Seminar by Zi-Kui Liu

Origin of Negative Thermal Expansion

Zi-Kui Liu, Ph.D.

The Pennsylvania State University

Solids typically exhibit positive thermal expansion upon heating though solids with negative thermal expansion, i.e. volume reduction upon heating, have been discovered serendipitously throughout the history. Recently, instead of considering the volume as a function of temperature only, we examined the thermal expansion from the combination of temperature and pressure. We show that the negative thermal expansion phenomenon originates from the existence of high pressure, small volume, and higher entropy phases/microstates with their configurations present in the matrix of stable microstate through thermal fluctuations. Some examples include Fe3PT as an Invar material, cerium with colossal thermal expansion, and water/ice with unique thermal expansion behaviors. We believe that the entropy contribution due to metastable microstates, termed microstate configurational entropy (MCE), is also responsible for other anomalies in materials due to unique properties of microstates and non-linear dynamic interactions among them. This new theory enables us to tailor thermal expansion of materials in particular and design materials with performance in general.

Dr. Zi-Kui Liu is a professor of Materials Science and Engineering at The Pennsylvania State University (  He obtained his BS from Central South University (China), MS from University of Science and Technology Beijing (China), Ph.D. from Royal Institute of Technology (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.  Dr. Liu's current research activities are centered on first-principles calculations, modeling of thermodynamic and kinetic properties, and their integration in understanding defects, phase stability, and phase transformations, and designing and tailoring materials processing and properties.  He was the founder and director of NSF Center for Computational Materials Design, published over 330 scientific papers (, and received the ASM International 2014 J. Willard Gibbs Phase Equilibria Award. 

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