Updated method considers system’s structure when calculating entropy

Configurational entropy plays a significant role in a system’s total entropy. It is usually calculated by treating all states as an ideal gas, regardless of the matter’s structure. However, because the symmetry of a system can affect its configurational entropy, systems with a crystalline structure may need an alternative approach to estimate this parameter.

Hu et al. offer an updated method for more accurately determining the configurational entropy of a system, taking its structure into account. Their calculations showed hexagonal-close-pack crystal structures to have higher configurational entropy than face-centered-cubic structures, and entropy increases nonlinearly with the number of atoms in the system.

This configurational entropy difference is not negligible. It dominates over intrinsic entropy at the nanoscale, making the total Gibbs free energy difference larger than expected. The conventional calculation only becomes valid as the mixing entropy of the system approaches that of an ideal gas with a sufficiently large number of atoms.

“This work points out the fact that difference of crystal symmetry between two crystal structures could have a significant effect on the early stage of phase transformation, which was ignored before,” said author Jien-Wei Yeh.

By properly considering the probability and degeneracy of each microstate, the researchers were able to determine how the geometry of a system affects its energy distribution. In this way, different structures are treated individually rather than as an ideal gas.

This is a first step to understanding how structural symmetries in a system affect entropy, and further research needs to be done to understand additional structures. Yeh noted important applications of this work include understanding plastic deformation mechanisms.

Source: “From symmetry to entropy: Crystal entropy difference strongly affects early stage phase transformation,” by C. H. Hu, Y. C. Chen, P. J. Yu, K. Y. Fung, Y. C. Hsueh, P. K. Liaw, J. W. Yeh, and A. Hu, Applied Physics Letters (2019). The article can be accessed at https://doi.org/10.1063/1.5114974 .