U and Th in Earth Reservoirs

Uranium and Thorium in Earth Reservoirs
Professor Ken Sims
Dept of Geology and Geophysics
University of Wyoming
Earth’s Heat Output
Earth’s heat energy is more than three times greater than
annual human energy consumption on the entire planet.
Earth Radioactivity
• Long-lived radioactive isotopes
“Present day geothermal heat (10’s TW) produced by U,Th series and 40K decay”
• Decay of heavy elements heats the Earth
• How much heat and from where are the main questions
• U/Th/K distribution in the core, mantle, crust
http://neutrino2004.in2p3.fr/slides/monday/fiorentini.pdf
Where do geoneutrinos come from?
– Nuclear reactors (fission products)
– The crust (enriched in K, U, Th)
– The mantle (what we’re really interested in)
Araki et al, 2005
The Age of the Elements
• An earlier generation star exploded (supernova)
creating a cloud of debris and elements
• Some time after, a compression occurs in the cloud,
due either to UV-bubbles or another supernova
• Gravitational collapse begins for our solar system and
sun:
– (our sun is a second-generation star)
• What is the timing of this?
Element building
• During supernova, there is a
massive efflux of neutrons:
the elements are built
upwards by n-capture
toward increasing N (and Z)
• Adjacent isotopes are
created with similar
abundances (ratios ~1)
decreasing upward
Uranium Isotopes
• All Uranium isotopes are unstable, but two
have very long half-lives:
– 238U decays with a half-life of 4.5 x 109 years
– 235U decays with a half-life of 710 x 106 years
• The lighter isotope was more abundant
during formation
235
U
238
U
1.3
Primordial
Uranium Isotopes
235
235
235t
238
238
238t
U
• The isotopes decay at
unequal rates
U
U 0e
U 0e
235
235
U
238
U
1.3
Primordial
U
238
U
0.0072
Present
Uranium Isotopes
235
235
235t
238
238
238t
U
Given
U
U0 e
U0 e
We then have
or
or
R
R0
Uranium Isotopes
• Taking natural
log of both
sides
R
ln
R0
±0.2 Ga due to 20%
uncertainty in
original ratio
238
235
238
t
t
or
ln
& substituting
the numbers
235
e
t
238
R
R0
235
0.0072
ln
1.3
1.537 x10 10 9.763x10
5.196
8.226 x10
10
10
6.3 0.2Ga
232Th
and 238U
• A similar exercise:
– (232Th:238U)0 ~ 1.6 ± 0.3
– 232Th half-life = 14.1 x 109 y
– 238U half-life = 4.5 x 109 y
– 238U decays faster than 232Th
– (232Th:238U)present ~ 2.8 ± 0.8
R
ln
R0
t
232
238
t
R
ln
R0
232
238
ln
4.916x10
11
2.8
1.6
1.5335x10 10
0.5596
1.0419x10 10
5.4Ga
232Th
vs. 238U
• Is 5.4 Ga different from 6.3 Ga ?
– (and whom do you believe?)
– If you vary the primordial ratios by ±20% (a reasonable
uncertainty) you get:
• T(235U/238U) = 6.1 - 6.5 Ga
• T(232Th/238U) = 3.5 - 7.2 Ga
– The better estimate for former is due to 235U’s short half-life
• Also, there are many processes in nature (i.e. during the
formation of the earth and subsequent reprocessing)
that can affect Th/U ratios
But wait… it’s more complicated than this!
• If nucleosynthesis is occurring continuously
– Nuclear “inventories” will grow until decay
balances production
– For U isotopes we have
P
N
which gives
N 235
N 238
ln
t
238
R
R0
Initial
235
235
235
P238
238
N 238
P235
P238
0.0072
0.20
1.537 x10 10 9.763 x10
235
238
ln
235
0.20
10
3.324
8.226 x10
10
4.04Ga
Th & U
K
from McDonough & Sun, Chem. Geol., 120, 223-253, 1995
Earth is Structured (Differentiation)
The interior of Earth is
layered:
– Lithosphere
Continental crust
Oceanic crust
– Upper mantle
Lower lithosphere,
upper
asthenosphere
– Lower mantle
– Outer core (liquid)
– Inner core (solid)
Mass Balance
Total Earth= Core + Bulk Silicate
Earth (BSE)
BSE= Mantle + Crust
Mantle lower mantle and upper
mantle; lithologically and
chemically heterogeneous;
mafic lavas- MORB, OIB,
CFBs…
Crust continental and oceanic;
lower, middle, upper;
lithologically and chemically
heterogeneous; loess,
xenoliths, shale composites,
seismic inferences…
147Sm 143Nd
144Nd
(alpha decay)
stable isotope
T1/2 of 147Sm = 106 Billion Years
DNd < DSm
?
Sims et al., 2008
Mantle Convection:
Continuous Differentiation and Remixing
What Does Mantle Convection Look Like?
Seismic Tomographic Maps
232Th/238U
of the depleted mantle and
enriched crust determined from
isotope systematics
• Pb Isotopes=> time integrated 232Th/238U
•
238U-230Th
disequilibria (current 232Th/238U)
U-Th-Pb governing equations
206
Pb
204
Pb
206
207
Pb
204
Pb
207
208
208
Pb
204
Pb
Pb
204
Pb
Pb
204
Pb
Pb
204
Pb
238
i
U
(e
204
Pb
t
1)
t
1)
t
1)
235
i
U
(e
204
Pb
232
i
Th
(e
204
Pb
* In all three decay schemes,
204Pb is used as a reference isotope
You can measure a date with all three
systems, and if those dates agree,
then you have concordant dates.
What processes can
make U-Th-Pb dates
Discordant?
After Smith and Farquhar (1989)
If
x=(238U/1204Pb)m
And y=(206Pb/204Pb)m
We have
y=b+mx
Where intercept
And slope
b=(206Pb/204Pb)i
m=(e t-1)
The U-Pb system and the age of the Earth
238U
= 206Pb + 8x4He
235U = 207Pb + 7x4He
= 1.55125x10-10 (4.5 Ga half life)
= 9.8485x10-10 (0.7 Ga half life)
204Pb
is a stable isotope
238U/235U is (nearly) constant in nature = 137.88
206Pb
204Pb
207Pb
204Pb
207Pb
204Pb
206Pb
204Pb
=
=
-
206Pb
0
204Pb
207Pb
0
204Pb
207Pb
204Pb
+
+
204Pb
235U
(e
t
- 1)
(e
t
- 1)
204Pb
0
204Pb
206Pb
238U
=
0
1
(e
t
- 1)
137.88
(e
t
- 1)
If
x=(206Pb/204Pb)m
And y=(207Pb/204Pb)m
We have
y=mx+(y0+x0)
Pb-Pb isochrons
207
Pb
204
Pb
207
206
206
Pb
204
Pb
Pb
204
Pb
Pb
204
Pb
i
i
1
e
137.88 e
5t
8t
1
1
Where (y0,x0)=primordial Pb isotopic
composition
And slope
1
e 5t 1
m
137.88 e 8t 1
The Geochron & Initial BSE Pb
Fe-S meteorite
stony meteorites
terrestrial sediment
Patterson (1954) Pb-Pb dating meteorites
and terrestrial sediments
1) Original Pb isotopic composition
estimated from troilite (FeS) in iron
meteorites. Troilite contains Pb but little
U or Th (DTh ≈ DU ≈ 0).
2) Meteorite Pb ratios are representative
of Bulk Earth initial ratios (i.e troilite
represent ‘solar system’ at early stage of
accretion)
3) ) Meteorites and Earth formed at the
same time (Geochron)
Isotope ratios of
Canyon Diablo Meteorite:
206Pb/204Pb
9.3066
207Pb/204Pb
10.293
208Pb/204Pb
29.475
Common (whole-rock) Pb-Pb dating
**Remember that this model only applies to
single stage leads (that’s one special lead!)
What geological circumstances would favor single-stage evolution?
Or where might you find these special leads?
What if you encounter a set of samples that indicate “future ages?”
with a single-stage Pb model? (see below plot)
Implies 2-stage evolution:
Bulk Earth was differentiated
into high- and low- reservoirs
a long time ago (episodic)
or continually differentiated
Very radiogenic Pb’s are due
to increasing partway through
source evolution.
“future”
ages?
Kappa = 232Th/238U
206
Pb
204
Pb
206
208
208
Pb
204
Pb
Pb
204
Pb
Pb
204
Pb
238
i
U
(e
204
Pb
t
1)
Kappa Conundrum
232Th/238U
measured
≠232Th/238U inferred by 208Pb/206Pb
232
i
Th
(e
204
Pb
t
1)
After Smith and Farquhar (1989)
Elliott et al., 1999
Continental Crust
Plumbo Tectonics- The Model
Zartman and Doe, 1981
U in the Worlds Oceans
There are about 1,344,420,000 cubic
kilometers or about 342,543,511 cubic miles of
water in the oceans of the world which
equates to about 1.34 x 1021 liters, or about
3.552 x 1020 gallons- NOAA.
The total amount of uranium dissolved in
seawater at a uniform concentration of 3 mg
238U/m3 normalized to a salinity of 35 is
4.5 billion tons.
Owens, Buesseler, Sims (submitted to Marine Chemistry)