Statistical Thermodynamics and Ordering Kinetics of D019-Type Phase: Application of the Models for H.C.P.-Ti-Al Alloy

TL;DR

This paper develops models using statistical thermodynamics and kinetics to describe atomic ordering in D019 phase of h.c.p.-Ti-Al alloy, analyzing phase transformation, order parameters, and temperature effects.

Contribution

It introduces a combined thermodynamic and kinetic modeling approach for D019 phase ordering in Ti-Al alloys, including temperature-dependent interatomic interactions.

Findings

Temperature-dependent interactions accelerate LRO relaxation.

Equilibrium LRO can be higher in non-stoichiometric compositions.

Model predictions align with experimental phase diagrams.

Abstract

Using the self-consistent field approximation, the static concentration waves approach and the Onsager-type kinetics equations, the descriptions of both the statistical thermodynamics and the kinetics of an atomic ordering of D019 phase are developed and applied for h.c.p.-Ti-Al alloy. The model of order-disorder phase transformation describes the phase transformation of h.c.p. solid solution into the D019 phase. Interatomic-interaction parameters are estimated for both approximations: one supposes temperature-independent interatomic-interaction parameters, while the other one includes the temperature dependence of interchange energies for Ti-Al alloy. The partial Ti-Al phase diagrams (equilibrium compositions of the coexistent ordered and disordered phases) are evaluated for both cases. The equation for the time dependence of D019- type long-range order (LRO) parameter is analyzed. The curves (showing the LRO parameter evolution) are obtained numerically for both temperature-independent interaction energies and temperature-dependent ones. Temperature dependence of the interatomic-interaction energies accelerates the LRO relaxation and diminishes a spread of the values of instantaneous and equilibrium LRO parameters versus the temperature. Both statistical-thermodynamics and kinetics results show that equilibrium LRO parameter for a non-stoichiometry (where an atomic fraction of alloying component is more than 0.25) can be higher than for a stoichiometry at high temperatures. The experimental phase diagram confirms the predicted (ordered or disordered) states for h.c.p.-Ti-Al.