Size dependence of the lattice parameters of carbon supported platinum nanoparticles: X-ray diffraction analysis and theoretical considerations

Carbon supported Pt nanoparticles with diameters ranging from 2 to 28 nm have been studied using X-ray diffraction. The unit cell parameter of synthesized Pt/C nanoparticles is always lower than that of bulk Pt. By decreasing the average particle size D to approximately 2 nm, the unit cell parameter a nonlinearly decreases by about 0.03 A which corresponds to a variation of 0.7% in comparison to bulk Pt, and the size effect is predominant for sizes ranging from 2 to 10 nm. The dependence a(1/D) is approximated well using a straight line with a slope of −0.0555 ± 0.0067 nm−1 and an intercept of −3.9230 ± 0.0017 A. For interpreting the obtained experimental dependence of the unit cell parameter of Pt/C nanoparticles, four different theoretical approaches such as the thermal vacancy mechanism, continuous-medium model, Laplace pressure, and bond order–length–strength correlation mechanism, were used. Comparison of the calculated dependencies, based on the above models, with the experimental ones, shows that the continuous-medium model agrees best with the experimentally found unit cell parameter dependence of our carbon supported Pt nanoparticles.