The analysis of morphological stability of a recrystallization front
A generalization of theoretical information about the patterns of trans-formation of a conversion front during phase reactions is carried out. The theory of concentration supercooling based on diffusional redistribution of alloy components in a melt near crystallization boundary is considered. Trans...
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Movchan, O.V. Chornoivanenko, K.O. 2020-04-15T17:11:11Z 2020-04-15T17:11:11Z 2018 The analysis of morphological stability of a recrystallization front / O.V. Movchan, K.O. Chornoivanenko // Progress in Physics of Metals. — 2018. — Vol. 19, No 2. — P. 185-194. — Bibliog.: 46 titles. — eng. 1608-1021 DOI: https://doi.org/10.15407/ufm.19.02.185 PACS numbers: 61.72.sh, 64.70.dg, 66.30.Fq, 68.35.Ja, 68.70.+w, 81.10.Aj, 81.10.Jt, 81.40.Ef https://nasplib.isofts.kiev.ua/handle/123456789/167909 A generalization of theoretical information about the patterns of trans-formation of a conversion front during phase reactions is carried out. The theory of concentration supercooling based on diffusional redistribution of alloy components in a melt near crystallization boundary is considered. Transformation mechanisms of flat front of crystallization with structure change into cellular and dendritic are studied. Regulations of the interfacial boundary instability during the phase transition are considered. The effect of alloying elements on the morphology of the transformation front is analysed. The conditions of the morphological stability of the recrystallization front in the high-alloyed iron alloys during chemical-thermal treatment are considered. As established, the transformation of the conversion front is carried out under the action of concentration gradients. This is caused by the redistribution of the base alloying elements ahead of the recrystallization front. Виконано узагальнення теоретичної інформації щодо закономірностей перетворення конверсійного фронту при фазових реакціях. Розглянуто теорію концентраційного переохолодження, основою якого є дифузійний перерозподіл компонентів стопу в розтопі поблизу межі кристалізації. Вивчаються механізми трансформації плаского фронту кристалізації та перекристалізації в комірковий і дендритний. Розглянуто питання нестійкости міжфазової межі в процесі фазових перетворень. Проведено аналізу впливу леґувальних елементів на морфологію фронту перетворення. Розглянуто умови морфологічної стабільности фронту перекристалізації у високолеґованих залізних стопах в процесі хеміко-термічного оброблення. Встановлено, що трансформація фронту перетворення здійснюється під дією концентраційних ґрадієнтів, спричинених перерозподілом основних леґувальних елементів попереду фронту перекристалізації. Выполнено обобщение теоретической информации о закономерностях превращения конверсионного фронта при фазовых реакциях. Рассмотрена теория концентрационного переохлаждения, основой которого является диффузионное перераспределение компонентов сплава в расплаве вблизи границы кристаллизации. Изучены механизмы трансформации плоского фронта кристаллизации и перекристаллизации в ячеистый и дендритный. Рассмотрены вопросы неустойчивости межфазной границы в процессе фазового перехода. Проводится анализ влияния легирующих элементов на морфологию фронта превращения. Рассматриваются условия морфологической стабильности фронта перекристаллизации в высоколегированных железных сплавах в процессе химико-термической обработки. Установлено, что трансформация фронта превращения осуществляется под действием концентрационных градиентов, вызванных перераспределением основных легирующих элементов впереди фронта перекристаллизации. en Інститут металофізики ім. Г.В. Курдюмова НАН України Успехи физики металлов The analysis of morphological stability of a recrystallization front Аналiз морфологічної стабільности фронту перекристалізації Анализ морфологической стабильности фронта перекристаллизации Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
The analysis of morphological stability of a recrystallization front |
| spellingShingle |
The analysis of morphological stability of a recrystallization front Movchan, O.V. Chornoivanenko, K.O. |
| title_short |
The analysis of morphological stability of a recrystallization front |
| title_full |
The analysis of morphological stability of a recrystallization front |
| title_fullStr |
The analysis of morphological stability of a recrystallization front |
| title_full_unstemmed |
The analysis of morphological stability of a recrystallization front |
| title_sort |
analysis of morphological stability of a recrystallization front |
| author |
Movchan, O.V. Chornoivanenko, K.O. |
| author_facet |
Movchan, O.V. Chornoivanenko, K.O. |
| publishDate |
2018 |
| language |
English |
| container_title |
Успехи физики металлов |
| publisher |
Інститут металофізики ім. Г.В. Курдюмова НАН України |
| format |
Article |
| title_alt |
Аналiз морфологічної стабільности фронту перекристалізації Анализ морфологической стабильности фронта перекристаллизации |
| description |
A generalization of theoretical information about the patterns of trans-formation of a conversion front during phase reactions is carried out. The theory of concentration supercooling based on diffusional redistribution of alloy components in a melt near crystallization boundary is considered. Transformation mechanisms of flat front of crystallization with structure change into cellular and dendritic are studied. Regulations of the interfacial boundary instability during the phase transition are considered. The effect of alloying elements on the morphology of the transformation front is analysed. The conditions of the morphological stability of the recrystallization front in the high-alloyed iron alloys during chemical-thermal treatment are considered. As established, the transformation of the conversion front is carried out under the action of concentration gradients. This is caused by the redistribution of the base alloying elements ahead of the recrystallization front.
Виконано узагальнення теоретичної інформації щодо закономірностей перетворення конверсійного фронту при фазових реакціях. Розглянуто теорію концентраційного переохолодження, основою якого є дифузійний перерозподіл компонентів стопу в розтопі поблизу межі кристалізації. Вивчаються механізми трансформації плаского фронту кристалізації та перекристалізації в комірковий і дендритний. Розглянуто питання нестійкости міжфазової межі в процесі фазових перетворень. Проведено аналізу впливу леґувальних елементів на морфологію фронту перетворення. Розглянуто умови морфологічної стабільности фронту перекристалізації у високолеґованих залізних стопах в процесі хеміко-термічного оброблення. Встановлено, що трансформація фронту перетворення здійснюється під дією концентраційних ґрадієнтів, спричинених перерозподілом основних леґувальних елементів попереду фронту перекристалізації.
Выполнено обобщение теоретической информации о закономерностях превращения конверсионного фронта при фазовых реакциях. Рассмотрена теория концентрационного переохлаждения, основой которого является диффузионное перераспределение компонентов сплава в расплаве вблизи границы кристаллизации. Изучены механизмы трансформации плоского фронта кристаллизации и перекристаллизации в ячеистый и дендритный. Рассмотрены вопросы неустойчивости межфазной границы в процессе фазового перехода. Проводится анализ влияния легирующих элементов на морфологию фронта превращения. Рассматриваются условия морфологической стабильности фронта перекристаллизации в высоколегированных железных сплавах в процессе химико-термической обработки. Установлено, что трансформация фронта превращения осуществляется под действием концентрационных градиентов, вызванных перераспределением основных легирующих элементов впереди фронта перекристаллизации.
|
| issn |
1608-1021 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/167909 |
| citation_txt |
The analysis of morphological stability of a recrystallization front / O.V. Movchan, K.O. Chornoivanenko // Progress in Physics of Metals. — 2018. — Vol. 19, No 2. — P. 185-194. — Bibliog.: 46 titles. — eng. |
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ISSN 1608-1021. Usp. Fiz. Met., 2018, Vol. 19, No. 2 185
https://doi.org/10.15407/ufm.19.02.185
PACS numbers: 61.72.sh, 64.70.dg, 66.30.Fq, 68.35.Ja, 68.70.+w, 81.10.Aj, 81.10.Jt, 81.40.Ef
O.V. mOVcHAN and K.O. cHORNOIVANENKO
National Metallurgical Academy of Ukraine,
4 Gagarin Ave.,
UA-49600 Dnipro, Ukraine
the analysis of MorPhological
staBility of a recrystallization front
A generalization of theoretical information about the patterns of trans-formation of
a conversion front during phase reactions is carried out. The theory of concentra-
tion supercooling based on diffusional redistribution of alloy components in a melt
near crystallization boundary is considered. Transformation mechanisms of flat
front of crystallization with structure change into cellular and dendritic are stud-
ied. Regulations of the interfacial boundary instability during the phase transition
are considered. The effect of alloying elements on the morphology of the transfor-
mation front is analysed. The conditions of the morphological stability of the re-
crystallization front in the high-alloyed iron alloys during chemical-thermal treat-
ment are considered. As established, the transformation of the conversion front is
carried out under the action of concentration gradients. This is caused by the redis-
tribution of the base alloying elements ahead of the recrystallization front.
Keywords: recrystallization front, phase transformations, front transformation, in-
terphase boundary, concentration gradients, chemical-thermal treatment.
analysis of the theory for transformation
of a Phase conversion front
The profile of the transformation front is an important characteristic of
the crystal growth process and depends on the thermophysical condi-
tions at the front, concentration of the alloying elements and impuri-
ties. Transformation of the flat transformation front into cellular and
then into dendritic is one of the most fundamental and important so-
lidification phenomena [1, 2], which determines the structural perfec-
tion of a material.
Regularities of morphology change of the crystallization front at
slow velocities of the front motion (∼10−7−10−4 m/s) have been inten-
186 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 2
O.V. Movchan and K.O. Chornoivanenko
sively studied since the early 1950s by W. Tiller, B. Chalmers, j. Ruter.
They created a theory of concentration supercooling based on concepts
of diffusion redistribution of alloy components in a melt near melt–
crystal interface [3]. This theory was later developed within the linear
stability model of Mullins and Sekerka [4, 5], and by Coriell and Sekerka
[6–8] that was later generalized to the nonlinear domain by Davis [9].
The authors have established that the cellular structure of the inter-
phase boundary arises in the case when the interphase surface becomes
unstable to wave distortions. This model was developed for flat and
spherical cases, as well as for the formation of a cellular front in the
process of directional crystallization, which determines the segregation
of impurities and dislocation structure of the crystal. As shown latter,
the cellular structure in binary alloys could be formed due to the con-
vective mechanism of heat and mass transfer near this boundary at low
crystallization rates [10]. The mass transfer is thermogravitation con-
vection at the melt−crystal interface. The paper [10] made it clear under
what control parameters a cellular front is formed, both under convec-
tion conditions at the melt−crystal interface and without it. Trivedi and
Kurz [11−13] extended the Mullins−Sekerka model for high velocities of
boundary movement (∼10−3 m/s) and higher without going beyond the
heat-diffusion mechanism for the redistribution of components of the
binary alloy near the melt−crystal interface. The theory of Mullins and
Sekerka was confirmed in many experimental works and numerical deci-
sion of the corresponding diffusion problem (see, for example, Refs.
[14−20]).
The cellular structure was studied at high drawing velocities in
[21]. It was shown that the solidifying surface becomes flat when the
certain high speed value is reached: ∼3 ⋅ 104Vc for the succinonitrile−argon
system (here, Vc denotes a critical solidification velocity). Such flat
front rebuilding was predicted as a particular consequence of a linear
analysis of the stability of Mullins and Sekerka [4] and is called absolute
stability. For a better understanding of this phenomenon, it is necessary
to model directional solidification at an atomic scale, which was done in
Ref. [22]. The kinetic modelling of directional solidification on an atom-
ic scale was performed by the Monte Carlo method for the lattice liquid
model. The presence of vacancies in the melt, which contributes to the
components diffuse, was taken into account.
The authors of Ref. [23] give an analysis of linear morphological
stability for the full range of crystallization rates: from low velocities
in the diffusion-limited regime to ultra-high velocities of the front
movement, when a diffusionless (chemically non-selective) regime is
performed.
It was shown in [24] that the growth of a two-phase zone as the
heterojunction zone from crystal to melt during crystallization of met-
ISSN 1608-1021. Usp. Fiz. Met., 2018, Vol. 19, No. 2 187
The Analysis of Morphological Stability of a Recrystallization Front
als and alloys is due to the reaction of the system to supercooling for
the fastest transition to a quasi-equilibrium state. Intensive deposition
of atoms at the interface between the liquid and solid phases leads to a
rapid decrease in the supercooling at the interface. The emergence of a
macrorough boundary of the cellular–dendritic structure is necessary to
isolate a large amount of latent heat of crystallization [25]. The deter-
mining role in the appearance of such cellular–dendrite forms has the
established balance between the force morphologically destabilizing the
front (proportional to gradient of the impurity-element concentration)
and the force stabilizing the front (proportional to the surface energy of
crystal–liquid interface). The morphological (in)stability of the initial
solidification front is reached, if one of the forces prevails. Therefore,
the growth of the two-phase zone passes through the stage of the mor-
phological instability of the microrough front to the appearance of sta-
ble macroscopic branched forms of the cellular–dendrite structure.
The paper [26] describes the multiphase model for predicting
cellular−dendrite transformation during solidification of binary alloys.
A mechanism of cellular structure formation associated with the occur-
rence of dislocations along the grain boundaries is known, for instance,
in the case when metals are irradiated with pulsed electron streams and
subsequent deformation [27]. The paper [28] is devoted to the study of
formation of cellular structures from a melt in binary systems. It has
been experimentally proved that there is the mechanism for the forma-
tion of a cellular structure associated with concentration supercooling
(diffusional redistribution of the alloy components at the melt−crystal
interface) in addition to the dislocation mechanism. The surface tension
anisotropy and growth kinetics also influence on cells formation during
directional crystallization [29].
According to the results of a theoretical analysis in [30], a mathe-
matical model of the process of structure change of metal alloys was
developed. The model was created for Fe−0.5% C alloy in the surface
layer of the order of several microns. The diffusion processes of redis-
tribution of components at the interface were taken into account.
The authors of Ref. [31] obtained experimental results, which allow
showing a close relationship between kinetics and morphology develop-
ment of dendritic structure in the studied alloys with the magnitude of
diffusion supercooling in the two-phase zone. At the same time, these
results show that cellular model of the two-phase zone reflects correctly
a nature of diffusion (liquation) processes determining the evolution of
dendrite structure in the elementary volume of the two-phase zone.
A physical model of convective heat and mass transfer in a melt
near the crystallization front has been developed in [32, 33] due to the
thermocapillary and concentration-capillary mechanisms acting on the
melt–crystal interface.
188 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 2
O.V. Movchan and K.O. Chornoivanenko
The authors of Ref. [34] obtained criteria for the formation of co-
lumnar and equiaxial grains by the process of dendritic crystallization.
It is shown that natural convection in a melt reduces local temperature
gradients. Thus, the convection extends a supercooling zone ahead of
the crystallization front and leads to increasing the potential for the
growth of equiaxial grains.
A fundamental problem in the process of formation of eutectic
structures is the question of a nature of morphological instability of the
simplest spatially periodic stationary states that lead to such a diverse
dynamics [35]. The variety of shapes and sizes of the resulting phase
structures is determined by nonequilibrium processes near a boundary
of the phase transition. Article [36] gives a comprehensive review of the
current state of solidification studies. Authors [36] consider the stabil-
ity of the interface during formation of three-dimensional dendrite
structures by directed growth of a dendrite vertex and the formation of
lateral branches, the stability of the interphase boundary in cellular
crystallization, as well as a morphological instability and the oscillation
of the interphase boundary during formation of eutectic structures. The
most popular theory that describes the process of crystallization of eu-
tectic melts with formation of periodic structures is the jackson−Hunt
theory [37]. However, it does not explain the reasons of periodic struc-
tures formation, and it cannot overcome difficulties in selecting the
decision of considered equations.
Many researchers believe that the main reason for appearance of
periodic structures is instability of the interphase boundary in the pro-
cess of phase transition. There are many theoretical calculations that
give qualitative correspondences of one or another mathematical model
of directional crystallization with observable structures since the classi-
cal paper [4].
As a rule, the presence of alloying elements leads to changes in
macro- and microstructures of a eutectic and to appearance of fan-like
structures that called colonial ones. As firstly shown by Weart and
Mack [38], the appearance of fan-shaped colonial structures is associ-
ated with the curvature of flat crystallization front and its transforma-
tion into a cellular one. The appearance of the cellular front during
single-phase solidification of binary alloys is due to a redistribution of
alloying elements between the phases.
Boiling and Tiller [39] attempted to relate size of the cells to veloc-
ity of the crystallization front on basis of the diffusion equation deci-
sion. However, it was not possible to achieve a good correspondence
with the experimental data. The authors explained this by a great sen-
sitivity of the calculated data to initial assumptions. The more advanced
models have been built using numerical methods by now. If thermody-
namic equilibrium was assumed in [39] at the interphase boundary, the
ISSN 1608-1021. Usp. Fiz. Met., 2018, Vol. 19, No. 2 189
The Analysis of Morphological Stability of a Recrystallization Front
authors of [40] constructed a nonequilibrium model of cellular structure
growth. The same authors [41] used combined numerical methods to pro-
vide the required level of accuracy. The authors of [42] obtained a good
agreement with their own experimental data in Al−4.5% Cu system.
They took into account diffusion in the solid phase and convective flow.
The authors of Refs. [43, 44] observed the phenomenon of flat front
transformation into cellular front at α→γ-recrystallization of carbur-
ized Fe−Si alloys. The effect of concentration supersaturation of ferrite
by carbon explained that. It was analogous to concentration supercool-
ing during crystallization of alloys.
The above-mentioned works mainly deal with the crystallization of
melts. There are no enough publications devoted to transformation of
the flat conversion front during the recrystallization [45]. That is why
an additional research is needed.
formation of a recrystallization
front in high-alloyed iron alloys during Decarburization
The transformation of recrystallization front into cellular and transfor-
mation of columnar ferrite grains into branched dendrites is observed
during decarburization of the experimental alloy T1 with ∼ 2% of carbon
by mass (Fig. 1). Decarburization of the investigated alloy was carried
out for 1.5 hours at 1050 °C in the first stage and 2 hours at 1200 °C in
the second stage in a wet hydrogen atmosphere in laboratory installa-
tion. Analysis of the isothermal section of Fe−W−C phase diagram at
the processing temperature (Fig. 2) suggested that the cause of α→γ-
front instability relates to the interphase redistribution of the basic al-
loying element (tungsten) in accordance with the equilibrium conditions.
Diffusion ferritization of surface layer in the investigated alloys is accom-
Fig. 1. Recrystallization
front during decarburi-
zation of the experimen-
tal T1 + 2% C alloy (sca-
ling ×50)
190 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 2
O.V. Movchan and K.O. Chornoivanenko
panied by interphase redistribution of tungsten atoms between the parent
phases and the growing α-phase. As a result, a chemical inhomogeneity
is formed that reflects on the nature of the transition zone structure.
The transformation of recrystallization front is due to various equi-
librium concentrations of tungsten at the interphase boundary, primar-
ily in austenite and the growing α-phase, as well as in carbide. Tungsten
is α-stabilizer, so its equilibrium content in the ferrite will be greater
than in austenite. Thus, carbon depletion of experimental alloy in the
three-phase equilibrium region (ferrite−austenite−M6C carbide) leads to
increasing in the difference between the equilibrium concentrations of
tungsten in these phases (Fig. 2). Consequently, γ + M6C→α-trans for-
mation is accompanied by redistribution of tungsten between the phases
during decarburization of the alloy.
formation of a recrystallization
front in high-alloyed iron alloys during carburization
Concentration gradients arising during the three-phase (ferrite−auste-
nite−carbide) transformation process cause diffusion redistribution of
the alloying elements ahead of the recrystallization front by diffusion
saturation with carbon in the T1 + 2% C alloy. It renders a significant
effect on the nature of the formed structures. Concentration supersatu-
Fig. 2. Chart of the isothermal cross-section for Fe−W−C ternary state diagram at
1200°C [46], where M is a metal and L is a liquid
ISSN 1608-1021. Usp. Fiz. Met., 2018, Vol. 19, No. 2 191
The Analysis of Morphological Stability of a Recrystallization Front
ration zone forms before the conversion front. It is similar to the con-
centration supercooling during crystallization (first observed by Weart
and Mack [38]). The flat α → γ-transformation front turns into a cellular
one in the presence of concentration supersaturation zone while losing
its stability (Fig. 3). The main alloying element (tungsten) is pushed
into the cavities between the protuberances at the front. Random protu-
berances are formed at the front under more preferable conditions. They
germinate into ferrite. Tungsten enriches the cavity by tangential dif-
fusion of it. Herewith, ferrite is even more stabilized.
conclusions
Within the framework of this work, we analysed theoretical informa-
tion dealing with morphological stability of the conversion front during
phase reactions. Factors affecting stability of flat front of crystalliza-
tion and recrystallization are revealed. The transformation of the re-
crystallization front into cellular and dendritic during chemical-thermal
treatment is considered. The concentration gradient of the main alloy-
ing element exists ahead the γ → α-transformation front at steady growth
of a ferrite layer during the decarburization of iron alloys alloyed by the
principle of high-speed steels. This is due to the thermodynamic feature
of the isothermal section of the Fe−W−C state diagram. It causes the
redistribution of components ahead front of recrystallization. A similar
situation is observed in high-alloyed iron alloys during carburizing. The
α → γ-flat front of recrystallization turns into a cellular one in case of
the presence of a concentration saturation zone, which occurs during
the three-phase transformation (ferrite → austenite + carbide). In this case,
the diffusion change in composition does not lead to a change in content
of alloying elements in the alloy.
Fig. 3. Microstructure
of the diffusion layer
of the T1 + 2% C alloy
after carburization at
1180°C (scaling ×250)
192 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 2
O.V. Movchan and K.O. Chornoivanenko
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Received May 15, 2018;
in final version, May 29, 2018
О.В. Мовчан, К.О. Чорноіваненко
Національна металургійна академія України,
просп. Гагаріна, 4,
49600 Дніпро, Україна
АНАЛІЗА МОРФОЛОГІЧНОї СТАБІЛЬНОСТИ
ФРОНТУ ПЕРЕКРИСТАЛІЗАЦІї
Виконано узагальнення теоретичної інформації щодо закономірностей перетво-
рення конверсійного фронту при фазових реакціях. Розглянуто теорію концен-
траційного переохолодження, основою якого є дифузійний перерозподіл компо-
нентів стопу в розтопі поблизу межі кристалізації. Вивчаються механізми транс-
формації плаского фронту кристалізації та перекристалізації в комірковий і
денд ритний. Розглянуто питання нестійкости міжфазової межі в процесі фазо-
вих перетворень. Проведено аналізу впливу леґувальних елементів на морфоло-
гію фронту перетворення. Розглянуто умови морфологічної стабільности фронту
перекристалізації у високолеґованих залізних стопах в процесі хеміко-термічного
оброблення. Встановлено, що трансформація фронту перетворення здійснюється
під дією концентраційних ґрадієнтів, спричинених перерозподілом основних ле-
ґувальних елементів попереду фронту перекристалізації.
Ключові слова: фронт перекристалізації, фазові перетворення, трансформація
фронту, міжфазова межа, концентраційні ґрадієнти, хеміко-термічне оброб лення.
194 ISSN 1608-1021. Prog. Phys. Met., 2018, Vol. 19, No. 2
O.V. Movchan and K.O. Chornoivanenko
А.В. Мовчан, Е.А. Черноиваненко
Национальная металлургическая академия Украины,
просп. Гагарина, 4,
49600 Днепр, Украина
АНАЛИЗ МОРФОЛОГИЧЕСКОЙ СТАБИЛЬНОСТИ
ФРОНТА ПЕРЕКРИСТАЛЛИЗАЦИИ
Выполнено обобщение теоретической информации о закономерностях превраще-
ния конверсионного фронта при фазовых реакциях. Рассмотрена теория концен-
трационного переохлаждения, основой которого является диффузионное пере-
распределение компонентов сплава в расплаве вблизи границы кристаллизации.
Изучены механизмы трансформации плоского фронта кристаллизации и пере-
кристаллизации в ячеистый и дендритный. Рассмотрены вопросы неустойчивос-
ти межфазной границы в процессе фазового перехода. Проводится анализ влия-
ния легирующих элементов на морфологию фронта превращения. Рассматриваются
условия морфологической стабильности фронта перекристаллизации в высоко-
легированных железных сплавах в процессе химико-термической обработки.
Установлено, что трансформация фронта превращения осуществляется под дей-
ствием концентрационных градиентов, вызванных перераспределением основных
легирующих элементов впереди фронта перекристаллизации.
Ключевые слова: фронт перекристаллизации, фазовые превращения, трансфор-
мация фронта, межфазная граница, концентрационные градиенты, химико-тер-
мическая обработка.
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