Theoretical studies on internal strain of face-centered-cubic metal nanoparticles

Combining the continuum elastic theory and the first-principles calculations, we systematically studied the internal strain of nanoparticles of face-centered-cubic (fcc) metals. By taking full account of the surface anisotropy, the theoretical results are found to be consistent with the previously reported experimental ones within a wide range of nanoparticle sizes. Furthermore, we demonstrate that among the fcc transition metals, the largest internal strain of the nanoparticles with size larger than 5 nm occurs in the last column of the Group VIII (Ni/Pd/Pt), which can be correlated with the filling status of $d$-band electrons of the metals. Most of the fcc metal nanoparticles tend to contract with decreasing size with the only exception of strontium, suggesting that most of the surfaces are dominated by the positive surface stress.