Rapid Alloy Solidification: A Quantitative Phase-Field Modelling Technique

The objective of this proposal is to put the modelling of microstructure formation during rapid solidification (RS) processing on the same firm footing as it is for conventional casting. A particular problem during the modelling of RS processing is that the exceptionally complex interactions between heat flow and solute distribution need to be considered. Consequently, while phase-field modelling is now the technique of choice for modelling the formation of solidification microstructure during conventional casting this is not the case for RS processing. The fundamental difference is that during conventional casting crystal growth is so slow that the release of latent heat can be ignored (the isothermal approximation). In RS processing this is not the case and thermal as well a chemical diffusion plays an essential role in determining the solidification microstructure. This in turn leads to a severe multi-scale problem due to the Lewis number (ratio of thermal to chemical diffusivity) typically being of the order 10000 in liquid metals. As a result even fundamental problems such as the predictions of length scale during dendritic growth cannot be tackled in anything but the most approximate of fashions in the RS regime, generally by relating length scale to a stability parameter, sigma, which is assumed constant. However, our previous work shows that sigma actually depends on a multiplicity of factors, including growth rate and cooling regime, and is therefore almost impossible to know a priori. In this proposal we describe how, with the application of advanced numerical techniques such as mesh adaptivity, implicit time-stepping, parallel processing and the use of a multigrid solver, it is feasible to construct a 3-dimensional phase-field model for simulating the formation of alloy microstructures during rapid solidification, using material parameters (including Lewis number) which are realistic for liquid metals. The model will solve for the diffusion of both heat and solute and will contain multiple solid phases such that a range of problems of practical interest in RS processing, such as competitive growth and the formation of metastable phases can be studied. Moreover, by formulating the problem in the 'thin-interface' limit, quantitatively correct predictions of length scales will be able to be made. By utilising the open-source development environment PARAMESH as the basis for our model, the resulting code will be deployable on a range of high performance computing platforms, typically being designed to run on 128-256 cores/processors (which, based upon current hardware trends, will be both widely available and moderately priced by the end of the project). The model will be applied to a number of problems of particular relevance in rapid solidification processing, such as the formation of eutectic dendrites and solidification of deeply undercooled alloys. In order to ensure the closest possible correspondence between modelling and reality a set of carefully controlled validation experiments will be conducted, against which the model can be tested at each stage of its development. These experiments will be undertaken by a PhD student, using a range of high vacuum containerless processing techniques already available at Leeds.

As stated in our summary, the objective of this research is to develop a phase-field modelling capability for the prediction of microstructure formation during rapid solidification which is on a par with the current capabilities for conventional (near isothermal) solidification. By far the largest commercial sector involved in rapid solidification processing is the powder metals industry, with an output in Europe and North America alone which is in excess of 1 billion tonnes of product annually. These powder metal products are technological vital in a number of key industries, including automotive and electronics. In the automotive industry most gears are now made via a powder metallurgical route for wear resistance. In the electronics industry solders pastes are routinely required using < 20 micron metal particles and as the track sizes requirements of modern CPU's an GPU's is reduced further there is an increasing demand for Type 7 and 8 solders (< 15 and < 10 micron particles respectively). However, the cooling rates during the production of such fine particulates can exceed 100000 K/s, well beyond the operating regime of conventional, isothermal phase-field models. A successful conclusion to this project would thus potentially equip the powder metallurgy industry with a tool for the prediction of the microstructure in their as-solidified product, under conditions that are appropriate to the formation of the product, using a thermodynamically consistent methodology. Our non-academic dissemination strategy is thus targeted primarily at the powder metals sector and includes the following specific actions: 1/ To present our work at PM trade conferences and meetings, particularly those organised by MPIF and EPMA, where the audience is predominantly drawn from the industry. 2/ To publish in the trade and in-house journals of MPIF and EPMA (e.g. International Journal of Powder Metals). 3/ To host a one day workshop towards the end of the project to show case the project, its results and the model developed. 4/ To freely share the code developed with potential academic collaborators and also to make it available to industry, probably on a consultancy basis. 5/ To maintain throughout the project a web-site which will showcase the model and that will publicise the availability of the model described above.