Original articleDiffusional Monte Carlo model of liquid-phase sintering
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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