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We present here an augmented space recursive technique in thek-representation which include diagonal, off-diagonal and the environmentaldisorder explicitly : an analytic, translationally invariant, multiplescattering theory for phonons in random binary alloys.We propose the augmentedspace recursion (ASR) as a computationally fast and accurate technique whichwill incorporate configuration fluctuations over a large local environment. Weapply the formalism to $Ni_{55}Pd_{45}$, $Ni_{88}Cr_12}$ and $Ni_{50}Pt_{50}$alloys which is not a random choice. Numerical results on spectral functions,coherent structure factors, dispersion curves and disordered induced FWHM's arepresented. Finally the results are compared with the recent itinerant coherentpotential approximation (ICPA) and also with experiments.Comment: 20 pages, LaTeX, 23 figure

Vibrational properties of phonons in random binary alloys: An augmented space recursive technique in thekrepresentation