Quantifying the degree of disorder and associated phenomena in materials through zentropy: Illustrated with invar Fe₃Pt

Disorder exists in all materials at finite temperatures, implicating that the degree of disorder (fDoD) is a key parameter to tailor macroscopic functionalities of materials. Here, we propose to quantify fDoD as a function of temperature using properties such as configurational entropy predicted by zentropy-a theory to represent total entropy of a system via a nested formula through the integration of quantum mechanics and statistical mechanics. Taking Invar Fe₃Pt as an example through first-principles based calculations from 0 K to finite temperatures, we demonstrate the capability of the present approach in predicting fDoD and associated phenomena in Fe₃Pt such as Curie temperature and negative thermal expansion, showing a good agreement with experimental data.