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

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.

scholarly journals The effect of density changes on crystallization with a mushy layer

2020 ◽  
Vol 378 (2171) ◽  
pp. 20190248 ◽  
Author(s):  
Irina G. Nizovtseva ◽  
Dmitri V. Alexandrov
Keyword(s):  
Solid Fraction ◽  
Solid Phase ◽  
Exact Analytical Solution ◽  
Medical Physics ◽  
Mushy Layer ◽  
Quasi Equilibrium ◽  
Directional Crystallization ◽  
Two Phase ◽  
Phase Layer ◽  
State Process

A nonlinear problem with two moving boundaries of the phase transition, which describes the process of directional crystallization in the presence of a quasi-equilibrium two-phase layer, is solved analytically for the steady-state process. The exact analytical solution in a two-phase layer is found in a parametric form (the solid phase fraction plays the role of this parameter) with allowance for possible changes in the density of the liquid phase accordingly to a linearized equation of state and arbitrary value of the solid fraction at the boundary between the two-phase and solid layers. Namely, the solute concentration, temperature, solid fraction in the mushy layer, liquid and solid phases, mushy layer thickness and its velocity are found analytically. The theory under consideration is in good agreement with experimental data. The obtained solutions have great potential applications in analysing similar processes with a two-phase layer met in materials science, geophysics, biophysics and medical physics, where the directional crystallization processes with a quasi-equilibrium mushy layer can occur. This article is part of the theme issue ‘Patterns in soft and biological matters’.

scholarly journals Monoclinic–orthorhombic first-order phase transition in K2ZnSi5O12 leucite analogue; transition mechanism and spontaneous strain analysis.

2021 ◽  
pp. 1-20
Author(s):  
Anthony M.T. Bell ◽  
Francis Clegg ◽  
Christopher M.B. Henderson
Keyword(s):  
Phase Transition ◽  
Strain Analysis ◽  
Phase Region ◽  
Martensitic Transition ◽  
Two Phase ◽  
Spontaneous Strain ◽  
First Order ◽  
Transition Mechanism ◽  
First Order Phase Transition ◽  
Increasing Temperature

Abstract Hydrothermally synthesised K2ZnSi5O12 has a polymerised framework structure with the same topology as leucite (KAlSi2O6, tetragonal I41/a), which has two tetrahedrally coordinated Al3+ cations replaced by Zn2+ and Si4+. At 293 K it has a cation-ordered framework P21/c monoclinic structure with lattice parameters a = 13.1773(2) Å, b = 13.6106(2) Å, c = 13.0248(2) Å and β = 91.6981(9)°. This structure is isostructural with K2MgSi5O12, the first cation-ordered leucite analogue characterised. With increasing temperature, the P21/c structure transforms reversibly to cation-ordered framework orthorhombic Pbca. This transition takes place over the temperature range 848−863 K where both phases coexist; there is an ~1.2% increase in unit cell volume between 843 K (P21/c) and 868 K (Pbca), characteristic of a first-order, displacive, ferroelastic phase transition. Spontaneous strain analysis defines the symmetry- and non-symmetry related changes and shows that the mechanism is weakly first order; the two-phase region is consistent with the mechanism being a strain-related martensitic transition.

Mathematical modeling of binary compounds with the presence of a phase transition layer

2020 ◽  
Author(s):  
Irina G. Nizovtseva ◽  
Ilya O. Starodumov ◽  
Eugeny V. Pavlyuk ◽  
Alexander A. Ivanov
Keyword(s):  
Mathematical Modeling ◽  
Phase Transition ◽  
Transition Layer ◽  
Binary Compounds

A Model for Cw Laser Recrystallization Including Reflectivity Effects

1983 ◽  
Vol 23 ◽  
Author(s):  
I.D. Calder
Keyword(s):  
Excellent Agreement ◽  
Solid Phase ◽  
Phase Region ◽  
Experimental Results ◽  
Two Phase ◽  
Cw Laser ◽  
Laser Recrystallization ◽  
Outer Annulus ◽  
Analytic Expressions ◽  
Practical Model

ABSTRACTA simple, practical model is developed for cw laser recrystallization of silicon and SOI structures, taking into account spatial variations in optical reflectivity. The power absorption is assumed to be uniform within each of three regions: the central molten spot, the annular two-phase region, and an outer annulus to account for absorption in the solid phase. Analytic expressions are obtained for the radial and depth dependence of the temperature, for the melt depth, the melt radius, the melt threshold, the crystallization threshold and the substrate melt threshold. SOI structures are considered and comparison with some experimental results shows excellent agreement.

Metastable copper-chromium alloy films

1992 ◽  
Vol 7 (6) ◽  
pp. 1370-1376 ◽  
Author(s):  
A.P. Payne ◽  
B.M. Clemens
Keyword(s):  
Phase Transition ◽  
Grazing Incidence ◽  
Phase Region ◽  
Heat Of Mixing ◽  
Chromium Alloy ◽  
Two Phase ◽  
Bcc Lattice ◽  
Bcc Structure ◽  
Nonequilibrium States ◽  
Cr System

Due to the large positive heat of mixing associated with the Cu–Cr binary system, solid solutions exist only as nonequilibrium states. In this study, a series of metastable Cu–Cr alloys ranging in composition from 14.1 to 75.4% copper was fabricated by sputter deposition. Symmetric, asymmetric, and grazing incidence x-ray diffraction geometries were used to trace the phase transition from bcc to fcc crystal structures with increasing Cu fraction. It is shown that the transition takes place not by a two-phase region suggested by equilibrium thermodynamics, but rather through gradual disordering of the bcc lattice as copper atoms are substitutionally accommodated. At a critical saturation near 71% Cu, the bcc structure becomes unstable relative to the fcc and a phase transition occurs. The free energies of the kinetically constrained Cu–Cr system are modeled and the results are found to agree well with observed behavior.

scholarly journals Nonlinear dynamics of mushy layers induced by external stochastic fluctuations

2018 ◽  
Vol 376 (2113) ◽  
pp. 20170216 ◽  
Author(s):  
Dmitri V. Alexandrov ◽  
Irina A. Bashkirtseva ◽  
Lev B. Ryashko
Keyword(s):  
Phase Transition ◽  
Liquid Phase ◽  
Analytical Solution ◽  
Friction Velocity ◽  
Solid Phase ◽  
Cumulative Effect ◽  
Atmospheric Temperature ◽  
Mushy Layer ◽  
Theme Issue ◽  
Stochastic Fluctuations

The time-dependent process of directional crystallization in the presence of a mushy layer is considered with allowance for arbitrary fluctuations in the atmospheric temperature and friction velocity. A nonlinear set of mushy layer equations and boundary conditions is solved analytically when the heat and mass fluxes at the boundary between the mushy layer and liquid phase are induced by turbulent motion in the liquid and, as a result, have the corresponding convective form. Namely, the ‘solid phase–mushy layer’ and ‘mushy layer–liquid phase’ phase transition boundaries as well as the solid fraction, temperature and concentration (salinity) distributions are found. If the atmospheric temperature and friction velocity are constant, the analytical solution takes a parametric form. In the more common case when they represent arbitrary functions of time, the analytical solution is given by means of the standard Cauchy problem. The deterministic and stochastic behaviour of the phase transition process is analysed on the basis of the obtained analytical solutions. In the case of stochastic fluctuations in the atmospheric temperature and friction velocity, the phase transition interfaces (mushy layer boundaries) move faster than in the deterministic case. A cumulative effect of these noise contributions is revealed as well. In other words, when the atmospheric temperature and friction velocity fluctuate simultaneously due to the influence of different external processes and phenomena, the phase transition boundaries move even faster. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

scholarly journals Statistical mechanics of binary systems

1942 ◽  
Vol 179 (978) ◽  
pp. 340-361 ◽  
Keyword(s):  
Phase Transition ◽  
Solid Solution ◽  
Partition Function ◽  
Binary Systems ◽  
Binary Solution ◽  
Phase Region ◽  
Atomic Fraction ◽  
Phase Boundaries ◽  
Binary Solid Solution ◽  
Two Phase

Mayer’s method for the expansion of the partition function of a gas is adapted to the calculation of the partition function of a binary solid solution. The partition function is expanded in powers of the atomic fraction. Singularities in this expansion correspond to a phase transition. The singularity can be calculated in the simplest case of a binary solution with a two-phase region. This case is treated in full; the limits of solubility and the specific heat are obtained. The latter is discontinuous at the phase boundaries.

DSC Investigations of the Phase Transitions of [M(H2O)6](NO3)2 , where M = Mn, Co, Ni, Cu and Zn

1999 ◽  
Vol 54 (10-11) ◽  
pp. 595-598
Author(s):  
E. Mikuli ◽  
A. Migdał-Mikuli ◽  
S. Wróbel ◽  
B. Grad
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Solid Phase ◽  
Melting Process ◽  
Melting Points ◽  
Two Stage ◽  
Two Phase ◽  
Solid Phase Transition ◽  
Cu And Zn

The phase transitions of [M(H2O)6 ](NO3)2 , where M = Mn2+ , Co2+ , Ni2+ , Cu2+ or Zn2+ have been studied at 100 -400 K by DSC. Two phase transitions connected with a two-stage melting process have been found for these five compounds. For the compound with M = Co, besides the two melting points a solid-solid phase transition at 272 K has been found.

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