A predictive equation for solute diffusivity in liquid metals

Liu, Yong; Long, Zhengyi; Wang, Haibing; Du, Yong; Huang, Baiyun

doi:10.1016/j.scriptamat.2006.04.019

Cited by 36 publications

(15 citation statements)

References 10 publications

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“…) in Liquid Si in m 2 s -1 . Experimental values given by Garandet [48] and those calculated with the models by Liu et al, [59] and by Sutherland-Einstein with the atomic radius suggested by either Goldshmidt [62] (S-E-G) or Protopapas and Parlee [63] (S-E-PP) are shown…”

Section: Appendixmentioning

confidence: 87%

“…The diffusion coefficients for most of the impurities important to the current work were not given by these authors. Therefore, they were calculated at the melting point of Si (1687 K [1414°C]) by two models: an adaptation proposed by Liu et al [59] of Cahoon's model, [60] which is based on the ''hole'' theory, and the Sutherland-Einstein equation [57] , given below, derived from the hydrodynamic theory:…”

Section: Appendixmentioning

confidence: 99%

“…[48] This error is within the usual order of magnitude of measurement errors for diffusion coefficients in liquid metals. [48,59] Consequently, the Sutherland-Einstein equation with the Goldshmidt atomic radius [62] was adopted to calculate the diffusion coefficient of Fe, Cu, Ti, V, Mn, Cr, Ni, and Zr in liquid Si (Table A1). For Al, B, P, and As, the values given by Garandet [48] were adopted.…”

Section: Appendixmentioning

confidence: 99%

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Macrosegregation of Impurities in Directionally Solidified Silicon

Martorano

Neto

Oliveira

et al. 2010

Metall Mater Trans A

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Directional solidification of molten metallurgical-grade Si was carried out in a vertical Bridgman furnace. The effects of changing the mold velocity from 5 to 110 lm seconds -1 on the macrosegregation of impurities during solidification were investigated. The macrostructures of the cylindrical Si ingots obtained in the experiments consist mostly of columnar grains parallel to the ingot axis. Because neither cells nor dendrites can be observed on ingot samples, the absence of precipitated particles and the fulfillment of the constitutional supercooling criterion suggest a planar solid-liquid interface for mold velocities £10 lm seconds -1 . Concentration profiles of several impurities were measured along the ingots, showing that their bottom and middle are purer than the metallurgical Si from which they solidified. At the ingot top, however, impurities accumulated, indicating the typical normal macrosegregation. When the mold velocity decreases, the macrosegregation and ingot purity increase, changing abruptly for a velocity variation from 20 to 10 lm seconds -1 . A mathematical model of solute transport during solidification shows that, for mold velocities ‡20 lm seconds -1 , macrosegregation is caused mainly by diffusion in a stagnant liquid layer assumed at the solid-liquid interface, whereas for lower velocities, macrosegregation increases as a result of more intense convective solute transport.

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Section: Appendixmentioning

confidence: 87%

Section: Appendixmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

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Macrosegregation of Impurities in Directionally Solidified Silicon

Martorano

Neto

Oliveira

et al. 2010

Metall Mater Trans A

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“…The range of applications shows the versatility of this simple approach. The diffusivities calculated using the Eq 12 derivated in the present manuscript; D E : The diffusivities predicted by Enskog Expression [17] ; D H : The diffusivities predicted by Liu's [30] method; D F : The diffusivities predicted by fluid theory [20] ; D(Exp …”

Section: Discussionmentioning

confidence: 95%

“…The diffusivities calculated by the new equation obtained in the present work were compared with the predictions of three available predictive methods: Enskog Expression, [17] Liu et al [30] and the fluid theory [20] over extended ranges of temperature. These methods have been reported in the corresponding references, and will not be detailed here.…”

Section: Derivation Of the New Equationmentioning

confidence: 99%

A New Equation for Temperature Dependent Solute Impurity Diffusivity in Liquid Metals

Yang

Wang

et al. 2010

J. Phase Equilib. Diffus.

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An equation to predict the temperature dependence of solute impurity diffusivity in liquid metals has been derived by combining the Sutherland-Einstein formula with Kaptay's unified equation on the dynamic viscosity of liquid metals. It has been demonstrated that consideration of the temperature dependence of the atomic radius of the diffusing species results in better agreement of the predicted diffusivities with the experimental data compared to when the temperature independent Goldschmidt atomic radius is used. Due to the simple-parameter nature of the equation, it could be very useful in predicting the solute impurity diffusivity in liquid metal when experimental data are scarce.

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