Ordered array of $\omega$ particles in $\beta$-Ti matrix studied by small-angle X-ray scattering

Abstract

Nanosized particles of $\omega$ phase in a $\beta$-Ti alloy were investigated by small-angle X-ray scattering using synchrotron radiation. We demonstrated that the particles are spontaneously weakly ordered in a three-dimensional cubic array along the $\langle 100\rangle$-directions in the $\beta$-Ti matrix. The small-angle scattering data fit well to a three-dimensional short-range-order model; from the fit we determined the evolution of the mean particle size and mean distance between particles during ageing. The self-ordering of the particles is explained by elastic interaction between the particles, since the relative positions of the particles coincide with local minima of the interaction energy. We performed numerical Monte Carlo simulation of the particle ordering and we obtained a good agreement with the experimental data.