Unveiling a crystal's entropy of disorder via electron diffraction. A statistical mechanics approach

TL;DR

This paper introduces a novel experimental method using electron diffraction to quantify the entropy of disorder in crystals, linking microscopic states to macroscopic thermodynamic properties.

Contribution

It presents a new approach to measure the molar entropy of disorder in crystals through electron diffraction, connecting statistical mechanics with experimental data.

Findings

Electron diffraction decay relates to microscopic state count Wd.

Method applies to tiny, thermally unstable crystals.

Disordering and crystallization are reciprocal processes governed by entropy.

Abstract

Upon melting, the molecules in the crystal explore numerous configurations, reflecting an increase in disorder. The molar entropy of disorder can be defined by Bolzmann's formula dSd = Rln(Wd) where Wd is the increase in the number of microscopic states, so far inaccessible experimentally. We found that the Arrhenius frequency factor A of the electron diffraction signal decay provides Wd via an experimental equation A = AINTWd where AINT is an inelastic scattering cross-section. The method connects Clausius and Boltzmann experimentally and supplements the Clausius approach, being applicable to a femtogram quantity of thermally unstable and biomolecular crystals. The data also showed that crystal disordering and crystallization of melt are reciprocal, both governed by the entropy change, but manifesting in opposite directions.