Adv. Studies Theor. Phys., Vol. 6, 2012, no. 4, 165 – 176 Thermodynamic Functions for Body Centred Lattice-Application on Lattice Green’s Function Jihad H. Asad Department of Physics, Tabuk University P. O. Box 741, Tabuk 71491, Saudi Arabia jhasad1@yahoo.com Abstract Thermodynamic functions of ionic systems were evaluated analytically using the Green’s Function for body centered cubic lattice. The free energy density, chemical potential, pressure, Spinodals, and Coulomb ionic potentials, are expressed in terms of hyper geometric functions 3 F 2 and complete elliptic integrals. Keywords: Lattice Green’s Function (LGF), Body Centered Cubic (BCC) Lattice, and Ionic Systems. 1 Introduction The Lattice Green's Function (LGF) is a basic function in the study of the solid state physics and condensed matter. It appears especially when impure solids are studied [Morita and Horiguchi, 1972]. Green was the first physicist who established the basic concepts of Green’s function in the potential theory, and his work was focused on solving Laplace's and Poisson's equations with different boundary conditions. The use of Green’s function method plays an important role in many-body problems [Fetter and Walecka, 1971], especially in problems of solid state physics where an enormous progress has been realized. In the mathematical problem of quantum theory which consists of solving linear