Simulation of Sinusoidal Diffuse Scattering Loci in the NonstoichiometricB8-Type Alloy PhasesA1+xB,A=(Co, Ni),B=(Ge, Sn)

Abstract

The alloys (Co, Ni)1+x(Ge, Sn) form a range of superstructures in which one [110] repeat of the hexagonalB8 substructure is preserved. Less well-ordered phases also occur in which continuous sinusoidal loci of diffuse scattering are observed trending parallel to c*. The curves can be modeled as cosine waves with maximumkatl=even and minimumkatl=odd. The shape of the curves vary with composition and annealing temperature. Computer simulation was used to generate two-dimensional projections of real-space occupancy patterns that produced similar diffraction patterns. The synthesized real-space arrays were characterized by sets of correlation coefficients. A Monte Carlo algorithm was then used to find sets of two-body interaction energies for which these structures lay at an energy minimum. Good fits between calculated and experimental diffraction patterns were found in all cases. The fitted interaction energies were mainly positive, implying that most two-body interactions were repulsive between sites of like occupancy. Magnitudes were significant out to third-nearest neighboring interstitial sites. The magnitudes tended to be largest nearx=0.5. Additional variations of both interaction energies and resulting correlations with composition and annealing temperature are discussed. It is shown that the double-locus diffraction pattern observed for the Ni–Ge system is not necessarily produced by a mechanical mixture of two structures, but can correspond to a single phase. InteractionsEijout tonth nearest neighbors include a larger number of symmetrically distinct 〈i,j〉 terms than the corresponding 〈u,v,w〉 terms in three dimensions, implying that only approximate three-dimensional energies can be obtained by fitting from the energies of this study. Mutual frustration of repulsive interactions on the interstitial sublattice, which has a large number of triangularly connected neighbors, is responsible for both breaking the hexagonal symmetry of the sublattice and the failure to form structures giving conventional “spot” diffraction patterns.