The work function of the surface of a material gives the energy (eV) required to extract an electron from the surface.  So the material structural properties affect the surface properties, and the surface properties affect the work function and the work function the electric breakdown in vacuum.  Of course, other effects such as electrode temperature influence things substantially (see thermionic emission), but that is the basic idea.  Material surfaces with high work functions require high voltages to extract their electrons in vacuum.

Thanks David. I understand the effect of work function and thermionic emission.

I was wondering is there any relation to material structure say for example copper (FCC) or some BCC or HCP and the dislocations in materials for breakdown. Because in theoretical explanations starts with field emission or kind of surface protrusions, which can be removed by machining of electrodes and some surface treatments.

but i think i should look forward to relation between lattice structure and workfunction which will help me in my research

Thanks David

So excited, I am also doing some research on this topic. In my opinion,the material structure indeed affacts the electron emission and the breakdown threshold, and it will be more significate while the electrode is at micro or nanoscale. Some works have shown that the discharge in the SiO2 layer developed along the grain boundary rather than the shortest distance due to the defect and the resitance. Similar to that result,the electron emission may become easier at the GB, the isolated atoms or some defects on the surface. They in fact change the local work function and then the emission. Breakdown at nanoscale is very interesting and it can tell us much.