Prediction of Ternary Liquidus Temperatures by Statistical Modeling of Binary and Ternary Ag–Al–Sn–Zn Systems

The relationship of liquidus temperatures among six binary and four ternary phases in a Ag-Al-Sn-Zn system was analyzed by means of statistical modeling. Four statistical models to predict changes in the liquidus temperatures in Ag-Al-Sn-Zn were proposed on the basis of different hypotheses derived from macroscopic and microscopic standpoints. The results of interpolation tests to evaluate the prediction accuracies of the ternary liquidus temperatures suggested that the multivariate regression model based on binary liquidus temperatures, interactive binary liquidus temperatures, and products of atomic ratios was found to be the most effective among the four models. It was numerically shown that the prediction accuracies of the liquidus temperatures in local ternary systems of Ag-Al-Sn-Zn can be improved further by using the models identified in their neighboring systems. Finally, the possibility to extract the general trend and the abnormal combination of elements for the prediction of liquidus temperatures was discussed on the basis of the statistical framework we considered.