# Phase field modeling of precipitation reactions in miscibility gap systems

Time: Fri 2022-10-14 13.00

Language: English

Subject area: Materials Science and Engineering

Doctoral student: Deepjyoti Mukherjee , Strukturer

Opponent: Professor Benoît Appolaire, Université de Lorraine

Supervisor: Professor Joakim Odqvist, Strukturer; Docent Henrik Larsson, Strukturer

## Abstract

As a backbone to the cutting tools and rock drilling industry, cemented carbides have been used widely due to their high hardness and wear resistance. Most commercially used cemented carbides contain a hard phase made of Tungsten carbide (WC) and a binder phase which is generally ductile. Lately, a secondary hard phase is desired by replacing W in WC partially with one or more metal substitutes such as Ti, V, Ta, Cr and Zr to better its mechanical properties. Some of these carbides are observed to exhibit unusual microstructures during ageing. For example, (Ti,Zr)C present along with WC, has been observed to undergo phase separation from a supersaturated phase, called $\gamma$, to Ti-rich and Zr-rich domains leaving behind an array of precipitates morphologically manifesting as lamellae. This phase separation process has been termed as discontinuous precipitation(DP) as it resembles the classical DP reaction observed in certain binary and multi-component systems. The behaviour comes from the presence of a miscibility gap in the carbide Ref. Borgh et al. 2014 and Ma et al. 2016 due to which the usual response of the system should be to undergo spinodal decomposition(SD), however, the carbide chooses a different path which questions the governing mechanism behind its decomposition process. Several factors are believed to affect such a process and one of such factors is the strain energy, which is generated due to the difference in lattice parameters of the separating phases. When compared to a different miscibility gap system, such as Fe-Cr, where the strain energy is quite low and the response is SD. Other factors such as grain boundary diffusion, atomic mobility, and gradient energy coefficient (κ) are also believed to have an effect on the decomposition process. Therefore, a thorough investigation of the factors is required and, a powerful tool to study the spatio-temporal evolution of the microstructure such as the phase field method, should be used.

According to some experiments the lamellae are generally observed to nucleate at grain boundaries and later grow with the help of grain boundary migration Ref. Borgh et al. 2014. The moving grain boundary leaves behind a series of alternate strands of Ti and Zr rich phases. The growth mechanism behind the moving boundary is believed to be assisted by diffusion of solutes along the grain boundary and generation of the elastic strain energy by it. The phenomenon is commonly known as diffusion induced grain boundary migration(DIGM) and it is believed to be a key part of DP Ref. Hillert and Purdy 1977 and Chongmo and Hillert 1981. In order to recreate DIGM and DP an energetic coupling between the mole fraction and phase field variable is required so that it accounts for the generated strain energy during the process. The main focus of this thesis will be to develop a phase field model accounting for such coupling which will predict DIGM in binary systems and use it further as a medium to model DP in (Ti,Zr)C. The model for DP could be used to predict and control its formation as its occurrence prone to increase the hardness of the carbides. Therefore, it can be used as a tool to design alloys and develop better alternatives. The alternatives could be used to prevent DP in the carbides which could be done by using different metal substitutes that will prefer SD over DP or vice versa.