1st Edition

Zentropy Theory and Fundamentals

Edited By Zi-Kui Liu Copyright 2025
    754 Pages 120 Color & 310 B/W Illustrations
    by Jenny Stanford Publishing

    754 Pages 120 Color & 310 B/W Illustrations
    by Jenny Stanford Publishing

    This book compiles selected publications authored or co-authored by the editor to present a comprehensive understanding of following topics: (1) fundamentals of thermodynamics, Materials Genome®, and zentropy theory; (2) zentropy theory for prediction of positive and negative thermal expansions. It is noted that while entropy at one scale is well represented by standard statistical mechanics in terms of probability of individual configurations at that scale, the theory capable of counting total entropy of a system from different scales is lacking. The zentropy theory provides a nested form for configurational entropy enabling multiscale modeling to account for disorder and fluctuations from the electronic scale based on quantum mechanics to the experimental scale based on statistical mechanics using free energies of individual configurations rather than their total energies in standard statistical mechanics. The predictions from the zentropy theory demonstrate remarkable agreements with experimental observations for magnetic transitions and associated emergent behaviors of strongly correlated metals and oxides, including singularity and instability at critical points and positive and negative thermal expansions, without the need of additional truncated models and fitting model parameters beyond density function theory. This paves the way to provide the predicted phase equilibrium data for high throughput predictive CALPHAD modeling of complex material systems, and those individual configurations may thus be considered as the genomic building blocks of individual phases in the spirit of Materials Genome®.

    Part I Fundamentals of Thermodynamics, Material Genome, and Zentropy Theory


    1. Computational Thermodynamics and Its Applications

    Zi-Kui Liu


    2. Perspective on Materials Genome

    Zi-Kui Liu


    3. Theory of Cross Phenomena and Their Coefficients beyond Onsager Theorem

    Zi-Kui Liu


    4. Thermodynamics and Its Prediction and CALPHAD Modeling: Review, State of the Art, and Perspectives

    Zi-Kui Liu


    5. Thermodynamics of Constrained and Unconstrained Equilibrium Systems and Their Phase Rules

    Zi-Kui Liu and John Ågren


    6. On Two-Phase Coherent Equilibrium in Binary Alloys

    Zi-Kui Liu and John Ågren


    7. Multiscale Entropy and Its Implications to Critical Phenomena, Emergent Behaviors, and Information

    Zi-Kui Liu, Bing Li, and Henry Lin


    8. Maximizing the Number of Coexisting Phases Near Invariant Critical Points for Giant Electrocaloric and Electromechanical Responses in Ferroelectrics

    Zi-Kui Liu, Xinyu Li, and Q. M. Zhang


    9. Mitigating Grain Growth in Binary Nanocrystalline Alloys through Solute Selection Based on Thermodynamic Stability Maps

    K. A. Darling, M. A. Tschopp, B. K. VanLeeuwen, M. A. Atwater, and Zi-Kui Liu


    10. On the Transition from Local Equilibrium to Paraequilibrium during the Growth of Ferrite in Fe–Mn–C Austenite

    Zi-Kui Liu and John Ågren


    Part II Zentropy Theory for Prediction of Positive and Negative Thermal Expansions


    11. Zentropy Theory for Positive and Negative Thermal Expansion

    Zi-Kui Liu, Yi Wang, and Shun-Li Shang


    12. Thermodynamics of the Ce γ–α Transition: Density-Functional Study

    Y. Wang, L. G. Hector, Jr., H. Zhang, S. L. Shang, L. Q. Chen, and Zi-Kui Liu


    13. A Thermodynamic Framework for a System with Itinerant-Electron Magnetism

    Y. Wang, L. G. Hector Jr., H. Zhang, S. L. Shang, L. Q. Chen, and Zi-Kui Liu


    14. Thermodynamic Fluctuations in Magnetic States: Fe3Pt as a Prototype

    Y. Wang, S.L. Shang, H. Zhang, L.-Q. Chen, and Zi-Kui Liu


    15. Thermodynamic Fluctuations between Magnetic States from First-Principles Phonon Calculations: The Case of bcc Fe

    Shun-Li Shang, Yi Wang, and Zi-Kui Liu


    16. Origin of Negative Thermal Expansion Phenomenon in Solids

    Zi-Kui Liu, Yi Wang, and Shun-Li Shang


    17. Thermal Expansion Anomaly Regulated by Entropy

    Zi-Kui Liu, Yi Wang, and Shun-Li Shang


    18. Nature of Ferroelectric-Paraelectric Phase Transition and Origin of Negative Thermal Expansion in PbTiO3

    Huazhi Fang, Yi Wang, Shun-Li Shang, and Zi-Kui Liu


    19. Fundamentals of Thermal Expansion and Thermal Contraction

    Zi-Kui Liu, Shun-Li Shang, and Yi Wang


    20. Density Functional Thermodynamic Description of Spin, Phonon and Displacement Degrees of Freedom in Antiferromagnetic-to-Paramagnetic Phase Transition in YNiO3

    J. L. Du, O. I. Malyi, S.-L. Shang, Y. Wang, X.-G. Zhao, F. Liu, A. Zunger, and Zi-Kui Liu


    Zi-Kui Liu is the Dorothy Pate Enright Professor in the Department of Materials Science and Engineering at the Pennsylvania State University, USA. He obtained his BS from Central South University, China, MS from the University of Science and Technology Beijing, China, and PhD from KTH Royal Institute of Technology, Sweden. He was a research associate at the University of Wisconsin-Madison and a senior research scientist at QuesTek Innovations LLC. He has been at the Pennsylvania State University since 1999, the editor-in-chief of CALPHAD journal since 2001, and the president of CALPHAD Inc. since 2013. Dr Liu coined the term "Materials Genome®" in 2002. He is a fellow of TMS and ASM International and has served as the president of ASM International and a member of the ASM International Board of Trustees and the TMS Board of Directors. He has graduated 32 PhD students and published over 650 papers.