Machine-learning-assisted multi-objective optimization in vertical zone refining of ultra-high purity indium

Abstract

Optimization of processing parameters cannot rely on the trial-and-error method for the production of ultra-high purity metals owing to the complexity of indium raw material and multi-pass processing procedure. A multi-objective optimization strategy was proposed to optimize the process parameters for vertical zone refining of 7N-grade ultra-high purity indium (In) by using machine learning (ML). Firstly, classification models were established for certain impurities (Si, S, Fe, Zn, Ni, Cu and As). In these models, the Synthetic Minority Over-sampling Technique (SMOTE) was introduced to overcome the sample imbalance problem of the experimental dataset. The accuracy of these classification models reached above 0.9. Secondly, a ridge regression model was built to predict the total impurity content in the product. The root mean square error (RMSE) was 0.023, the Pearson correlation coefficient (r) was 0.91, and R-squared (R2) value was 0.79. Using these models, high-throughput virtual screening was performed to conduct vertical zone-refining experiments, which in turn validated the reliability of the models. Feature analysis by Shapley additive explanations (SHAP) revealed that the total impurity content in the final product strongly depended on the content of Ni and Sn impurities in the 6N-grade indium raw material and on the velocity parameter of the 2rd through 4th zone passes (V2). A lower V2 is favorable for eliminating impurities from indium raw material with total impurity content ranging from 0.2 ppm to 0.4 ppm.