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Pattern Selection in the Eutectic Growth - Thermodynamic Interpretation

Wołczyński W.

Archives of Metallurgy and Materials

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2020

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Vol. 65, iss. 2

653--666

EN

The (Zn) – single crystal strengthened by the E = (Zn) + Zn16 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 Zn16 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 reappear 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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Thermodynamic pattern selection in the stripes generated periodically during the (Zn) - single crystal growth

Wołczyński W.

Archives of Metallurgy and Materials

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2013

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Vol. 58, iss. 2

309--313

EN

The (Zn) - hexagonal single crystal growth was performed by the Bridgman system. Some eutectic stripes were generated periodically in the single crystal. The stripes consisted of the strengthening inter-metallic compound, Zn16Ti and (Zn) - solid solution. Two morphology transitions were recorded. At the first threshold growth rate, L-shape irregular rods transformed into regular lamellar structure. The transition was accompanied by the irregular into regular morphology alteration. The regular lamella into regular rods transition occurred at the second threshold growth rate. The new, proposed thermodynamic pattern selection criterion (PSC) of the lower minimum entropy production was applied to describe the structural transitions. The solid/liquid interface perturbation of the (Zn) - phase was referred to the marginal stability.

PL

Heksagonalny monokryształ roztworu stałego (Zn) został wyprodukowany w układzie Bridgmana. Prążki eutektyczne zostały wygenerowane periodycznie w monokrysztale. Prążki składały się z umacniającego związku międzymetalicznego Zn16Ti oraz roztworu stałego (Zn). Zarejestrowano dwa przejścia morfologiczne. Przy pierwszej prędkości progowej nieregularne włókna o przekroju L doznały transformacji w regularne płytki. Temu przejściu towarzyszyła przemiana morfologii nieregularnej w regularna. Regularne płytki dokonały transformacji w regularne włókna przy drugiej prędkości progowej. Niższe minimum produkcji entropii to proponowane, nowe kryterium termodynamiczne dla selekcji struktur, jakie zastosowano by opisać przejścia strukturalne. Perturbacja frontu krystalizacji fazy (Zn) została odniesiona do stanu stabilności marginalnej.

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Pattern selection within the stripes strengthening the hexagonal (Zn)-single crystal

Wołczyński W., Boczkal G.

Inżynieria Materiałowa

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2012

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Vol. 33, nr 5

349--352

EN

A new thermodynamic criterion according to which this structure is formed which evinces lower situated minimum entropy production has been successfully applied. Calculation of the entropy production has required, however, to introduce the anisotropy of the specific surface free energy (surface tension). Therefore, a model of changes of the specific surface free energy with the rotating crystallographic orientation has been applied. However, the model takes directly into account some changes of the specific surface free energy versus varying growth rates, only. It has been shown that the crystallographic orientation varying with growth rates results in the rotation of the mechanical equilibrium observed at the triple point of the solid/liquid interface. Additionally, an oscillation between stationary state and marginal stability justifies thermodynamically the structural oscillation between regular structure formation and irregular eutectic structure formation.

PL

Z powodzeniem zastosowano nowe termodynamiczne kryterium, zgodnie z którym ta struktura jest formowana, która przejawia niżej usytuowane minimum produkcji entropii. Obliczenia produkcji entropii wymagały uwzględnienia anizotropii napięcia międzyfazowego na granicy faza stała /faza ciekła. Zaproponowano zatem model zmian napięcia międzyfazowego w funkcji zmieniającej się orientacji krystalograficznej. Jednakże model bezpośrednio uwzględnia jedynie zmiany napięcia międzyfazowego w funkcji zmieniającej się prędkości krystalizacji. Pokazano, że orientacja krystalograficzna zmieniająca się wraz ze zmianami prędkości krystalizacji skutkuje rotacją równowagi mechanicznej obserwowanej w potrójnym punkcie frontu krystalizacji. Oscylacją między stanem stacjonarnym a stabilnym marginalnie uzasadniono termodynamicznie oscylacje strukturalne między formowaniem eutektycznej struktury regularnej i eutektycznej struktury nieregularnej.

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Eutectic solidification as explained by the thermodynamics of irreversible processes

Wołczyński W., Guzik E.

Archives of Foundry Engineering

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2009

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Vol. 9, iss. 1

113-116

EN

The grain size diameter is the main parameter characterizing a given metallic alloy. In the case of Al-Si or Fe-C eutectic alloy the average inter-lamellar spacing is a good parameter which seems to be adequate to describe this irregular structure. To define the average inter-lamellar spacing the regular areas within generally irregular structure has been distinguished. It has been postulated that the formation of regular structure could be related to the minimum entropy production criterion. From the other side the maximum destabilization of the non-faceted phase interface could be referred to marginal stability. The criterion of minimum entropy production allows to formulate the growth law for regular lamellar structure solidifying under stationary state. It defines the regular eutectic spacing versus growth rate. The marginal stability concept allows to define the maximum wavelength which can be developed at the solid / liquid interface of non-faceted (Al) phase. It defines the maximum spacing within irregular structure taking into account the wavelength of instability (marginal stability) created at the non-faceted phase interface. An average inter-lamellar spacing results from the relationship formulated on the basis of both spacings. It should be emphasized that both conditions (criteria) are deduced from the thermodynamics of irreversible processes. The simplified scheme of irregular structure incorporates, additionally the intermediate lamella of faceted phase that is also taken into account in the definition of average inter-lamellar spacing, [...] . The intermediate morphology existing between two distinguished distances is treated as being under oscillation between stationary state and marginal stability. The state of marginal stability is defined by a vanishing excess entropy production. Therefore, it is suggested that the structural oscillation takes place between an attractor and point of bifurcation in the system.