Configurational and residual entropies of nonergodic crystals and the entropy’s behavior on glass formation

Abstract

We use thermodynamics of lattice vacancies to test the merits of the view that (i) statistical entropy, k(B) ln Omega, vanishes on vitrification of a liquid and hence there is no residual entropy and (ii) k(B) ln Omega of a nonergodic state would increase with time t as its structure relaxes. We argue that this view conflicts with the precepts of the configurational entropy of a crystal, -R[x ln x+(1-x)ln(1-x)], where x is the fractional population of vacancies, and with the observed decrease in x with t on structural relaxation. The issue of whether the entropy of a kinetically arrested crystal state is equal to k(B) ln Omega or 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 energy landscapes of a crystal and liquid differ, and point out that since crystals are in a nonequilibrium state, their thermodynamic data are inappropriate for testing the validity of the third law.