From symmetry to entropy: Crystal entropy difference strongly affects early stage phase transformation

Abstract

Although the connection between symmetry and entropy is not clear, researchers calculate configurational entropy with an ideal gas mixing model all along regardless of which structure they are considering. However, it is obvious that crystalline structures have symmetry, while an ideal gas does not. Therefore, the same ideal gas mixing value should not be assigned to other structures, such as face-centered-cubic (fcc) and hexagonal-close-packed (hcp) structures. Here, we offer a precise definition for determining the configurational entropy of crystals. We calculate the difference in configurational entropy between fcc and hcp structures based on Burnside's lemma in combinatorial mathematics and crystallographic rotation-point groups.