On the determination of the metastable miscibility gap in ternary alloys from small-angle measurements. I. Theoretical background

Metastable precipitation as the formation of GP zones is governed by a metastable miscibility gap. It is shown that the limits of this gap in a ternary system can be determined from combined analysis of the small-angle scattering (SAS) of X-rays and of neutrons. The necessary condition is a significantly different ratio β = (b_C−b_A)/(b_B−b_A) of the atomic scattering amplitudes b of the components A, B and C for both the X-rays and the neutrons. This difference enables one to determine the slope of the tie-line passing through an individual alloy by comparing the integrated SAS intensities of the two types of radiation. Thereafter, the determination of the gap limits follows the same procedure as already known for binary alloys. The change of the mean atomic volume with composition influences the result, but this can be taken into account provided the same Vegard's law is valid for both the depleted matrix and the precipitate.