Melting entropy of crystals determined by electron-beam–induced configurational disordering

Abstract

Upon melting, the molecules in a crystal explore numerous configurations, reflecting an increase in disorder. The molar entropy of disorder can be defined by Boltzmann’s formula Δ S d = R ln( W d ), where W d 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 W d through an experimental equation A = A INT W d , where A INT 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.