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