The evolution and morphological stability of a particle in a binary alloy melt

Chen, M.W.; Wang, Z.D.

doi:10.1016/j.jcrysgro.2023.127113

Cited by 4 publications

(4 citation statements)

References 26 publications

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“…(5) Уравнения возмущений поверхности раздела будут иметь вид: (6) Соответственно, граничные условия (2) примут вид: (7) Проведение линейного анализа устойчивости требует знания аналитического вида градиентов невозмущенной температуры, входящих в уравнения (6). Для их получения необходимо решить краевую задачу (4), (5).…”

Section: постановка задачиunclassified

“…Соответственно, граничные условия (7) имеют вид (штрихом обозначена производная по радиальной координате): (11) Как и в уравнении [1], зависимость амплитудных значений возмущений скорости межфазной границы от максимальных значений возмущений температуры и концентрации имеет вид:…”

Section: постановка задачиunclassified

“…В настоящее время эта неустойчивость изучается разными авторами [7 -10]. В работе [7] данная неустойчивость изучалась для бинарных сплавов. Были сформулированы критерии абсолютной и относительной устойчивости сферического зародыша кристаллизации для этих сплавов и показано, что по мере роста частицы начальная концентрация в разбавленном бинарном расплаве сначала подавляет, а затем повышает морфологическую стабильность частицы.…”

Section: Introductionunclassified

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Formation of the gradient of structural-phase states of high-speed steel during surfacing. Part 2. The role of the Mullins–Sekerka instability in formation of crystallization structures

Nevskii,

Bashchenko,

Gromov

et al. 2024

Izv. vysš. učebn. zaved., Čern. metall.

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The authors studied the crystallization process of the Fe – W system, which is the basis of heat-resistant high-speed steel used in plasma arc surfacing on the surface of rolls and various cutting tools. The structure of this material consists of two components: cellular and dendritic. Histogram of the structural elements distribution shows the presence of a single maximum. The most probable size takes a value in the range of 10 – 15 μm. The paper considers the morphological instability of crystallization front (the Mullins-Sekerka instability). The model includes the equations of convective thermal conductivity and diffusion. The Stefan conditions for temperature were set at interface of the phases. Linear analysis of this instability is carried out for two cases: when the convective term in the equations of thermal conductivity and diffusion can be neglected; when convection prevails over diffusion processes. In all cases, it was assumed that the value (1 – ks ) was close to zero, which corresponds to a concentration of the alloying element approximately equal to or exceeding the eutectic one, and a short-wave approximation was also used. In the first case, the analytical view of dependence of the wavelength, which accounts for the maximum rate of interface disturbances growth, coincides with generally accepted concepts. In the second case, the value of this wavelength is directly proportional to square root of the interphase boundary velocity. The limits of applicability of these approximations for various mechanisms of crystal growth were determined. In the case of normal growth, both approximations provide an adequate explanation for the formation of structural elements up to 5 μm in size at a crystallization front velocity of about 2 m/s. For the case of growth due to screw dislocations, the wavelength value corresponding to the fastest-growing perturbation mode in the first case coincides with experimental data at a crystallization front velocity of the order of 10–7 m/s, whereas in the convective approximation such a coincidence is observed at 10–4 m/s. Further development of the model consists in simultaneous consideration of the convective and diffusion components. The results obtained will serve as a material for the research of the Mullins–Sekerka instability for two interface boundaries.

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Section: постановка задачиunclassified

Section: Introductionunclassified

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Formation of the gradient of structural-phase states of high-speed steel during surfacing. Part 2. The role of the Mullins–Sekerka instability in formation of crystallization structures

Nevskii,

Bashchenko,

Gromov

et al. 2024

Izv. vysš. učebn. zaved., Čern. metall.

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“…Таким образом, при построении математических моделей плазменного воздействия на структуру материалов необходимо учитывать как движение границ фазового перехода, так и границ прогрева. Поиск механизмов формирования градиента структуры и фазового состава теплостойких сплавов при плазменной наплавке на вращающийся валок необходимо проводить с использованием представлений о возникновении и развитии неустойчивости Маллинза-Секерки [15], анализ которой позволяет определить условия возникновения этих состояний с учетом движения границы прогрева. Изучение этой неустой-movable cylindrical boundaries that separate three regions.…”

Section: Introductionunclassified

Formation of the gradient of structural-phase states of high-speed steel during surfacing. Part 1. Solving the Stefan problem with two movable boundaries

Nevskii,

Bashchenko,

Peregudov

2023

Izv. vysš. učebn. zaved., Čern. metall.

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The article considers theoretical study of solidification of the binary iron–tungsten system at a tungsten content of 18 wt. %. Such tungsten content is typical for heat-resistant alloys used in plasma-arc surfacing on the rolls surface. The axisymmetric Stefan thermal problem is solved for two movable cylindrical boundaries that separate three regions. In region 1, the melt is at the melting point; in region 2, the substance is in a two‒phase state, and in region 3 – a solid. The liquidus temperature was set at the interface of regions 1 and 2, and the solidus temperature – at the interface of regions 2 and 3. At these boundaries, a condition for the heat flows balance was given, from which a system of kinetic equations was obtained. This system was solved by numerical methods, without hypothesizing that the fronts of phase transformations move according to the law R ~ t1/2. Solution of the system of kinetic equations shows that the solidus boundary moves almost linearly. The liquidus boundary moves according to the parabolic law. For regions of the micrometer range in size, the processes of phase transformations take place in a time of about 5 ns, whereas for regions of the order of 10 μm in size – in a time of about 50 ms. Dependences of temperature fields on the radial coordinate at various points in time show that with increasing time, the dimensions of region 2 decrease, and as soon as coordinates of the liquidus and solidus boundaries become close, thecrystallization process stops. Further development of the model consists in taking into account the rotation of one of the media. The results obtained will serve as a material for the study of the Mullins-Sekerka two-front instability.

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The reversible inward growth of a particle in an alloy melt induced by anisotropic interface kinetics

Chen,

Wang

2024

Chinese Journal of Physics

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The evolution and morphological stability of a particle in a binary alloy melt

Cited by 4 publications

References 26 publications

Formation of the gradient of structural-phase states of high-speed steel during surfacing. Part 2. The role of the Mullins–Sekerka instability in formation of crystallization structures

Formation of the gradient of structural-phase states of high-speed steel during surfacing. Part 2. The role of the Mullins–Sekerka instability in formation of crystallization structures

Formation of the gradient of structural-phase states of high-speed steel during surfacing. Part 1. Solving the Stefan problem with two movable boundaries

The reversible inward growth of a particle in an alloy melt induced by anisotropic interface kinetics

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