Simulation of Crystal Growth in Multicomponent Metastable Alloys

Dudorov, M. V.; Рощин, В. Е.

doi:10.3103/s0967091219120039

Cited by 5 publications

(16 citation statements)

References 14 publications

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“…Thereby, simultaneous growth of "equilibrium" nuclei of A and Z E phases as well as metastable nuclei of Z phase, occur during cooling of the melt with eutectic composition, i. e. phase transformation takes plaсe: Initial melt → A +Z +Z E It is important to note that in the case of nuclei Z forming the local equilibrium condition is not executed, thereby use of the equations ( 1) and Onsager principle is not correct. In this connection, the variational theory was proposed in our previous works [13,14]; use of this theory for physicalchemical description of the system "nucleus -phase boundary -initial melt" allows to obtain the equation for nucleus growth speed in the case of deviation from equilibrium. The obtained equations can be easily transformed for the case of nucleus growth in eutectic overcooled melt.…”

Section: Regularities Of Eutectic Melt Crystallizationmentioning

confidence: 99%

“…The expression for molar speed of product forming on the surface square unit was obtained for the phase Z [13,14] in the following way:…”

Section: Regularities Of Eutectic Melt Crystallizationmentioning

confidence: 99%

“…The corresponding "metastable" line for Fe 3 B nuclei on the phase equilibrium diagram was built, whereas this line takes into account deviations from the equilibrium state. The previously developed technique [14] is used for it. Consideration of crystallization of metastable alloys showed, based on calculations, slight deviation from equilibrium state.…”

Section: Calculation Of the Metastable Phase Equilibrium Diagram For Fe-b Meltmentioning

confidence: 99%

“…Then let's apply the theory of ideal solutions, taking into account the influence of surface effects on the value of nucleus chemical potential. Consequently, it can be expressed as follows [14]:…”

Section: Calculation Of the Metastable Phase Equilibrium Diagram For Fe-b Meltmentioning

confidence: 99%

“…The authors previously developed the new variational approach for description of crystal growth [13,14]. The advantages of this approach conclude in complex description of mutually connected thermal and diffusion processes in the system "growing crystal -melt", taking into account the influence of non-linear effects on the phase boundary.…”

Section: Introductionmentioning

confidence: 99%

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Variational theory of crystal growth and its application for analysis of forming processes for metastable phases in overcooled metallic melts with eutectic composition

Dudorov¹,

Drozin²,

Stryukov³

et al. 2021

cisisr

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The new crystallization theory for overcooled metastable melt is developed; it is based on variational mechanical principles and takes into account regularities of forming and diffusion growth of equilibrium crystals as well as diffusion-free growth of metastable crystals. Calculations for the melt Fe 83 B 17 were conducted on the model; they displayed that simultaneous nucleation and growth of Fe and Fe 2 B with metastable phase Fe 3 B are observed in overcooled melt, and growth speed of near-critical dimensional crystals of Fe 3 B exceeds crystal growth speed of Fe and Fe 2 B. The effect of diffusion-free growth is observed for Fe 3 B crystals, when quickly growing Fe 3 B crystal surface catches boron atoms. Quasi-equilibrium phase diagram for overcooled Fe-B melt was built on the base of the developed theory; it takes into account both equilibrium crystal growth and metastable phase growth. The obtained diagram allows to predict the values of components concentration near the surface of growing crystals both for Fe and Fe 2 B crystals meeting the requirements of local equi-librium condition on their surface and for Fe 3 B metastable crystals which are characterized by diffusion-free growth stipulated by high motion speed of crystal surface.

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Section: Regularities Of Eutectic Melt Crystallizationmentioning

confidence: 99%

“…The expression for molar speed of product forming on the surface square unit was obtained for the phase Z [13,14] in the following way:…”

Section: Regularities Of Eutectic Melt Crystallizationmentioning

confidence: 99%

Section: Calculation Of the Metastable Phase Equilibrium Diagram For Fe-b Meltmentioning

confidence: 99%

Section: Calculation Of the Metastable Phase Equilibrium Diagram For Fe-b Meltmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Variational theory of crystal growth and its application for analysis of forming processes for metastable phases in overcooled metallic melts with eutectic composition

Dudorov¹,

Drozin²,

Stryukov³

et al. 2021

cisisr

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Theory of Metastable Crystallization of Supercooled Eutectic Melt

Dudorov,

Drozin,

Stryukov

et al. 2021

Chem

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A new theory of crystallization of a supercooled metastable melt, based on the variational principles of mechanics, was developed. The theory takes into account the regularities of the dif-fusion growth of equilibrium crystals, as well as the regularities the diffusionless growth of meta-stable crystals. Mathematical modeling showed that in the supercooled melt Fe83B17 there is sim-ultaneous nucleation and growth of the stable Fe and Fe2B phases with the metastable Fe3B phase. The growth rate of crystals of near-critical sizes of the Fe3B phase exceeds the growth rate of the Fe and Fe2B crystals. For the Fe3B crystals the effect of diffusionless growth has been ob-served; in this case, the rapidly growing surface of the Fe3B crystal captures the boron atoms. On the basis of the developed theory, a quasi-equilibrium phase diagram for a supercooled Fe-B melt was constructed. The phase diagram takes into account both the equilibrium crystal growth and the growth of the metastable phase. The resulting diagram makes it possible to pre-dict the values of the concentration of components at the surface of growing crystals for the Fe and Fe2B crystals, for which the condition of local equilibrium is observed on their surface, and for the metastable Fe3B crystals, whose diffusionless growth is due to the high speed of the crys-tal surface movement. The performed mathematical modeling of the nucleation and growth of crystals in the over-cooled eutectic melt Fe83B17 showed that in a supercooled melt there is simultaneous nucleation and growth of the stable Fe and Fe2B phases with the metastable Fe3B phase. The regularities of nucleation and growth of the metastable Fe3B phase have been studied. The growth mechanism of the Fe3B nuclei differs from the growth of the Fe and Fe2B nuclei due to diffusionless capture of the boron atoms by the growing surface of the Fe3B crystals.

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Variational Theory of Crystal Growth in Multicomponent Alloys

2022

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The provisions for a new variational theory of crystal growth in multicomponent metal melts were formulated. The developed theory is the generalization of the previously conducted studies of crystal growth under conditions of deviation from local equilibrium at the phase boundary. The description of the methods of non-equilibrium thermodynamics of interrelated physico-chemical processes occurring in the initial phase, on the interface of phases and inside the growing crystal, was compared with the variational description of the crystal growth as a macrobody. The developed approach made it possible to find the general expression for the crystal growth rate, considering the influence of thermal and diffusion processes, as well as taking into account the influence of nonstationary effects associated with deviation from the local equilibrium on the surface of the growing nucleus. The justification of the new method showed that when the condition of the local equilibrium on the surface of the growing crystal is satisfied, the resulting equations take the form of expressions that can be obtained by constructing the equation of a mass and internal energy balance for the system under consideration. As an example, the problem of crystal growth from a melt of eutectic composition was considered. The equation of the growth rate of the two-component nucleus of the stoichiometric composition was obtained, taking into account the influence of the local non-equilibrium effects on growth. The expressions obtained were compared with the known equations of the solute trapping theory.

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Simulation of Crystal Growth in Multicomponent Metastable Alloys

Cited by 5 publications

References 14 publications

Variational theory of crystal growth and its application for analysis of forming processes for metastable phases in overcooled metallic melts with eutectic composition

Variational theory of crystal growth and its application for analysis of forming processes for metastable phases in overcooled metallic melts with eutectic composition

Theory of Metastable Crystallization of Supercooled Eutectic Melt

Variational Theory of Crystal Growth in Multicomponent Alloys

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