Phonons in random alloys: The itinerant coherent-potential approximation

We present the itinerant coherent-potential approximation (ICPA), an analytic, translationally invariant, and tractable form of augmented-space-based multiple-scattering theory¹⁸ in a single-site approximation for harmonic phonons in realistic random binary alloys with mass and force-constant disorder. We provide expressions for quantities needed for comparison with experimental structure factors such as partial and average spectral functions and derive the sum rules associated with them. Numerical results are presented for Ni₅₅Pd₄₅ and Ni₅₀Pt₅₀ alloys which serve as test cases, the former for weak force-constant disorder and the latter for strong. We present results on dispersion curves and disorder-induced widths. Direct comparisons with the single-site coherent potential approximation (CPA) and experiment are made which provide insight into the physics of force-constant changes in random alloys. The CPA accounts well for the weak force-constant disorder case but fails for strong force-constant disorder where the ICPA succeeds.