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... Read more

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

Biography

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.