Phase-field crystal modeling of early stage clustering and precipitation in metal alloys

Abstract

A phase field crystal model is used to investigate the mechanisms of formation and growth of early clusters in quenched/aged dilute binary alloys, a phenomenon typically outside the scope of molecular dynamics time scales. We show that formation of early sub-critical clusters is triggered by the stress relaxation effect of quenched-in defects, such as dislocations, on the energy barrier and the critical size for nucleation. In particular, through analysis of system energetics, we demonstrate that the growth of sub-critical clusters into overcritical sizes occurs due to the fact that highly strained areas in the lattice locally reduce or even eliminate the free energy barrier for a first-order transition.

Atomic-scale pathway of early-stage precipitation in Al–Mg–Si alloys

“…The descriptions of such methodologies can be found in detail in Refs. 40,41,43 . Below, we present the details of the above PFC calculations and simulation methodologies for clustering in a ternary alloy system in 3D.…”

“…The analysis of Fallah et al 40,41,43 on Al-Cu-(Mg) system clearly showed that the presence of quenched-in dislocations in the matrix of a supersaturated solid solution system could lead to stress relaxation effects associated with the sum of dislocation Burger's vectors, Σb 2 i , and thus effectively reduce, or even eliminate, the local energy barrier for nucleation. This effect can be similarly shown in the current system (see the inset of Fig.…”

Multicomponent phase-field crystal model for structural transformations in metal alloys

“…This in turn draws nearby dislocations to the cluster in attempts to relieve these additional stresses caused by solute accumulation. An extensive investigation of solute clustering mechanisms, in presence of quenchedin bulk crystal defects, has been done through a quantitative analysis of the system energetics in binary alloys in [34] and recently in ternary alloys, using the present model [40].…”

Phase-field crystal model for a diamond-cubic structure

“…This model has been shown to stabilize crystal structures such as bcc, face-centered cubic (f cc), simple cubic (sc), and hexagonal closepacked (hcp) structures [12] and has been used to study many phenomena including solute drag effects on grain boundary motion [13], clustering and precipitation in an Al-Cu alloy [14,15], and the stability of stacking faults and partial dislocations [16]. However, a diamondcubic (dc) structure, to the knowledge of the authors, had not been shown to be stable within the PFC model.…”