1st Edition

Zentropy Tools, Modelling, and Applications

Edited By Zi-Kui Liu Copyright 2025
    854 Pages
    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) density functional theory and CALPHAD modeling; (2) computational tools; and (3) applications of computational thermodynamics. 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 Density Functional Theory and CALPHAD Modeling


    1.       First-Principles Calculations and CALPHAD Modeling of Thermodynamics

    Zi-Kui Liu


    2.       Thermodynamics of the Cr-Ta-W System by Combining the Ab Initio and CALPHAD Methods

    Larry Kaufman, P. E. A. Turchi, Weiming Huang, and Zi-Kui Liu


    3.       Ab initio Lattice Stability in Comparison with CALPHAD Lattice Stability

    Y. Wang, S. Curtarolo, C. Jiang, R. Arroyave, T. Wang, G. Ceder, L.-Q. Chen, and Zi-Kui Liu


    4.       Thermodynamic Properties of Al, Ni, NiAl, and Ni3Al from First-Principles Calculations

    Y. Wang, Zi-Kui Liu, and L.-Q. Chen


    5.       First-Principles Study of Binary bcc Alloys Using Special Quasirandom Structures

    Chao Jiang, C. Wolverton, Jorge Sofo, Long-Qing Chen, and Zi-Kui Liu


    6.       An Integrated Framework for Multiscale Materials Simulation and Design

    Zi-Kui Liu, L.-Q. Chen, P. Raghavan, Q. Du, J. O. Sofo, S. A. Langer, and C. Wolverton


    7.       First-Principles Calculation of Self-Diffusion Coefficients

    M. Mantina, Y. Wang, R. Arroyave, L. Q. Chen, Zi-Kui Liu, and C. Wolverton


    8.       Ocean of Data: Integrating First-Principles Calculations and CALPHAD Modeling with Machine Learning

    Zi-Kui Liu


    9.       First-Principles Thermodynamic Theory of Seebeck Coefficients

    Yi Wang, Yong-Jie Hu, Brandon Bocklund, Shun-Li Shang, Bi-Cheng Zhou, Zi-Kui Liu, and Long-Qing Chen


    10.    An Alternative Approach to Predict Seebeck Coefficients: Application to La3–xTe4

    Yi Wang, Xiaoyu Chong, Yong-Jie Hu, Shun-Li Shang, Fivos R. Drymiotis, Samad A. Firdosy, Kurt E. Star, Jean-Pierre Fleurial, Vilupanur A. Ravi, Long-Qing Chen, and Zi-Kui Liu


    11.    Quantifying the Degree of Disorder and Associated Phenomena in Materials through Zentropy: Illustrated with Invar Fe3Pt

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


    12.    Parameter-Free Prediction of Phase Transition in PbTiO3 through Combination of Quantum Mechanics and Statistical Mechanics

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


    13.    Genomic Materials Design: CALculation of PHAse Dynamics

    G. B. Olson and Zi-Kui Liu


    Part II Computational Tools


    14.    Efficient Stochastic Generation of Special Quasirandom Structures

    A. van de Walle, P. Tiwary, M. de Jong, D.L. Olmsted, M. Asta, A. Dick, D. Shin, Y. Wang, L.-Q. Chen, and Zi-Kui Liu


    15.    YPHON: A Package for Calculating Phonons of Polar Materials

    Yi Wang, Long-Qing Chen, and Zi-Kui Liu


    16.    pycalphad: CALPHAD-Based Computational Thermodynamics in Python

    Richard Otis and Zi-Kui Liu


    17.    ESPEI for Efficient Thermodynamic Database Development, Modification, and Uncertainty Quantification: Application to Cu–Mg

    Brandon Bocklund, Richard Otis, Aleksei Egorov, Abdulmonem Obaied, Irina Roslyakova, and Zi-Kui Liu


    18.    Quantified Uncertainty in Thermodynamic Modeling for Materials Design

    Noah H. Paulson, Brandon J. Bocklund, Richard A. Otis, Zi-Kui Liu, and Marius Stan


    19.    DFTTK: Density Functional Theory ToolKit for High-throughput Lattice Dynamics Calculations

    Yi Wang, Mingqing Liao, Brandon J. Bocklund, Peng Gao, Shun-Li Shang, Hojong Kim, Allison M. Beese, Long-Qing Chen, and Zi-Kui Liu


    20.    Extensible Structure-Informed Prediction of Formation Energy with Improved Accuracy and Usability Employing Neural Networks

    Adam M. Krajewski, Jonathan W. Siegel, Jinchao Xu, and Zi-Kui Liu


    21.    Predictive Crystal Plasticity Modeling of Single Crystal Nickel Based on First-Principles Calculations

    John D. Shimanek, Shipin Qin, Shun-Li Shang, Zi-Kui Liu, and Allison M. Beese


    22.    Density Functional Theory-Informed Dislocation Density Hardening within Crystal Plasticity: Application to Modeling Deformation of Ni Polycrystals

    Adnan Eghtesad, John D. Shimanek, Shun-Li Shang, Ricardo Lebensohn, Marko Knezevic, Zi-Kui Liu, and Allison M. Beese


    Part III Applications of Computational Thermodynamics


    23.    Application of the Le Chatelier Principle on Gas Reactions

    Zi-Kui Liu, John Ågren, and Mats Hillert


    24.    Morphology of Cementite Decomposition in an Fe-Cr-C Alloy

    Zi-Kui Liu and John Ågren


    25.    The Development of Phase-Based Property Data Using the CALPHAD Method and Infrastructure Needs

    Carelyn E. Campbell, Ursula R. Kattner, and Zi-Kui Liu


    26.    Developing Gradient Metal Alloys through Radial Deposition Additive Manufacturing

    Douglas C. Hofmann, Scott Roberts, Richard Otis, Joanna Kolodziejska, R. Peter Dillon, Jong-ook Suh, Andrew A. Shapiro, Zi-Kui Liu, and John-Paul Borgonia


    27.    The Penn State-Georgia Tech CCMD: Ushering in the ICME Era

    Zi-Kui Liu and David L. McDowell


    28.    Synthesis Science of SrRuO3 and CaRuO3 Epitaxial Films with High Residual Resistivity Ratios

    Hari P. Nair, Yang Liu, Jacob P. Ruf, Nathaniel J. Schreiber, Shun-Li Shang, David J. Baek, Berit H. Goodge, Lena F. Kourkoutis, Zi-Kui Liu, Kyle M. Shen, and Darrell G. Schlom


    29.    Suitability of Binary Oxides for Molecular-Beam Epitaxy Source Materials: A Comprehensive Thermodynamic Analysis

    Kate M. Adkison, Shun-Li Shang, Brandon J. Bocklund, Detlef Klimm, Darrell G. Schlom, and Zi-Kui Liu


    30.    Adsorption-Controlled Growth of Ga2O3 by Suboxide Molecular-Beam Epitaxy

    Patrick Vogt, Felix V. E. Hensling, Kathy Azizie, Celesta S. Chang, David Turner, Jisung Park, Jonathan P. McCandless, Hanjong Paik, Brandon J. Bocklund, Georg Hoffman, Oliver Bierwagen, Debdeep Jena, Huili G. Xing, Shin Mou, David A. Muller, Shun-Li Shang, Zi-Kui Liu, and Darrell G. Schlom


    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.