself (see Brown, 1988 for references). Nonetheless, the first set of fully consistent calculations that account for convection in the fluid, and its coupling with thermo-solutal field, heat diffusion in the solid and a non-planar interface appear to be due to Chang & Brown 16 and Adornato & Brown"'. By assuming a quasi-steady growth when the transient scale is small, they calculate the nonlinear steady states numerically.…”

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confidence: 99%

Convection effects on radial segregation and crystal–melt interface in vertical Bridgman growth

Tanveer

1994

Physics of Fluids

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The influence of convection caused by horizontal heat transfer through the sides of a vertical Bridgman apparatus is studied analytically. The case when the heat transfer across the side walls is small is considered, so that the resulting interfacial deformation and fluid velocities are also small. This allows one to linearize the Navier–Stokes equations and express the interfacial conditions about a planar interface through a Taylor expansion. Using a no-tangential stress condition on the side walls, asymptotic expressions for both the interfacial slope and radial segregation at the crystal–melt interface are obtained in closed form in the limit of large thermal Rayleigh number. It is suggested that these can be reduced by appropriately controlling a specific heat transfer property at the edge of the insulation zone on the solid side.

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Chemical Segregation in Vertical Bridgman Growth of GaInSb Alloys

Barat

Duffar

Dussere

et al. 1999

Cryst. Res. Technol.

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Cryst. Res. Technol. 34 1999 4 449-456 A set of experiments on the solidification of Ga 1-x In x Sb alloys with a large variation of the sample diameter (from 1mm to 10mm), of the growth rate (from 0.7 to 7 µm/s) and of the concentration (from x=0.01 to x= 0.1) is described. The associated radial and longitudinal segregation of the In have been analysed by SIMS or electron microprobe. Numerical simulation of the experiments, taking into account thermal, hydrodynamic and chemical behaviour has been carried out with the help of FIDAP. It is shown from these numerical results that a plateau of concentration can be reached even if a convective loop is present close to the interface, provided that the convection does not extend into the bulk of the liquid. This is in full agreement with the experimental results obtained. Supporting this analysis, in some experiments, a defect in term of verticality of the crucible led to complex 3-D convection involving the whole liquid, and in that case no plateau was obtained.For the radial segregation ∆C R , three regimes of transport are found, characterised by the convective level:-A diffusive one, with a low, constant, ∆C R related to the interface curvature.-A quasi-diffusive one (weak convection) in which ∆C R increases with convection. -A convective one in which it decreases. Measured radial segregations are in good agreement with predictions from the numerical simulations.

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Radial segregation induced by natural convection and melt/solid interface shape in vertical bridgman growth

Cited by 229 publications

References 35 publications

Scaling analysis of convective solute transport and segregation in Bridgman crystal growth from the doped melt

Scaling analysis of convective solute transport and segregation in Bridgman crystal growth from the doped melt

Convection effects on radial segregation and crystal–melt interface in vertical Bridgman growth

Chemical Segregation in Vertical Bridgman Growth of GaInSb Alloys

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