Using Taylor expansion, 

a) derive the expression for the chemical potential difference between Zr atoms at flat surfaces and hollow surfaces (at the surface of a spherical hole with radius r). 

b) If the spherical hole has a radius of 10 nm and the partial molar volume of  compute the chemical potential difference Zr atoms feel between a flat surface and the hollow surface in units of eV/atom.r

av. ON of Zr is 14.1 cm/mole,