Application of the Weibull density function to describe the δ′ (Al 3Li) particle size distribution in binary AlLi alloys

Abstract

In this paper the results of a quantitative transmission electron microscopy investigation of the shape of the δ′ (Al 3Li) particle size distribution (PSD) in a series of binary AlLi alloys containing between 2.4 and 4.5 wt. % Li are described. The isothermal aging times were varied from 12 h to 10 days at 200 and 225°C. PSDs were determined for the various aging conditions. The shape of the PSDs was found to be a function of lithium content. Alloys containing 2.4 wt. % Li tended to have a long tail on the left side of the distribution curve (a coefficient of skewness of less than zero), and alloys with more than 4 wt.% Li tended to have a long tail on the right side of the distribution curve (a coefficient of skewness greater than zero). The PSDs were modeled using the Weibull density function which has the form p(x) = abx b−1 exp( −ax b) Both the a and the b parameters systematically decreased with increasing lithium content. The changes in a and b resulted in a series of distributions in which the shape of the PSD changed progressively from a negatively to a positively skewed distribution with increasing lithium content. The linear regression equations relating lithium content [Li] in weight per cent to the value of the respective parameters were determined to be a = 0.94 − 0.03[ Li] b = 5.80 − 0.52[ Li] The above expressions were found to be independent of aging time and temperature over the ranges investigated. With these expressions the shape of the δ PSD can be predicted, simply by knowing the composition.