  The solid diffusive phase transformation involving the nucleation and growth
of one nucleus is universal and frequently employed but has not yet been fully
understood at the atomic level. Here, our first-principles calculations reveal
a structural formation pathway of a series of topologically close-packed (TCP)
phases within the hexagonally close-packed (hcp) matrix. The results show that
the nucleation follows a nonclassical nucleation process, and the whole
structural transformation is completely accomplished by the shuffle-based
displacements, with a specific 3-layer hcp-ordering as the basic structural
transformation unit. The thickening of plate-like TCP phases relies on forming
these hcp-orderings at their coherent TCP/matrix interface to nucleate ledge,
but the ledge lacks the dislocation characteristics considered in the
conventional view. Furthermore, the atomic structure of the critical nucleus
for the Mg2Ca and MgZn2 Laves phases was predicted in terms of Classical
Nucleation Theory (CNT), and the formation of polytypes and off-stoichiometry
in TCP precipitates is found to be related to the nonclassical nucleation
behavior. Based on the insights gained, we also employed high-throughput
screening to explore several common hcp-metallic (including hcp-Mg, Ti, Zr, and
Zn) systems that may undergo hcp-to-TCP phase transformations. These insights
can deepen our understanding of solid diffusive transformations at the atomic
level, and constitute a foundation for exploring other technologically
important solid diffusive transformations.
