Despite the lack of translational symmetry in random substitutional alloys, their description in terms of single Bloch states has been used in most phenomenological models and spectroscopic practices. We present a new way of analyzing the alloy electronic structures based on a "majority representation" phenomenon of the reciprocal space spectrum P͑k͒ of the wave function. This analysis provides a quantitative answer to the questions: When can an alloy state be classified according to the crystal Bloch state symmetry, and under what circumstances are the conventional theoretical alloy models applicable.

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The coherent phase stability of fcc-based Al-Zn and Al-Cu alloys is studied theoretically by first-principles total energy calculations, a mixed-space cluster expansion approach, and Monte Carlo thermodynamic simulations. We find that a large portion of the differences between Al-Zn and Al-Cu can be explained by the differences between fcc-Zn and fcc-Cu: While Zn is stable in the hcp structure, fcc-Zn shows an instability when deformed rhombohedrally along ͑111͒. In contrast, fcc-Cu is the stable form of Cu and is elastically extremely soft when deformed along ͑100͒. These elastically soft directions of the constituents permeate the phase stability of the alloys: ͑111͒ superlattices are the lowest energy coherent structures in Al-Zn, while ͑100͒ superlattices are stable coherent phases in Al-Cu. The short-range order of both Al-rich solid solutions show clustering tendencies, with the diffuse intensity due to short-range order in Al-Zn and Al-Cu showing streaks along ͑111͒ and ͑100͒, respectively. The mixing enthalpies and coherent phase boundaries are also calculated and found to be in good agreement with experimental data, where available. ͓S0163-1829͑99͒01146-7͔

The electronic structure of abrupt (InAs) n /(GaSb) n superlattices is calculated using a plane wave pseudopotential method and the more approximate eight band k•p method. The k•p parameters are extracted from the pseudopotential band structures of the zinc-blende constituents near the ⌫ point. We find, in general, good agreement between pseudopotential results and k•p results, except as follows. ͑1͒ The eight band k•p significantly underestimates the electron confinement energies for nр20. ͑2͒ While the pseudopotential calculation exhibits ͑a͒ a zone center electron-heavy hole coupling manifested by band anticrossing at nϭ28, and ͑b͒ a light hole-heavy hole coupling and anticrossing around nϭ13, these features are absent in the k•p model. ͑3͒ As k•p misses atomistic features, it does not distinguish the C 2v symmetry of a superlattice with no-commonatom such as InAs/GaSb from the D 2d symmetry of a superlattice that has a common atom, e.g., InAs/GaAs. Consequently, k•p lacks the strong in-plane polarization anisotropy of the interband transition evident in the pseudopotential calculation. Since the pseudopotential band gap is larger than the k•p values, and most experimental band gaps are even smaller than the k•p band gap, we conclude that to understand the experimental results one must consider physical mechanisms beyond what is included here ͑e.g., interdiffusing, rough interfaces, and internal electric fields͒, rather than readjust the k•p parameters. ͓S0163-1829͑99͒07531-1͔