| Autor: |
Liubov V. Toropova, Dmitri V. Alexandrov |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Scientific Reports, Vol 12, Iss 1, Pp 1-9 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2045-2322 |
| DOI: |
10.1038/s41598-022-15137-2 |
| Popis: |
Abstract In this paper, we develop a theory of solid/liquid phase interface motion into an undercooled melt in the presence of nucleation and growth of crystals. A set of integrodifferential kinetic, heat and mass transfer equations is analytically solved in the two-phase and liquid layers divided by the moving phase transition interface. To do this, we have used the saddle-point method to evaluate a Laplace-type integral and the small parameter method to find the law of phase interface motion. The main result is that the phase interface Z propagates into an undercooled melt with time t as $$Z(t)=\sigma \sqrt{t}+\varepsilon \chi t^{7/2}$$ Z ( t ) = σ t + ε χ t 7 / 2 with allowance for crystal nucleation. The effect of nucleation is in the second contribution, which is proportional to $$t^{7/2}$$ t 7 / 2 whereas the first term $$\sim \sqrt{t}$$ ∼ t represents the well-known self-similar solution. The nucleation and crystal growth processes are responsible for the emission of latent crystallization heat, which reduces the melt undercooling and constricts the two-phase layer thickness (parameter $$\chi |
| Databáze: |
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