In particular, it is interesting to determine how the nucleus is formed and how the crystal grows. Therefore, it is desirable to contribute to understanding these phenomena with experimental evidence at the particle level, where each particle is followed as it slows down its dynamics while the system diminishes its effective temperature. However, due to the microscopic nature of the crystallisation processes, direct experimental evidence describing the phenomena at the particle level is hard to find in the literature. Some experimental results 15, 16 and numerical simulations 17, 18 support this two-step non-classical nucleation theory. In this second-step process, thermal perturbations and the interaction of the aggregate with the free particles are crucial in the reordering process that should be detailedly understood 14. After that, the system must overpass a second energy barrier to reorder the aggregate to become the nucleus. Experimentally, it has been found that in order to occur the first step, the barrier energy that needs to be over-passed is lower than that predicted by the CNT. Then it is ordered in the second step 13. In one of the non-classical nucleation theories 11, 12, specifically the two-step nucleation theory, it is predicted that an amorphous aggregate is initially formed in the first step. Therefore, there is a search for a theory capable of describing nucleation in those systems for which CNT fails. For instance, it fails to predict the critical size of the nucleus and the height of the energy barrier, among other quantities that do not correspond to what is observed in some systems 8, 9, 10. This theory has successfully described nucleation and crystal growth in some systems but fails in others. CNT assumes that the nucleus has been an ordered structure since its generation. Then, to form a nucleus, it is necessary to overpass an energy barrier. At this point, the aggregate becomes a stable nucleus and grows to form the crystal. For specific conditions, aggregates reach a critical size when free bulk energy surpasses the free surface energy. Starting from a fluid-like state, as the effective temperature diminishes, unstable aggregates form and become larger as the effective temperature decreases 5, 6, 7. According to CNT, particle concentration inhomogeneities lead to the formation of the nucleus in just one step, from which the crystal grows. Non-classical nucleation theories arise as alternatives to describe crystallisation in various systems for which classical nucleation theory (CNT) fails 1, 2, 3, 4. We studied the structural changes and features in the system by using the sixth orientational order parameter and the packing fraction. On the contrary, the structures are more branched for a smaller depth of the parabolic potential. Also, aggregates are more clearly round-shaped as parabolic potential depth increases. In the explored range of the depths of the parabolic potential, crystallisation generally occurs quicker as the deeper parabolic potential is. The crystal growth occurs similarly small disordered groups of particles join the nucleus, forming an amorphous shell of particles which experiments a rearranging while the aggregate grows. However, if the depth of the parabolic potential exceeds a certain value, the reordering process of the second step does not occur. The nucleus size is larger for deeper concaveness of the parabolic potential. In an ulterior second step, this disordered aggregate, due to the effective temperature and the perturbations caused by the impacts of free particles moving in the surrounding region, evolves to an ordered crystalline structure. At the initial formation of the nucleus, as a first step, in the central region of the lens an amorphous aggregate is formed. We have observed that the two-step features of the crystallisation process are more evident as the depth of the parabolic potential increases. We studied the two-step crystallisation process of a magnetic active 2D-granular system placed on different lens concaveness and under the action of an alternating magnetic field which controls its effective temperature.
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