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.