Nanocrystalline (nc) metals show significant differences in their thermodynamic properties, such as specific heat at constant pressure and thermal expansion, in comparison to polycrystalline metals. These properties are explained in terms of a macroscopic analysis. Based on a quasiharmonic approximation, the thermodynamic quantities are calculated as functions of the excess volume of the grain-boundary component in nc metals. The enhancements of the specific heat and the thermal expansion coefficient are accompanied by a reduction of the Debye temperature. The results show good agreement with experimental data.
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Michael Wagner (1992) studied this question.
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