Energy and entropy of crystals, glasses and melts

Abstract

The molar entropy, S, and enthalpy (energy), H, of crystals, glasses and melts of the same one-component systems have been suitably visualized including the transformadon from the melt into a glass or crystallization. For the temperature T → 0 Κ the enthalpy and entropy of the glass are larger by ΔH0 and ΔS0 as compared to the stable crystal. The S and Η functions of glasses correspond to a simple continuation of these functions from the molten State to lower temperatures. Crystallization occurs as a spontaneous process under production of entropy. Extrapolating the entropy of the molten and crystalline states from the melting range to lower temperatures, which is the basis of "Kauzmann's paradox", is ambiguous and misleading, as the extrapolated data deviate considerably from the experimental temperature dependencies of S of glasses and crystals. A proper extrapolation does not cause an entropy catastrophe as claimed in "Kauzmann's paradox", since the enthalpy difference between the undercooled melt and the corresponding crystals must be taken into account, and the respective entropies in both states are not connected by an isothermal process. The molar entropy and enthalpy are visualized as functions of temperature by numerical results of a Debye model. The molar entropy is a universal function of the ratio T/TD, wherein TD is the Debye temperature of the well known specific heat capacity, CD. Between 0 K and TD the entropy increases by 1.36 × 3R ≈ 4R irrespective of TD. Above TD it increases approximately as 3R × ln (T/TD). The entropy capacity, CD/T scales with 1/TD and the enthalpy with TD, both considered as functions of T/TD. The entropy capacity shows a maximum of 2.033 × 3R/TD for T/TD = 0.28.