Grain-boundary enthalpy of nanocrystalline materials crystallized from the amorphous state

An evident inequality between the enthalpy of crystallization of amorphous selenium, $\Delta H_x,$ and the enthalpy difference between the undercooled liquid and the conventional polycrystalline selenium, $\Delta H^{l\to c},$ was observed, which is inconsistent with the widely accepted idea that the two enthalpies should be equal. The inequality between the two enthalpies is attributed to the excess enthalpy of the nanocrystallized selenium with respect to the conventional polycrystalline selenium. The maximum excess enthalpy of the nanocrystalline selenium amounts up to 30% of the heat of fusion. Based on the assumption that the excess enthalpy of the nanocrystalline sample is concentrated in the high density of grain boundaries, the grain-boundary enthalpies of the nanocrystalline selenium samples were determined. The obtained grain-boundary enthalpies of the nanocrystalline selenium samples are found to increase from 0.27 to $0.32{\mathrm{J}/\mathrm{m}}^2$ with the mean crystallite size increment from 9 to 22 nm. It is predicted that an inequality between the two enthalpies of $\Delta H_x$ and $\Delta H^{l\to c}$ will always occur in the nanocrystallization process of an amorphous solid and that the grain-boundary enthalpies of the nanocrystallized products can then be determined.