| Abstract: | Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation（103lna）.Based on the density functional theory,we investigated how the average Ca–O bond length and the reduced partition function ratios（103lnb）and103lna of44Ca/40Ca in forsterite（Fo）are affected by its Ca concentration.Our results show that Ca–O bond length in forsterite ranges from 2.327 to 2.267 A?with the Ca/（Ca+Mg）varying between a narrow range limited by an upper limit of 1/8 and a lower limit of 1/64.However,outside this narrow range,i.e.,Ca/（Ca+Mg）is lower than1/64 or higher than 1/8,Ca–O bond length becomes insensitive to Ca concentration and maintains to be a constant.Because the 103lnb is negatively correlated with Ca–O bond length,the 103lnb significantly increases with decreasing Ca/（Ca+Mg）when 1/64\Ca/（Ca+Mg）\2/16.As a consequence,the 103lna between forsterite and other minerals also strongly depend on the Ca content in forsterite.Combining previous studies with our results,the heavier Ca isotopes enrichment sequence in minerals is:forsteriteorthopyroxeneclinopyroxenecalcite&diopsidedolomitearagonite.Olivineand pyroxenes are enriched in heavier Ca isotope compared to carbonates.The 103lna between forsterite with a Ca/（Ca+Mg）of 1/64 and clinopyroxene（Ca/Mg=1/1,i.e.,diopside）is up to～0.64%at 1200 K.The large 103lnaFodiopsiderelative to the current analytical precision for Ca isotope measurements suggests that the dependence of103lnaFo-diopsideon temperature can be used as a thermometer,similar to the one based on the 103lna of44Ca/40Ca between orthopyroxene and diopside.These two Ca isotope thermometers both have a precision approximate to that of elemental thermometers and provide independent constraints on temperature. |
