https://doi.org/10.1140/epjb/s10051-026-01165-8
Research – Statistical and Nonlinear Physics
Phase-field crystal simulation of bi-crystal phase and liquid pool evolution in grain boundary premelting region under the strain
1
School of Materials Science and Engineering, Nanjing University of Science and Technology, 210094, Nanjing, People’s Republic of China
2
Department of Physics, Abdul Wali Khan University, 23200, Mardan, KPK, Pakistan
3
School of Mechanical and Electrical Engineering, Hainan Vocational University of Science and Technology, 571126, Haikou, People’s Republic of China
a
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Received:
11
December
2025
Accepted:
6
April
2026
Published online:
18
April
2026
Abstract
The phase-field crystal (PFC) model is used to study liquid pools and phase transformations in premelting zones. The investigation reveals distinct transformations, including the conversion of the liquid-triangular-striped phase into triangular phase, the transition from liquid-triangular to triangular phase, and the transformation of triangular-striped phase into striped configurations. Furthermore, the study observes the presence of extensive liquid pools and occurrences of triangular melting. It is shown that grain boundaries alter during premelting with variations of temperature and strain, and the solid phase transforms into the liquid phase at the grain boundaries. We observed that premelting first appears at the grain boundary of a bi-crystal liquid phase due to the aggregation of dislocations and the minimization of free energy over time. A decrease in atomic density and an increase in undercooling contribute to the transition of dislocation arrays, leading to the formation of a liquid-like state with disrupted atomic order. Atom density is inversely proportional to liquid pool width. When a strain is applied, dislocation pairs encounter and form a single crystal as the temperature decreases. It is found that increasing rates accelerate the evolution of liquid pools and dislocation absorption at grain boundaries, promoting lattice distortion and the solid–liquid transition in the premelting zone. These findings reveal that fracture propagation is influenced by strain and undercooling, and the presence of liquid pools in crystal materials also affects fracture propagation. This research holds valuable implications for understanding and controlling phase transformations in various crystals.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
