# Mg2SnSi Thermoelectric System Microstructure Data Over CALPHAD and Elastic Parameters Space

The total free energy of a heterogeneous system is ascribed by Eq.~\ref{eqn:tot_energy} where bulk free energy density ($f^{bulk}$), interfacial free energy density ($f^{int}$), and elastic energy density ($f^{elas}$), are the contributing factors.

$latex <\mathcal{F}^{tot} = f^{int} + f^{bulk} + f^{elas}>$

`The process of solid-state phase transition in materials is influenced by elastic anisotropy, and the hardness enhancement observed upon the age hardening relies on a shear modulus difference between the formed domains as well as their coherency strain. Thus, it is of primary interest to determine the elastic properties of the alloy system to study the induced variation in the microstructure. The Ab-initio-based calculated, and experimental lattice parameters for cubic Mg$_2$Sn$_{1-x}$Si$_x$ system at room/high temperatures, and also different compositions are taken from different studies in the literature. The values are either provided for individual phases (Mg$_2$Sn and Mg$_2$Si), or for the parent phase as a function of composition. Using these data, the stress-free transformation strain (SFTS) ($\epsilon^{0}_{ij}$) for Mg$_2$Sn, and Mg$_2$Si was calculated. Accordingly, the range is used to initiate a uniform sample set for the propagation of uncertainty in the phase-field model. The range of all parameters used in dataset 3.0 is shown in Table \ref{table:1st_order_elastic_cts}. This database is used in our recent paper \cite{attari2020uncertainty}. For complete interpretation of the generation of the database, the reader is referred to \cite{attari2020uncertainty,honarmandi2019bayesian,sanghvi2019uncertainty}`