Analysis of small-angle scattering patterns from precipitating alloys

The structure of an alloy containing a high density of precipitate particles is analyzed with the Percus-Yevick hard-sphere model to represent the spatial arrangement of precipitates. A commercial aluminum-lithium alloy was heat treated to produce a structure containing a high density of nearly spherical precipitates having the nominal composition Al₃Li in a matrix of almost-pure aluminum. Small-angle x-ray scattering from foils of the alloy was analyzed by nonlinear fitting to a theoretical scattering curve based on a hard-sphere-liquid model which satisfactorily represented the particle size, particle-interaction distance, and particle density. Fitting the calibrated scattering cross section permits determination of the precipitate and matrix composition. While the Percus-Yevick model has been used in modeling micelle solution structures and liquids, this is the first known application to the structure of precipitate alloys.