Time-dependent paths,fictive temperatures and residual entropy of glass

After describing the Clausius limits of entropy, determined from the C _pd ln T integral, and its current use in determining the entropy of metastable (atomic) crystals, we determine two fictive temperature T _f values of four glasses – one from the integral of C _pdT and the other from C _pd ln T. The C _p data of the two metal–alloy glasses are from this calorimetric study; the C _p data of (i) quenched basalt composition glass fibers before and after partial annealing, and (ii) quenched NBS-710 composition glass fibers are taken from the literature. The C _pd ln T integral, which is not the entropy change, and the C _pdT integral yield the same T _f values. Therefore, the effect of the difference between the cooling and heating paths in the liquid–glass transformation range is too small to indicate whether the residual entropy, S _res, is a result of using the C _pd ln T integral. This questions the notion that S _res stems from use of the C _pd ln T integral. Extrapolation of the C _p values of the liquid and glass to high temperatures lead to erroneous T _f values, as do permanent (irreversible) loss of the strain and surface energies of glass on initial heating.