First-principles investigation of equilibrium K isotope fractionation among K-bearing minerals

The 41K/39K reduced partition function ratios, 103lnβ, of 17 major K-bearing minerals have been calculated using the density functional theory (DFT) method. Their 103lnβ decrease in the order of alunite (KAl3(SO4)2(OH)6) ∼ K-hollandite I (KAlSi3O8) > niter (KNO3) > potassium carbonate (K2CO3) ∼ potassium bicarbonate (KHCO3) > muscovite (KAl2(AlSi3O10)(OH)2) > potassium hydroxide monohydrate (KOH·H2O) ∼ hydrated potassium carbonate (K2CO3·1.5H2O) > nepheline (Na3KAl4Si4O16) > potassium hydroxide dihydrate (KOH·2H2O) > kalsilite (KAlSiO4) > microcline (KAlSi3O8) ∼ phlogopite (KMg3AlSi3O10(OH)2) > lepidolite (KLi2AlSi4O10(OH)2) > sylvite (KCl) > leucite (KAlSi2O6) > djerfisherite (K6CuFe24S26Cl). The calculated 103lnβ varies from 6.80‰ in alunite to 2.08‰ in djerfisherite at 300 K, and from 0.63‰ to 0.19‰ at 1000 K. At 1000 K, there is only small variation (<0.12‰) in 103lnαmineral-microcline of 41K/39K, defined as 103lnβmineral − 103lnβmicrocline, for K-bearing silicate minerals except K-hollandite I, indicating no measurable K isotope fractionation among these end-member K-bearing minerals during high-temperature geochemistry processes. However, the K concentration variation in K-feldspar shows a significant effect, as large as 0.21‰, on the equilibrium K isotope fractionation between K-feldspar and microcline, which cannot be ignored in high-temperature geochemistry processes. Finally, because KOH·H2O and KOH·2H2O are enriched in heavy K isotope relative to all calculated silicate minerals except muscovite, we infer that the interaction between water and silicate minerals likely enrichs 41K in the fluid, which probably explains the relatively higher 41K/39K in river and sea water relative to silicate minerals.