First-principles investigation of the concentration effect on equilibrium fractionation of K isotopes in feldspars

Abstract

The K concentration effects on K-O bond length and the reduced partition function ratios of 41K/39K in alkali feldspars have been explored using the density functional theory (DFT) method. In alkali feldspars, the average K-O bond length increases with increasing K content, measured as K/(K + Na) molar ratio, ranging from 2.724 Å in alkali feldspar with a K/(K + Na) of 1/16 to 2.880 Å in microcline (K/(K + Na) = 1). Our results show large K concentration effect on the calculated reduced partition function ratio. For example, 103ln41K/39Kαfeldspar-microcline between alkali feldspar with a K/(K + Na) of 1/16 and microcline are 2.21‰ at 300 K and 0.42‰ at 700 K, which are comparable to the 41K/39K variation observed in natural samples. Furthermore, isotope fractionation, 103ln41K/39Kαfeldspar-microcline, is negatively linearly correlated with the average K-O bond length in alkali feldspars. Therefore, the concentration effect on K isotope fractionations needs to be considered in the applications of K isotopes in the fields of geochemistry and cosmochemistry, such as the formation of the lunar anorthositic crust and the evolution of the Earth’s crust.