Based on Thomas-Fermi model, the effect of external electric field on inner boundary potential was studied and the new atomic potential boundary condition was established. Thomas-Fermi model was extended to solid solution and compound with the volume adding method. The entropy energy of various system was calculated and analyzed taking Al, Mg, Li, Cu, Au, Zn single atoms, Al-Mg solid solution and Mg5Al8 for instances. The results show that the entropy energy decreases first and then increases in the whole electric field; the trendline of entropy energy at the electrode voltage is mainly same as at the boundary potential in each system, but the trendline of entropy energy is different about zero point.