Dendritic solidification: The role of heat conduction in the solid

Lasse Makkonen

    Research output: Contribution to journalArticleScientificpeer-review


    Ivantsov’s equation of dendritic solidification under a given supercooling ΔT provides the product of the growth velocity V and the tip radius of curvature R, but not V and R separately. However, experimentally, it is observed that both V and R are uniquely determined by ΔT. Assumptions, such as maximum velocity criterion, marginal stability criterion and solvability criterion, have been proposed to deal with the paradox, but it has been repeatedly pointed out that another fundamental equation must be missing from the treatment, since Ivantsov’s single equation includes two unknowns. Here, such a first-principles equation is proposed based on the dissipation and heat transfer of interfacial energy within the solid. It is demonstrated that combining this previously unrecognized mechanism with the conventional heat transfer to the liquid, provides a dendrite growth selection law in harmony with experimental data.
    Original languageEnglish
    Pages (from-to)1328-1331
    JournalCrystallography Reports
    Issue number7
    Publication statusPublished - Dec 2021
    MoE publication typeA1 Journal article-refereed


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