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The structural and the electronic properties of the ternary Sr_xCa_1-xS, Ba_xCa_1-xS and Ba_xSr_1-xS alloys have been calculated using the full-potential linear muffin-tin-orbital (FP-LMTO) method based on density functional theory, within both local density approximation (LDA) and generalized gradient approximation (GGA). The calculated equilibrium lattice constants and bulk modulus are compared with previous results. The concentration dependence of the electronic band structure and the direct and indirect band gaps are investigated. Using the approach of Zunger and co-workers, the microscopic origins of the band gap bowing are investigated also. A reason is found from the comparison of our results with other theoretical calculations

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