A differential cluster variation method for analysis of spiniodal decomposition in alloys

TL;DR

This paper introduces a differential cluster variation method (DCVM) to analyze spinodal decomposition in alloys, enabling more accurate calculations of gradient energy and decomposition wavelengths, with implications for understanding alloy microstructure evolution.

Contribution

The paper develops a novel DCVM that incorporates lattice symmetry and composition gradients to improve analysis of spinodal decomposition in alloys.

Findings

Gradient coefficient in ordered Al-Li alloys is significantly larger than in disordered alloys.

Calculated fastest growing wavelength is about 10 nm, larger than experimental domain sizes.

The method explains the dominance of antiphase boundaries in post-ordering spinodal decomposition.

Abstract

A differential cluster variation method (DCVM) is proposed for analysis of spinoidal decomposition in alloys. In this method, lattice symmetry operations in the presence of an infinitesimal composition gradient are utilized to deduce the connection equations for the correlation functions and to reduce the number of independent variables in the cluster variation analysis. Application of the method is made to calculate the gradient energy coefficient in the Cahn-Hilliard free energy function and the fastest growing wavelength for spinodal decomposition in Al-Li alloys. It is shown that the gradient coefficient of congruently ordered Al-Li alloys is much larger than that of the disordered system. In such an alloy system, the calculated fastest growing wavelength is approximately 10 nm, which is an order of magnitude larger than the experimentally observed domain size. This may provide a theoretical explanation why spinodal decomposition after a congruent ordering is dominated by the antiphase boundaries.