Estimation of molecular and thermodiffusion coefficients for non‐ideal molten metal alloys and its implication in solidification process

Abstract

In this paper an expression is proposed for the estimation of thermodiffusion factor in liquid metal alloys. The expression can be readily used given that it requires properties that could be easily obtained from the physical properties of the mixture constituents, such as viscosity and molar volume. The predictive power of the proposed expression, as well as other pertinent models is examined against the experimental data. The estimated thermodiffusion factor is then used to study thermo‐solutal convection in an enclosure filled with molten Sn–Bi alloy by solving the transport equations numerically. Two simulations were carried out in a vertical rectangular cell encapsulated by a quartz container: top heating and bottom heating. The sidewalls in both cases were exposed to the external natural convection and surface radiation to the ambient. Numerical results show that in the top heating case, the distribution of temperature and concentration are linear, but species segregation occurs due to the thermodiffusion effect. In the bottom heating case, boundary‐driven convective flow develops with a large Rayleigh number (Ra) where an increase in the Ra number negates the thermodiffusion effect due to the development of strong mixing.

Numerical investigation of heat transfer and solidification in a cavity filled with molten metal alloys in the presence of thermodiffusion

“…Bearing in mind that for thermodiffusion, for a coupled heat and mass transfer phenomenon to be present the phenomenological coefficients L ik are non-zero, and one may show that the summation of all terms in the square brackets in Eq. 2.2 is zero [25]. This operation produces two equations relating and .…”

“…Those equations, combined with Eq. 2.1 and the Gibbs-Duhem relationship (∑ = 0) at constant pressure and temperature, results in the thermodiffusion factor of the first component in terms of the net heat of transport [25]:…”

“…2.14, when the natural logarithm of the relative concentration of solute is plotted against 1/RT, an almost linear curve is obtained through a temperature range. The slope of that line has been studied as the net heat of transport [25].…”

On the effect of thermodiffusion on solute segregation during the growth of semiconductor materials by the vertical Bridgman method

“…The prediction power of the proposed expression along with some other existing thermodiffusion models for liquid mixtures (such as the Haase, Kempers, Drickamer and Firoozabadi formulas) were finally examined against available experimental data obtained on ground or in microgravity environment. These models were refined and compared with other available data by Eslamian and Saghir [52] and Jafar Salehi et al [53]. Most recently, the relevance of these phenomena to semiconductor processing has been reemphasized by Eslamian and Saghir [54], who have reviewed advances and patents that employ thermodiffusion to fabricate semiconductor, micro-electromechanical systems (MEMS), nanoelectromechanical systems (NEMS), micro and nano thin films.…”

In situ Measurement of Thermodiffusion in Liquid Alloys

“…However, reliable predictive theories for liquid alloys are still lacking. Recently, improved models were proposed [19], but experimental values needed to validate these models are scarce.…”