Modeling and predicting microstructure evolution in lead/tin alloy via correlation functions and stochastic material reconstruction

The binary lead/tin (Pb/Sn) alloy is widely used as an interconnect in microelectronics. The physical properties of this heterogeneous material critically depend on its complex bulk microstructure containing Pb-rich and Sn-rich phases, which can be both laminar and globular. In this paper, we devise a procedure to model and predict the microstructure evolution (i.e. coarsening) in a Pb–Sn alloy aged at elevated temperatures below its melting point using statistical morphological descriptors, i.e. the two-point correlation functions S2 associated with the phases. We verify via phase-field simulations that the growing length scale characterizing microstructure coarsening can be well captured by the corresponding correlation functions, which enables us to predict the S2 of intermediate microstructures given the initial and final microstructures. Stochastic material reconstruction techniques are employed to generate virtual three-dimensional microstructures that are consistent with the predicted correlation functions, which are quantitatively compared with the actual alloy microstructures when available.