Mathematical model of solidification of melt with high-speed cooling

Abstract

A new mathematical model of supercooled melt crystallization based on the variational principles of thermodynamics has been developed. The model takes into account the crystal formation and diffusion growth regularities, as well as the diffusionless crystal growth with the deviation from the local equilibrium at the surface. The model also takes into account the growing crystals mutual influence on the components concentration in the melt. The calculations for the supercooled eutectic melt Fe83B17 showed that the nucleation and growth of the phases Fe and Fe2B with a metastable phase Fe3B occure in the melt. The local equilibrium on the surface of the growing Fe3B crystals with the melt probably does not maintained. The regularities of the nucleation and mutual influence of the growing crystals of the phases are studied. The nucleation and growth rate of the Fe3B nuclei differs from the growth of Fe and Fe2B nuclei due to the diffusionless capture of boron atoms by the growing Fe3B crystals surface. The model will help to calculate the melt cooling technology mode for producing amorphous ribbons on a copper rotating drum.The calculation made it possible to analyze changes in the temperature and the crystallization degree in the various ribbon layers. The calculation results have been verified experimentally by X-ray diffraction and calorimetric studies of the obtained ribbons. The correspondence of the calculation and the experimental results confirms the effectiveness developed methodology for studying the regularities of crystal growth in supercooled melts.

The Degree of Metallic Alloys Crystallinity Formed under Various Supercooling Conditions

“…In [5], an attempt was made to estimate the degree of crystallinity in an amorphous sample by comparing the heat of crystallization of the studied material with the sample containing a given fraction of the crystalline phase. Similar studies were also carried out by the authors of this article when comparing the crystallization heat of amorphous ribbons of various thicknesses [6].…”

“…As a part of the investigation, the ribbons with a thickness of 28, 34 and 38 microns previously obtained [6] when casting the melt of the composition (Fe-79.89%, B-15.40%, Si-4.40%, C-0.32%) were studied. All samples were made from the one ribbon.…”

“…An important task of such study is to determine the conditions when this transition can be considered to have taken place. The research on the obtained amorphous materials [2][3][4][5] shows the presence of crystals in their structure, which cannot always be detected by X-ray diffraction analysis (XRD) [5][6][7] and transmission electron microscopy methods (TEM) [8,9]. The investigation of the dependences of the nucleation and mutual growth of various crystal phases in changing the temperature field makes it possible to study the regularities of the processes occurring in supercooled melts.…”

“…Using experimental methods, it is difficult to determine the patterns of changes in the degree of crystallinity in different layers of the material under study. In this regard, a promising direction of research is mathematical modeling that provides extensive opportunities for studying crystal growth patterns under various cooling modes of the metallic melt [1,[3][4][5][6]. Such studies are very relevant, for example, for the study of amorphous ribbons obtained by supercooling the melt on a rotating drum.…”

“…To estimate the degree of crystallinity, calorimetric studies of ribbons of various thicknesses were carried out. In this case, the previously developed mathematical model [6] was used, describing the crystallization processes in supercooled eutectic melts. The model takes into account the patterns of formation and mutual growth of various crystal phases in relation to the given melt cooling mode.…”