Partial phonon densities of states ofFe57in Fe-Cr: Analysis by a local-order cluster expansion

Abstract

Nuclear resonant inelastic x-ray scattering spectra were measured for $^{57}\mathrm{Fe}$ in disordered body-centered-cubic alloys of Fe-Cr. Partial phonon density of states (DOS) curves were obtained from these data. These results, in conjunction with the results of Ruckert et al. [Hyperfine Interact. 126, 363 (2000)] on Fe-Cr thin-film multilayers and alloys, were analyzed with a local-order cluster expansion method. Interaction partial phonon DOS functions for the different short-range correlation functions were obtained from the disordered alloys. These interaction DOS functions were used in reconstructing the $^{57}\mathrm{Fe}$ partial DOS curves measured by Ruckert et al. on a set of thin-film multilayer samples of $^{57}\mathrm{Fe}∕^{56}\mathrm{Fe}∕\mathrm{Cr}$. The method worked well using terms up to a combined first- and second-nearest-neighbor triangle cluster, which were obtained reliably from the disordered alloys. The limitations of a basis set of correlation functions from disordered alloys are discussed but shown to be acceptable for the chemical trends of phonons in the Fe-Cr system.