Configurational and residual entropies of nonergodic crystalsand the entropy's behavior on glass formation

摘要

We use thermodynamics of lattice vacancies to test the merits of the view that (i) statistical entropy,kB In St vanishes on vitrification of a liquid and hence there is no residual entropy and (ii) k_BIn 1Zof a nonergodic state would increase with time t as its structure relaxes. We argue that this viewconflicts with the precepts of the configurational entropy of a crystal,-R[x In x+ (1-x)ln(1-x)],where x is the fractional population of vacancies, and with the observed decrease in x with t onstructural relaxation. The issue of whether the entropy of a kinetically arrested crystal state is equal to k_BIn Ωor equal to -R[x ln x+ (1-x)ln(1-x)] can be resolved by measuring the vapor pressure,the emf of an electrolytic cell, and by scanning calorimetry. We also consider how the energylandscapes of a crystal and liquid differ, and point out that since crystals are in a nonequilibriumstate, their thermodynamic data are inappropriate for testing the validity of the third law.