It seems clear that the work function of a metal is dependent on the surface orientation and that it has to do with the density of atoms at the surface. Wouldn´t this give that when the metal becomes liquid, the work function will change? Or will it be the same as for the random oriented solid surface?
The work function of a solid metal is different from that of the liquid metal. The work function of a crystal surface can even be different depending on the orientation of crystal plains relative to the surface.
Check out https://books.google.de/books?isbn=0849396069 page 1908 and following
https://books.google.de/books?isbn=0849396069
Since the structure of the metal is different in the solid state, where you have to take into account the lattice energy, and in the liquid state you don't have this energy, and the behaviour of the metal is as a liquid with random movement of the particles, the kinetic energy of metal in the liquid state should determine the work you are looking for.
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