年代學(xué)2013-05

1、同位素地質(zhì)年代學(xué)同位素地質(zhì)年代學(xué)Isotope Parent-Daughter SystemD = D0 + N (elt-1)87Sr/86Sr = (87Sr/86Sr)0 + 87Rb/86Sr(elt 1)t =(D-D0)Nlnl1+ 187Sr/86Sr = (87Sr/86Sr)0 + 87Rb/86Sr(elt 1)The values of 87Sr/86Sr ratio of samples can be obtained by the measurement using a mass spectrometerThe initial values of 87Sr/86Sr

2、ratio of samples can be estimated or obtained by the isochron methodHow about the value of 87Rb/86Sr ratio?For calculation of the value of 87Rb/86Sr ratio, we need to know:Contents of Rb and SrSr isotopic abundance of individual sample or Sr isotopic ratios (84Sr/86Sr, 87Sr/86Sr, 88Sr/86Sr)Rb isotop

3、ic abundance or 85Rb/87Rb ratio (2.59265, we have already known)Methods to obtain the contents of Rb and SrMeasurements using the x-ray fluorescence (XRF), inductively-coupled spectrometry (ICP) techniquesMeasurements using the isotope dilution method (同位素稀釋法同位素稀釋法), the most accurate methodHow to c

4、alculate atomic amounts (mol) of 87Rb and 86Sr and 87Rb/86Sr atomic ratios of individual sample from the contents of Rb and Sr (ppm) and isotopic ratios of Rb and Sr?85Rb87Rb72.17%27.83%銣銣 (Rubidium)Group 1 alkali metal, trace element in the EarthAtomic abundance Atomic abundance ratio:85Rb/87Rb = 2

5、.59265a constant throughout the Earth, moon and most meteorites due to isotopic homogenization in the solar nebula.Calculation of atomic amounts of 87Rb (mol) Concentration of Rb = CRbAverage atomic weight of Rb85Rb/87Rb = 2.5926585Rb = 2.59265 * 87RbAWRb = 1/(1+2.59265)*AW87 + 2.59265/(1+2.59265)*A

6、W85Atomic amounts of Rb (mol) = CRb / AWRbAtomic amounts of 87Rb (mol) I87Rb = 1/(1+2.59265)*(CRb/AWRb)I87Rb = CRb*Ab87Rb/AWRbor鍶 (Strontium)Group 2 alkaline earth metal, trace element in the EarthStable isotopes: 84Sr, 86Sr and 88Sr Radiogenic isotope: 87SrAtomic abundance ratio:88Sr/86Sr = 8.37528

7、7Sr/86Sr ratio changes with time. 86Sr88Sr9.87%82.53%Atomic abundance 87Sr84Sr7.04%0.56%AverageCalculation of atomic amounts of 87Sr (mol) Concentration of Sr = CSrAssume:Based on the measured value of 87Sr/Sr86 ratio of individual samples to calculate average atomic weight AWSrValue of 84Sr/86Sr ra

8、tio = r1Value of 87Sr/86Sr ratio = r2Value of 88Sr/86Sr ratio = r3Average atomic weight of SrAWSr = r1/(r1+r2+r3+1)*AW84 + 1/(r1+r2+r3+1)* AW86 + r2/(r1+r2+r3+1)*AW87 + r3/(r1+r2+r3+1)*AW88Atomic amounts of Sr (mol) = CSr / AWSrAtomic amounts of 86Sr (mol) I86Sr = 1/(r1+r2+r3+1)*(CSr/AWSr)I86Sr =CSr

9、*Ab86Sr/AWSr)87Rb / 86Sr atomic ratio = I87Rb / I86Sr878786862.692920.283096RbSrCRbSrSrCSrI87Rb = 1/(1+2.59265)*(CRb/AWRb)I86Sr = 1/(r1+r2+r3+1)*(CSr/AWSr)or87878686RbSrSrRbCAWRbAb RbSrCAb SrAWPbPb的平均原子量計(jì)算的平均原子量計(jì)算依據(jù)測得的樣品某元素同位素組成依據(jù)測得的樣品某元素同位素組成( (或比值或比值) )自然界鉛的主要同位素有自然界鉛的主要同位素有: : 204Pb、206Pb、207Pb、2

10、08Pb238U 206Pb235U 207Pb232Th 208Pb衰變測得某樣品鉛同位素組成測得某樣品鉛同位素組成( (原子數(shù)比原子數(shù)比):): a= 206Pb/204Pb = 18.8 b= 207Pb/204Pb = 15.6 c= 208Pb/204Pb = 39.2 204Pb/204Pb = 1該樣品的鉛平均原子量該樣品的鉛平均原子量 (AWPb)？鉛同位素的原子質(zhì)量 204Pb = 203.97302 (A204) 206Pb = 205.97444 (A206) 207Pb = 206.97587 (A207) 208Pb = 207.97663 (A208)A*A206a

11、+b+c+1B*A207a+b+c+1C*A208a+b+c+11*A204a+b+c+1+AWPb = 同位素稀釋法是一種準(zhǔn)確的化學(xué)成分定量分析的方法，通過同位素稀釋法是一種準(zhǔn)確的化學(xué)成分定量分析的方法，通過同位素比值的質(zhì)譜精密測定和化學(xué)計(jì)量的準(zhǔn)確稱重，實(shí)現(xiàn)對同位素比值的質(zhì)譜精密測定和化學(xué)計(jì)量的準(zhǔn)確稱重，實(shí)現(xiàn)對某一基體中的同位素、元素或分子個(gè)數(shù)的高精度測量某一基體中的同位素、元素或分子個(gè)數(shù)的高精度測量基本原理：基本原理：針對某一待測物質(zhì)的待分析的元素，準(zhǔn)確地加入針對某一待測物質(zhì)的待分析的元素，準(zhǔn)確地加入適量的該元素的稀釋劑，均勻混合到達(dá)化學(xué)平衡后，采用質(zhì)適量的該元素的稀釋劑，均勻混合到達(dá)化學(xué)

12、平衡后，采用質(zhì)譜方法準(zhǔn)確的測定混合物的同位素比值，在已知待測物質(zhì)、譜方法準(zhǔn)確的測定混合物的同位素比值，在已知待測物質(zhì)、稀釋劑和混合物的同位素比值（或豐度）以及待測物質(zhì)和稀稀釋劑和混合物的同位素比值（或豐度）以及待測物質(zhì)和稀釋劑的準(zhǔn)確稱樣量的情況下，可以計(jì)算得到待測元素的濃度釋劑的準(zhǔn)確稱樣量的情況下，可以計(jì)算得到待測元素的濃度或質(zhì)量或質(zhì)量待測物質(zhì)和稀釋劑的同位素比值（豐度）可以同樣采用質(zhì)譜待測物質(zhì)和稀釋劑的同位素比值（豐度）可以同樣采用質(zhì)譜法預(yù)先獲得法預(yù)先獲得樣品稀釋劑Isotope dilution analysis銣同位素為例銣同位素為例85Rb87Rb85Rb87Rb85Rb87Rb樣品樣

13、品稀釋劑稀釋劑混合物混合物同位素豐度同位素豐度We know: 1、Value of 87Rb/85Rb ratio of sample; 2、Value of 87Rb/85Rb ratio of spike; 3、Concentration of the Rb spike； 4、Sample and spike are exactly weightedWe have measured 87Rb/85Rb ratio for the mixture of the sample and spike,How can we obtain Rb concentration of the sample

14、?Rbmixture Rbsample + Rbspike87Rbsam + 87Rbspi85Rbsam + 85Rbspi87Rb85Rb()mix=87Rb85Rb()measured=(85Rb/87Rb)sam = a; (2.59265, constant value) 85Rbsam = a x 87RbsamWeight of sample: Wsam (g)Sample:Atomic abundance and weight of Rb isotopes in natural sample85Rb: 72.17 %; 84.9117487Rb: 27.83 %; 86.909

15、19Value of atomic 85Rb/87Rb ratio: 2.59265(85Rb/87Rb)spi = c;Spike Rb concentration: CRb = b (mol/g)Weight of spike: Wspi (g)Spike:稀釋劑85Rbspi = c/(c+1) x b x Wspi (mmol)87Rbspi = 1/(c+1) x b x Wspi (mmol)87Rbsam + 87Rbspi85Rbsam + 85Rbspi=87Rb85Rb()measured87Rbsam + 1/(c+1)*b*Wspia*87Rbsam + c/(c+1)

16、*b*Wspi =87Rbsam can be obtained85Rbsam = a x 87RbsamRbsam = 87Rbsam + 85Rbsam = (1+a) x 87Rbsam (mmol)Total Rb of the sample:Rb concentration of sample (Csam):Csam = Rbsam/Wsam (mmol/g) = (Rbsam/Wsam) x ARb (mg/g or ppm)ARb: average atom weight of Rb = 85.4678最佳稀釋比例最佳稀釋比例在實(shí)驗(yàn)分析過程中，根據(jù)不同的巖石類型，即在實(shí)驗(yàn)分析過程

17、中，根據(jù)不同的巖石類型，即不同的同位素母體和子體含量大小，加入不同不同的同位素母體和子體含量大小，加入不同重量的同位素稀釋劑，或者考慮使用不同濃度重量的同位素稀釋劑，或者考慮使用不同濃度或不同類型的稀釋劑，如混合型（或不同類型的稀釋劑，如混合型（87Rb-84Sr)或或單一型（單一型（87Rb，84Sr）稀釋劑。這樣可以使母體）稀釋劑。這樣可以使母體和子體同位素的稀釋比同時(shí)達(dá)到最佳稀釋比例和子體同位素的稀釋比同時(shí)達(dá)到最佳稀釋比例同位素稀釋劑同位素稀釋劑人工富集的或制造的、不具有自然界同位素豐度人工富集的或制造的、不具有自然界同位素豐度( (或比值或比值) )的、強(qiáng)烈地富集在自然界豐度相對較低的

18、、強(qiáng)烈地富集在自然界豐度相對較低的某一個(gè)或幾個(gè)同位素的某一個(gè)或幾個(gè)同位素常用的稀釋劑常用的稀釋劑, 如：如：87Rb、84Sr149Sm、 150Nd202Pb、205Pb、208Pb、233U、235U、230Th自然界自然界Rb同位素豐度同位素豐度稀釋劑稀釋劑87Rb同位素豐度同位素豐度85Rb87Rb98%Atomic abundance 85Rb87Rb72.17%27.83%Atomic abundance 86Sr88Sr9.87%82.53%Atomic abundance 87Sr84Sr7.04%0.56%自然界自然界Sr同位素豐度同位素豐度稀釋劑稀釋劑84Sr同位素豐度同位

19、素豐度86Sr88Sr1%5%Atomic abundance 87Sr84Sr95%205Pb208Pb24.1%52.3%Atomic abundance 207Pb204Pb22.6%1.4%0%206Pb自然界自然界Pb同位素豐度同位素豐度稀釋劑稀釋劑205Pb同位素豐度同位素豐度205Pb208Pb0.1%0.1%207Pb204Pb0.1%99.9%206PbAtomic abundance 稀釋劑制備稀釋劑制備 不同稀釋劑的賦存介質(zhì)不同稀釋劑的賦存介質(zhì)( (不同酸介質(zhì)不同酸介質(zhì)) ) 不同分析對象不同分析對象( (巖性或礦物種類巖性或礦物種類) ) 配制稀釋劑的濃度配制稀釋劑的濃度 混合稀釋劑或單種稀釋劑混合稀釋劑或單種稀釋劑 混合稀釋劑中不同稀釋劑的比例混合稀釋劑中不同稀釋劑的比例稀釋劑組成和濃度的標(biāo)定稀釋劑組成和濃度的標(biāo)定 同位素組成標(biāo)定同位素組成標(biāo)定 采用質(zhì)譜計(jì)測量同位素比值采