najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2026-17-4-424-431najo-1904Research ArticlePHYSICSФИЗИКАTwo-phase core-shell nanoparticle modelДвухфазная модель наночастицы типа «ядро–оболочка»https://orcid.org/0000-0003-1514-857XРехвиашвилиС.RekhviashviliS.

Sergo Rekhviashvili 

Nalchik

rsergo@mail.ruInstitute of Applied Mathematics and Automation, KBSC RASRussian Federation202631082026174424431Copyright © Rekhviashvili S., 20262026Рехвиашвили С.Rekhviashvili S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1904

A two-phase core-shell model for nanoparticle melting is proposed, in which a solid core is sur- rounded by a quasi-liquid shell. The model provides self-consistent analytical expressions for the size-depen- dent melting temperature and effective surface tension, along with kinetic equations describing the temporal evolution of the shrinking solid core under external heating. The analysis identifies distinct melting regimes, including a pronounced acceleration in the final stage caused by curvature-induced melting-point depression. Numerical estimates for silver and copper nanoparticles demonstrate that size effects can significantly reduce melting time. The results offer simple and physically transparent relations that clarify nanoscale melting behav- ior, provide an intuitive interpretation of the Tolman length, and explain the overheating observed in molecular dynamics simulations.

Предложена двухфазная модель плавления наночастицы типа «ядро–оболочка», в которой твердое ядро окружено квазижидкой оболочкой. Модель позволяет получить самосогласованные аналитические выражения для температуры плавления и эффективного поверхностного натяжения, зависящих от размера наночастицы, а также кинетические уравнения, описывающие временную эволюцию сокращающегося при нагреве твердого ядра. Анализ выявляет различные режимы плавления, в том числе выраженное ускорение на заключительной стадии, обусловленное понижением температуры плавления вследствие кривизны поверхности. Численные оценки для наночастиц серебра и меди показывают, что размерные эффекты способны существенно сократить время плавления. Полученные результаты дают простые и физически наглядные соотношения, позволяющие лучше понять процесс плавления на наноуровне, дают простую интерпретацию длины Толмена и объясняют перегрев, часто наблюдаемый при моделировании методом молекулярной динамики.

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The authors declare that there are no conflicts of interest present.