Predicting growth of γ′ in nickel alloys

Abstract

Individual experiments on the growth at elevated temperature of γ′ particles in nickel alloys do not cover a range of conditions sufficient to permit unambiguous discrimination between the growth laws a = (kt)^⅓ and a = (k′t)^½, where a is half the mean particle size (half the cube edge or sphere diameter as appropriate), k and k′ are constants, and t is time. This paper assembles six studies of Ni-Al binary alloys, Ni-Cr-Al ternary alloys, and the commercial IN 738 alloy, which together cover temperatures from 500 to 1000°C. By compensating for temperature and composition according to the theory from which the growth laws are derived, the experimental times are converted to equivalent times, which range from a few minutes to 50 years. The plot of a = (kt)^⅓ over this considerable time span is linear, but that of a = (k′t)^½ has the curved form to be expected when the former is linear. Growth of γ′ particles in these alloys, therefore, is correctly described, within the experimental times, by the first equation and k = (2.3 × 10¹⁵ c/T) exp(−32 520/T) nm³ S⁻¹ with the matrix concentration c in wt-%. Further, no process is foreseen which prevents this conclusion from being true for indefinite time. In these experiments, a varied fiftyfold, but the distribution of particle sizes varied little; the growth process, therefore, can be fairly described as steady state. The volume fraction of γ′ ranged from 2.5 to 40% and had no obvious effect on k or on particle size distribution, nor was there any detectable influence of particle shape, cubic or spherical. The most recent theory of steady state growth predicts k correctly if the γ′ matrix interface energy is given the reasonable value of 0.022 J m⁻², and the two most recent theories each predict the particle size distribution, and also the growth law for individual particles as a function of their position in this distribution, to within the experimental error.