Estimate the difference in chemical potential of a spherical Pt nanocrystal compared to a large Pt crystal. Assume that the surface free energy per unit area g = 2 J m-2 is isotropic and the radius is R=5 nm. The fcc lattice constant of Pt is 0.392 nm.
Assume that the binding energy (minus the zero point vibrational energies) of Ne on graphite(0001) is e0 = 20 meV. Estimate the temperature at which the Ne coverage will be 1014 cm-2 using both the 2D ideal gas and the Langmuir model for a pressure of 10-6 Torr. For the Langmuir model, you can assume that the site density is 1015 cm-2. You can also simplify the statistical mechanics by assuming that the vibrational partition functions are equal to 1.
