Entropy production in steady‐state eutectic growth

Wołczyński, W.

doi:10.1002/crat.2170240203

Cited by 9 publications

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References 23 publications

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“…The fulfilment of the above conditions, Eq. ( 17) has already been confirmed, [23]. On the other hand, the thermodynamics of irreversible processes provides the general criterion which is substantiated mathematically (the Liouville's theorem) for the stationary process itself: ∂P/∂X C |X T = 0.…”

Section: Discussionmentioning

confidence: 88%

Archives of Metallurgy and Materials

Wołczyński¹

2020

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The (Zn) -single crystal strengthened by the E = (Zn) + Zn 16 Ti eutectic precipitate is subjected to directional growth by the Bridgman's system and current analysis. Experimentally, the strengthening layers (stripes) are generated periodically in the (Zn) -single crystal as a result of the cyclical course of precipitation which accompanies the directional solidification. These layers evince diversified eutectic morphologies like irregular rods, regular lamellae, and regular rods. The L -shape rods of the Zn 16 Ti -intermetallic compound appear within the first range of the growth rates when the irregular eutectic structure is formed. Next, the branched rods transform into regular rods and subsequently the regular rods into regular lamellae transitions can be recorded. The regular lamellae exist only within a certain range of growth rates. Finally, the regular rods re-appear at some elevated growth rates.A new solution to the diffusion equation is provided to describe the micro-field of the solute concentration in the liquid adjacent to the front of the growing eutectic structure. The solution is based on the mass balance in the considered system. Moreover, the existence of the protrusion of the leading eutectic phase over the wetting one is required by the mass balance. The appearance of the d -protrusion in the growing eutectic is well confirmed by the experimental observations of the frozen solid/liquid interface. The mentioned solution satisfies the concept of the eutectic coupled growth according to which undercooling of the leading phase is less than undercooling of the wetting eutectic phase. Also, the Ti -solute micro-segregation / redistribution is analyzed within the matrix of the single crystal. The micro-segregation is described as a result of the solution to the adequate, newly developed differential equation. The definition for the solute redistribution is given by the subsequently / separately formulated relationship. This definition takes into account both extent -, and intensity of the solute redistribution.Finally, the entropy production is calculated for the regular lamellae -, and for the regular rods formation, respectively. The entropy production is a function of some parameters which define the eutectic phase diagram, coefficient of the diffusion in the liquid, and some capillary parameters connected with the mechanical equilibrium located at the triple point of the solid/liquid interface. Branches formation is related to the marginal stability. A new criterion is formulated and subjected to successful verification. It is: in the structural -thermodynamic competition the winner is this kind of the pattern for which minimum entropy production has a lower value

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Section: Discussionmentioning

confidence: 88%

Archives of Metallurgy and Materials

Wołczyński¹

2020

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Contribution to the determination of the entropy production for steady state eutectic growth

Wołczyński

1989

Cryst. Res. Technol.

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I n order to find a generalized entropy production for steady-state eutectic growth the entropy production per unit time and volume is to be determined. A relationship which expresscs tho entropy production per unit time and volume as a function of KRUPKOWSKI'S equations is shown. It is in a qualitative accuracy with LESOULT-TURPIN'S theory. The above quantity is to be integrated over a distinguished volume of the unidirectionally solidified euteetio structure. A correlation between this volume and entropy production is discussed.

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Lamellar eutectic growth at minimum entropy production

Wołczyński

1989

Cryst. Res. Technol.

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A mode of determination of entropy production per unit time for regular eutectic growth is presented. I n order to integrate this thermodynamic quantity, both diffusion equation and coefficient of the interplay between curvature of an interface and concentration field are taken into account. The adaptation of the criterion of minimum entropy production allowed to show the equation (growth law) describing the lamellar structure formation under imposed temperature gradient and given growth rate for an alloy under investigation.

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Entropy production in steady‐state eutectic growth

Cited by 9 publications

References 23 publications

Archives of Metallurgy and Materials

Archives of Metallurgy and Materials

Contribution to the determination of the entropy production for steady state eutectic growth

Lamellar eutectic growth at minimum entropy production

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