  In the framework of density functional theory, the structural and magnetic
properties of Fe$_{100-x}$Al$_x$ alloys (${5 \leq x \leq 25}$~at.\%) with the
different structural order are investigated. Using the Korringa-Kohn-Rostoker
Green's function method with a coherent potential approximation, the
equilibrium lattice parameters, ground-state energy, and shear moduli for
D0$_3$, B2, and A2 structures are calculated. For all structures, the optimized
lattice constant increases while the shear modulus demonstrates a decreasing
behavior with increasing Al content. The tetragonal magnetostriction constants
are estimated by the torque method. The A2 and B2 structures provide a positive
contribution to the tetragonal magnetostriction. With the help of Monte Carlo
simulations of the Heisenberg model, the Curie temperatures are obtained in a
wide concentration range.
