Integrating quantum, statistical, classical, and irreversible thermodynamics for prediction, discovery and design of materials

Zi-Kui Liu

Department of Materials Science and Engineering

Pennsylvania State University, University Park, PA 16802, USA

EXTENDED ABSTRACT: Thermodynamics is a science concerning the state of a system, whether it is stable, metastable or unstable, when interacting with the surroundings. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs*s combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibb's combined law, so it is only applicable to equilibrium systems, thus termed as classical thermodynamics (CT). Gibbs further derived the classical statistical mechanics (CSM) in terms of the probability of configurations in a system in 1900Js. With the quantum mechanics (QM) developed in 1920's, the QM-based statistical mechanics (QSM) was established and connected to CSM at the classical limit as shown by Landau in 1930*s. The development of density fimction theory (DFT) by Kohn and co-workers in 1960*s enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager in 1930's and Prigogine and co-workers in 1950's. The digitization of thennodynamics was developed by Kauftnan in the framework of the CALculation of PHAse Diagrams (CALPHAD) modeling of individual phases with internal degrees of freedom in 1970's, which has enabled computational materials design in last 50 years. Our recently termed Zentropy theory integrates DFT, QSM and CSM, particularly replace the total energy of each individual configuration in QSM by its DF匚predicted free energy. The Zentropy theory is capable of accurately predict transition temperatures and properties of magnetic materials with inputs only from DFT-based calculations and without fitting parameters, including the singularity at critical points and the strongly correlated physics. This has the potential in next 50 years to shift the paradigm of CALPHAD modeling of thermodynamics from partial reliance on experimental inputs to fully predictive with inputs solely from DFT-based calculations and machine learning models built on those calculations. Furthennore, through the combined law of thermodynamics with the entropy production as a function of internal degrees of freedom, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal, and the cross phenomena originates from the dependence of the conjugate potential of the molar quantity in a flux on nonconjugate potentials, which can be predicted by the Zentropy theory and CALPHAD-based thermodynamic modeling (https://doi.Org/10.1016/j.actamat.2020.08.008, https://d0i.0rg/l0.1080/21663831.2022.2054668, abs/2301.02132).

Keywords:Thermodynamics; Statistical mechanics; CALPHAD

Brief Introduction of Speaker
Zi-Kui Liu

Zi-Kui Liu is the Dorothy Pate Enright Professor at The Pennsylvania State University. He obtained his BS from Central South University (China), MS from University of Science and Technology Beijing (China), PhD from Royal Institute of Technology (KTH, Sweden). He was a research associate at University of Wisconsin-Madison and a senior research scientist at Questek Innovation, LLC. He has been at the Pennsylvania State University since 1999, and his current research activities are centered on first-principles calculations, machine learning, prediction and modeling of thermodynamic, kinetic and mechanical properties, and their integration for understanding defects, phase stability, and phase transformations, and designing materials. Dr. Liu has been the Editor-m-Chief of CALPHAD journal since 2001. He is Fellow of ASM International and TMS and served as the President of ASM International and a member of ASM Board of Trustees and the TMS Board of Directors. Dr. Liu coined the term ''Materials Genome®'' in 2002 and has over 600 publications in peer-reviewed journals.