Correction of common lead in U–Pb analys
that do not report 204Pb
Tom Andern
Department of Geology,Laboratory for Isotope Geology,University of Oslo,PO Box 1047,Blindern,N-0316Oslo,Norway
Received 20November 2001;accepted 11July 2002
Abstract
The prence of common lead contamination in zircons ud for U–Pb geochronology is a potentially rious source of error.Traditionally,common lead is measured by analysis of 204Pb,and the isotopic composition of lead corrected accordingly.Some analytical methods (e.g.LAM-ICPMS)do not report 204Pb.Correction methods are available for such analys,but the assume that the only source of discordance in a zircon is the prence of common lead.Using such a correction on a lead analysis that contains a discordance component caud by lead loss will invariably lead to overcorrection,and hence to a meaningless,young age.By assuming that the obrved 206Pb/238U,207Pb/235U and 208
Pb/232Th ratios of a discordant zircon can be accounted for by a combination of lead loss at a defined time,and the prence of common lead of known composition,a correction method can be designed that neither us 204Pb nor assumes concordance.The method propod here involves a numeric solution to a t of equations relating the content of radiogenic lead in a zircon or other U/Th-enriched mineral to its total lead content,the amount of common lead prent,the age of initial crystallization,the age of lead loss and the amount of lead lost in that process.An estimate for the age of lead loss is needed,but in the abnce of prior knowledge of this age,the recalculation procedure can be t up in such a way that the bias in initial age caud by a systematic error in the age of lead loss is minimized.Despite this limitation,the method will give less bias in the corrected ages than alternative correction methods.D 2002Elvier Science B.V .All rights rerved.
Keywords:Geochronology;Uranium–lead;Common lead;Lead isotopes
1.Introduction
The U–Th–Pb system of high U–Pb minerals such as zircon provides us with some of the most versatile,preci and robust geochronometers cur-rently available.Common lead is lead of nonradio-genic origin incorporated into a mineral during its
initial formation,in subquent recrystallization pro-cess or by contamination during analysis.As the prence of even small amounts of unsupported lead in a zircon or other datable mineral will increa its apparent U–Th–Pb ages,the prence of undetected or uncorrected common lead is very detrimental to U–Pb dating.In U–Pb geochronology using thermal or condary ionization mass spectrometers,the minor,nonradiogenic isotope 204Pb is analyd as a monitor of common lead,and the signals of the
0009-2541/02/$-e front matter D 2002Elvier Science B.V .All rights rerved.PII:S 0009-2541(02)00195-X
王者荣耀女E-mail address:tom.andern@ (T.Andern).
减肥喝什么茶
/locate/chemgeo
Chemical Geology 192(2002)59–
79
radiogenic isotopes206Pb,207Pb and208Pb are cor-rected in proportion to their relative abundances in common lead.The u of this correction is critically dependent on preci measurement of204Pb,which is routine in a thermal or condary ionization mass spectrometry.
The u of plasma-ionization mass spectrometry with in situ lar-ablation microsampling(LAM-ICPMS)is a new and promising analytical approach to U–Pb dating of U-enriched ircon). The method combines the lateral spatial resolution of the ion microprobe with greater speed of analysis and considerably less capital investment.Unfortunately, the method ud to compensate for the prence of common lead in thermal or condary ionization mass spectrometry cannot generally be applied to LAM-ICPMS analys.This problem aris primarily becau the low peak/background ratio of the204Pb peak is compounded by the ubiquitous prence of Hg in the argon nebulizer gas;204Hg interferes on204Pb, while the202Hg peak is so small that reliable measure-ment is difficult,if not impossible,and hence an overlap correction of sufficient precision is ldom feasible.
Current methods for common lead correction of such U–Pb analys make assumptions of ideal con-cordance of206Pb/238U and207Pb/235U or208Pb/232Th (e.g.Ludwig,2001),which may not always be justi-fied.In this paper,an alternative approach to common lead correction of U–Pb data is
prented,which neither requires knowledge of the amount of204Pb prent,nor assumes that corrected compositions plot on the concordia.This method is thus applicable to U–Pb analys which do not report204Pb,and to grains which have suffered lead loss in addition to contamination by common lead.
2.Theoretical background
In a U-bearing mineral,radiogenic lead isotopes (206Pb,207Pb and208Pb)will accumulate with time due to radioactive decay of uranium and thorium isotopes.For the238U–206Pb parent–daughter pair, the growth equation is given by:
206Pb
r ¼238Uðe k238tÀ1Þ
where k238is the decay constant for238U,and sub-
script r denotes radiogenic lead.Similar equations
apply to the235U–207Pb and232Th–208Pb decay
ries;decay constants and other relevant data can
be found in standard introductory Faure,
1986;Dickin,1995).
If the system remains clod and the lead contained
in the system(zircon or other U-enriched mineral)is
entirely radiogenic in origin,three simple parent–
daughter ages can be calculated from U–Th–Pb
isotope data:
t206¼
1
k238
ln
206Pb r
U
þ1
;
t207¼
1
k235
ln
207Pb r
U
þ1
;
t208¼
1
k232
ln
208Pb r
232Th
þ1
;
where k235and k232are the decay constants of235U
and232Th,respectively.
A fourth age(t7/6)can be determined from the
relationship between207Pb/206Pb and time:
207Pb r
206Pb r
¼
235U
238U
e k235tÀ1
e k238tÀ1
¼
1
137:88
e k235tÀ1
e k238tÀ1
;
where the prent-day238U/235U is constant at137.88.
If the zircon has suffered lead loss after its crys-
tallization,a systematic age-discordance pattern will
result,in which t208<t206<t207<t7/6V t true.In the
ca of lead loss late in the history of the sample,
the t7/6age still reprents the true crystallization age;
for ancient lead loss the t7/6is a minimum estimate of
the true age.
However,if nonradiogenic lead is incorporated
into the mineral at the time of initial crystallization
or in some later event,the lead prent in the system is
no longer exclusively due to in situ radiogenic accu-
mulation,for example:
206Pb¼206Pb
c
þ206Pb r¼206Pb cþ238Uðe k238tÀ1Þ;
where206Pb c is the206Pb component in the non-
radiogienic lead incorporated into the system,known
as common lead.If common lead is prent,the ages
T.Andern/Chemical Geology192(2002)59–79
60
determined from obrved U–Th–Pb isotope ratios no longer reflect the crystallization age,for example:
t obs206¼
1
k238
ln
206Pb rþ206Pb c
U
þ1
>t true
206
The increa in the apparent age of U–Pb systems is illustrated by Fig.1,which shows the effect of 0.1%,1%and2%common lead on the age of a zircon with constant U/Th=3as a function of true age.As can be en,t7/6is strongly affected at all ages;the systematic error induced by1%common lead in a Proterozoic zircon is100Ma or more,and the effect increas towards younger ages.For U/Th=3,the effect of1%common lead on t208exceeds that on t7/6for Mesoproterozoic or older zircons.For reason-able U/Th ratios,common lead-contaminated Precam-brian zircons of this composition will in general show one of the age quences:t7/6>t207>t208>t206>t true, t7/6>t208>t207>t206>t true or t208>t7/6>t207>t206>t true.
In U–Pb geochronology bad on thermal ioniza-tion(TIMS)or condary ion(SIMS)mass spectrom-etry,the minor,nonradiogenic lead isotope204Pb is measured as a monitor of common lead.Using a model for the isotopic composition of common lead, 206Pb
c
,207Pb c and208Pb c can be estimated,and the obrved radiogenic isotope ratios corrected accord-ingly.If204Pb is not reported,as would normally be the ca for quadrupole LAM-ICPMS data,this cor-rection cannot be ud.
2.1.The3D,classical U–Th–Pb concordia
A3D view of the classical concordia diagram is shown in Fig.2.An ancient zircon which has suffered neither lead loss nor contamination with common lead will plot on a line in space(the‘‘3D concordia’’), which is curved in both206Pb/238U–207Pb/ the classical U–Pb concordia)and206Pb/238U–208Pb/ 232Th projections.A zircon of age t
1
and with no common lead,which has lost lead in a subquent event(at t2),will plot on the straight line connecting the two points C1and C2,corresponding to concordant lead compositions at t1and t2,respectively.
A zircon of age t1which has picked up common lead at the time of crystallization will plot on a line from C1towards the composition of common lead, which lies at infinity.A zircon of age C1with a given
fraction,fc,of common lead will plot at A;lead loss at t2will displace its composition along a straight line (AC2)towards concordant lead composition at age t2 (i.e.point C2),to an intermediate composition at A V. The lines C1A,C1C2and AC2define a plane in 206Pb/238U–207Pb/235U–208Pb/232Th space.
Correcting a zircon which contains common lead and which has lost part of its total lead content in a
later Fig.1.The change in apparent U–Th–Pb ages induced by contamination with0.1%,1%and2%common lead in a zircon with U/Th=3,as a function of age.Curves are labeled by the percentage of common lead.
T.Andern/Chemical Geology192(2002)59–7961
event is equivalent to moving its composition along the line from its measured composition (at A V ),along the broken line A V B ,until interction with the common lead free lead loss line C 1C 2at B ,which is the radio-genic lead component in the zircon.Since common lead is situated at infinity,this line is fixed in space,parallel with C 1A ,and confined to the plane C 1C 2A .For a given t 2,there is only one such plane,and hence only one pair of points C 1and B .The initial age (t point C 1),the fraction of lead lost (fl,reprenting the relative displacement from A to A V or from C 1to B )and the fraction of common lead (fc,corresponding to the distance from A V to B )are therefore interdependent,and can,in principle,be determined in a single oper-ation.The 206Pb/238U,207Pb/235U and 208Pb/232Th ratios of a zircon at point B is uniquely given by the composition of concordant lead of age t 1,the age of lead loss (t 2)and the amount of lead lost at t 2.
In geometrical terms,determining the amount of common lead in a zircon which has lost lead amount
s to determining the orientation of the plane C 1AC 2.This can be done by making an initial guess of t 1(as,for example,indicated by the interction between the
concordia and the plane with broken outline in Fig.2),and rotating this plane with the line AC 2as a hinge,by reducing t 1,until coincident with the line A V B .3.The correction algorithm
To avoid unnecessarily cluttered equations,a short-hand notation defined in Table 1is introduced for the derivation of the expressions ud to determine the amount of common lead and the error propagation.Let fc be the atomic fraction of common 206Pb in an analyd lead,defined by:fc =206Pb c /206Pb =206Pb c /(206Pb c +206Pb r )where 206Pb r is the radiogenic lead and 206Pb c is the common lead.The radiogenic lead component of a common lead-bearing zircon is then given by:y r ¼y ð1Àfc Þð1Þx r ¼x Àyc 7k fc ð2Þz r ¼z Àyc 8u fc
ð3
Þ
Fig.2.A 3D view of the classical U –Th–Pb concordia diagram.The concordia is shown as the heavy,curved line starting at the origin.It is terminated at the point where it pierces the arbitrarily chon front surface of the diagram.Points C 1and C 2are concordant lead compositions at times t 1and t 2,respectively.Point A reprents the prent-day composition of a zircon of age t 1with a fraction fc of common 206Pb.Loss of a fraction fl of its total lead at t 2moves this point to A V ,which is the analyd composition of the mineral.Correcting for common lead amounts to projecting back along the dash-dot line (defined by A V and the composition of common lead at infinity)to B ,which lies at the cord C 1C 2.If the U/Th ratio has not been disturbed,all of the points lie within a single plane in three dimensions,shown by shading.The correction method propod in this paper determines the position of point B by simultaneous solution of Eqs.(1)–(6).The thin,dotted outline reprents a plane hinged on A V C 2,which intercts the concordia at t >t 1,and which thus cannot include point B or the line A V B .
T.Andern /Chemical Geology 192(2002)59–79
62
The points C1,C2and B in Fig.2are collinear in three dimensions,and must therefore be related by the expressions:
y rÀy t
2
y t
1Ày t
2
¼
x rÀx t
2
x t
脸部松弛下垂怎么办
1
Àx t
节日营销2
ð4Þ
and
z rÀz t
2
z t
1Àz t
2
¼
y rÀy t
2
y t
1
Ày t
2
ð5Þ
The common lead corrected composition is related to
the composition of concordant lead at t1and t2and the
fraction of lead lost at t2:
y r¼y t
1
ð1Àf lÞþy t
2
f lð6Þ
Substituting the composition of radiogenic lead as
given by Eqs.(1)–(3)into Eqs.(4)and(5),and
eliminating fc from the resulting pair of equations,
yields an equation which relates the composition of
concordant lead at point C1in Fig.2)to
measured composition(A V)and the composition of
concordant lead of age t2:
yðx t
1
Àx t
2
ÞÀy t
2
x t
1
þxðy t
2
Ày t
1
Þþx t
2
y t
1
x t
1
Àx t
2
Àc7ky t
1
þc7ky t
2
À
zðy t
2
Ày t
1
Þþz t
2
y t
1
þyðz t
1
Àz t
2
ÞÀy t
2
z t
1
印度独立z t
1
Àz t
2
Àc8uy t
1
þc8uy t
2
¼0
ð7Þ
Substituting the relevant expressions for concord-
ant lead compositions at t1and t2yields an equation
which can be solved numerically for t1.Once t1has
been determined,the amount of common lead can be
calculated from one of the two equivalent expressions
for fc which can be derived from Eqs.(4)and(5)
above after substitution of the composition of radio-
genic lead given by Eqs.(1)–(3),e.g.
fc¼
Àyx t
1
þyx t
2
þy t
2
x t
1
þxy t
1
Àxy t
2
Àx t
2
y t
1
t1t27t17t2
ð8Þ
比较好玩的单机游戏The composition of the radiogenic lead component in
the zircon can then be calculated from Eqs.(1)–(3)
above,and the fraction of lead lost at t2from the
expression:
f l¼
y t
1
Ày r
y t
1
Ày t
2
ð9Þ
which is derived from Eq.(6).
3.1.The systematic error introduced by the age of
lead loss
The t1determined by solving Eq.(7)is dependent on
the assumed age of lead loss.The bias introduced by an
erroneous choice of t2is independent of the amount of
common lead removed by the correction algorithm,but
Table1
Parameters ud in correction of common lead
Parameter Standard
notation
Shorthand
Radiogenic
206Pb/238U ratio 206Pb
r
/238U y r
Radiogenic
207Pb/235U ratio 207Pb
r
/235U x r
Radiogenic
208Pb/232Th ratio 208Pb
r
/232Th z r
Concordant isotopic ratios at t1206Pb
t1
/238U,
207Pb
t
1
/235U,
208Pb
t
1
/232Th
y t
1
,x t
1
,z t
1
Concordant ratios at t2206Pb
t2
/
238U,etc.y t
2
,x t9月节日
2
,z t
2
207Pb/206Pb of common lead 207Pb
C
/206Pb C c7
208Pb/206Pb of common lead 208Pb
C
/
206Pb C c8
Isotope ratio in
prent-day uranium
238U/235U=137.88k 238U/232Th
ratio in sample
u
Obrved, uncorrected ratios 206Pb/238U,
207Pb/235U,
208Pb/232Th诚信名言
y,x,z
Fraction of
common206Pb
fc Fraction of
lead lost at t2
fl Real age of zircon
(upper intercept age)
t1 Age of lead loss
(known or assumed)
t2 Error(standard deviation)
in parameter a
r a Correlation coefficient of
errors in measured
206Pb/238U and207Pb/235U
q
Correlation coefficient of errors in corrected
206Pb/238U and207Pb/235U
q r
T.Andern/Chemical Geology192(2002)59–7963
