On the entropy difference between the vitreous and the crystalline state

The paper deals with the entropy difference between frozen-in phases and their equilibrium counterparts. First, the nature of data compiled in thermochemical data collections are briefly reviewed, comprising data for non-equilibrium phases. Then, experimental evidence from earlier literature is compiled showing that the conventional entropy of a frozen-in phase at zero Kelvin assumes a non-zero residual value S(0). Based on calorimetric data from multiple sources, the same evidence is elaborated for diopside glass, yielding Sglass(0) = 24.8 ± 3 J/(mol K), a value reproducing a result publishes earlier. The zero Kelvin enthalpy of this glass is Hglass(0) = 81±8 kJ/mol. For Sglass(0), a structural interpretation in terms of silicate chain mixing is proposed, yielding a lower threshold for Sglass(0). From the point of view of statistical mechanics, non-zero residual entropies of frozen-in phases can be derived from ensemble averages, however, not from time averages.