Revisiting Hume-Rothery’s Rules with artificial neural networks

Hume-Rothery’s breadth of knowledge combined with a quest for generality gave him insights into the reasons for solubility in metallic systems that have become known as Hume-Rothery’s Rules. Presented with solubility details from similar sets of constitutional diagrams, can one expect artificial neural networks (ANN), which are blind to the underlying metals physics, to reveal similar or better correlations? The aim is to test whether it is feasible to predict solid solubility limits using ANN with the parameters that Hume-Rothery identified. The results indicate that the correlations expected by Hume-Rothery’s Rules work best for a certain range of copper or silver alloy systems. The ANN can predict a value for solubility, which is a refinement on the original qualitative duties of Hume-Rothery’s Rules. The best combination of input parameters can also be evaluated by ANN.

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