Nucleation and phase transition of spherical crystals and quasicrystals
Abstract
We investigated the nucleation, growth, and solid-to-solid phase transition processes of spherical six-fold symmetric crystals (C6) and ten-fold symmetric quasicrystals (DQC) using the Lifshitz-Petrich model. By combining the spherical-harmonic pseudospectral method with a nullspace-preserving saddle-point search technique, we resolved the critical nucleus structures and phase transition pathways. Although both transitions from the homogeneous state to the ordered state involve the formation of localized critical nuclei, their subsequent growth processes exhibit distinct modes of accommodating geometric mismatch: C6 forms branched domain structures and persistent line defects associated with orientation and phase mismatches, whereas DQC relaxes collision-induced defects through local coordination rearrangements. The resolved DQC-to-C6 pathway proceeds through a series of metastable intermediates that progressively connect these distinct modes of mismatch accommodation. Its multi-step character reflects the coupled adjustment of local coordination and compatibility between the emerging C6 domains. These results reveal the intrinsic link between the multi-step nature of the phase transition and the distinct structural requirements for accommodating geometric mismatch.
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BibTeX
@misc{zhou2026nucleation,
title = {{Nucleation and phase transition of spherical crystals and quasicrystals}},
author = {Tiejun Zhou and Aibei Xie and Gang Cui and Xianbo Huang and Li Peng and Kai Jiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00931},
eprint = {2610.00931},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00931},
}
RIS
TY - UNPB
TI - Nucleation and phase transition of spherical crystals and quasicrystals
AU - Tiejun Zhou
AU - Aibei Xie
AU - Gang Cui
AU - Xianbo Huang
AU - Li Peng
AU - Kai Jiang
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00931
UR - https://arxiv.org/abs/2610.00931
AB - We investigated the nucleation, growth, and solid-to-solid phase transition processes of spherical six-fold symmetric crystals (C6) and ten-fold symmetric quasicrystals (DQC) using the Lifshitz-Petrich model. By combining the spherical-harmonic pseudospectral method with a nullspace-preserving saddle-point search technique, we resolved the critical nucleus structures and phase transition pathways. Although both transitions from the homogeneous state to the ordered state involve the formation of localized critical nuclei, their subsequent growth processes exhibit distinct modes of accommodating geometric mismatch: C6 forms branched domain structures and persistent line defects associated with orientation and phase mismatches, whereas DQC relaxes collision-induced defects through local coordination rearrangements. The resolved DQC-to-C6 pathway proceeds through a series of metastable intermediates that progressively connect these distinct modes of mismatch accommodation. Its multi-step character reflects the coupled adjustment of local coordination and compatibility between the emerging C6 domains. These results reveal the intrinsic link between the multi-step nature of the phase transition and the distinct structural requirements for accommodating geometric mismatch.
ER -