geothermochronology based on noble gases: i. stability of the u-xe isotopic system in nonmetamict...

1

ISSN 0869-5911, Petrology, 2009, Vol. 17, No. 1, pp. 1–24. © Pleiades Publishing, Ltd., 2009.Original Russian Text © Yu.A. Shukolyukov, M.M. Fugzan, I.P. Paderin, S.A. Sergeev, D.P. Krylov, 2009, published in Petrologiya, 2009, Vol. 17, No. 1, pp. 3–27.

INTRODUCTION

In 1905, Rutherford (1906) proposed an U–Th–Hemethod of isotopic dating, which was subsequentlymodified and modernized by many researchers at vari-ous laboratories worldwide (Strutt, 1910; Holmes andPaneth, 1936; Keevil et al., 1944; Hurley, 1954; Hurleyand Fairbarn, 1953). In the Soviet Union, E.K. Gerlinggreatly contributed to both the modernization of the U–Th–He geochronologic method itself and the under-standing of

4

He (and radiogenic

40

Ar) migration

through the structures of natural minerals (Gerling,1939, 1961).

However, accumulated factual data eventually madeit obvious that the original imperfectness of the struc-tures and its secondary distortions, first of all, duringthe radioactive decay of U, Th, and members of theirradioactive families, results in the variable escape ofradiogenic He from virtually all minerals, and hence,the U–Th–He isotopic clock yields underestimatedtime values. This led to the gradual loss of interest inthis method.

Geothermochronology Based on Noble Gases: I. Stability of the U–Xe Isotopic System in Nonmetamict Zircons

Yu. A. Shukolyukov

a, b, d

, M. M. Fugzan

c

, I. P. Paderin

d

, S. A. Sergeev

a,d

, and D. P. Krylov

b

a

Geological Faculty, St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199034 Russiae-mail: [email protected]

b

Institute of Precambrian Geology and Geochronology, Russian Academy of Sciences, nab. Makarova 2, St. Petersburg, 199034 Russia

e-mail: [email protected]

c

Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, ul. Kosygina 19, Moscow, 119991 Russia

e-mail: [email protected]

d

Karpinskii All-Russia Research Institute of Geology (VSEGEI), Srednii pr. 74, St. Petersburg, 199106 Russiae-mail: [email protected]

Received November 2, 2007; in final form, January 9, 2008

Abstract

—The paper presents data on persistent tendencies and relations in the migration of noble gases inU-bearing minerals of various composition: uraninite, pitchblende, metamict zircon, khlopinite, samarskite,betafite, and ampangabeite from various regions worldwide. The escape curves of all noble gases (starting withradiogenic He, Kr, and Xe and ending with nucleogenic

38

Ar) during annealing in the laboratory are demon-strated to include three or four extrema, which suggest a change (increase or decrease) in the escape of raregases at certain temperatures. This, in turn, implies that noble gas atoms are contained in the structures of min-erals in various energy states and that all calculations of migration parameters of noble gases according to theclassic diffusion model based on Fick’s laws are inaccurate. The paper presents a brief description of an alter-native mechanism underlain by an exponential dependence of the migration kinetics on temperature and time.A principle is proposed for the isotopic dating of minerals based on the application of the neutron-inductionU

−

Xe techniques. The paper presents a technique for studying the escape of noble gases from minerals. Exper-imental data are obtained on the escape kinetics of radiogenic and neutron-induced (in a nuclear reactor) Xecomponents from four nonmetamict zircon samples. One of them (zircon from Sri Lanka) is characterized bya particularly homogeneous crystal structure. Its optical examination indicates that this transparent gem-qualityzircon contains no inclusions or structural flaws or defects. Its cathodoluminescence images show only thin,weakly contrasting zoning of the magmatic type. Mass spectrometric SHRIMP II data reveal a very homoge-neous distribution of U and Th in the zircon grain. Nevertheless, the curve of Xe escape kinetics for this sampleshows well pronounced extrema, which suggest that Xe atoms are characterized by different settings in the zir-con structure: they can be accommodated at defects and structural zones of various types (crystalline, amor-phous, and metamict). According to literature data, such zones are nanometer-sized. For each of the detectedextrema, which correspond to the discrete energy settings of Xe atoms in the structure, migration parametersare calculated: the activation energy and frequency factor, which are proved to be strongly correlated. The sta-bility of radiogenic Xe in the structure of crystalline (nonmetamict) zircons calculated from these parameterswas demonstrated to be extremely high.

DOI:

10.1134/S0869591109010019

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PETROLOGY

Vol. 17

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SHUKOLYUKOV et al.

Recent years were marked by the revival of interestin the U–Th–He method of isotopic geochronology inthe form of the application of the U–Th–He isotopicsystem to studying the temperature history of rocks.Starting in 1987, a new scientific avenue started todevelop: geothermochronology based on the U–Th–Hesystem (Zeitler et al., 1987; Wolf et al., 1996, 1998;Farley, 2000; Farley and Stockkli, 2002). The readercan find a comprehensive review of the current state ofthe problem in (Risso, 2005). Along with this, the ther-mal history of rocks is also actively investigated withthe application of the K–Ar isotopic system (

39

Ar

/

40

Arvariant) and such “classic” systems as U–Pb, Sm–Nd,Lu–Hf, the fission track technique, and other isotopicmethods (Levskii et al., 2003).

The general goal of this research avenue is not onlythe reproduction of the thermal histories of magmaticand sedimentary rocks but also, what is even moreimportant, the study of geological processes in correla-tion with these histories.

We believe that one of the highly promising researchavenues in this field of isotopic geology is the simulta-neous application of genetically interrelated isotopicgeochronological systems of noble gases: not only U–Th–He but also U–Xe

s

, U–Xe

n

, U–Kr

s

, and U–Kr

n

(Shukolyukov, 1970, 1989; Shukolyukov et al., 1974,1974, 1975, 1977, 1985, 1992, 1993, 1994; Teitsmaet al., 1975; Teitsma and Clarke, 1978; Shukolyukovand Meshik, 1987) in combination with the U–Th–Pbisotopic system.

1

First, the coincidence of ages obtained by two or

more isotopic system of the same mineral in whichradiogenic isotopes have principally differentgeochemical and migration characteristics notablyimproves the geochronologic reliability of the age val-ues. It is hard to imagine natural conditions underwhich, for example, radiogenic isotopes of the inert gasXe (

136

ïÂ,

134

ïÂ,

132

ïÂ,

and

131

Xe), which are productsof the spontaneous fission of

238

U and radiogenic iso-topes of the chemically active element Pb (

206

Pb and

207

Pb) and the inert gas

4

He (which are products of the

α

-decay of

238

U and

235

U) can migrate with equal veloc-ities and according to the same mechanisms from U-bearing minerals. Because of this, the coincidence ofage values experimentally obtained by these threemethods is a definite indication of the absence of migra-tion and justifies the plausibility of the estimates.

Second, differences between apparent age valuesobtained with the use of various but genetically interre-lated isotopic systems (

136

Xe

s

-

238

U

,

86

Kr

s

-

238

U

,

136

Xe

n

-

235

U

,

86

Kr

n

-

235

U

,

4

He

-

232

Th

,

4

He

-

238

U

,

and

235

U)in the same sample of a mineral offer unique ther-

1

The s and n subscript indexes correspond to Xe and Kr producedby the spontaneous fission of

238

U and the neutron-induced fis-sion of

235

U in the same U-bearing sample preliminarily irradi-ated with a flux of thermal-velocity neutrons in the laboratory;see below for details.

mogeochronologic possibilities, because radiogenicisotopes migrate according to the same mechanism butwith different kinetic parameters. Having experimen-tally determined these migration parameters and thelosses of radiogenic isotopes in a given sample of amineral, one can derive information on the thermal his-tory of this mineral. Hence, there is a possibility ofimplementing a new geochronologic apparatus.

In order to make this approach applicable to prac-tice, it is necessary to carry out extensive studies ofmigration characteristics of He, Xe, and Kr and the sta-bility of their isotopic systems in mineral geochronom-eters. This publication presents recently obtained dataon the stability of the

136

Xe

s

-

238

U system in zircons, asa supplement to our earlier data (Shukolyukov et al.,1979, 1992, 1994; Matukov et al., 1981; Krylov et al.,1992; Krylov and Shukolyukov 1994, 2003; and oth-ers). This paper is the first publication of a seriesdevoted to the exploration of the possibility of the broadapplication of a complex of isotopic systems (U–Xe,U–Kr, and He–U) to the isotopic geochronology andgeothermochronology of various minerals (from U-bearing minerals at Au and U deposits to high-temper-ature accessory minerals, such as zircon, baddeleyite,and others), whose isotopic systems can be variablyaffected by secondary processes.

Our present research was conducted on a well-known gem-quality zircon from Sri Lanka. The mineralhas a chemically and crystallographically homoge-neous matrix, a perfect crystalline structure, and ischaracterized by a single-stage geological history. Weattempted (1) to experimentally determine the migra-tion parameters of radiogenic Xe of both spontaneousand neutron-induced U fission and the energy charac-teristics of the U–Xe isotopic system; (2) to use tech-niques of microprobe analysis (which is characterizedby a high spatial resolution) to study and compare thestates of the U–Pb and U–Xe isotopic systems by deter-mining the corresponding isotopic ages; (3) to explorethe possibility of applying the conclusions drawn fromthe data obtained on the migration characteristics ofradiogenic Xe to other accessory zircons having non-metamict (crystalline) structures from rocks of variouscomposition and age; and (4) to evaluate the possibilityof utilizing our samples as laboratory standards for theXe

s

-

Xe

n

method of the isotopic geochronology of mag-matic rocks.

MATERIALS

Our comparative studies on a modernized MI 1201gas mass spectrometer and SIMS SHRIMP-II were car-ried out with zircon samples of perfect structure andwithout any discernible traces of metamictness, whichwere made available for us by courtesy of Prof. H. Lip-polt of the Heidelberg University and W.A. Todt of theMax-Plank Institute in Mainz.

PETROLOGY

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No. 1

2009

GEOTHERMOCHRONOLOGY BASED ON NOBLE GASES 3

The samples were: (1) a large fragment of a gem-quality zircon crystal from Sri Lanka, from whichsmaller chips were split away (Fig. 1); (2) zircon fromNigeria, which had a nonmetamict undisturbed struc-ture of grains; we also examined zircons from Antarc-tica (from D.P. Krylov’s collection at the Institute ofPrecambrian Geology and Geochronology, RussianAcademy of Sciences); (3) sample 11v32-b from pla-giogranite (enderbite) from MacMaxon Island; thematerial consisted of opaque lilac–yellow grains withfused crystal faces; and (4) sample 11g-1/32 from pla-giogranite (enderbite) from MacMaxon Island, Antarc-tica; the material consisted of almost transparent long-prismatic crystals with very rare inclusions.

METHODOLOGY, METHODS, AND TECHNIQUES

Methodology of Xe

s

-

Xe

n

Isotopic Dating

The principles of the U–Xe (Xe

s

-

Xe

n

) method ofisotopic geochronology, which was first proposed byone of the authors of this paper and his colleagues, andthe fundamentals of the experimental methodologywere described in much detail in our earlier publica-tions. Nevertheless, it is pertinent to recall the essentialsof U–Xe isotopic geochronology and describe the suc-cession of dating operations by the Xe

s

-

Xe

n

method.Along with the

α

-decay of the nuclei of the

238

U and

235

U isotopes in U-bearing minerals, a process generat-ing the

206

Pb and

207

Pb isotopes,

238

U spontaneouslydecays (at a rate 2.5

×

10

7

times lower than the rate of

α

-decay) into fragments with mass numbers of ~70 and~160. They include the stable isotopes

136

ïÂ,

134

ïÂ,

132

ïÂ,

131

ïÂ

, and a very insignificant amount of

129

Xe.The atomic concentrations of radiogenic Xe and

238

Uand the age

t

of the mineral are related through the fol-lowing equation, with regard for both types of

238

Udecay (its spontaneous fission and

α

-decay):

(1)

where

λ

α

and

λ

s

are the rate constants of

α

-decay and

238

U fission, respectively, and

y

s

is the relative Xe yieldduring

238

U spontaneous fission.However, attempts to date U-bearing minerals by

this Xe–U method, which was first proposed in (Khlo-pin and Gerling, 1948; Khlopin et al., 1947), have dem-onstrated that it yields significantly underestimatedapparent age values because of variable losses of radio-genic Xe.

In order to determine the actual (not affected by Xelosses) age, we proposed a method of Xe

s

-

Xe

n

age spec-tra (Shukolyukov et al., 1974, 1974, 1975, 1977;Teitsma and Clarke, 1978), which was applied in thecourse of this research.

During

the first methodological step,

instead ofdetermining

238

U concentration in the sample to be

tU–Xe1λα-----

Xes

U238----------

λα

λsys--------- 1+⎝ ⎠

⎛ ⎞ ,ln=

dated, we determined the Xen concentration, which isformed from 235U upon the irradiation of the samplewith a known integral flux of thermal-velocity neutronsΦ in a nuclear reactor

(2)

where σ235 is the cross section of 235U fission under theeffect of thermal neutrons, yn is the relative Xe yieldduring neutron-induced fission, and R = 235U/238U.

This leads to

(3)

Substituting (3) into (1) allows us to calculate theage of the zircons irradiated by a thermal neutron fluxwithout direct determination of U concentration in themineral

(4)

The exact determination of the flux of thermal neu-trons Φ in a nuclear reactor and the spatial heterogene-ity of this flux faces significant methodological difficul-ties. Moreover, the known values of Xe yield during thefission yn and ys and the constant of the spontaneous fis-sion λs involve fairly high uncertainties (Gorbachevet al., 1976). We solved this problem by irradiating amonitor mineral of known age, together with the sam-ple to be dated, in the nuclear reactor. Because Eq. (4)holds for the monitor mineral, the values of yn, ys, λs,and Φ can be eliminated from the two equations

(5)

Hence, the age of the sample is now a function ofonly two values: the ratio of the concentrations of spon-

Xen UΦσ235yn235 URΦσ235yn,238= =

U238 Xen

RΦσ235yn------------------------.=

tXes Xen–1λα-----

Xes

Xen---------

λαRΦσ235yn

λsys------------------------------ 1+⎝ ⎠

⎛ ⎞ .ln=


Xes/Xen( )sample

Xes/Xen( )mon

------------------------------------ etmonλα 1–( )ln .=

Fig. 1. Zircon from Sri Lanka with a flawless nonmitamictstructure and the same zircon as a faceted gem.

4

PETROLOGY Vol. 17 No. 1 2009

SHUKOLYUKOV et al.

taneous and neutron-induced components in the sampleto be dated and in the monitor mineral. We calculatedthese ratios from the isotopic composition of Xe in theirradiated monitor mineral and the sample to be dated

(6)

Isotope i can be 134ïÂ, 132ïÂ, or 131Xe, depending onthe conditions under which the measurements are car-ried out, for example, on the contamination of Xe in thesample with atmospheric Xe. Here we utilize i = 134.

With regard for formula (5), Eq. (4) was simplifiedto the form

(7)

where

(8)

The second methodological step involved measur-ing the (ïÂs/Xen)sample/(ïÂs/Xen)monitor in the gas frac-tions escaping from the sample during its stepwiseannealing and holding for a certain time (in our experi-ments it was usually equal to 35 min) at any specifiedtemperature step. At low temperatures, Xe escapesfrom perturbed zones in the mineral that have partlylost their radiogenic Xe. At higher temperatures, the gasis released from crystal zones that completely retaintheir radiogenic isotopes. This provides the possibilityof dating a mineral even if it has partly lost its radio-genic Xe. This age is calculated for a number of high-temperature steps, which define a plateau in the appar-ent age spectrum. The average value of the ages of thesegas fractions (coinciding within the analytical errors) isassumed as the true age of the mineral.

Methods Used to Measure Radiogenic Xe Concentrations

The fundamentals of experimental methods appliedto determine concentrations of radiogenic Xe in miner-als were worked out in (Shukolyukov, 1970, 1975,1977; Shukolyukov et al., 1974). These methods werelater specified and modernized (Shukolyukov et al.,1985, 1992; Shukolyukov and Meshnik, 1987, 1989;Reimond et al., 1995).

The sample and monitor mineral mounted in contactwith it in an aluminum container were irradiated by anintegral flux of thermal-velocity neutrons in the cooledtunnel of a nuclear reactor. The sample was then takenfrom the container and degassed for no less than 12 h

X136 es

X136 en

---------------

Xei

Xe136-------------⎝ ⎠

⎛ ⎞n

Xei

Xe136-------------⎝ ⎠

⎛ ⎞meas

–

Xei

Xe136-------------⎝ ⎠

⎛ ⎞meas

Xei

Xe136-------------⎝ ⎠

⎛ ⎞s

–

-----------------------------------------------------.=


Xes

Xen---------⎝ ⎠

⎛ ⎞sample

J 1+⋅ ,ln=

Je

tmonλα 1–Xes

Xen---------⎝ ⎠

⎛ ⎞mon

----------------------.=

(evacuation of the monitor and sample wrapped into Nifoil to vacuum at a temperature of~200°ë). After this,each of them was successively dropped into a vacuumfurnace with a Ta heater for stepwise heating. The tem-perature was measured by an optical pyrometer, whichwas calibrated on a W–Re thermocouple.

Xe was extracted from zircon in a resistance furnacewith a Ta heater at a step of 100–150°ë within a tem-perature range of 1100– 1800°ë. The extracted chemi-cally active gases were adsorbed at getters in a double-step purification system. Xe was separated from othergases by an adsorbent (activated carbon) cooled to adesired temperature.

The isotopic composition of Xe was measured on aMI 1201 mass spectrometer in quasistatic vacuummode. The detection limit of Xe was ~1 × 10–14 cm3 of136Xe. The blank with Al foil that was completely anal-ogous to the foil in which the sample was wrapped didnot exceed 5 × 10–14 cm3 of 136Xe. A correction for iso-topic mass discrimination was introduced according tothe isotopic composition of a reference standard sampleof atmospheric Xe, which was measured before andafter the analysis of Xe from the sample. The fraction-ation coefficients was no higher than 0.5% per amu. Acorrection for an admixture of atmospheric Xe wasintroduced according to the ion current of the isotope130Xe, which was absent from the mass spectrum of Xeof spontaneous and neutron-induced fission. The mon-itor mineral was analyzed in the same series and by ananalogous method and was irradiated in the nuclearreactor in the same container, in immediate contactwith the zircon. The monitor mineral was zircon fromrapakivi sampled at the Berdyaush Massif, SouthernUrals. The monitor had an U–Pb concordant age of1.354 ± 0.010 Ga (Krasnobaev, 1986) and an U–Xe ageof 1.40 Ga (Krylov et al., 1993).

The experimental data on the monitor mineralneeded to calculate the Xes–Xen age are presented inTable 1. This table also reports data on the isotopiccomposition of Xe generated by various fission types(Shukolyukov, 1970, 1980), which were needed toevaluate the proportions of Xe concentrations producedby spontaneous and neutron-induced fission (Xes/Xen)in the minerals.

SHRIMP-II Study of the Zircon

We utilized a SHRIMP-II secondary-ion mass spec-trometer and a CamScan 2500 MX electron micro-scope, respectively, to obtain U–Pb age values (to com-pare them with the results of the U–Xe method) and toevaluate the heterogeneity of the distribution of U, Pb,and other elements in zircon grains.

Sample preparation. Individual zircon grainsselected to be dated and grains of the standard zircon91500 (Wiedenbeck et al., 1995) were placed into anadhesive tape and covered with epoxy resin. Upon itssolidification, the standard-sized (1 inch in diameter)



Table 1. Xe isotopic composition of the monitor mineral (zircon from rapakivi, Berdyaush Massif, Southern Urals) irradiatedby a thermal-velocity neutron flux

Material 136Xe 134Xe 132Xe 131Xe 130Xe 129Xe 128Xe 126Xe 124Xe

Monitor mineral, 1800°C

≡1.000 0.923 ± 0.015 0.607 ± 0.013 0.190 ± 0.003 0 0.015 ± 0.009 0 0 0

Xes ≡1.000 0.825 0.578 0.082 0 ≤0.001 0 0 0

Xen ≡1.000 1.238 0.680 0.456 0 0.105 0 0 0

Xeatm ≡1.000 1.176 3.031 0.239 0.458 2.981 0.216 0.00997 0.0107

Note: The assumed reference isotope was 136Xe. For comparison, the table also lists the Xe isotopic composition expressed in various com-ponents: Xes is Xe of 238U spontaneous fission, Xen is Xe of neutron-induced 235U fission, and Xeatm is atmosphere Xe.

pellet was polished with fine diamond paste to exposethe mid-sections of the zircon grains at a flat polishedsurface.

Optical microscopy. The heterogeneity of the zir-con grains was examined and photographed in trans-mitted and reflected light at 25–50× magnification.

The cathodoluminescence of the crystals wasexamined to get insight into their inner structure and thetype of their zoning. These studies were carried outwith the use of a CamScan 2500 MX scanning electronmicroscope at a beam current of ~5 nA, an acceleratingvoltage of 15 kV, and a working distance of ~35 mm.

The U–Pb dating of zircons was made on aSHRIMP-II SIMS at the Center for Isotopic Studies atthe Karpinskii All-Russia Research Institute of Geol-ogy (VSEGEI). The U–Pb ratios were measured by themethod described in (Williams, 1998). The intensity ofthe primary beam of molecular negatively charged oxy-gen ions was 3.3 nA, and the diameter of the spot (cra-ter) was 25 µm.

Although neither optical nor cathodoluminescenceexaminations have revealed any differences in thestructures of individual fragments of zircon SL-13 fromSri Lanka or any structural heterogeneities within thesefragments, we analyzed all available fragments, andsome of them were analyzed twice (to improve the reli-ability).

The raw data were processed with the SQUID com-puter program (Ludwig, 2000). The U–Pb ratios werenormalized to 0.17917, a value assumed for the stan-dard zircon 91500, which corresponds to an age of1062.4 Ma (Wiedenbeck et al., 1995). The errors of theindividual analyses (age ratios) are reported at an 1σlevel, and the errors in the ages of concordant ages andthose calculated from intersections with a concordia arereported for a 2σ level. The concordia plots were con-structed with the ISOPLOT/EX computer program(Ludwig, 1999).

RESULTS AND DISCUSSION

For each zircon sample, we determined parametersof Xe migration in the crystal structure, quantitativelyevaluated the stability of the U–Xe isotopic system,determined the U–Xe age by the Xes-Xen method; wealso compared the U–Xe and U–Pb SHRIMP-II agevalues of the zircon from Sri Lanka. The latter wasmade possible because the sample was highly homoge-neous in composition and had a perfect crystal struc-ture, as is manifested in the absence of any traces ofmitamictization. We also obtained experimental data oncharacteristics of the actual structure and chemicalcomposition of the zircon sample from Sri Lanka.

Stability of the U–Xe Isotopic System in the Zircons

Our experimental data on the stepwise annealing ofzircons (amount of Xe and its isotopic composition) arereported in Table 2. Based on these data, we con-structed curves for the escape kinetics of Xe producedby the spontaneous and neutron-induced fission of the238U and 235U isotopes, respectively (Fig. 2). Note thatthe most detailed study of the Xe escape kinetics fromminerals requires annealing with as many as possiblenumber of temperature steps to ensure a greater “reso-lution” of the method. Although we managed to carryout annealing with a relatively small number of temper-ature steps, this enabled us to identify the principal fea-tures of Xe migration in the samples.

The dissymmetric and complicated curves of radio-genic Xe escape based on our experimental data showclearly pronounced evidence of Xe migration from anumber of crystal-chemical settings (i.e., differentenergy states) of Xe atoms in the structure of real zirconcrystals. We considered integral Xe escape curves to bea superposition of symmetrical curves (peaks of theescape rates from various crystal-chemistry settings).While the three maxima of radiogenic Xe escape ratesfrom the zircon from Sri Lanka occur at temperatureranges of 1800–1850, 1630–1700, and 1250–1450°ë,zircons from Antarctica display four maxima of Xeescape rates (at 1220–1250, 1400–1430, 1600–1620,

6


SHUKOLYUKOV et al.

Table 2. Xe isotopic composition and concentrations of Xe produced by the spontaneous-fission of 238U (Xes) in our samples

Sample Escape tempera-ture Xe, °C

136Xes, 10–10 cm3/g

134Xe/136Xe 132Xe136Xe 131Xe/136Xe 129Xe/136Xe

Gem-quality zircon from Sri Lanka: large yellow trans-parent crystals with a non-metamict perfect structure

1100 0.078 1.0478 ± 25 0.6330 ± 15 0.2838 ± 8 0.0571 ± 281200 0.0150 1.0586 ± 16 0.6357 ± 10 0.2935 ± 4 0.0598 ± 301350 0.304 1.0597 ± 5 0.6360 ± 3 0.2945 ± 4 0.0601 ± 301450 0.580 1.0008 ± 7 0.6215 ± 4 0.2412 ± 4 0.0453 ± 231600 0.866 0.9931 ± 8 0.6195 ± 5 0.2342 ± 4 0.0433 ± 221700 0.941 0.9935 ± 7 0.6196 ± 4 0.2346 ± 4 0.0434 ± 221800 1.139 1.0004 ± 10 0.6213 ± 6 0.2408 ± 4 0.0452 ± 24

Sum of fractions 3.852 1.0039 ± 10 0.6222 ± 5 0.2440 ± 4 0.0461 ± 23Zircon from Nigeria with a nonmetamict structure

1100 0.0140 1.122 ± 3 0.6515 ± 26 0.3515 ± 18 0.0759 ± 781250 0.0280 1.030 ± 3 0.6286 ± 25 0.2676 ± 13 0.0526 ± 551380 0.0401 1.011 ± 3 0.6241 ± 26 0.2511 ± 13 0.0480 ± 481500 0.0902 1.029 ± 3 0.6284 ± 25 0.2669 ± 12 0.0524 ± 481600 0.279 1.023 ± 3 0.6268 ± 24 0.2610 ± 13 0.0508 ± 511700 0.401 1.013 ± 3 0.6244 ± 23 0.2522 ± 13 0.0483 ± 511850 1.19 1.011 ± 3 0.6237 ± 22 0.2497 ± 12 0.0476 ± 48

Sum of fractions 2.042 1.015 ± 33 0.6250 ± 27 0.2542 ± 13 0.0489 ± 50Zircon from plagiogranites (enderbites) from MacMax-on Island, Antarctica (sam-ple 11v32-b): lilac-yellow-ish subhedral crystals with fused crystal faces, opaque

1100 0.036 1.1679 ± 35 0.6637 ± 29 0.3925 ± 19 0.087 ± 91200 0.185 1.1660 ± 35 0.6626 ± 28 0.3909 ± 20 0.087 ± 91300 0.247 1.1578 ± 34 0.6602 ± 29 0.3838 ± 19 0.083 ± 91400 0.473 1.1460 ± 35 0.6573 ± 26 0.3726 ± 18 0.082 ± 81500 1.051 1.1101 ± 33 0.6488 ± 25 0.3401 ± 17 0.073 ± 81600 2.101 1.1103 ± 33 0.6484 ± 27 0.3403 ± 16 0.072 ± 81700 0.999 1.1162 ± 32 0.6499 ± 26 0.3459 ± 17 0.074 ± 71800 0.513 1.1129 ± 30 0.6491 ± 24 0.3425 ± 18 0.074 ± 81880 0.401 1.1078 ± 29 0.6478 ± 24 0.3381 ± 18 0.072 ± 7

Sum of fractions 6.010 1.1210 ± 34 0.6511 ± 25 0.3502 ± 18 0.076 ± 8Zircon from plagiogranites (enderbites) from MacMax-on Island, Antarctica (sam-ple 11g-1/32): almost trans-parent long-prismatic crys-tals with very rare minute inclusions

1100 0.0383 1.151 ± 3 0.6580 ± 26 0.3770 ± 19 0.083 ± 81200 0.0817 1.164 ± 4 0.6620 ± 33 0.3885 ± 19 0.086 ± 91300 0.0826 1.158 ± 4 0.6622 ± 33 0.3834 ± 19 0.085 ± 81400 0.105 1.165 ± 4 0.6600 ± 27 0.3896 ± 19 0.086 ± 91500 0.0942 1.118 ± 3 0.6603 ± 30 0.3470 ± 17 0.075 ± 81600 0.214 1.121 ± 3 0.6512 ± 26 0.3503 ± 18 0.076 ± 81700 0.169 1.102 ± 3 0.6460 ± 27 0.3326 ± 17 0.071 ± 71800 0.114 1.120 ± 3 0.6515 ± 26 0.3494 ± 17 0.075 ± 81880 0.0551 1.103 ± 3 0.6470 ± 26 0.3341 ± 17 0.071 ± 7

Sum of fractions 0.954 1.135 ± 4 0.6468 ± 26 0.3624 ± 18 0.079 ± 8

Note: In the reported isotopic composition, 136Xe ≡ 1.000, 130Xe ≡ 0.

and 1800–1830°ë), which correspond to four distinctenergy states of Xe atoms in the real crystal structure ofzircon.

In order to understand these data, one has to select aphysical mechanism to interpret data on Xe migrationthrough a real crystal structure.

The migration processes of atoms of Xe and otherradiogenic noble gases through minerals is usuallydescribed using two main techniques. Beginning withthe very first publications by Gerling (1939, 1961), themajority of Russian and some foreign researchersapplied the formalism of a monomolecular first-orderreaction, which is underlain by the concept that adomain of the crystal structure of natural minerals (real

crystals) where an atom of a radiogenic isotope isformed is so defective that it is sufficient for a migratingatom to accomplish a single “jump” to pass into amobile state. Because of this, the behavior of a migrat-ing radiogenic atom is formally analogous to the behav-ior of atoms during simple chemical interactions.Indeed, a single fission act of U nucleus that gives riseto a single atom of radiogenic Xe in the structure of acrystal is associated with the release and dissipation ofapproximately 200000000 eV in this structure,whereas atoms in a crystal structure are bound to oneanother with energy of 2–4 eV.

This mathematical apparatus of the theory of mono-molecular chemical reactions of the first order isapplied in many modern isotopic–geochemical models



for the evolution of the system Earth’s mantle–crust–atmosphere, which also includes other (not necessarilygaseous) elements (see, for example, Azbel’ and Tol-stikhin, 1988).

We proceeded from the fact that the migrationvelocity of radiogenic Xe atoms can be representedwithin the framework of this approach as

(9)

where k is the frequency factor, which is calculated as

(10)

dXedt

---------- –kXe t( )=

k k0e–

ERT-------

,=

1

1200 1400 1600 1800 200010000

3

5

7

9

1112

2

4

6

8

10

Zircon from Sri Lanka

136 X

e s, 1

0–11 c

m3/g

1

1200 1400 1600 1800 200010000

3

5

7

9

1112

2

4

6

8

10

Zircon from Nigeria

136 X

e s, 1

0–11 c

m3/g

1

1200 1400 1600 1800 200010000

3

5

7

9

2

4

6

8

136 X

e n, 1

0–11 c

m3/g

1

1200 1400 1600 1800 200010000

3

5

7

9

2

4

6

8

10

136 X

e n, 1

0–11 c

m3/g

1200 1400 1600 1800 200010000

5

15

20

10

Zircon from Antarctica (sample 11v32-b)

136 X

e s, 1

0–11 c

m3/g

1200 1400 1600 1800 200010000

0.5

1.0

2.0

1.5

Zircon from Antarctica (sample 11g-1/32)

136 X

e s, 1

0–11 c

m3/g

1

1200 1400 1600 1800 200010000

3

5

2

4

6

136 X

e n, 1

0–11 c

m3/g

1200 1400 1600 1800 200010000

20

30

40

50

10

136 X

e n, 1

0–11 c

m3/g

T,°CT,°C

Fig. 2. Escape curves of spontaneous and neutron-induced fission Xe from zircons from Sri Lanka, Nigeria, and Antarctica.

8


SHUKOLYUKOV et al.

where k0 is the value of the frequency factor at T 0,E is the activation energy of migration, R is the gas con-stant, and í is temperature in K. The integral form ofthe Xe migration law in minerals that follows from thisdifferential form is

(11)

In order to determine the migration characteristics(the activation energy Ö and the frequency factor k),expression (11) can be modified as

(12)

(13)

Inasmuch as this is an equation for a straight line ina lnln(Xe0/Xet) – 1/T vs. 1/T diagram, the parameters ofthis line can be used to calculate the values of the acti-vation energy E and frequency factor k0.

An advantage of this approach is the proved exist-ence of zones of real crystals characterized by differentdisturbance of the crystal structure, the possibility ofmigration of various radiogenic atoms through thestructure, the probable existence of various primarydefects and traps for such migrating atoms in minerals,the possibility for U to be contained in minerals in var-ious modes and, consequently, a heterogeneous distri-bution of radiogenic Xe in the crystal structure or, inother words, the possibility of various energy states ofradiogenic Xe atoms in real mineral structures. Theseissues can more or less account for the observable com-plicated curves for the kinetics of radiogenic Xe migra-tion in minerals. Another advantage of this formalism isthe relative simplicity of the mathematical proceduresused to determine the migration parameters Ö and kfrom experimental data. Disadvantages of thisapproach involve, first of all, the absence of rigorousproofs for the migration mechanism and the not alwayssufficient resolution of the method, which makes it dif-ficult to distinguish between migration processes withdifferent kinetic parameters.

An alternative approach is based on Fick’s diffusionlaws that describe variations in the concentrations ofatoms of radiogenic gases in minerals at temperaturechanges (Fechtig and Kalbitzer, 1966). The methodrelies on rigorously specified assumptions: diffusionproceeds from mineral grains of equal size of sphericalor another a priori specified shape, starting with ini-tially homogeneous concentrations of both the radioac-tive (parental) isotope and the radiogenic noble-gas iso-tope. The change in the remaining concentration of gasatoms with time is described by a complicated function,which depends on the diffusion coefficient D, tempera-ture T, and the size of the mineral grains, for example,the radius of the sphere R (Fechtig and Kalbitzer, 1966;Carslaw and Jaeger, 1959). The fraction of lost gas can

Xet Xe0e–kt.=

Xe0

Xet

--------- ek0e

–E

RT-------

t= ,

Xe0

Xet

---------lnln k0ln tlnE

RT-------.–+=

be accurately calculated by the expression correspond-ing to the assumed migration model according to clas-sic diffusion laws

(14)

where

(15)

Knowing the diffusion coefficient as a temperaturefunction and the exact effective sizes of the diffusioncells (which are far from always the same as the sizesof the real crystals), one can calculate the important dif-fusion parameters: the activation energy of diffusionand the frequency factor

(16)

Unfortunately, exact as it is, expression (14) is aconvergent infinite series that can be applied in calcula-tions only at very significant gas losses (F > 90%). Atlow (F ≤ 10%) and intermediate (10 ≤ F ≤ 90%) gaslosses from minerals, various (often fairly inaccurate)formulas should be applied to evaluate the diffusioncoefficient and calculate the migration parameters: theactivation energy and frequency factor k0. We considerthis to be one of the disadvantages of the approach.

However, the main problem in interpreting experi-mental data on the migration of noble gases in the struc-ture of real minerals is the fundamental differencebetween the actual conditions of migration and the con-cept of the originally homogeneous distribution ofgases with equal energy states of all atoms of themigrating gas in the crystal structure.

It is well known that U is extremely heteroge-neously distributed in the crystal structure of most sam-ples of zircon and other accessory minerals (Tugarinovand Bibikova, 1980; Krasnobaev, 1986; Shukolyukov,1970). Starting with Gerling’s pioneering publicationsdevoted to the escape kinetics of radiogenic He and Arfrom U-bearing minerals (Gerling, 1939, 1961), it isalso known that the escape rate of gases during theannealing of any mineral has a number of maximumand minimum values. The kinetic curves of gas escapewith a number of clearly pronounced and pervasivelypresent maxima of the migration velocities of Xe, Kr,Ar, Ne, and He during the heating of U minerals andzircons were obtained later by other researchers. This isa common feature of radiogenic noble gases.

For example, the escape curves of radiogenic Xefrom a few dozen pitchblende samples from quartz–cal-cite–pitchblende veins at the Schlema-Alberodadeposit in the Erzgebirge, Germany (Shukolyukov

F 16

π2----- 1

n2-----e–n

2Bt,

n 1=

∞

∑–=

B π2 D

R2-----.=

D D0e–

ERT-------

.=



et al., 1992) display three pervasively occurring max-ima (of different amplitude) in the migration velocities.

The kinetic curves (Fig. 3) of radiogenic Xe escapefrom uraninite from the Witwatersrand Au deposits(Reimond et al., 1995) also show three major maximaof the escape rare at temperatures of 500–700, 1000–

1100, and 1600°ë (Figs. 4a–4d). Our earlier data onpartly metamict zircons indicate that their escapecurves for radiogenic Xe also display clearly pro-nounced maxima (Figs. 4e–4i). In general, any U-bear-ing mineral exhibits clearly pronounced maxima at theescape curves not only of fission Xe and Kr but also ofother noble gases: radiogenic 4He and 40Ar and nucleo-

1500500 1000

1500500 1000

1500500 1000

1500500 1000

1500500 1000

1500500 1000

1500500 1000

1500500 1000

1500500 1000Temperature, °C

Relative rateof radiogenic Xe escape

XeR 3638

578M-1

21/58

R 3661

164 M

633/58

R 3691a

R 3680

1500500 1000

1500500 1000

1500500 1000

1500500 1000

1500500 1000

1500500 1000

1500500 1000

476/58

730/58

217/9

186/66

780 /55

201/66

C 66

Sh/810

Temperature, °C

Fig. 3. Escape curves of spontaneous-fission Xe from pitchblende from the Schlema-Alberoda deposit in the Erzgebirge, Germany(Shukolyukov et al., 1992). The age determined for the plateau for samples from veins of different spatial orientation ranges from120 to 300 Ma. Maxima in the Xe migration velocities at various temperatures correspond to three or four energy states of Xe atomsin the pitchblende structure.

10


SHUKOLYUKOV et al.

genic 38Ar (Shukolyukov, 1970) (Fig. 5). The tempera-tures of the peaks are roughly the same for various sam-ples, whereas the amplitudes of the peaks strongly dif-fer. The examples of the minerals khlopiniute andsamarskite from the Vishnevye Mountains, Urals,betafite from Ol’khon Island in Lake Baikal, andampangabeite from Ukraine (Shukolyukov and Ashki-nadze, 1987) confirm that the nonmonotonous depen-dence of the escape rate on temperature (Fig. 6) is typ-ical of the migration of noble gases in likely all miner-als. Because of this and considering that the realstructures of natural minerals differ from the idealizedconcept of classic diffusion, the stability of the U–Xe

isotopic system in zircons was evaluated according tothe model for the kinetics of first-order monomolecularreactions. All calculations of the migration parameterswere accomplished by the techniques described above.

According to the above formalism, we constructedlnln(Xe0/Xet) – 1/T (where ïÂ0 and ïÂt are the initialXe concentration and the Xe concentration remainingafter annealing at a specified temperature during a timeperiod t) for each peak on the escape curves of Xe ofspontaneous and neutron-induced fission at each tem-perature step (Fig. 2) (at each of the steps the samplewas annealed for 35 min).

T,°C

10

500 1000 1500 20000

20

30(d)

5

1000 1500 20005000

10

25 (i)

5

500 1000 1500 20000

10

20

(b)

5

500 1000 1500 20000

2025 (a)

1510

15

Relative Xe yield, %30

2015

5

1000 1500 20005000

10

30 (h)

2015

5

1000 1500 20005000

10

35 (g)

2515

5

1000 1500 20005000

10

25 (f)2015

5

1000 1500 20005000

10

30(e)

2015

25

3020

25

Relative Xe yield, %

T, °C

5

500 1000 1500 20000

10

20 (c)

15

Fig. 4. Kinetic curves of radiogenic Xe escape from U and U-bearing minerals. (a–d) Uraninite samples from mineral deposits inWitwatersrand, Central Kaapvaal Craton (Reimold et al., 1995): (a) Blyuvooruitzicht, 0.832 ± 0.016 Ga; (b) Sub Nigel, 1.115 ±0.036 Ga; (c) Free State Geduld, 1.044 ± 0.024 Ga; (d) Ventersdorp Contact Reef from the Kloof gold mine, 1.300 ± 0.058 Ga.Isotopic Xes-Xen ages are calculated for plateaus. All curves show extrema that correspond to two, three, or four energy states ofradiogenic Xe atoms in the uraninite structure. (e–i) Samples of partly metamict Archean zircons from the Napier Complex, easternAntarctica (Shukolyukov et al., 1994; Krylov and Shukolyukov, 2003): (e) sample 202g from garnet quartzite, 2.59 ± 0.22 Ga,(f) sample 22b from mesoperthitic granulite, 3.83 ± 0.24 Ga, (g) gneiss from the Fyfe Hills, 3.51 ± 0.10 Ga; (h) zircon from garnetfrom Mount Napier, 3.24 ± 0.15 Ga; (i) zircon from gneiss from Mount King, the weighted mean age of the fractions released at1480–1800°C is 3.61 ± 0.26 Ga. The Xes-Xen isotopic ages are calculated for plateaus. All Xe escape curves show extrema corre-sponding to two, three, or more energy states of radiogenic Xe states in the structure of ancient zircons.



As an illustrative example of these calculations,Fig. 7 shows such dependences for the zircon from SriLanka. Using these and analogous data on other sam-ples, we calculated the tangents of the curves and thenthe corresponding activation energy values Ö. Thelength of the segments intercepted by the straight lineon the ordinate were utilized to calculate the frequencyfactor k0 (Table 3). As can be seen from the table, theactivation energy of Xe escape and the frequency factorof the zircons vary for distinct energy states of Xe in thesame sample (El is the low-energy, Ei1 is the first inter-mediate-energy, Ei2 is the second intermediate-energy,and Eh is the high-energy states, respectively). Forexample, the activation energy of the escape of Xesatoms from the low- (El) and high-temperature (Eh)states of zircon from Nigeria differ by a factor of morethan 6 (18 and 116 kcal/mol, respectively). Evengreater differences occur between the values of the fre-quency factor in the Xe escape equation for theseenergy states: k0 = 2.8 × 10–1 and 1.6 × 1012 year–1.

The kinetic parameters Ö and k0 of radiogenic Xeescape from distinct energy settings of Xe atoms in thesame sample and from the same setting in the structuresof various zircons also vary (Table 3, Fig. 8). Even non-metamict and almost perfect zircon grains are charac-terized by certain features that predetermine strikinglydifferent values of the activation energy and frequencyfactor and, correspondingly, different behavior ofradiogenic Xe in these grains. We still have not under-stood both the nature of these feature and their positionin the mineral structure. An empirical dependence wasestablished between the parameters of Xe migration Öand k0 (Fig. 9), which is valid (as a rough approxima-tion) for Xe in all energy states of the zircons, i.e., at alltemperatures

or

(17)

A dependence between the activation energy ofradiogenic Xe migration and the frequency factor wasfirst identified when Xe migration was examined in zir-cons based on the classic diffusion concept and was dis-cussed in (Krylov and Shukolyukov, 1994).

Knowing the migration parameters of Xe, we wereable to evaluate the thermal stability of the U–Xe sys-tem in our zircon samples. An important parametercharacterizing this stability is the closure temperatureof isotopic–geochemical systems of minerals, which iscalculated from empirical data. We do not share the cur-rently widely accepted opinion that atoms can com-pletely stop to migrate from minerals at a certain tem-perature (so-called closure temperature). In fact, this isat variance with the mathematical expression for themigration concept adopted here

k0ln 13.7 Eln 41.2–=

k0 12.8 10–18× e13.7 Eln= .

(18)

Indeed, a mineral may be an absolutely closed sys-tem with respect to Xe migration if the Xe loss rate –dXe/dt = 0, which is possible only at ïÂ(t) = 0, i.e.,when the mineral contains no more Xe atoms or at

The latter is possible only if k0 = 0 (i.e., with regardfor the meaning of the frequency term, at absolute zero

–dXedt

---------- k0e–

ERT-------

Xe t( )= .

k0e–

ERT-------

0.=

0.2

500 1000 15000

0.81.0

4He0.60.4

0.2

500 1000 15000

0.81.0

38Ar0.60.4

0.2

500 1000 15000

0.81.0 86Kr

0.60.4

0.2

500 1000 15000

0.81.0

0.60.4

5

500 1000 15000

2025

136Xe1510

0.2

500 1000 15000

0.6

0.4

136Xe

86Kr

0.2

500 1000 15000

0.6

0.4

0.2

500 1000 15000

0.6

0.4

4He

38Ar

Temperature, °C

Fraction of escaped gas,rel. units.

BL MF

Fig. 5. Escape curves of various noble gases (spontaneousfission Xe and Kr, nucleogenic 38Ar generated by α,n andαp reactions, and radiogenic 4He) from uraninite (Shukoly-ukov and Ashkinadze, 1967). BL and MF are uraninite sam-ples from granitic pegmatites in northern Karelia, BalticShield, age 1.95 Ga. The curves show clearly pronouncedescape maxima that testify that atoms of each noble gas arecontained in more than a single energy state in the uraninitecrystal structure.

12


SHUKOLYUKOV et al.

temperature, when the oscillation frequency of the

atoms is zero), or if = 0, and this conditions is ful-filled also only at absolute zero temperature. Becauseof this, we use here the concept of relative closure tem-perature of the mineral system Tr as a criterion of thestability of the U–Xe isotopic systems. This tempera-ture is understood as a temperature at which 98% Xes isretained in the mineral for a specified time (for exam-ple, a time equal to the age of the mineral). Tr is calcu-lated by (13), based on our experimental data (Table 3).

It should be stressed that we take into account notthe accumulation of radiogenic Xe but merely thechange in the proportion of the original and final Xeconcentrations in the course of heating. Figure 10 andTable 4 demonstrate that much Xe produced by thespontaneous fission of U (Xes) in our samples is gener-ally tightly held by the crystal structures. For example,the relative closure temperature of the zircon from Ant-arctica (sample 11v32-b) is 510°ë and ensures >98%retention of radiogenic Xes at an intermediate energystate (Ei2, 44% of the total concentration) for 1 Ga, i.e.,

e–

ERT-------

the whole lifetime of the sample. The heating ofanother sample from the same area in Antarctica (sam-ple 11g-1/32) to 700°ë during 1 Ga may result in theretention of >65% radiogenic Xes at Ei2.

Amazing stability is displayed by the U–Xe isotopicsystem of zircon from Sri Lanka (Fig. 10). The crystalstructure of this sample is such that its heating to1200°ë during 650 Ma ensured the preservation of98% Xes at a high-temperature state (28% radiogenicXe). At a temperature of ≤ 1100°ë, this zircon couldretain all of its radiogenic Xe for a much longer time.At 1300°ë, the zircon could held close to 70% of its Xefor 600 Ma.

A visual representation of radiogenic fission Xemigration in the zircon structure is offered in Fig. 11,which shows the dependence of Xes preservationdepending on temperature and heating duration at agiven activation energy of gas migration in zircons.

Our data demonstrate that zircons with prefectstructures ensure the preservation of all (or much of)their radiogenic Xe in the structure, in spite of the pos-sibility of the partial loss of spontaneous fission Xe

9

2

500 1000 15000

468

1210

4He

2

500 100015000

468

14

10

4He

1

500 1000 15000

35

86Kr

500 1000 15000

5

10

20

154He

5

500 100015000

101520

3025

4He

5

500 100015000

101520

3025 136Xe

7

12

1

500 1000 15000

3

586Kr

715105

500 1000 15000

2025

86Kr10

5

500 100015000

15

20

86Kr

1

5001000 15000

3

136Xe

5

500 100015000

101520

3025 136Xe

5

500 100015000

10

15 136Xe7

5

Temperature, °C

Khlopinite Samarskite Betafite Ampangabeite Released gas fraction, %

Fig. 6. Escape curves of radiogenic Xe, Kr, and He from U-bearing minerals of various chemical composition: khlopinite (Ti-tan-talo-niobate from Transbaikalia, 140 Ma), samarskite (tantaloniobate from the Southern Urals, 293 Ma), betafite (Ti-tantaloniobatefrom the Southern Urals, 293 Ma), and ampangabeite (Ti-tantalo-niobate from Ukraine, 1950 Ma, determined by the U–Pb isotopictechnique).The curves show no less than three clearly pronounced energy states in which atoms of various noble gases are contained in thestructures of these minerals.



from the mineral during its geological lifetime. Thisfeature of Xe migration kinetics in the zircon crystalstructure warrants the dating of minerals by the Xes-Xenmethod with the use of age spectra. One of the distinc-tive features of these spectra is young ages at relativelylow annealing temperatures because of the partial lossof radiogenic Xe in the course of its geological history,and another pervasive feature is the occurrence of an

age plateau at high temperatures, which corresponds tothe crystallization time of the mineral.

Zircon Dating by the Xes–Xen Method

Based on experimental data and Eqs. (6)–(8), weobtained 136Xes/136Xen ratios and the coefficient J for ali-quots of neutron-irradiated monitor mineral (Table 1).

lnln

(136 X

e 0/13

6 Xe)

–2.5

0.00048 0.00050–3.0

–2.0

–1.5

–1.0

–0.5

0

0.5

1.0E = 152 kcal/molk0 = 6.0 × 1011 year–1

–2.5

0.00055–3.0

–2.0

–1.5

–1.0

–0.5

0

1.0

1.5

1/T, K–1

E = 133 kcal/molk0 = 3.6 × 1011 year–1

–2.5

0.00060 0.00065–3.0

–2.0

–1.5

–1.0

–0.5

0

0.5

1.5E = 100 kcal/molk0 = 3.7 × 108 year–1

0.5

0.00050

1.0

0.00055

Fig. 7. An example of the graphical determination of the activation energy and frequency factor in an equation for the escape kineticsof the spontaneous-fission Xe for discrete temperature steps during the laboratory annealing of zircon from Sri Lanka.

Table 3. Parameters of Xe migration from the structure of our zircon sample

Sampling site

Tempera-tures of maxi-ma on the ki-netic curves

of Xes escape, T, °C

Energy position

of Xe atoms in zircon structure

Fraction of Xes

in a given state

Activation energy of Xes

migration, kcal/mol

Frequency factor k0,

year–1

Xen fraction in a given

state

Activation energy of Xen

migration, E, kcal/mol

Frequency factor k0,

year–1

Sri Lanka 1450 El ~32% 100 3.7 × 108 ~29% 64 1.9 × 104

1630 Ei2 ~40% 133 3.6 × 1011 ~31% 118 2.5 × 109

1790 Eh ~28% 152 6.0 × 1011 ~40% 147 1.9 × 1011

Nigeria 1250 El ~7% 18 2.8 × 10–1 ~6% 13 6.9 × 10–2

1700 Ei2 ~34% 76 9.0 × 107 ~30% 50 6.1 × 103

1850 Eh ~59% 116 1.6 × 1012 ~64% 82 2.0 × 107

MacMaxon Island, Ant-arctica (sam-ple 11v32-b)

1250 El ~7% 23 4.6 × 100 ~9% 24 9.2 × 100

1430 Ei1 ~14% 42 1.2 × 103 ~22% 41 6.1 × 103

1600 Ei2 ~65% 46 2.0 × 103 ~56% 45 2.8 × 103

1830 Eh ~14% 78 4.5 × 106 ~13% 65 9.1 × 104

MacMaxon Island, Ant-arctica (sam-ple 11v32-g)

1220 El ~16% 24 2.8 × 100 ~25% 29 4.1 × 100

1400 Ei1 ~17% 55 2.5 × 106 ~25% 60 1.8 × 107

1600 Ei2 ~44% 57 9.1 × 104 ~31% 50 1.4 × 104

1800 Eh ~23% 106 9.9 × 108 ~19% 117 2.7 × 1012

14


SHUKOLYUKOV et al.

Table 5 lists experimental data on radiogenic Xecomponents in the zircon from Sri Lanka and the136Xes/136Xen ratio (the ratio of the concentrations ofspontaneous and induced fission of 238U and 235U).Based on these data, we constructed the plots inFig. 12 (apparent age vs. temperature and apparentage vs. the cumulative fraction of released neutron-induced Xe).

A “classic” age spectrum of the “upward staircase”type was obtained for zircon in sample 11v32-b fromAntarctica. At temperatures lower than ~1400°ë, thestepwise escape of Xe takes place from low-tempera-ture states, and the apparent age is obviously underesti-mated due to the partial loss of radiogenic Xe. At 1400–1900°ë, the age values obtained for various Xe frac-tions (at various heating steps) remain constant (within

E, kcal/mol

20

1 2 3 410

40

60

80

100

120130140150160

30

50

70

90

110

EÇ

Ei2

Eç

k0, year–1

1E+000

1 2 3 41E–001

1E+002

1E+0041E+005

1E+007

1E+009

1E+011

1E+013

1E+001

1E+003

1E+006

1E+008 k0B

k0i2

k0H

1E+012

1E+010

Fig. 8. Ranges of the migration parameters of radiogenic fission Xe: activation energy E and frequency factor k0 for various energystates of Xe atoms in the same sample and the same state in various zircon samples. Plotted along the x axis: (1) zircon from SriLanka, (2) zircon from Nigeria, (3, 4) zircons from Antarctica (samples 11v32-b and 11g-1/32, respectively).

50 100 150E, kcal/mol

0 200

1E+0001E–001

1E+002

1E+005

1E+007

1E+009

1E+011

1E+014

1E+001

1E+0031E+004

1E+006

1E+008

1E+012

1E+010

1E+013

lnk0 = 13.7lnE – 41.2k 0, y

ear–1

Fig. 9. Empirical dependence between Xe migration parameters: activation energy E and frequency factor k0 for our samples.



the errors) and independent of their escape temperature.This is a convincing argument in support of the com-plete preservation of Xes in the corresponding crystal-chemical settings and the realistic character of theobtained age values. The Xe fraction in this stable statein zircon grains is 84%, and the age of this zircon sam-ple from Antarctica is 1075 ± 26 Ma.

Qualitatively similar relations were revealed inanother zircon from Antarctica (sample 11g-1/32).Underestimated ages are obtained at temperatures of≤1400°ë, but these values are quite close for all Xefractions: from 549 to 650 Ma. The other temperaturefractions (from 1400 to 1900°ë), which account for68% ïÂs, define an age plateau corresponding to an age

0.1

600 700 8000

0.3

0.5

0.70.80.91.0

900

0.2

0.4

0.6

500

Eç

0.1

10000

0.3

0.5

0.70.80.91.0

1200

0.2

0.4

0.6

800

Ei2

0.1

50 1500

0.3

0.5

0.70.80.91.0

250

0.2

0.4

0.6 Eç

0.1

500 600 7000

0.3

0.5

0.70.80.91.0

800

0.2

0.4

0.6

400

Ei2

0.1

12000

0.3

0.5

0.70.80.91.0

1400

0.2

0.4

0.6

1000

0.1

700 800 900 11000

0.3

0.5

0.70.80.91.0

1000

0.2

0.4

0.6EÇ

0.1

100 2003000

0.3

0.5

0.70.80.91.0

400

0.2

0.4

0.6 Eç

EÇ

0.1

200 600

0.3

0.5

0.70.80.91.0

0.2

0.4

0.6 Ei1

400

0.1

500300

0.3

0.5

0.70.80.91.0

0.2

0.4

0.6 Ei2

0.1

0 100 200

0.3

0.5

0.70.80.91.0

300

0.2

0.4

0.6Eç

0.1

400200

0.3

0.5

0.70.80.91.0

0.2

0.4

0.6 Ei1

0.1

700500

0.3

0.5

0.70.80.91.0

900

0.2

0.4

0.6 Ei2

0.1

900 10001100800

0.3

0.5

0.70.80.91.0

1200

0.2

0.4

0.6 EÇ

0.1

900800

0.3

0.5

0.70.80.91.0

1100

0.2

0.4

0.6 EÇ

700 1000

600

ln(Xe0/Xet)

ln(Xe0/Xet)

ln(Xe0/Xet)

ln(Xe0/Xet) Zircon from Antarctica, sample 11v-32b

Zircon from Antarctica, sample 11g-1/32

Zircon from Nigeria


Temperature, °C

Fig. 10. Calculated relative closure temperature (�) for the U–Xe isotopic system in zircons at which no less than 98% radiogenicXe is retained in zircon for a specified time period.The relative closure temperatures are different for Xe atoms in various energy states in the mineral structure (El—low-temperaturestate, Ei1 and Ei2—intermediate-temperature states, Eh—high-temperature state).

16


SHUKOLYUKOV et al.

of 1040 ± 85 Ma, although these age values show a sig-nificant scatter of the apparent age. Inasmuch as sam-ples 11v32-b and 11v32-g were taken from the samearea, the coincidence (within the experimental error) oftheir age values testifies that these are true age values.

The age spectrum of the zircon from Nigeria alsodisplays a plateau. This tendency is disturbed only bythe gas fraction released at 1380°ë (Fig. 12). Theextended plateau (78% of all Xes escaping from themineral) is defined by two high-temperature fractions,which correspond to temperatures of 1700 and 1850°ë.The corresponding age of this zircon is 1023 ± 13 Ma.

Although Xe fractions escape during the annealingof zircon from Sri Lanka within a broad temperaturerange (1100–1350°ë), they account for no more than8% ïÂs and 11% Xen. Radiogenic Xe almost com-pletely (92% Xes) escapes at 1450–1800°C. These tem-perature fractions correspond to a high-temperatureplateau (Fig. 12) with an age of 621 ± 22 Ma. This zir-con is the most interesting among all of our samplebecause of the high degree of Xe preservation and therecord-high temperature required to disturb the U–Xeisotopic system. Because of this, we conducted theSHRIMP-II study on this zircon sample from SriLanka.

Electron Microscopic and SHRIMP-II Dataon Zircon from Sri Lanka

We studied large zircon fragments (Fig. 1); theiroptical examination in transmitted and reflected light(Fig. 13) has not revealed any inclusions or defects inthis water-clear zircon. The cathodoluminescenceexamination of these fragments was carried out to getinsight into their inner structure and the possible type oftheir zoning. The CL images display only weakly con-trasting thin zoning of the magmatic type (Fig. 14).

Our SHRIMP-II data on eight analytical spots in theselected zircon grain are presented in Fig. 6. This distri-bution of the U and Th concentrations is very homoge-neous, with variations in the U and Th concentrations atvarious sites in the grain being no greater than 2–3% ofthe U concentrations, 5% of the Th concentration, 2.8%of the 238U/232Th ratio, and 2.5% of the radiogenic 206Pbconcentration. The U–Pb isotopic system of this zirconremained closed, as follows from the coincidence of theisotopic ages calculated by independent decayschemes. Hence, the age values calculated by the206Pb/238U and 207Pb/235U ratios with the use of the ISO-POLOT computer program and the software incorpo-rated in data processing programs of SHRIMP-IIyielded an age of 593.5 ± 1.9 Ma, and the calculatedrelative error of the age is 0.3% (Fig. 15). As can beseen from Table 6, the average measurement error ofthe isotopic ratios themselves was three to ten times

Table 4. Relative closure temperature of zircons at heating throughout the whole lifetime of the sample

Sampling site

Temperatures at which the migration of Xes atoms

from various levels in the zircon structure is activated, kcal/mol

Radiogenic Xes fraction in a given energy state

Relative closure temperature of zircon, °C

Antarctica (sample 11v-32g); MacMaxon Island, sample 11g-1/32

El = 24 ~16% 180

Ei1 = 55 ~17% 420

Ei2 = 57 ~44% 510

Eh = 106 ~23% 890

MacMaxon Island, Antarctica, sample 11v32-b

El = 23 ~7% 165

Ei1 = 42 ~14% 430

Ei2 = 46 ~65% 700

Eh = 78 ~14% 920

Nigeria El = 18 ~7% 110

Ei2 = 76 ~34% 620

Eh = 112 ~59% 850

Sri Lanka El = 100 ~32% 650

Ei2 = 133 ~40% 1020

Eh = 152 ~28% 1180



0.1

1000

0.6

0.91.0

0.4

0.8

0.3

0.7

0.2

0.5

0.1

500 10000

0.6

0.91.0

0.4

0.8

0.3

0.7

0.2

0.5

300 500

ln(Xet/Xe0)700°C

800°C

900°C

1000°C

Eç = 100 kcal/mol

0.1

1000

0.6

0.91.0

0.4

0.8

0.3

0.7

0.2

0.5

300 500

900°C1100°C

1200°C

Ei2 = 133 kcal/mol

0.1

1000

0.6

0.91.0

0.4

0.8

0.3

0.7

0.2

0.5

300 500

1100°C

1200°C

1300°C

1400°C

EÇ = 147 kcal/mol

ln(Xet/Xe0)100°C

200°C

250°C

Eç = 18 kcal/mol

0.1

500 10000

0.6

0.91.0

0.4

0.8

0.3

0.7

0.2

0.5

600°C

700°C

750°C

Ei2 = 76 kcal/mol

0.1

500 10000

0.6

0.91.0

0.4

0.8

0.3

0.7

0.2

0.5

900°C

1000°C

1050°C

EÇ = 116 kcal/mol

0.1

500 10000

0.6

0.91.0

0.4

0.8

0.3

0.7

0.2

0.5

900°C

1000°C

1100°C

EÇ = 106 kcal/mol

0.1

500 10000

0.6

0.91.0

0.4

0.8

0.3

0.7

0.2

0.5

500°C

600°C

700°C

Ei2 = 57 kcal/mol

0.1

500 10000

0.6

0.91.0

0.4

0.8

0.3

0.7

0.2

0.5

200°C

300°C

350°C

Eç = 23 kcal/mol

0.1

500 10000

0.6

0.91.0

0.4

0.8

0.3

0.7

0.2

0.5

150°C

250°C

Eç = 23 kcal/mol

0.1

500 10000

0.6

0.91.0

0.4

0.8

0.3

0.7

0.2

0.5

450°C

500°C

600°C

Ei2 = 46 kcal/mol

0.1

500 10000

0.6

0.91.0

0.4

0.8

0.3

0.7

0.2

0.5

700°C

800°C

900°C

EÇ = 78 kcal/mol

ln(Xet/Xe0)

ln(Xet/Xe0)

200°C

Zircon from Antarctica, sample 11v-32b

Zircon from Antarctica, sample 11g-1/32

Zircon from Nigeria


Time, Ma

Fig. 11. Dependence of the preservation of spontaneous-fission Xe (Xet/Xe0) on temperature and the duration of heating during theexperimental determination of Xe migration parameters in our zircon samples from Antarctica, Nigeria, and Sri Lanka.

higher: 0.8–1.1% for the 206Pb/238U ratio and 2.6–4.0%for the 207Pb/235U ratio.

With regard for these data, we compared the agedetermined by the Xes-Xen method with that calculateddirectly from independent isotopic ratios (206Pb/238U,207Pb/235U, and 208Pb/232Th) without mathematical pro-cessing of the data by the software of SHRIMP-II

(Fig. 16). Within the probable analytical error, theXes-Xen age (621 ± 22 Ma) coincides with the averageage value of 613 ± 38 Ma obtained by the U–Th–Pb iso-topic method (the difference between the values is closeto 1%, although with regard for the probable errors, thiscoincidence should rather be incidental) and is close tothe age of 593.5 ± 1.9 Ma determined by J. Wetherill’smethod (statistical difference from 1 to 4.5%).

18


SHUKOLYUKOV et al.

Table 5. Concentrations of Xe produced by the spontaneous (Xes) and neutron-induced (Xen) fission of 238U and 235U in zir-cons irradiated by a thermal-velocity neutron flux and their Xes-Xen age (136Xe ≡ 1.000, 130Xe ≡ 0)

Sample Xe escape temperature, °C

136Xes, 10–10 cm3/g

136Xen, 10–10 cm3/g

136Xes/136Xen

Age, Ma

ApparentWeighted average,

on plateau

Zircon, MacMaxon Island, Antarctica, sample 11v-32b

1100 0.036 0.176 0.204 ± 0.004 510

1200 0.185 0.876 0.211 ± 0.004 540

1300 0.247 1.025 0.242 ± 0.005 607

1400 0.473 1.65 0.287 ± 0.005 719

1500 1.051 2.34 0.449 ± 0.009 1090

1075 ± 26(84% Xes)

1600 2.101 4.69 0.448 ± 0.009 1090

1700 0.999 2.39 0.418 ± 0.008 1020

1800 0.513 1.18 0.435 ± 0.008 1060

1880 0.401 0.871 0.460 ± 0.009 1120

Sum of fractions 6.010 15.22 0.395 ± 0.008 968

MacMaxon Island, Antarcti-ca, sample 11v-32g

1100 0.0383 0.143 0.268 ± 0.005 660

1200 0.0817 0.371 0.220 ± 0.005 562

1300 0.0826 0.343 0.241 ± 0.004 607

1400 0.105 0.486 0.216 ± 0.004 549

1500 0.0942 0.229 0.411 ± 0.008 1006

1040 ± 85(68% Xes)

1600 0.214 0.543 0.394 ± 0.008 969

1700 0.169 0.343 0.493 ± 0.007 1185

1800 0.114 0.286 0.399 ± 0.008 978

1880 0.0551 0.114 0.483 ± 0.009 1171

Sum of fractions 0.954 2.858 0.334 ± 0.007 827

Zircon from Nigeria 1100 0.0140 0.0361 0.388 ± 0.011 345

1250 0.0280 0.0276 1.015 ± 0.030 865

1380 0.0401 0.0331 1.212 ± 0.036 1021

1500 0.0902 0.0882 1.023 ± 0.025 875

1600 0.279 0.256 1.090 ± 0.021 925

1700 0.401 0.335 1.197 ± 0.023 1009 1023 ± 13(78% Xes)1850 1.19 0.967 1.231 ± 0.022 1036

Sum of fractions 2.042 1.743 1.102 ± 0.023 990

Zircon from Sri Lanka 1100 0.0078 0.0091 0.854 ± 0.017 385

1200 0.0150 0.020 0.768 ± 0.016 347

1350 0.304 0.401 0.760 ± 0.038 345

1450 0.580 0.430 1.349 ± 0.030 598

621 ± 22(92% Xes)

1600 0.866 0.594 1.457 ± 0.032 644

1700 0.941 0.649 1.451 ± 0.029 641

1800 1.139 0.841 1.355 ± 0.026 600

Sum of fractions 3.852 2.944 1.309 ± 0.024 621



Age

, Ma

100

1200 1400 1600 1800T, °C

10000

200

300

400

500

600

700


Age

, Ma

100

1200 1400 1600 180010000

300

500

700

900

11001200

Zircon from Antarctica,

Age

, Ma

100

1200 1400 160010000

200

400

600

800

10001100

Zircon from Nigeria

Age

, Ma

100

1200 1400 1600 180010000

300

500

700

900

11001200


1800

300

500

700

900

sample 11g-1/32200

400

600

800

1000

sample 11v-32b

200

400

600

800

1000

Age

, Ma

100

0.5 0.7 0.90.10

300

500

700

900

11001200

Zircon from Antarctica, sample 11v-32b

200

400

600

800

1000

Age

, Ma

100

0.1 0.2 0.3 0.5 0.6 0.7 0.9 1.00

300

500

700

900

11001200


0.8

sample 11g-1/32200

400

600

800

1000

Age

, Ma

100

0.1 0.2 0.3 0.4 0.6 0.7 0.8 1.00

200

400

600

800

10001100

Zircon from Nigeria

0.9

300

500

700

900

Age

, Ma

100

0.1 0.2 0.3 0.4 0.5 0.6 0.9 1.0Cumulate Xe yield Xen

0

200

300

400

500

600

700


0.7 0.8

0.5

0.4

0.3

Fig. 12. Evaluated plateau-age values depending on temperature (T, °C) and the cumulate relative yield of neutron-induced fissionXe from zircon samples from Antarctica, Nigeria, and Sri Lanka.

20


SHUKOLYUKOV et al.

Hence, the coincidence of age values for two princi-pally different isotopic systems indicates that radio-genic Xe is very tightly held by the crystal structure ofzircon from Sri Lanka. In order to evaluate the possibledistortion of the structure of this zircon, we calculatedthe ideal dose of α-radiation that could have affected itsstructure. With regard for the age (613 ± 38 Ma), con-centrations of U (673 ± 16 ppm) and Th (109 ± 5 ppm),and data from (Reiners, 2005), the radiation dose was~1.5 × 1018 α-particles/g of mineral, is lower than ~2 ×1018 α-particles/g of mineral required to induce defectsresponsible for a drastic increase in the losses of radio-genic He (Holland, 1954; Hurley et al., 1956; Reiners,2005). This validates the plausibility of the evaluationsand conclusions based on the determined Xe migrationcharacteristics in our zircon samples. The zircon fromSri Lanka has characteristics that enable its utilizationas a standard sample during dating by the Xes-Xenmethod.

CONCLUSIONS

The analysis of the migration kinetic curves of U-fission Xe from zircon and the comparison of our datacompiled from the literature led us to conclude thatatoms of each noble gas can be contained in the struc-tures of real minerals in a diversity of energy states and,hence, escape, with different migration parameters(activation energy and frequency factor) in the courseof zircon annealing. These atoms are likely contained in

the structures of minerals in defects and structuralzones of different types (nanometer-sized crystalline,amorphous, and metamict) (Utsunomiya et al., 2007).The proportions of the concentrations of each noble gasin such defects and structural zones depends on the geo-logical history of the sample. This casts doubts onto thepossibility of applying the classic diffusion formalismin describing the migration of noble gases in minerals.Within the framework of this formalism, it is difficult toexplain experimental data indicating a nonmonotonousdependence of the migration velocity of noble gasesfrom zircon grains of the same size on temperature. Theoccurrence of maxima of escape rates from these grainsat characteristic temperatures is not consistent withclassic migration laws.

Our data indicate that atoms of radiogenic Xe arevery strongly bound in the flawless structure of non-metamict zircons from Sri Lanka, Nigeria, and Antarc-tica. Much or even all Xe contained in this state can beretained in the mineral for hundreds of million years atheating to temperatures of >1000°ë. The migrationcharacteristics of radiogenic Xe in zircons are such thatits atoms are completely retained in the “high-tempera-ture state” in spite of significant Xe losses from its“low-temperature states”. This validates the principleof obtaining an age plateau that underlies the Xes-Xenmethod of isotopic dating.

The experimentally determined migration parame-ters of radiogenic Xe of the spontaneous and neutron-

(b)

(‡)

Fig. 13. (a) Transmitted and (b) reflected light photographsof one of the large fragments of zircon from Sri Lanka (seeFig. 1).

Fig. 14. Cathodoluminescence images showing the innerstructure of possible zoning in the zircon (taken on a Cam-Scan 2500 MX electron microscope). The fragment hasonly weakly contrasting zoning of the magmatic type.



206Pb/238U

0.72 0.76 0.80 0.84 0.88

207Pb/235U

0.680.092

0.094

0.096

0.098

0.100

0.102

0.92

580

600

620

Concordia age = 593.5 ± 1.9 Ma(1σ, included

in the errors of the decay

MSWD (concordance) = 0.00020

Probability (concordance) = 0.99

Òconstants)

Fig. 15. Wetherill’s diagram based on experimental data on the zircon from Sri Lanka.The age value was calculated from the 206Pb/238U and 207Pb/235U isotopic ratios, using the ISOPLOT computer program and thesoftware incorporated into the data processing programs of SHRIMP-II.

Table 6. SHRIMP-II data on zircon from Sri Lanka

Analytical spot in the thin section

238U, ppm

232Th, ppm

232Th/238

U206Pb*/

238U207Pb*/

235U207Pb*/206Pb*

208Pb*/232Th

Age, Ma

t(206Pb/238U)

t(207Pb/206Pb)

t(208Pb/232Th)

SL-SH-1.1 674 108 0.17 0.09549 ±0.0086

0.794 ±0.023

0.063 ±0.0017

0.0300 ±0.0011

587.9 ±5.0

615 ± 60 598 ± 22

SL-SH-1.2 651 103 0.16 0.09615 ±0.00091

0.799 ±0.033

0.0603 ±0.0024

0.0346 ±0.0029

591.8 ±5.4

614 ± 86 687 ± 57

SL-SH-2.1 678 110 0.17 0.09552 ±0.00086

0.782 ±0.023

0.0594 ±0.0017

0.0326 ±0.0011

588.1 ±5.1

581 ± 62 648 ± 23

SL-SH-2.2 686 112 0.17 0.09664 ±0.00088

0.798 ±0.026

0.0599 ±0.0019

0.0297 ±0.0016

594.7 ±5.2

599 ± 69 591 ± 32

SL-SH-3.1 696 118 0.17 0.09531 ±0.00084

0.780 ±0.020

0.0593 ±0.0014

0.0305 ±0.0011

586.8 ±4.9

580 ± 51 607 ± 21

SL-SH-4.1 682 111 0.17 0.09860 ±0.00099

0.807 ±0.021

0.0594 ±0.0014

0.0325 ±0.0034

606.3 ±6.0

580 ± 53 647 ± 25

SL-SH-5.1 658 106 0.17 0.09759 ±0.00090

0.797 ±0.034

0.0593 ±0.0025

0.0367 ±0.0013

600.3 ±5.3

576 ± 92 729 ± 69

SL-SH-5.2 658 104 0.16 0.0971 ±0.0011

0.813 ±0.030

0.0607 ±0.0021

0.0335 ±0.0027

597.6 ±6.1

630 ± 76 665 ± 54

22


SHUKOLYUKOV et al.

induced fission of U and the results obtained by com-paring two independent isotopic systems, Xe–U andPb–U, in a sample of gem-quality zircon from SriLanka, which is highly homogeneous (both composi-tionally and crystallographically), has a perfect crystalstructure, and is characterized by a relatively simplegeological history of its U–Xe and U–Pb isotopic sys-tems led us to conclude that this sample can be utilizedas a laboratory reference sample for the Xes-Xenmethod of isotopic geochronology.

ACKNOWLEDGMENTS

The authors thank Prof. H. Lippolt (University ofHeidelberg, Germany) for fruitful scientific coopera-tion and for numerous samples provided for thisresearch. Many interesting zircon samples were madeavailable for us by courtesy of Prof. W. Todt (Max-

Palnk-Institut für Chemie, Mainz, Germany). Prof.E.V. Bibikova (Vernadsky Institute of Geochemistryand Analytical Chemistry, Russian Academy of Sci-ences) is thanked for the very scrupulous reviewing themanuscript and valuable comments, all of which weretaken into account. We appreciate A.P. Meshik’s partic-ipation in certain phases of this research and thank himfor working out the methodology and techniques of theexperimental studies. This study was financially sup-ported by the Russian Foundation for Basic Research,project no. 07-05-00634-a.

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1

580 590 600 610 620 630 640 660 6705700

2

3

650

1

580 590 600 610 620 630 640 660 6705700

2

4

650

0.4

580 590 600 610 620 630 640 660 6705700

0.8

2

650

580 590 600 610 620 630 640 660 670570 650

3

1.6

1.2

t(206Pb/238U), Ma

t(207Pb/235U), Ma

t(208Pb/232U), Ma

average of U–Th/Pb data, Ma

SHRIMP-II, concordia, Ma

t(Xes/Xen), Ma

Ma

Fig. 16. Comparison of age values for the zircon from Sri Lanka yielded by various isotopic systems:206Pb-238U, 207Pb-235U,208Pb-232Th, and 136Xes-

136Xen



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geothermochronology based on noble gases: i. stability of the u-xe isotopic system in nonmetamict...

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