年代学2013-02

1、同位素地质年代学同位素地质年代学放射性核素衰变类型放射性核素衰变类型按释放的按释放的/ /捕获的粒子捕获的粒子a a衰变衰变b-/b+b-/b+衰变衰变/ /电子捕获衰变电子捕获衰变g g衰变衰变按衰变方式或途径按衰变方式或途径1. 1. 简单衰变类型简单衰变类型放射性核素放射性核素 （母体）（母体） 稳定核素（子体）稳定核素（子体）2. 2. 分支衰变类型分支衰变类型 稳定核素稳定核素1 1（子体（子体1 1） 稳定核素稳定核素2 2（子体（子体2 2）放射性核素放射性核素 （母体）（母体） 3. 系列衰变类型系列衰变类型放射性核素放射性核素 （母体）（母体） 不稳定核素（子体不稳定核素（子

2、体1） 不稳定核素（子体不稳定核素（子体2） 稳定核素（子体稳定核素（子体N） 238U系列衰变系列衰变235U系列衰变系列衰变232Th系列衰变系列衰变4. 4. 其它衰变类型其它衰变类型自发裂变自发裂变 (Spontaneous Fission)Nuclei of certain isotopes of elements having high actomic numbers disintegrate spontaneously and form isotopes of two product elementsFlerov & Petrzhak (1940) 首次首次报道报道92U同位素的

3、裂变同位素的裂变其它可裂变元素有其它可裂变元素有: 94Pu、95Am、96Cm、 105HaFriedlander et al., 1981Decrease in activation energy (D DE) with increasing atomic number implies an increase in the susceptibility of these nuclides to nuclear fission 放射性成因同位素的积累放射性成因同位素的积累Growth of radiogenic daughters简单衰变类型简单衰变类型A long-lived radion

4、uclide (N) decays in a closed system toA stable radiogenic daughter (D*)N = N0e-ltD* = N0 - N = N0 - N0e-ltWhen t , D* = N0= N0 (1 - e-lt)由于由于N0不易获得，可以转换为不易获得，可以转换为:N0 = N eltD* = N0 - N = N elt - N = N (elt - 1)若岩石或矿物形成时，有若岩石或矿物形成时，有D存在，即存在，即D0，则有，则有:D = D0 + D* = D0 + N (elt - 1)若保持体系封闭，形成年龄可得到若保持

5、体系封闭，形成年龄可得到: :岩石或矿物同位素年代学的基本条件岩石或矿物同位素年代学的基本条件: : Rock or mineral sample being dated has not gained or lost parent (N) or daughter (D) atoms - closed system The decay constant of the parent nuclide (N) is independent of time and is not affected by any physical condition to which the nuclide may hav

6、e been subjected Value of the decay constant is known accurately An appropriate value of D0 is used in calculation based on either knowledge of the chemical properties of the daughter element or its isotope composition in the terrestrial reservoir from which the rock or mineral originated The measur

7、ed values of D and N contents are accurate and representative of the rock or minerals being dated 1. Decay constants （衰变参数衰变参数)Decay of radionuclides by emission of negatrons, positrons, and a a-particles and by spontaneous fission is a nuclear process, which is not affected by electron density in t

8、he vicinity of the nucleus or by external pressure and temperature of the environment to which these radionuclides may be subjectedDecay constants of negatron, positron, and a a-emitters are invariant with respect to time and unaffected by environmental conditionsOnly electron capture decay and inte

9、rnal conversion of isomers may be affected by extranuclear environmentHahn et al. (1976) have proposed, electron density in the vicinity of the nucleus may affect the probability of decay of the both decay typesHensley et al. (1973) observed an increase of 0.59% in the decay constant of 7Be (electro

10、n capture), when this nuclide was subjected to a pressure of 270 kbar2. Isotope closed system (同位素封闭体系同位素封闭体系)主要影响因素主要影响因素The extent to which rocks and minerals have actually remained closed to parent and daughter elements depends on many factors, mainly: Retentivity of the minerals for parent (N) a

11、nd daughter (D) elements Physical and chemical properties of the parent and daughter elements history of metamorphic alteration of the rock or minerals in response to episodic changes of pressure and temperature rate of cooling following the last thermal episodeInteraction with aqueous solutionsClos

12、ure Temperature of Isotope SystemRb-Sr system:Muscovite 450-500 OC Biotite 350 OCK-Ar system:Hornblende 450-500 OC Biotite 300 OCMuscovite 350-400 OC Microcline 150-250 OCU-Pb system:Zircon 900 OC Garnet 800 OCMonazite 650-740 OC Sphene (titanite) 500-670 OC Rutile 420-380 OC Apatite 350 OC 20040060

13、08001000120014000.00010.0010.010.1110Effective diffusion radius (cm)Closure Temperature (C)Nd, GarnetSm, ApatiteSm, ZirconNd, TitanitePb, ZirconAfter Cherniak et al. (1997); Lee et al. (1997); Metzger et al. (1989); etc.问题：问题：采用不同同位素体系对同一岩石样品的不同矿采用不同同位素体系对同一岩石样品的不同矿物，分别进行同位素年代学测试，获得多个同物，分别进行同位素年代学测试

14、，获得多个同位素体系的年龄位素体系的年龄在什么情况下，这些年龄值相同？在什么情况下，这些年龄值相同？在什么情况下，这些年龄值存在差异？在什么情况下，这些年龄值存在差异？如何解释现象？代表什么地质意义？如何解释现象？代表什么地质意义？200300400500600700800800850900950100010501100Time (Ma)Temperature ( C)OMezger (1990)石榴石 (U-Pb)独居石 (U-Pb)榍石 (U-Pb)角闪石 (Ar-Ar)金红石 (U-Pb)黑云母 (Ar-Ar)Cooling history3oC/Ma1oC/MaAdirondackHi

15、ghlands3. Initial value (子体元素的初始值确定子体元素的初始值确定, D0)(1) In some cases, the initial value , D0 can be estimated(2) The initial value, D0, can also be determined by using the isochron (等时线等时线) method40K 40Ar, 矿物矿物D0 0238U 206Pb, 锆石锆石D0 087Rb 87Sr, 地幔成因岩石地幔成因岩石D0 0.7044. Determination of decay constants

16、( (衰变参数衰变参数l l的确定）的确定）5. Accurate determination of isotopic composition and contents of mother and daughter nuclides放射性母体和放射性成因子体同位素组成和含量的放射性母体和放射性成因子体同位素组成和含量的准确测量准确测量 Accurate measurement of isotopic composition by mass spectrometer (质谱计同位素比值或丰度的精确测定质谱计同位素比值或丰度的精确测定） determination of contents of m

17、other and daughter nuclides (放射性母体和放射性成因子体含量测定放射性母体和放射性成因子体含量测定) - 同位素稀释法测定同位素稀释法测定分支衰变类型分支衰变类型A long-lived radionuclide (N) decays in a closed system to more than one stable radiogenic daughter36Ar38Ar40Ar40K39K182019182122Number of neutronsNumber of protons41K2043,44,46,48Ca40Ca42Ca19le = 0.581 x

18、10-10 (year-1)40K 40Ar (10.5%)b-capture40K 40Ca + b- (89.5%)lb = 4.962 x 10-10 (year-1)l = le + lb = 5.543 x 10-10 (year-1)T1/2 = 1.28 x 109 (year)The atmospheric ratio of 40Ar/36Ar is known to be 295.5. By measuring the amount of 36Ar present, we can deduce the amount of atmospheric 40Ar initially

19、present.40Ar36Ar36Ar40Klle= 295.5 +(elt -1) 40Ar40Klle(elt -1) = 40Ar0 + DiNlli(elt -1) = Di0 + l l = l l1 + l l2 + + l li + + l ln系列衰变类型系列衰变类型A long-lived radionuclide (N1) decays in a closed system to a unstable radiogenic daughter (N2), which can subsequently decay to an another unstable or a sta

20、ble one (N3)N1 (radioactive) N2 Nn (stable)For the simple case N1 N2 N3A radionuclide (N1) decays to a radioactive daughter (N2) that subsequently decays to a third daughter (N3)The rate of decay of N2 is the difference between the rate at which N2 is produced by decay of its parent (N1) and its own

21、 rate of decayThe rate of decay of the parent (N1):The rate of decay of the first daughter (N2):111dNNdtl-222dNNdtl-The net rate of change of the number of daughter N2:21122dNNNdtll-The number of atoms of parent N1 remaining at any time (t): 1011tNN el-Hence we have: 10222110tdNNN edtlll-+-122001212

22、21tttNNeeN ellllll-+-If 020N 12012121ttNNeelllll-The general solution of a radioactive decay series: N1 N2 N3 Nnwhen 00023.0nNNN1212.ntttnnNC eC eC elll-+where 01211121311.nnNCl llllllll- 01211212322.nnNCl llllllll- 01211313233.nnNCl llllllll-If n = 33123123tttNC eC eC elll-+0123112131NCl l lllll-0123121232NCl l lllll-0123131323NCl l lllll-系列衰变过程中，系列衰变过程中，母子体变化规律母子体变化规律系列衰变的平衡系列衰变的平衡When the parent (N1) of a decay chain has a longer halflife than its unstable daughter (N2), thenl1 l2, and l2 l1 l212012121ttNNeelllll-The equation can become 1201212ttNNeellll-approaches zero faster than as