The thermal features of the nanograin boundary were described by a developed thermodynamic model. Using the nanocrystalline Cu as an example, the pressure, the bulk modulus, and the volume thermal expansion coefficient were calculated to characterize the thermodynamic properties of the grain boundaries on the nanoscale. Based on the parabola-type relationship between the excess free energy and the excess volume of the nanograin boundary, the thermal stability, as well as its evolution characteristics, was analyzed. The experimental results of the temperature-varying grain growth in the nanocrystalline Cu, which exhibited the discontinuous nanograin growth behavior, verified the thermodynamic predictions. In addition, the quantitative relationships correlating the excess volume and the lattice expansion with the nanograin size were discussed.
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