Figure 4

Effects of size on the mechanical and thermodynamic properties of nanocrystalline materials. Size dependence of (A) heat capacity C _m [46–48] and (B) Young’s modulus Y for Ag [43, 45–47], (C) Debye temperature Θ _D , [49, 19, 50–52] and (D) diffusion activation energy Q _d for Au [53, 19, 50–52]. Solid lines refer to parameters calculated from Equation 9 (our model prediction). The white circle is plotted using Equation 4 and experimental data for the melting points T _m . The solid triangles show the experimental data (r_0Ag = 0.1444 nm, σ_Ag = 1.998 N/m, C_{m Ag} = 25.36 J/mol · K, Y_Ag = 80 GPa; r_0Au = 0.1442 nm, σ_Au = 1.331 N/m, Θ_{D Au} = 184.59 K, Q_{d Au} = 108 KJ/mol [39, 40, 48, 54]).