Original article
Diffusional Monte Carlo model of liquid-phase sintering

https://doi.org/10.1016/j.matcom.2011.05.005Get rights and content

Abstract

Liquid-phase sintering (LPS) is a consolidation process for metallic and ceramic powders. At given temperature conditions, the process occurs with constant amount of liquid phase. However, the evolution of solid-particle shape is observed, namely, the rounding of particles and the growth of big particles at the expense of the small ones, which is known as Ostwald ripening.

In this work, we propose a Monte Carlo (MC) model to simulate the microstructural evolution during LPS. The model considers the change of state of the discretising elements, namely voxels, of the system. The microstructural evolution proceeds accounting for both the geometrical characteristics of the particles, such as the number of solid neighbours, and the amount of solute contained in or surrounding a randomly chosen voxel. This has been implemented in terms of two probability distribution functions (PDFs). The diffusion of solute has also been considered by means of the implementation of a three-dimensional finite-difference algorithm.

The diffusional MC model that we present is able to reproduce the Ostwald ripening behaviour and, in particular, results match the case in which the process is limited by the diffusion of the solute in the liquid phase.

Introduction

The present work is a follow-up of the work presented in Ref. [15]. In that work, we first made a brief description of multi-scale computational modelling, paying special attention to the micro-scale techniques, in which the Monte Carlo (MC) method is included. Then, we introduced the concept of sintering, in general, and the particularities of liquid-phase sintering. We summarized the theoretical background of these processes and included the main assumptions to tackle the problem of particle coarsening, either by Ostwald ripening [19] or by particle coalescence, from an analytical point of view. Finally, the geometrical MC model of liquid-phase sintering was defined. After that, the method was validated and some simulation results were shown.

In this article, we propose a MC method that combines the geometrical MC model of Ref. [15] with a diffusional MC model, in order to take into account the presence of a solute and its diffusion through the liquid phase. The main features of the geometrical model will be summarized below (see Section 2) for clarity. Once the method is defined and validated, some results obtained using the proposed complete model will be shown.

Section snippets

Geometrical MC model of LPS

The computer models of LPS presented in Ref. [15] and the model that we will present here are based on the Monte Carlo (MC) technique. This technique consists of the random modification of the elements that form the system [18]. Thus, the simulated microstructures have to be divided into volume elements, called “voxels”, which, in this work, are cubes of constant size, although other microstructural discretisation shapes (for instance, tetrakaidecahedra [17]) could be used. This is one of the

Diffusional MC model of LPS

As mentioned, the diffusional model that we propose is also based on the Monte Carlo technique, and therefore, it benefits from the advantages of tackling with a discretised system and a real distribution of particles, compared to other analytical models [14], [30], [3]. Nevertheless, in this case, voxels are assigned not only a state (“solid” or “liquid”) but also a new parameter, namely the solute concentration, which represents the amount of solute contained in the voxel, ranging between 0

Conclusions

We have developed a diffusional model, based on the Monte Carlo technique, for the microstructural evolution of liquid-solid systems, in which coarsening by Ostwald ripening and by particle coalescence can take place. The main advantages of this model compared to other models is that a second component and the diffusion of this component can be taken into account. Besides, because we are working with a discretised system, we can analyse the local behaviour of the model, which is an improvement

Acknowledgement

The authors would like to thank Unilever R&D Colworth (UK) for the support of this research.

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