Transcript Chapter 2x - Earth and Atmospheric Sciences

Chapter 2
K-Ar, Rb-Sr, Sm-Nd, Lu-Hf and Re-Os
Figure 2.1
Radioactive Decay
 Unstable nuclei decay to stable ones at rates independent of all environmental influences.
 Modes
 Beta
 electron or positron emission plus neutrino
 Electron capture
 functionally equivalent to positron emission - neutrino emitted; x-ray also emitted
 Alpha
 emission of 4He nucleus
 Fission
 rare - effectively only 238U
 Gamma ray emission (energetic photon) generally accompanies all of the above
 Radioactive decay obeys all conservation laws: mass-energy, spin, momentum.
 Mass of daughter and particles plus energy released must sum to mass of parent.
 Radioactive decay is a major source of the Earth’s internal energy driving plate tectonics and other
geologic processes.
3
Decay Systems
 Geochronologists have a variety of decay systems to work
with. Each is in some ways unique. Success in dating
depends on choosing the right tool. Factors to consider:
 Half-life: shorter half-live better for younger samples
 Chemical behavior of parent and daughter: specifically
 abundance
 fractionation of parent and daughter in different minerals
 mobility of parent and daughter
 ‘closure temperature’ of system: at what temperature is the clock
reset?
Basic Equations
 Basic Equation
dN
= -l N
dt
 Rearrange and integrate:
t
dN
=
òN0 N ò0 -l dt
N
ln
N
= lt
N0
N = N 0 e- l t
 Half-life:
1
ln 2
ln = lt1/2 t1/2 =
2
l
Case where some daughter
already present
 D, daughter; D* =N0 – N, radiogenically produced
daughter
D* = N0 - N = Nelt - N = N(elt -1)
 Since some daughter is initially present (D0):
D = D0 + N(elt -1)
 Its more convenient to work with ratios than absolute
numbers, so we divide by the amount of another, nonradioactive, non-radiogenic isotope. For Sr:
87
Sr / 86 Sr = ( 87 Sr / 86 Sr)0 + 87 Rb / 86 Sr(elt -1)
Isochron Dating
 In the general case:
R = R0 + RP/D (elt -1)
 we have two unknowns, R0 and t (we measure R and
R0).
 We need two equations. If we have two samples with
(presumably) identical R0 and t, subtracting one from
the other, we have: ∆ R = ∆ RP/D (elt -1)
 Rearranging:
∆R
= elt-1
∆ RP/D
t=
or
ln(∆ R /∆ RP/D +1)
l
Isochrons
 From equ. 2.20, we see that t is
proportional to the slope on a
plot of R vs. RP/D.
 Looking at equation 2.19 with
this in mind:
R = R0 + RP/D (elt -1)
 we see that it has the form y=a
+xb, where a is the intercept and
b the slope.
 So we can determine the age by
determining the slope through a
set of cogenetic samples.
 This line is called an isochron.
Assumptions
 We are assuming each sample analyzed has the same value
of R0 and t.
 In other words, they are cogenetic: they formed at the same time
with the same isotope ratio at the time.
 The latter requires isotopic homogeneity (isotope equilibrium).
Typically achieved by diffusion (± convective mixing), requiring
elevated temperature. Hence we are usually dating thermal
events.
 We also assume the only change in R and RP/D is due to
radioactive decay. In other words, we assume the system
has remained closed, no migration of parent or daughter in or
out (we’ll see some ‘work-arounds’ for this).
Additional Considerations
 In addition to a closed system that was initially
isotopically homogenized, an accurate date requires:
 Large amount of radiogenic isotope to have been
produced (essentially requiring a large parent/daughter
ratio)
 For isochron dating, we want a large range of parentdaughter ratios, which minimizes the uncertainly on the
isochron.
Determining the slope
 Relations between observations are commonly determined using
regression (commonly included in calculators, Excel, etc.).
 Classical regression assumes x values are known absolutely – not the case
with analytical data.
 We should take errors in both x and y into account in computing our slope
– this is done by weighting each point inversely by its associated analytical
error.
 Known as two-error regression, mathematically a bit more complicated and
requires iteration.
 In practice, many geochronologists use the Isoplot Excel add-in from the
Berkeley Geochronology Laboratory (unfortunately, latest version runs only
on Excel for Windows).
 http://bgc.org/isoplot_etc/isoplot.html.
The K-Ca-Ar System

40K

The ratio of electron captures to beta decays is called
the branching ratio and is defined as:
is can decay to either 40Ca (by β– decay) or 40Ar by
electron capture (or more rarely β+ decay).
R=
lec
lb

Total decay constant, sum of these two, is 5.5 x 10-10
yr-1 corresponding to a half-life of ~1.28 Ga.

Most (~90%) decays to 40Ca, but 40Ca is doubly magic
and a very abundant nuclide. Thus the radiogenic
fraction is small. 40Ar, on the other hand is a rare gas
and fairly rare (on the Earth anyway). Thus mostly we
are interested in the decay to 40Ar.

The usually large K/Ar ratio in rocks and the relatively
short half-life makes this a good choice for many
dating applications, particularly young events.

Because Ar is a gas and mobile (K also readily
mobilized), the system is readily reset. This can be a
good thing for dating low temperature events.
K-Ar Dating
 Our relevant decay equation is:
 where λis the total decay constant.
 Most rocks have little Ar; lavas, for example, almost
completely degas. What little Ar is present is generally
adsorbed atmospheric Ar, whose isotopic composition is
well known. Thus our equation becomes:
296.16
Diffusion, Cooling and Closure
Temperature
 We mentioned radiogenic chronometers are generally reset
by thermal events.
 This occurs when diffusion is sufficiently rapid to isotopically
homogenize our system.
 Or, the case of K-Ar, Ar is able to diffuse out of the rock.
 The temperature at which the chronometer is reset is known
as the closure temperature. It differs for each decay system,
mineral, and, as we’ll see, cooling rate.
 Let’s first consider diffusion.
Temperature Dependence of
Diffusion
 The diffusio flux is given by Fick’s first law:

æ ¶C ö
J = -D ç
è ¶x ÷ø
where D is the diffusion coefficient and
∂C/∂x the concentration gradient.
 Diffusion coefficient in solids depends on
temperature according to:

EA is the activation energy
= D0e- EA / RT and D is the
frequencyD
factor.
 We can determine these by making
measurements at multiple temperatures,
taking the log of the above equation, then
plotting up the results.
Ar in biotite
Figure 2.2
Closure Temperature
 Using the data in the previous figure, we would find there is
no significant loss of Ar at 300˚C even on geologic time
scales. At 600˚C, loss would be small but significant. At
700˚C, about 1/3 of Ar would be lost from a 100 µ biotite in 2
to 3 weeks!
 If the rock cools rapidly from 700˚C, it will quickly close. If it
cools slowly, closure will come much later.
 Think about Ar in a cooling intrusive igneous or metamorphic
rock. Unlike a lava, cooling will occur on geologic time scales.
At first, most Ar is lost, but as the rock cools, loss slows.
 What is the closure temperature?
Diffusion Calculations
 To determine the distribution of a diffusion species with
time c(x,t), we use Fick’s Second Law:
æ ¶2 c ö
æ ¶c ö
=
D
çè ÷ø
çè ¶x 2 ÷ø
¶t x
 Solutions depend on circumstances. Easy way to solve
it is to look in Crank (1975) who gives this equation for
diffusion out of a cyclinder of radius a
4 æ Dt ö
f @ 1/2 ç 2 ÷
p èa ø
1/2
Dt
1 æ Dt ö
- 2 - 1/2 ç 2 ÷
a
3p è a ø
 where ƒ is the fraction lost
3/2
Ar loss from biotite
Figure 2.3. Fraction of Ar lost from a 150 µ cylindrical crystal as a
function of temperature for various heating times. All Ar is lost in 10
Ma at 340°C, or in 1 Ma at 380° C.
Dodson’s Closure
Temperature
 Dodson (1973) derived an equation for ‘closure temperature’
(also sometimes called blocking temperature) as a function
of diffusion parameters, grain size and shape, and cooling
rate:
Tc =
EA
æ ARTc2 D0 ö
R ln ç - 2
÷
è a E At ø
 where Tc is the closure temperature, τ is the cooling rate,
dT/dt (for cooling, this term will be negative), a is the
characteristic diffusion dimension (e.g., radius of a
spherical grain), and A is a geometric factor (equal to 55
for a sphere, 27 for a cylinder, and 9 for a sheet) and
temperatures are in Kelvins.
 Unfortunately, this is not directly solvable since Tc occurs
both in and out of the log, but it can be solved by indirect
methods (MatLab, Solver in Excel).
40Ar–39Ar
 You might wonder what this is all
about. 39Ar has a 269 yr half-life
and does not occur naturally.

40Ar–39Ar
dating is simply a specific
analytical technique for 40K–40Ar
dating.
 The sample is irradiated with
neutrons in a reactor and 39Ar is
created from 39K by: 39K(n,p)39Ar.
 Since the amount of 39Ar is
proportional to the amount of 39K
and that is in turn proportional to
the amount of 40K, the 39Ar/40Ar
ratio is a proxy for the 40K/40Ar
ratio.
Dating
40Ar–39Ar
Technique
 The amount of 39Ar produced is a function of the amount of 39K present, the
reaction cross-section (analogous to the neutron capture cross-section), the
neutron flux, neutron energies, and the irradiation time:
39
Ar = 39 Kt ò fes e de
 The
Ar * le
=
39
Ar
l
40
40Ar*/39Ar
is then:
40
39
K(elt -1)
Kt ò fes e de
 This is way too much nuclear physics for simple geochemists. The trick is
to combine several of these terms in a single term, C:
C=
le
1
l t f s de
ò e e
 then determine C by irradiating a ‘standard’ of known age and solving this
equation for C:
Ar *
=C
39
Ar
40
40
K ( elt -1)
39
K
Advantages
 The parent-daughter ratio can be determined simply by
determining the isotopic composition of Ar in the
irradiated sample (rather than having to separately
measure K).
 Ar can be extracted from a sample simply by heating it
in vacuum. This can be done in temperature steps,
allowing for multiple cases and multiple isotope ratio
measurements.
 In fact, this is what is typically done.
 Even newer techniques involve spot heating with a
laser, allowing for high spatial resolution.
A Textbook Plateau
Figure 2.4. Here, there has been some diffusional loss from
the edges of the biotite, giving a younger age, but
subsequent temperature steps all give the same age.
Partial reseting in contact
metamorphic aureole
Figure 2.5. Ar release spectra for hornblendes taken from varying distance from a 114 million yea
Curves show calculated release spectra expected for samples that lost 31, 57, and 78% of their a
Figure 2.6. Ar release spectrum of a hornblende in a Paleozoic gabbro
reheated in the Cretaceous by the intrusion of a granite. Anomalously old
apparent ages in the lowest temperature release fraction results from diffusion
of radiogenic Ar into the hornblende during the Cretaceous reheating.
Figure 2.7. Ar release spectrum from a calcic plagioclase from Broken Hill,
Australia. Low temperature and high temperature fractions both show
erroneously old ages. This peculiar saddle shaped pattern, which is
common in samples containing excess Ar, results from the excess Ar being
held in two different lattice sites.
40Ar-39Ar
Isochrons
 The data from various
temperature release steps are
essentially independent
observations of Ar isotopic
composition. Because of this,
they can be treated much the
same as in conventional
isochron treatment.
 Since for all release fractions of
a sample the efficiency of
production of 39Ar from 39K is
the same and 40K/39K ratios are
constant, we may substitute
39Ar × C for 40K:
Ar æ 40 Ar ö
=
+
36
Ar çè 36 Ar ÷ø 0
40
Ar
C(elt – 1)
36
Ar
39
Figure 2.8
Inverse Isochrons
 The problem with that
approach is 36Ar will not be
very abundance and there will
be a relatively large error in
measurement - not something
we want when it occurs as both
denominators.
 We can invert that ratio and
plot it vs 39Ar/40Ar.
 The x intercept is then the age
(case of no trapped Ar) and the
y-intercept gives the isotopic
composition of trapped Ar.
Figure 2.9
Inverse Isochrons
 The problem with that approach
is that 36Ar is not very abundance
and there will be a relatively large
error in measurement - not
something we want when it
occurs as both denominators.
 We can invert that ratio and plot
it vs 39Ar/40Ar.
 The x intercept then gives the
age (case of no unradiogenic Ar)
and the y-intercept gives the
isotopic composition of trapped
Ar.
Figure 2.9
Two Trapped Components
after correction for inherited Ar
Figure 2.10
Rb-Sr System
 Rb: alkali; soluble, mobile, highly incompatible, substitutes for K
 Sr: alkaline Earth; soluble, somewhat mobile, incompatible, substitutes
for Ca
 Both concentrated in the Earth’s crust; particularly Rb. High Rb/Sr in
granitic rocks and their derivatives.
Sr chronostratigraphy
 Sr present in relatively high
concentration is seawater.
 Also concentrated in carbonates
(abundant marine bio-sediment).
 Long residence time; therefore
 Sr isotopic composition of open ocean
water is uniform (in space).
 Sr isotope ratio varies in time, mainly
due to changes in the relative fluxes
from the continents (erosion) and
mantle (ridge-crest hydrothermal
activity).
 Particularly in the Tertiary, Sr isotope
ratio of marine sediment can be used to
date the horizon..
Figure 2.12
Sm-Nd System
Figure 2.13
Sm-Nd characteristics
 Long half-life (~106 Ga).
 Sm and Nd both rare earths elements (REE), similar
behavior, typically small variation in Sm/Nd
 generally more variation in mafic igneous rocks that granitic
ones and their derivatives
 garnet has quite high Sm/Nd.
 REE behavior well understood.
 Both form 3+ ions and are quite insoluble and immobile.
 High closure temperature.
Cosmic Rare Earth Abundances
Figure 2.14
Normalized abundances
Figure 2.15
Ionic Radii and Partition Coefficients
The Epsilon Notation
 Because Sm and Nd are refractory lithophile elements
(condensed at high T in solar nebula and partition into
silicate part of the planet) and because the Sm/Nd
differs little in nebular materials (i.e., chondritic
meteorites), it was assumed the Earth had a chondritic
Sm/Nd ratio and therefore that the evolution of
143Nd/144Nd in the Earth should follow that of chondrites.
Furthermore, variations in 143Nd/144Nd are small. Thus
the ε notation was introduced by DePaolo and
Wasserburg (1976):
e Nd
é 143 Nd / 144 Ndsample - 143 Nd / 144 Ndchondrites ù
=ê
ú ´10, 000
143
Nd / 144 Ndchondrites
ë
û
Nd isotopic evolution of the Earth
 CHUR: “Chondritic Uniform
Reservoir” – (silicate Earth if it
is chondritic)
 Mantle is Nd depleted relative
to Sm, has high Sm/Nd,
evolves to high εNd.
 Continental crust is Nd
enriched relative to Sm, has
high Sm/Nd, evolves to low
εNd.
Figure 2.16
Figure 2.17. Garnet-bearing granulite from Dabie UHP metamorphic
belt in China.
Crustal Residence Times
 Basic idea is that there is a relatively large fractionation between Sm
and Nd during melting to form new additions to crust. Subsequent
crustal processing produces little change in Sm/Nd.
 Consider our
isochron
equation:
143
144
143
Nd /
Ndsam =
Nd /144 Nd0 +147 Sm /144 Ndsam (elt -1)
 Since λt << 1, we can use the approximation that for x<<1, ex ≈ x+1
143 this
and linearize
Nd /144equation:
Ndsam @143 Nd /144 Nd0 +147 Sm /144 Ndsam lt
 On a plot of 143Nd/144Nd vs. t, the slope = 147Sm/144Ndλ
 We want to know t assuming 143Nd/144Nd0 is the mantle value at the
time the material was added to crust.
 We project back along the slope defined by 147Sm/144Nd to the point of
intersection on the mantle evolution curve.
Sm-Nd Model Ages (aka Crustal
Residence Times)
Figure 2.18
Lu-Hf System
Lu-Hf in Chondrites
Figure 2.19
Lu-Hf System

176Lu
is another odd-odd nuclide.
 Decays to 176Hf with half-life of 36 Ga
(possible it might also decay to 176Yb, but
extremely infrequently – not demonstrated.
 Lu and Hf both refractory lithophile
elements -implies silicate Earth has
chondritic Lu/Hf (?).
 Lu slightly incompatible, Hf moderately
incompatible.
 Lu has 3+ valance state, Hf 4+ valance
state, both quite insoluble and immobile.
 Strong chemical similarity of Hf to Zr;
therefore Hf strongly partitioned into zircon
(ZrSiO4) – a highly resistance accessory
mineral in many crustal rocks.
epsilon Hf notation
 176Hf/177Hf ratio commonly represented as εHf – exactly
analogous to εNd:
e Hf
é 176 Hf / 177 Hfsample - 176 Hf / 177 Hfchondrites ù
=ê
ú ´10, 000
176
177
Hf / Hfchondrites
ë
û
Hf in the crust
 Unlike Sm/Nd, the Lu/Hf ratio does change significantly during weathering and other
crustal processes – mainly related to zircon.
 Zircon is extremely resistant chemically and physically and when weathering occurs
will go into the sand fraction (taking Hf with it).
 Lu will mainly go in the clay fraction.
 Thus sedimentary processes act to fractionate Lu/Hf.
 Thus sediments sometimes deviate from the otherwise strong correlation between ε Hf
and εNd.
 So there is no analogous Lu-Hf crustal residence time.
 On the other hand, zircons have very low Lu/Hf, so preserve, or nearly so, their
initial εHf. This together with U-Pb ages of zircons provides analogous information on
provenance of sediments.
Figure 2.20
Lu-Hf in dating
 Lu and Hf are immobile - good for dating older rocks.
 Lu half-life relatively short.
 Lu/Hf ratio more variable that Sm/Nd.
 Consequently, larger variation in Hf isotope ratios
than Nd isotope ratios.
 Lu very strongly concentrated in garnet, so this system
again very useful for dating garnet-bearing rocks.
Figure 2.21
Re-Os

187Re
decays to 187Os with a half-live of 42 Ga.
 Also a decay of 190Pt to 186Os with very long half-life (450 Ga), so that resulting
variation is usually not detectable
 Unlike most elements we’ve considered, Re and Os are siderophile (and also
chalcophile) meaning they are concentrated in the Earth’s core.
 Consequently, Re and Os concentrations in the crust and mantle are very low
(ppb and usually lower).
 Within the silicate part of the Earth, Os behaves as a very compatible element
(hence remains in the mantle with very low concentrations in the crust), while Re
is moderately incompatible and concentrates in the crust.
 Large variation in Re/Os leads to quite large variations in 186Os/188Os.
Gamma notation
 In a manner somewhat analogous to the epsilon
notation, Os isotope ratios are often reported as γOs :
percent deviations from Primitive Upper Mantle:
g Os
æ 186Os / 188Ossam - 186Os / 188OsPUM ö
=ç
186
÷ø ´100
Os / 188OsPUM
è
Figure 2.22
Figure 2.23: Re/Os isochron for a komattite from
Munro Township, Ontario.
Re-Os dating of diamond inclusions
Figure 2.24: sulfide inclusion in diamond
Tracing Os isotope evolution of seawater from
hydrogenous sediments and black shales.
Figure 2.26
Dating Hydrocarbon Generation (?)
Figure 2.27