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1

Pattern Selection in the Frame of Thermodynamic Similarity between Eutectics: Cu-Cu2O and (Zn)-Zn16Ti – Experiment

Wołczyński W.

Archives of Metallurgy and Materials

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2018

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Vol. 63, iss. 3

1555--1564

EN

Coagulation and solidification of the copper droplets suspend in the liquid slag are usually accompanied by the appearance of the Cu-Cu2 O eutectic. Locally, this eutectic is created in the stationary state. Therefore, frequently it has a directional morphology. Since the E = (Zn) + Zn16 Ti – eutectic is similar in the asymmetry of the phase diagram to the Cu-Cu2 O – eutectic, the (Zn) single crystal strengthened by the E = (Zn) + Zn16 Ti 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 re-appear at some elevated growth rates. The entropy production per unit time and unit volume is calculated for the regular eutectic growth. It will allow to formulate the entropy production per unit time for both eutectic structure: rod-like and lamellar one.

2

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.

3

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.

4

The criterion of minimum entropy production in eutectic growth

Trepczyńska-Łent M.

Archives of Foundry Engineering

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2012

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Vol. 12, iss. 2

85-88

EN

The paper presents adaptation problem of lamellar/rod growth of eutectic. The transformation of eutectic microstructure was investigated systematically. A interpretation of the eutectic growth with theory minimum entropy production was presented.

5

Control of the structural parameters in the (Zn) - Zn16Ti single crystal growth

Wołczyński W., Boczkal G., Musielak P., Sibiga G., Mikułowski B.

Archives of Foundry Engineering

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2011

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Vol. 11, iss. 4

149-156

EN

The (Zn) - single crystal was obtained by means of the Bridgman system. Several growth rates were applied during the experiment. The graphite crucible was used in order to perform the solidification process. The unidirectional solidification occurred with the presence of the moving temperature field. The thermal gradient was positive so that the constrained growth of the single crystal was ensured. The (Zn) single crystal was doped with small addition of titanium and copper. The titanium formed an intermetallic compound Zn16-Ti. The copper was solved in the solid solution (Zn). The precipitates of (Zn) and Zn16-Ti formed a stripes localized cyclically along the single crystal length. The intermetallic compound Zn16-Ti strengthened the (Zn) single crystal. The structural transitions were observed in the stripes with the increasing solidification rate. Within the first range of the solidification rates ( 0 -v1) the irregular L-shape rod-like intermetallic compound was revealed. At the 1 v - threshold growth rate branches disappear continuously till the growth rate equal to [...]. At the same range of growth rates the regular lamellar eutectic structure (Zn) - Zn16-Ti appeared continuously and it existed exclusively till the second threshold growth rate equal to v2 . Above the second threshold growth rate the regular rod-like eutectic structure was formed, only. The general theory for the stationary eutectic solidification was developed. According to this theory the eutectic structure localized within the stripes is formed under stationary state. Therefore, the criterion of the minimum entropy production defines well the stationary solidification. The entropy production was calculated for the regular rod-like eutectic structure formation and for the regular lamellar eutectic structure formation. It was postulated that the observed structure are subjected to the competition. That is why the structural transition were observed at the revealed threshold growth rates. Moreover, it was postulated that this structure is winner in the competition which manifests a lower minimum entropy production within a studied range of growth rates. Exceptionally, the phenomenon of branching was formed under the marginal stability. Therefore, the spacing of the regular structure selected by the criterion of minimum entropy production depends on the growth rate only. In the case of the irregular eutectic structure the average spacing depends on both growth rate and thermal gradient. The irregular eutectic structure localized within the stripes contains some areas with regular rods and some areas with maximum destabilization of solid / liquid interface of the (Zn) - non-faceted phase. The length of the destabilized non-faceted phase is treated as equal to the wavelength of the perturbation which appears at the solid / liquid interface of the non-faceted phase, (Zn). In spite of the interface destabilization the selection of a given structure depends on the localization of the minimum entropy production, only.

6

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.