The universe naturally tends toward disorder, and only through an input of energy can we combat this inevitable chaos. This idea is encapsulated in the concept of entropy, which is evident in everyday phenomena such as ice melting, fire burning, and water boiling. However, the theory of "entropy" introduces another layer of meaning to this understanding.
This theory was proposed by a team led by Zikui Liu, Distinguished Dorothy Pate Enright Professor in the Department of Materials Science and Engineering at Penn State. The "Z" in zentropy comes from the German term "Zustandssumm", which means the "sum of states" of entropy.
Liu said "zentropy" can also be seen as a homophone of the Buddhist term "Zen" and entropy, which is used to reveal the nature of a system. The idea, Liu said, is to consider how entropy occurs at multiple scales within a system to help predict potential outcomes when the system is affected by its surrounding environment.
Liu and his research team published their latest paper on this concept, demonstrating that this approach can provide a way to predict experimental results and enable more efficient discovery and design of new ferroelectric materials. The work, published in ScriptaMaterialia, combines some intuition with a wealth of physics knowledge to provide a parameter-free approach to predicting the behavior of advanced materials.
Ferroelectrics have unique properties that make them valuable in a variety of applications, both currently and in development, the researchers say. One such property is spontaneous electrical polarization that can be reversed by the application of an electric field, which has enabled the development of technologies ranging from ultrasound to inkjet printers and energy-efficient RAM in computers to ferroelectrically driven gyroscopes in smartphones, enabling smooth videos and sharp photos.
To develop these techniques, researchers need to experimentally understand the behavior of this polarization and its reversal. To improve efficiency, researchers often design experiments based on predicted outcomes. Typically, such predictions require adjustments called "fitting parameters" to closely match real-world variables, which take time and effort to determine. But Zen entropy can integrate top-down statistical mechanics and bottom-up quantum mechanics to predict experimental measurements of a system without the need for such adjustments.
"Of course, in the end, experiments are the ultimate test, but we found that zentropy can provide quantitative predictions that greatly narrow the range of possibilities," Liu said. "We can design better experiments to explore ferroelectric materials, and research efforts will progress faster, which means time, energy and money can be saved and more efficient."
While Liu and his team have successfully applied Zen entropy theory to predict the magnetic properties of a range of materials under various phenomena, discovering how to apply it to ferroelectric materials has been a thorny problem. In the current study, the researchers report that they have found a way to apply Zen entropy theory to ferroelectric materials, focusing on lead titanate. Like all ferroelectric materials, lead titanate has an electrical polarity that can be reversed when an external electric field, temperature change, or mechanical stress is applied.
When an electric field reverses the electrical polarization, the system changes from order to disorder in one direction, and then back to order again when the system stabilizes in the new direction. However, this ferroelectricity only occurs below a critical temperature unique to each ferroelectric material. Above this temperature, ferroelectricity - the ability to reverse polarization - disappears, and paraelectricity - the ability to polarize - appears. This change is called a phase change. Measurements of these temperatures can reveal key information about various experimental results, Liu said. However, predicting phase transitions before experiments is nearly impossible.
"There is no theory or method that can accurately predict the free energy and phase transition of ferroelectric materials before experiments," Liu said. "The best prediction of the transition temperature differed from the actual temperature in the experiment by more than 100 degrees."
The reason for this difference is unknown uncertainties in the model and the inability of the fitting parameters to take into account all salient information that affects the actual measurements. For example, one commonly used theory describes the macroscopic features of ferroelectricity and quasielectricity, but does not take into account microscopic features such as dynamic domain walls - the boundaries between regions with different polarization characteristics within the material. These configurations are the building blocks of the system and fluctuate significantly with changes in temperature and electric field.
In ferroelectrics, the configuration of the electric dipoles in the material changes the direction of polarization. The researchers used Zen entropy to predict the phase transitions of lead titanate, including identifying three possible configurations in the material.
The researchers' predictions are valid and consistent with experimental observations reported in the scientific literature. They used publicly available domain wall energy data to predict a transition temperature of 776 Kelvin, which agrees well with the observed experimental transition temperature of 763 Kelvin. Liu said the research team is working to further narrow the gap between predicted and observed temperatures by better predicting domain wall energy as a function of temperature.
Liu said that this ability to predict the transition temperature so closely to actual measurements can provide valuable insights into the physical properties of ferroelectric materials and help scientists better design experiments: "This basically means that you can have some intuition and prediction methods about the microscopic and macroscopic behavior of the material before conducting the experiment. We can start to accurately predict the results before the experiment."
Other Penn State researchers who worked with Liu on the study include Shunli Shang, research professor of materials science and engineering, Yi Wang, research professor of materials science and engineering, and Jinglian Du, a materials science and engineering researcher at the time of the study.