The composition design of sealing alloys still inevitably relies on the trial-and-error method, leading to the unnecessary waste of time and materials. The main goal of this study is to introduce an electronic structure model, named the nearest-neighbor two-shell (NNTS) model, to guide the composition design of the face-centered cubic (fcc) solid solution alloy. The chemical structure formula of the model is [X–Y12]Z2, where X, Y, and Z are the composited atomics in the alloy. The atomic structure of the model is developed by comparing with the Friedel sphere periodic electronic resonance structure. We applied the proposed model to analyze various iron–nickel (Fe–Ni) binary and ternary alloys, and the obtained results were consistent with those calculated using the Cowley parameters. The discovery of the model is conducive to gaining a deeper understanding of the composition distribution of alloys and also provides a new way to design the alloy composition.