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Nucleation plays a critical role in many physical and biological phenomenaranging from crystallization, melting and evaporation to the formation ofclouds and the initiation of neurodegenerative diseases. However, nucleation isa challenging process to study in experiments especially in the early stagewhen several atoms/molecules start to form a new phase from its parent phase.Here, we advance atomic electron tomography to study early stage nucleation at4D atomic resolution. Using FePt nanoparticles as a model system, we revealthat early stage nuclei are irregularly shaped, each has a core of one to fewatoms with the maximum order parameter, and the order parameter gradient pointsfrom the core to the boundary of the nucleus. We capture the structure anddynamics of the same nuclei undergoing growth, fluctuation, dissolution,merging and/or division, which are regulated by the order parameterdistribution and its gradient. These experimental observations differ fromclassical nucleation theory (CNT) and to explain them we propose the orderparameter gradient (OPG) model. We show the OPG model generalizes CNT andenergetically favours diffuse interfaces for small nuclei and sharp interfacesfor large nuclei. We further corroborate this model using molecular dynamicssimulations of heterogeneous and homogeneous nucleation in liquid-solid phasetransitions of Pt. We anticipate that the OPG model is applicable to differentnucleation processes and our experimental method opens the door to study thestructure and dynamics of materials with 4D atomic resolution.

Capturing Nucleation at 4D Atomic Resolution