Electronic and positron band structures and charge densities of GaN, AlN, and their alloy Ga0.5Al0.5N in zinc-blende structure using the empirical pseudopotential method are investigated. For the ternary alloy Ga1-xAlxN, the virtual crystal approximation is coupled with the pseudopotential method. The energies along Γ, X, and L of Ga1-xAlxN alloy as a function of the alloy concentration are calculated. Angular correlation of positron annihilation radiation along different crystallographic directions in GaN, AlN, and Ga0.5Al0.5N is calculated. Other quantities such as ionicity character and bulk modulus by means of recent models with respect to the alloy concentration are discussed. © 2003 American Institute of Physics.