First-principle Calculation Of Inter-mineral Equilibrium K,Ca And N Isotope Fractionation

The cycle of the materials in the earth,the formation and evolution of planets are important in the geoscience.Stable isotope fractionation is one of major tools to trace these processes with complete theory and profound application,which has formed a new subject,Stable Isotope Geochemistry.However,whether the isotope fractionation reachs equilibra in the natural samples is crucial for the further discussion and analyzing.In the experiment,direct measurement of isotope equilibrium fractionation is difficult.Recent years,theoretical prediction of equilibrium isotope fractionation causes more and more attention because of its high convenience and repeatability.First-principles calculations have successfully predicted equilibrium inter-mineral isotope fractionation factors of many elements including C,O,Mg,Si,Ca and Fe.Here we use Quantum ESPRESSO software,which is based on the density functional theory?DFT?,to predict the inter-mineral K,Ca and N isotope equilibrium fractionation factors.The research of K isotopes are rare and the mechanism of the K isotope fractionation is unknown.However,the K isotope would be a good candidate to trace many important geochemistry and cosmochemistry processes,such as the formation and evolution of the planets,the crust weathering and the circulation of the materials in the earth.There are lots of work on the Ca isotopes,and the prediction of reduced partition function ratio of many mantle minerals,such as olivine,orthopyroxene?opx?and clinopyroxene?cpx?,were also reported.But,garnet,one of the Ca-dominant mantle mineral,has not been researched.In the past,most of the N isotope research is often related with the biosphere,hydrosphere and atmosphere.Recent year,the geology N circle is more and more important for understanding the global N circulation and deducing the process of core formation.The K concentration effects on K-O bond length and the reduced partition function ratios of 41K/39K in alkali feldspars have been explored.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 � in alkali feldspar with K/?K+Na?of 1/16 to 2.880 � in microcline?K/?K+Na?=1?.The results show large K concentration effect on the calculated reduced partition function ratio.For example,103 in 41K/39K ?feldspar-microcline between alkali feldspar with K/?K+Na?=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,103 ln 41K/39K ?feldspar-microcline is negatively,linearly correlated with the average K-O bond length in alkali feldspars.Therefore,the concentration effect on K isotope fractionation 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.The 41K/39K reduced partition function ratios,103ln?,of 17 major K-bearing minerals have been predicted.The calculated 103ln? 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 103ln?minieral-microcline of 41K/39K,defined as 103ln?minieral-103ln?microcline,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.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.To better understand the Ca isotope behaviors in the Earth's interior,the Ca concentration effects on the average Ca-O bond length and the reduced partition function ratio?103ln??of 44Ca/40Ca in garnet?grt?have been investigated using first-principles calculations.The average Ca-O bond length increases with the Ca concentration in garnet,which causes a significant variation of 103ln? of 44Ca/40Ca?near 0.47� at 1000 K?.In contrast to Ca in orthopyroxene?opx?and forsterite?fo?,whose bond length and 103ln? are sensitive to concentration only in a narrow range,the bond length and 103ln? of garnet vary with Ca concentration in a much larger range.Ca concentration effects on the 103ln? of 44Ca/40Ca in garnet and clinopyroxene?cpx?can well explain the variation of ?44/40Cagrt-cpx of the natural samples and the negative correlation between ?44/40Cagrt-cpx and Ca concentration in garnet.The simulation shows a limited Ca isotope composition variation??44/40Ca<0.04�?for the depleted mid-ocean ridge basalts?MORB?partial melting without garnet crystallization but a large?44/40Ca up to 0.15� for the depleted MORB melt with garnet crystallization.We predicted the 103ln? of 17 nitrogen-bearing minerals,including nitrate-and ammonium-bearing salts,ammonium-bearing silicate minerals,and nitrides.The results show large nitrogen isotope fractionations between different nitrogen species with 15N most enriched in nitrate minerals and most depleted in nitride minerals.However,the nitrogen isotope fractionations between minerals with the same nitrogen speciation?e.g.,within the nitrate group,or the ammonium group?are very small.Particularly,in silicate minerals,while there exist small magnitudes of nitrogen isotope fractionations among plagioclase,K-feldspar,and mica minerals,the nitrogen isotope fractionations between minerals within these groups are close to 0�,though the concentration effects are found in these solid solution series.These results suggest that nitrogen isotopes may not serve as a good geothermometer,but can be robust tool to trace material sources and infer geological processes that may cause isotope disequilibrium,such as metamorphic devolatilizaton,hydrothermal alteration,crust-mantle interaction.The large variation of 103ln? among nitrites may be useful to deduce the processes of core formation.