The kinetics of diffusive phase transformations in the light of trans-interface diffusion

Abstract

A variety of models with detailed coupling of thermodynamics and kinetics at a migrating interface has been developed for simulating diffusive phase transformations. A classification of such models is possible by the way the processes associated with the migrating interface are treated. In case of sharp interface models, the interfacial processes are assumed to be fast enough to not influence overall phase transformation kinetics (i.e. local equilibrium holds), or an effective mobility is attributed to the interface, which is also known as mixed-mode approach. In case of models treating an interface with finite thickness, the kinetic processes inside the interface are described in detail. In this work, a quasi-sharp interface model is analysed using the thermodynamic extremal principle. By this procedure, the implicit assumptions behind the modelling approach are revealed, and the evolution equations are derived. By means of a thick interface model, the contact conditions at both sides of a migrating interface are calculated, and the driving forces for interface migration and trans-interface diffusion are obtained. Based on these driving forces, the quasi-sharp interface model is evaluated and an effective interface diffusion coefficient is calculated.

In Situ High-Temperature EBSD and 3D Phase Field Studies of the Austenite–Ferrite Transformation in a Medium Mn Steel

“…Many models have been proposed to incorporate the effect of various parameters on the rate of interface migration during ferrous phase transformations, as nicely summarized in a comprehensive review paper (Gouné et al, 2015). In such models, the phase transformation is modeled by reducing the actual interface to a mathematical surface characterized with multiple variables and parameters such as the interface thickness (Svoboda et al, 2011), trans-interface diffusivity (Gamsjäger & Rettenmayr, 2015), interface energy (Militzer et al, 2014) and crystallographic orientation relationship (OR) between two crystals in contact (Ecob & Ralph, 1981). Yet, all these models explicitly or implicitly assume that the local interface movement is the same for each interface and does not vary along a particular interface, except near triple lines and quadrupole points.…”

The thermodynamics of non-equilibrium interfaces during phase transformations in concentrated multicomponent alloys

“…As in the present model, other sharp-interface models allow for bulk diffusion on both sides of the interface, which is essential for modeling solid-state phase transformations. The approach of Hillert, Rettenmayr, and coworkers [13,14,71,72,73] differs from those previously described in that a composition x tr b (x i or…”

Influence of Finite Mobilities of Triple Junctions on the Grain Morphology and Kinetics of Grain Growth

“…Similarly, triple points T 12 , T 13 and T 14 are equivalent to T 4 , T 5 and T 6 , respectively. The triple points T 10 and T 11 are equivalent to T 3 and T 4 shifted by the vector v. The triple points T 15 and T 16 are equivalent with T 6 and T 7 shifted by the vector (u − v). The system contains 19 grain boundaries, where the equivalent grain boundaries follow from analogous considerations.…”

“…Numerous theoretical and experimental investigations were thus conducted for many decades to better understand the physical processes governing grain growth. As an example the effect of solute drag on migrating grain boundaries and interfaces had been investigated theoretically and experimentally in earlier days, see e.g., [1][2][3][4][5], and remains a hot topic until today, e.g., [6][7][8][9][10][11][12][13][14][15][16][17][18].…”