双稀释剂计算及校正方法
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摘要
随着高精度同位素测量技术的发展,双稀释剂方法被证明是很多同位素体系测量的必要方法。尽管双稀释剂方法的原理和计算过程在多篇文献中已有介绍,但双稀释剂本身的测量和校正方法还没有被系统地讨论过。本文从介绍同位素质量分馏定律入手,简明阐述了双稀释剂测量原理并推导了双稀释剂计算公式及计算方法。同时进一步讨论了双稀释剂校正方法与其对同位素测量结果的影响,提出了双稀释剂方法的完整公式,以及相应的双稀释剂误差传递推导过程。
In recent years, the double-spike technique has been widely used to correct mass-dependent isotope fractionation during sample preparation and mass spectrometric analysis in many isotope systems. Although the principle of the double-spike technique and its calculation procedure have been introduced in different ways, the way to calibrate the isotopic ratios of double-spike has not been fully described. This paper aims at systematically describing the principle, calculation and calibration procedure of the double-spike technique. Then, we come up with a revised formulas of double-spike calculation. Besides, we also provide error propagation based on every measured isotopic ratio in our new calculation method, which is the base of further study and optimation on the double-spike technique.
In recent years, the double-spike technique has been widely used to correct mass-dependent isotope fractionation during sample preparation and mass spectrometric analysis in many isotope systems. Although the principle of the double-spike technique and its calculation procedure have been introduced in different ways, the way to calibrate the isotopic ratios of double-spike has not been fully described. This paper aims at systematically describing the principle, calculation and calibration procedure of the double-spike technique. Then, we come up with a revised formulas of double-spike calculation. Besides, we also provide error propagation based on every measured isotopic ratio in our new calculation method, which is the base of further study and optimation on the double-spike technique.
引文
[1]朱祥坤,王跃,闫斌,李津,董爱国,李志红,孙剑.非传统稳定同位素地球化学的创建与发展[J].矿物岩石地球化学通报,2013,32(6):651-688.Zhu Xiang-kun,Wang Yue,Yan Bin,Li Jin,Dong Ai-guo,Li Zhi-hong,Sun Jian.Developments of non-traditional stable isotope geochemistry[J].Bull Mineral Petrol Geochem,2013,32(6):651-688(in Chinese with English abstract).
[2]Albarède F,Beard B.Analytical methods for non-traditional isotopes[J].Rev Mineral Geochem,2004,55(1):113-152.
[3]Maréchal C N,Télouk P,Albarède F.Precise analysis of copper and zinc isotopic compositions by plasma-source mass spectrometry[J].Chem Geol,1999,156(1):251-273.
[4]Dodson M.A theoretical study of the use of internal standards for precise isotopic analysis by the surface ionization technique:Part I.General first-order algebraic solutions[J].JSci Instrum,1963,40(6):289.
[5]Compston W,Oversby V M.Lead isotopic analysis using a double-spike[J].J Geophys Res,1969,74(17):4338-4348.
[6]Galer S J G.Optimal double and triple spiking for high precision lead isotopic measurement[J].Chem Geol,1999,157(3/4):255-274.
[7]Rudge J F,Reynolds B C,Bourdon B.The double-spike toolbox[J].Chem Geol,2009,265(3):420-431.
[8]李津,朱祥坤,唐索寒.钼同位素比值的双稀释剂测定方法研究[J].地球学报,2011,32(5):601-609.Li Jin,Zhu Xiang-kun,Tang Suo-han.Mo isotope measurements using double-spike techniques[J].Acta Geosci Sinica,2011,32(5):601-609(in Chinese with English abstract).
[9]李津,朱祥坤,唐索寒.双稀释剂法在非传统稳定同位素测定中的应用--以钼同位素为例[J].岩矿测试,2011,30(2):138-143.Li Jin,Zhu Xiang-kun,Tang Suo-han.The application of double-spike in non-traditional stable isotopes-A case study on mo isotopes[J].Rock Mineral Anal,2011,30(2):138-143(in Chinese with English abstract).
[10]Hamelin B,Manhes G,Albarede F,Allegre C J.Precise lead isotope measurements by the double-spike technique-Areconsideration[J].Geochim Cosmochim Acta,1985,49(1):173-182.
[11]郑永飞,陈江峰.稳定同位素地球化学[M].北京:科学出版社,2000:10-13.Zheng Yong-fei,Chen Jiang-feng.Stable Isotope Geochemistry[M].Beijing:Science Press,2000:10-13(in Chinese).
[12]Kehm K,Hauri E H,Alexander C M O,Carlson R W.High precision iron isotope measurements of meteoritic material by cold plasma ICP-MS[J].Geochim Cosmochim Acta,2003,67(15):2879-2891.
[13]Eberhardt A,Delwiche R,Geiss J.Isotopic effects in single filament thermal ion sources[J].Z Naturfo A,1964,19(6):736-740.
[14]Rees C.Fractionation effects in the measurement of molybdenum isotope abundance ratios[J].Int J Mass Spectrom Ion Phys,1969,3(1):71-80.
[15]Habfast K.Fractionation correction and multiple collectors in thermal ionization isotope ratio mass spectrometry[J].Int JMass Spectrom,1998,176(1):133-148.
[16]Russell W,Papanastassiou D,Tombrello T.Ca isotope fractionation on the Earth and other solar system materials[J].Geochim Cosmochim Acta,1978,42(8):1075-1090.
[17]Young E D,Galy A,Nagahara H.Kinetic and equilibrium mass-dependent isotope fractionation laws in nature and their geochemical and cosmochemical significance[J].Geochim Cosmochim Acta,2002,66(6):1095-1104.
[18]Hofmann A.Fractionation Corrections for mixed-isotope spikes of Sr,K,and Pb[J].Earth Planet Sci Lett,1971,10(4):397-402.
[19]Johnson C M,Beard B L.Correction of instrumentally produced mass fractionation during isotopic analysis of Fe by thermal ionization mass spectrometry[J].Int J Mass Spectrom,1999,193(1):87-99.
[20]Albarède F.Introduction to Geochemical Modeling[M].Cambridge:Cambridge University Press,1996:142-144.
[21]Eugster O,Tera F,Wasserburg G J.Isotopic analyses of barium in meteorites and in terrestrial samples[J].J Geophys Res,1969,74(15):3897-3908.
[22]Siebert C,N?gler T F,Kramers J D.Determination of molybdenum isotope fractionation by double-spike multicollector inductively coupled plasma mass spectrometry[J].Geochem Geophys Geosyst,2001,2.DOI:10.1029/2000GC000124.
[23]Han R,Qin L,Brown S T,Christensen J N,Beller H R.Differential isotopic fractionation during Cr(VI)reduction by an aquifer-derived bacterium under aerobic versus denitrifying conditions[J].Appl Environ Microbiol,2012,78(7):2462-2464.
[2]Albarède F,Beard B.Analytical methods for non-traditional isotopes[J].Rev Mineral Geochem,2004,55(1):113-152.
[3]Maréchal C N,Télouk P,Albarède F.Precise analysis of copper and zinc isotopic compositions by plasma-source mass spectrometry[J].Chem Geol,1999,156(1):251-273.
[4]Dodson M.A theoretical study of the use of internal standards for precise isotopic analysis by the surface ionization technique:Part I.General first-order algebraic solutions[J].JSci Instrum,1963,40(6):289.
[5]Compston W,Oversby V M.Lead isotopic analysis using a double-spike[J].J Geophys Res,1969,74(17):4338-4348.
[6]Galer S J G.Optimal double and triple spiking for high precision lead isotopic measurement[J].Chem Geol,1999,157(3/4):255-274.
[7]Rudge J F,Reynolds B C,Bourdon B.The double-spike toolbox[J].Chem Geol,2009,265(3):420-431.
[8]李津,朱祥坤,唐索寒.钼同位素比值的双稀释剂测定方法研究[J].地球学报,2011,32(5):601-609.Li Jin,Zhu Xiang-kun,Tang Suo-han.Mo isotope measurements using double-spike techniques[J].Acta Geosci Sinica,2011,32(5):601-609(in Chinese with English abstract).
[9]李津,朱祥坤,唐索寒.双稀释剂法在非传统稳定同位素测定中的应用--以钼同位素为例[J].岩矿测试,2011,30(2):138-143.Li Jin,Zhu Xiang-kun,Tang Suo-han.The application of double-spike in non-traditional stable isotopes-A case study on mo isotopes[J].Rock Mineral Anal,2011,30(2):138-143(in Chinese with English abstract).
[10]Hamelin B,Manhes G,Albarede F,Allegre C J.Precise lead isotope measurements by the double-spike technique-Areconsideration[J].Geochim Cosmochim Acta,1985,49(1):173-182.
[11]郑永飞,陈江峰.稳定同位素地球化学[M].北京:科学出版社,2000:10-13.Zheng Yong-fei,Chen Jiang-feng.Stable Isotope Geochemistry[M].Beijing:Science Press,2000:10-13(in Chinese).
[12]Kehm K,Hauri E H,Alexander C M O,Carlson R W.High precision iron isotope measurements of meteoritic material by cold plasma ICP-MS[J].Geochim Cosmochim Acta,2003,67(15):2879-2891.
[13]Eberhardt A,Delwiche R,Geiss J.Isotopic effects in single filament thermal ion sources[J].Z Naturfo A,1964,19(6):736-740.
[14]Rees C.Fractionation effects in the measurement of molybdenum isotope abundance ratios[J].Int J Mass Spectrom Ion Phys,1969,3(1):71-80.
[15]Habfast K.Fractionation correction and multiple collectors in thermal ionization isotope ratio mass spectrometry[J].Int JMass Spectrom,1998,176(1):133-148.
[16]Russell W,Papanastassiou D,Tombrello T.Ca isotope fractionation on the Earth and other solar system materials[J].Geochim Cosmochim Acta,1978,42(8):1075-1090.
[17]Young E D,Galy A,Nagahara H.Kinetic and equilibrium mass-dependent isotope fractionation laws in nature and their geochemical and cosmochemical significance[J].Geochim Cosmochim Acta,2002,66(6):1095-1104.
[18]Hofmann A.Fractionation Corrections for mixed-isotope spikes of Sr,K,and Pb[J].Earth Planet Sci Lett,1971,10(4):397-402.
[19]Johnson C M,Beard B L.Correction of instrumentally produced mass fractionation during isotopic analysis of Fe by thermal ionization mass spectrometry[J].Int J Mass Spectrom,1999,193(1):87-99.
[20]Albarède F.Introduction to Geochemical Modeling[M].Cambridge:Cambridge University Press,1996:142-144.
[21]Eugster O,Tera F,Wasserburg G J.Isotopic analyses of barium in meteorites and in terrestrial samples[J].J Geophys Res,1969,74(15):3897-3908.
[22]Siebert C,N?gler T F,Kramers J D.Determination of molybdenum isotope fractionation by double-spike multicollector inductively coupled plasma mass spectrometry[J].Geochem Geophys Geosyst,2001,2.DOI:10.1029/2000GC000124.
[23]Han R,Qin L,Brown S T,Christensen J N,Beller H R.Differential isotopic fractionation during Cr(VI)reduction by an aquifer-derived bacterium under aerobic versus denitrifying conditions[J].Appl Environ Microbiol,2012,78(7):2462-2464.