Structural pathway for nucleation and growth of topologically close-packed phase from parent hexagonal crystal

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

On the complexity of undominated core and farsighted solution concepts in coalition games

ABSTRACT In this paper, we study the computational complexity of solution concepts in the context of coalitional games. Firstly, we distinguish two different kinds of core, the undominated core and excess core, and investigate the difference and relationship between them. Secondly, we thoroughly investigate the computational complexity of undominated core and three farsighted solution concepts-farsighted core, farsighted stable set and largest consistent set