Theory of transport in liquid metals

Protopapas, Pavlos; Parlee, N. A. D.

doi:10.1016/0301-0104(75)80052-8

Cited by 20 publications

(17 citation statements)

References 22 publications

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“…In this paper the adaptation was accomplished by using the correction function of Protopapas and Parlee [18] which is given in terms of the packing fraction η. The classical hard sphere expressions for g ij (σ ij ) was corrected with the factor (2 − η)/((1 − η)(2 + η)).…”

Section: Resultsmentioning

confidence: 99%

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The viscosity of liquid alloys

Terzieff

2008

Journal of Alloys and Compounds

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Section: Resultsmentioning

confidence: 99%

“…(2) The formalism of Djemili et al [13] based on the vicosity model of Takeuchi and Iida [14] and the thermodynamic approach of Hicter et al [15]. (3) The rigid-sphere approach of Enskog [16] and Tham and Gubbins [17] as has been represented by Protopapas and Parlee [18].…”

Section: Resultsmentioning

confidence: 99%

The viscosity of liquid alloys

Terzieff

2008

Journal of Alloys and Compounds

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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: 98%

“…where D li is the diffusion coefficient of impurity i; j B is the Boltzmann constant; T is temperature; l is the viscosity of liquid Si (measured by Kimura and Terashima [61] ); and r i is a suitable atomic radius of the impurity atom, assumed equal to either the Goldschmidt radius [62] or the effective hard-sphere radius proposed by Protopapas and Parlee, [63] as suggested by Chauhan et al [64] The calculated values are given in Table A1, indicating that the Sutherland-Einstein equation (Eq. [A1]) using the Goldshmidt atomic radius gives the smallest average relative error (57 pct) in relation to Garandet's values.…”

Section: Appendixmentioning

confidence: 99%

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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“…The computed are in (Star). z=1.56 Exp Bruson [20] Exp Henderson [21] Simu Protopapas [22] Simu Pasternak [23] Self-diffusion coefficient of copper (a)…”

Section: Resultsmentioning

confidence: 99%

Diffusion coefficient of copper, tin and copper tin alloy

Mouas

Gasser

Slimane

et al. 2011

EPJ Web of Conferences

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Abstract. Pseudopotential formalism is used to construct an ionic effective potential (ion-ion potential screened by electrons). Molecular Dynamics is used in conjunction with the constructed effective potential to get the atomic structure factor of the pure components copper and tin which are compared to the experimental ones. We selected the Shaw Optimized Model Potential having proved that it adequately describes the atomic structure, we used it to calculate the velocity autocorrelation function and to deduce the self diffusion of pure metals: copper, tin and the diffusion coefficient of copper in the Sn 95,6% Cu 4,4% .

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Theory of transport in liquid metals

Cited by 20 publications

References 22 publications

The viscosity of liquid alloys

The viscosity of liquid alloys

Macrosegregation of Impurities in Directionally Solidified Silicon

Diffusion coefficient of copper, tin and copper tin alloy

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