From a ground-state analysis of the Ising model applied to the A15 crystalline structure with first-, second-, and weak third- and seventh-neighbor pair interactions, additional ordered states are predicted at the compositions ${\mathit{A}}_5$${\mathit{B}}_3$ and ${\mathit{A}}_7$B. Low-temperature expansions are performed and stability properties as a function of temperature and concentration are investigated by means of variational methods, within the Bragg-Williams and cluster-variation-method approximations. The results are compared with those from Monte Carlo simulations. Typical prototype A15-based order-disorder phase diagrams and short-range-order diffuse-intensity calculations are presented and discussed in relation to experiment.

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