Theory of alloys. III. Embedded-cluster calculations of electronic spectra for a one-dimensional ternary alloy

The embedded-cluster method is modified to treat electronic spectra in ternary alloys and is applied to the calculation of the electronic density of states for the one-dimensional, one-state-peratom, ternary alloy $A_x{B}_{1-x}C$ in the nearest-neighbor tight-binding approximation. As a test of this method, the spectra for some representative cases of alloys in the "persistence" and "amalgamation" regimes are presented and compared with "exact" spectra for the same cases obtained for 10 000-atom random chains by the use of the negative-eigenvalue theorem. For a cluster containing eight unit cells embedded in a coherent-potential-approximation effective medium, the embedded-cluster method reproduces all of the major features of the exact spectra for all alloy compositions and over wide range of atomic energies of the alloy constituents.