On the theory of non-stationary directional solidification with a phase transition layer

Ferromagnetic shape memory alloy is a kind of new smart material. Directional solidification method in producing polycrystalline Ni2MnGa is mature and effective. In order to increase the strain of Ni2MnGa polycrystalline prepared by directional solidification, mechanical training is an effective method. In this paper, the tests of temperature-induced strain are carried out in different directions of Ni2MnGa prepared by directional solidification using three kinds of specimens with various mechanical training. Through analyzing the mechanical properties in different directions, the influence of mechanical training on the temperature-induced strain are investigated. Some conclusions which may provide references for the engineering applications of this material are gained.

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On reconstitutive phase transitions and the jump of the chemical potential

Analysis ◽

10.1524/anly.2008.0905 ◽

2008 ◽

Vol 28 (1) ◽

Author(s):

Thomas Blesgen

Keyword(s):

Phase Transition ◽

Phase Transitions ◽

Weak Solutions ◽

Transition Layer ◽

Chemical Potential ◽

Sharp Interface ◽

Free Energies ◽

Diffusion In Solids ◽

Existence Of Weak Solutions ◽

Two Phases

This article studies diffusion in solids in the case of two phases under isothermal conditions where due to plastic effects the number of vacancies changes when crossing a transition layer, i.e. a reconstitutive phase transition. A segregation model is derived and the equations are studied in the limit of a sharp interface. A Gibbs–Thomson law is derived and it is shown that the vacancy component of the chemical potential jumps across the transition layer thereby explaining recent experimental observations. The thermodynamic correctness of the model is shown as well as the existence of weak solutions with logarithmic free energies.

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Mathematical modeling of bulk and directional crystallization with the moving phase transition layer

10.22541/au.163250947.73804831/v1 ◽

2021 ◽

Author(s):

Liubov Toropova ◽

Danil Aseev ◽

Sergei Osipov ◽

Alexander Ivanov

Keyword(s):

Mathematical Modeling ◽

Phase Transition ◽

Transition Layer ◽

Solid Phase ◽

Phase Region ◽

Mushy Region ◽

Solidification Velocity ◽

Mushy Layer ◽

Two Phase ◽

Phase Layer

This paper is devoted to the mathematical modeling of a combined effect of directional and bulk crystallization in a phase transition layer with allowance for nucleation and evolution of newly born particles. We consider two models with and without fluctuations in crystal growth velocities, which are analytically solved using the saddle-point technique. The particle-size distribution function, solid-phase fraction in a supercooled two-phase layer, its thickness and permeability, solidification velocity, and desupercooling kinetics are defined. This solution enables us to characterize the mushy layer composition. We show that the region adjacent to the liquid phase is almost free of crystals and has a constant temperature gradient. Crystals undergo intense growth leading to fast mushy layer desupercooling in the middle of a two-phase region. The mushy region adjacent to the solid material is filled with the growing solid phase structures and is almost desupercooled.

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