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The structural and electronic properties of the B_{x}Ga_{1-x}N, B_{x}Al_{1-x}N, Al_{x}Ga_{1-x}N and B_{x}Al_{y}Ga_{1-x-y}N compounds were studied using the full-potential linearized augmented plane wave method, within the generalized gradient approximation. We have compared the Al and B compositions dependence on the ground state properties: lattice parameters, bulk moduli and their pressure derivative, and band gap energies. The lattice parameters are found to change linearly for Al_{x}Ga_{1-x}N, exhibit a downward bowing for both B_{x}Al_{1-x}N and B_{x}Ga_{1-x}N, and has a very small deviation when Al is added and a large deviation when B is incorporated for B_{x}Al_{y}Ga_{1-x-y}N. The calculated band gap variation for the ternaries shows that the B_{x}Ga_{1-x}N has a phase transition from direct-gap to indirect-gap for high boron contents (x > 0.75). As for B_{x}Al_{1-x}N, a direct-gap is found in the boron content range 0.07 < x < 0.83. For Al_{x}Ga_{1-x}N and B_{x}Al_{y}Ga_{1-x-y}N compounds, they have been found to be direct-gap materials. The results show that the B_{x}Ga_{1-x}N, B_{x}Al_{1-x}N, Al_{x}Ga_{1-x}N and B_{x}Al_{y}Ga_{1-x-y}N materials may well be useful for optoelectronic applications.
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