Direct measurement of the Gibbs free energy of mixing via atom probe tomography

The concept of thermodynamic free energy plays a central role across various disciplines, providing critical insights into system dynamics, energy flow, and sustainability. In materials science, Gibbs free energies are typically determined through phase diagram modeling, which relies on a broad range of thermodynamic data. This process requires the investigation of well-equilibrated materials, a task that can be time-consuming or even impractical for systems with low mobility. In this study, we introduce a novel methodology for extracting the composition dependence of the Gibbs free energy of mixing from local composition fluctuations in solids using atom probe tomography (APT). We present both the theoretical framework and practical implementation through computational simulations, as well as experimental validation using APT data from Cu–Ni alloys. The experimental phase diagram constructed from the resulting Gibbs free energy of mixing shows excellent agreement with CALPHAD-based predictions. This approach provides superior accuracy and efficiency, as equilibration on the nanometer scale can be achieved in a relatively short time. It holds promising potential for application to multi-component solids, liquids, and organic systems, particularly with emerging techniques like cryo-APT.