About

Dr. Zi-Kui Liu is the Corning Faculty Fellowship in Materials Science and Engineering at Penn State. He obtained his B.S. in Metallurgy from Central South University in China, his M.S. in Materials Engineering from the University of Science and Technology Beijing, and his Ph.D. in Physical Metallurgy from the Royal Institute of Technology (KTH) in Sweden. He has held positions as a research associate at the University of Wisconsin-Madison and as a senior research scientist at Questek Innovation, LLC. Since 1999, he has been part of the Pennsylvania State University faculty. Dr. Liu is the Editor-in-Chief of the CALPHAD journal and has served as the President of CALPHAD, Inc. He co-founded the NSF Center for Computational Materials Design and served as its director from 2005 to 2014. He is credited with coining the term “Materials Genome®” in 2002 and led the incorporation of the nonprofit Materials Genome Foundation in 2018. His research focuses on first-principles calculations, machine learning, thermodynamic and kinetic modeling, and their integration for understanding defects, phase stability, and phase transformations, as well as designing materials processing and properties. His team developed the zentropy theory capable of predicting macroscopic functionalities from quantum mechanics and statistical mechanics. Dr. Liu has published over 600 papers, graduated 31 PhD students, and authored a textbook on Computational Thermodynamics of Materials. He is a Fellow of TMS and ASM International, and has received numerous awards including the William Hume-Rothery Award, the ASM J. Willard Gibbs Phase Equilibria Award, and the Lee Hsun Award. His research group’s website is at www.phases.psu.edu.

Research topics

• Computer Science
• Materials science
• Metallurgy
• Thermodynamics
• Artificial Intelligence
• Machine Learning
• Quantum mechanics
• Chemistry
• Physics
• Statistical physics
• Composite material
• Condensed matter physics
• Physical chemistry
• Geology
• Organic chemistry
• Computational chemistry
• Crystallography
• Mechanical engineering
• Computational science
• Operating system
• Inorganic chemistry
• Engineering physics

Selected publications

• Gas phase alloyed functionally graded titanium nitride: Investigation of phase formation and mechanical properties

  Additive manufacturing · 2026-04-01

  article
  PublisherDOI

• pyzentropy: A Python package implementing recursive entropy for first-principles thermodynamics

  ArXiv.org · 2026-04-19

  articleOpen accessSenior author

  While the recursive property of entropy is well known in information theory, it is rarely utilized in thermodynamics, despite entropy originating in this field. Moreover, computational tools to implement this concept within first-principles thermodynamics remain lacking. In this work, we introduce an open-source Python package, pyzentropy, to implement this approach. We demonstrate its effectiveness using $Fe_3Pt$ as a case study, considering a 12-atom supercell with multiple magnetic configurations. By applying the recursive formulation of entropy to compute the total entropy of the system, we reproduce the Invar behavior, along with the anomalous temperature dependence of the linear coefficient of thermal expansion (LCTE), heat capacity $C_P$, and bulk modulus $B$. We also construct the $T$-$V$ and $P$-$T$ phase diagrams in good agreement with experimental observations. Finally, we highlight the importance of determining key high-probability configurations to accurately capture material properties.

  PublisherOA PDF

• Temperature-dependent thermodynamic properties of CrNbO4 and CrTaO4 by first-principles calculations

  International Journal of Refractory Metals and Hard Materials · 2026-02-10

  preprintOpen accessSenior author
  PublisherOA PDFDOI

• Symmetry-broken superconducting configurations from density functional theory for bcc and hcp metals and Nb3Sn

  arXiv (Cornell University) · 2026-01-19

  preprintOpen accessSenior author

  We recently proposed a unified theoretical framework for superconductivity that broadens the applicability of Bardeen-Cooper-Schrieffer (BCS) theory to both conventional and unconventional superconductors. Within this framework, superconductivity arises from the formation of a symmetry-broken superconducting configuration (SCC) generated by atomic perturbations of the normal conducting configuration (NCC). The SCC emerges through electron-phonon interaction and gives rise to distinct straight one-dimensional tunnels (SODTs) in the charge density difference of electrons and/or holes. These SODTs originate from regular and systematic atomic displacements between the SCC and NCC, a phenomenon revealed by density functional theory (DFT) calculations. To further verify this framework, we performed DFT-based calculations for 12 hexagonal close-packed (hcp) elements (Be, Mg, Sc, Y, Ti, Zr, Hf, Tc, Re, Ru, Os, and Zn), 5 body-centered cubic (bcc) elements (V, Nb, Ta, Mo, and W), and the compound Nb3Sn. Our results indicate that all these materials exhibit superconductivity at 0 K and 0 GPa, as evidenced by the predicted SODTs. Notably, Mg, Sc, and Y are predicted to be superconducting under ambient pressure, a finding that awaits experimental confirmation.

  PublisherDOI

• Tuning γ/γ′ lattice misfit to discover Pt-Al-Hf superalloys with superior high-temperature compressive strength

  Journal of Material Science and Technology · 2026-04-27

  article
  PublisherDOI

• pyzentropy: A Python package implementing recursive entropy for first-principles thermodynamics

  arXiv (Cornell University) · 2026-04-19

  preprintOpen accessSenior author

  While the recursive property of entropy is well known in information theory, it is rarely utilized in thermodynamics, despite entropy originating in this field. Moreover, computational tools to implement this concept within first-principles thermodynamics remain lacking. In this work, we introduce an open-source Python package, pyzentropy, to implement this approach. We demonstrate its effectiveness using $Fe_3Pt$ as a case study, considering a 12-atom supercell with multiple magnetic configurations. By applying the recursive formulation of entropy to compute the total entropy of the system, we reproduce the Invar behavior, along with the anomalous temperature dependence of the linear coefficient of thermal expansion (LCTE), heat capacity $C_P$, and bulk modulus $B$. We also construct the $T$-$V$ and $P$-$T$ phase diagrams in good agreement with experimental observations. Finally, we highlight the importance of determining key high-probability configurations to accurately capture material properties.

  PublisherDOI

• ZENN: A thermodynamics-inspired computational framework for heterogeneous data–driven modeling

  Proceedings of the National Academy of Sciences · 2026-01-02 · 1 citations

  articleOpen access

  Traditional entropy-based methods—such as cross-entropy loss in classification problems—have long been essential tools for representing the information uncertainty and physical disorder in data and for developing artificial intelligence algorithms. However, the rapid growth of data across various domains has introduced new challenges, particularly the integration of heterogeneous datasets with intrinsic disparities. To address this, we introduce a zentropy-enhanced neural network (ZENN), extending zentropy theory into the data science domain via intrinsic entropy, enabling more effective learning from heterogeneous data sources. ZENN simultaneously learns both energy and intrinsic entropy components, capturing the underlying structure of multisource data. To support this, we redesign the neural network architecture to better reflect the intrinsic properties and variability inherent in diverse datasets. We demonstrate the effectiveness of ZENN on classification tasks and energy landscape reconstructions, showing its superior generalization capabilities and robustness-particularly in predicting high-order derivatives. In image and text classification tasks, ZENN demonstrates superior generalization by introducing a learnable temperature variable that models latent multisource heterogeneity, allowing it to surpass state-of-the-art models on CIFAR-10/100, BBC News, and AG News. As a practical application in materials science, we employ ZENN to reconstruct the Helmholtz energy landscape of Fe 3 Pt using data generated from density functional theory and capture key material behaviors, including negative thermal expansion and the critical point in the temperature–pressure space. Overall, this work presents a zentropy-grounded framework for data-driven machine learning, positioning ZENN as a versatile and robust approach for scientific problems involving complex, heterogeneous datasets.

  PublisherOA PDFDOI

• Symmetry-broken superconducting configurations from density functional theory for bcc and hcp metals and Nb3Sn

  ArXiv.org · 2026-01-19

  articleOpen accessSenior author

  We recently proposed a unified theoretical framework for superconductivity that broadens the applicability of Bardeen-Cooper-Schrieffer (BCS) theory to both conventional and unconventional superconductors. Within this framework, superconductivity arises from the formation of a symmetry-broken superconducting configuration (SCC) generated by atomic perturbations of the normal conducting configuration (NCC). The SCC emerges through electron-phonon interaction and gives rise to distinct straight one-dimensional tunnels (SODTs) in the charge density difference of electrons and/or holes. These SODTs originate from regular and systematic atomic displacements between the SCC and NCC, a phenomenon revealed by density functional theory (DFT) calculations. To further verify this framework, we performed DFT-based calculations for 12 hexagonal close-packed (hcp) elements (Be, Mg, Sc, Y, Ti, Zr, Hf, Tc, Re, Ru, Os, and Zn), 5 body-centered cubic (bcc) elements (V, Nb, Ta, Mo, and W), and the compound Nb3Sn. Our results indicate that all these materials exhibit superconductivity at 0 K and 0 GPa, as evidenced by the predicted SODTs. Notably, Mg, Sc, and Y are predicted to be superconducting under ambient pressure, a finding that awaits experimental confirmation.

  PublisherOA PDF

• Thermal oxidation and high temperature structural behavior of uranium carbide

  npj Materials Degradation · 2026-01-09 · 1 citations

  articleOpen access

  Uranium monocarbide (UC) exhibits physiochemical characteristics well-suited for nuclear fuel applications in Generation IV reactors, but its high susceptibility to oxidation remains a major barrier to deployment. A detailed understanding of the U-C-O system, including UC thermal oxidation, crystal chemistry, and thermodynamic/kinetic properties, is essential to predict its behavior under normal and off-normal reactor conditions. In this work, in situ high temperature synchrotron X-ray diffraction was conducted under sealed and open-air conditions to characterize UC thermal expansion and oxidation behaviors. From the sealed experiment, the mean coefficient of thermal expansion of UC was determined to be 9.8 × 10−6 K−1 from room temperature to 970 K. Open-air experiments conducted from room temperature to 773 K revealed the oxidation sequence UC → UO2 → U3O8. Notably, a tetragonal U(C1-xOx)2 phase, absent from current thermodynamic predictions, was observed at 840 K, lower than previously considered, suggesting potential relevance for advanced reactor fuel applications. These findings reveal ambiguities in existing knowledge of the U-C-O system, emphasizing the need for continued investigation to facilitate the use of UC-based TRISO and other carbide fuels in emerging reactor designs.

  PublisherOA PDFDOI

• Computational investigations of the formation of intermetallic compounds in Al/Cu joints

  Journal of Manufacturing Processes · 2025-07-25 · 3 citations

  articleSenior author
  PublisherDOI

Recent grants

• Collaborative Research: Accurate Prediction of Phase Stability for Chemistry and Process Design of Ni-based Superalloys

  NSF · $354k · 2018–2021

• Computational and Experimental Investigations of Magnesium Alloys

  NSF · $506k · 2010–2017

• POSE: Phase I: A Path to Sustaining a New Open-Source Ecosystem for Materials Science (OSEMatS)

  NSF · $300k · 2022–2024

• CDMR: Design and Processing of High-Energy-Density Cathodes for Li-ion Batteries

  NSF · $360k · 2013–2016

• I/UCRC CGI: Center for Computational Materials Design (CCMD), Phase II

  NSF · $161k · 2010–2013

Frequent coauthors

• Shun‐Li Shang

  Pennsylvania State University

  507 shared

• Yi Wang

  SAIC Motor (China)

  234 shared

• Long‐Qing Chen

  Pennsylvania State University

  128 shared

• M. Lethuillier

  Institute of Nuclear Physics of Lyon

  120 shared

• V. Sordini

  Institute of Nuclear Physics of Lyon

  116 shared

• S. Perriès

  Institute of Nuclear Physics of Lyon

  113 shared

• M. Titov

  Institut de Recherche sur les Lois Fondamentales de l'Univers

  113 shared

• G. Hamel de Monchenault

  Université Paris-Saclay

  111 shared

Education

• PhD, Materials Science and Engineering

  Royal Institute of Technology

  1992

Awards & honors

• Corning Faculty Fellowship in Materials Science and Engineer…
• Fellow of TMS (2022)
• Dorothy Pate Enright Professor (2020)
• PyCalphad: Runner-up (2nd place) in 2019 NASA Software of th…
• Distinguished Professor, Pennsylvania State University (2018…