Cluster Expansion Applied to Inelastic Scattering Experiments

Abstract

In this thesis the cluster inversion method of Connolly and Williams is performed on measurements of properties of random solid solutions. This is possible when the number of terms required for the expansion is small. The interaction parameters are extended to interaction functions, which become physically significant when only a few terms are required. The focus of this thesis is on the phonon density of states (DOS), which is determined from the results of inelastic scattering experiments. Nuclear resonant inelastic X-ray scattering (NRIXS) is utilized to probe the phonon modes of 57Fe atoms in binary body-centered cubic alloys of Fe-V, Fe-Cr, and Fe-Co. Alloying with 3d series atoms causes a softening of the Fe phonon partial density of states (PDOS) curves with decreasing average atomic number. For Fe-Cr, the interaction phonon partial density of states (IPDOS) functions obtained from the disordered alloys up to a combined first- and second-nearest-neighbor triangle cluster were successful in reconstructing the 57Fe PDOS curves of thin-film multilayer samples. To obtain the phonon properties of the Cr atoms, inelastic neutron scattering spectra were measured on disordered solid solutions of BCC Fe-Cr alloys. These data were reduced from time-of-flight histograms to energy spectra that resemble the DOS, but were distorted by differences in efficiencies of the atom species for phonon scattering. Cluster expansion formalisms were developed to both correct for this neutron weighting problem, and to isolate the PDOS of Fe and Cr atoms. An asymmetry in the phonon entropy of mixing was identified, and attributed to the larger number of low-energy modes associated with like and unlike pairs in the first- and second-nearest-neighbor shells of Cr atoms, compared to Fe atoms. The results of inelastic neutron scattering on Cu-Au are re-analyzed with the cluster expansion technique. The neutron weight correction changes both the magnitude and sign of the phonon entropy of mixing. Although a low number of terms works very well for the low-energy modes, the optical modes are poorly treated. The failure of the cluster expansion to reproduce the optical phonon modes in the ordered Cu3Au sample indicates a much higher dependence on the local chemical arrangement.