Transcript Radiogenic Isotope Geochronology •Radiogenic isotope dating (or radiometric dating) • Techniques based on spontaneous decay of longlived naturally occurring radioactive isotopes • Radioactive.

Radiogenic Isotope Geochronology
•Radiogenic isotope dating (or radiometric dating)
• Techniques based on spontaneous decay of longlived naturally occurring radioactive isotopes
• Radioactive parent isotopes decay to stable
daughter isotopes at rates that can be measured
experimentally, and are constant over time
• From the amount of parent and daughter isotopes in
a rock, along with the known rate of decay, can
calculate the time elapsed since the rock formed
Radiogenic Isotope Geochronology
• The power of
radioisotopic dating
•Link tectonic,
paleobiologic,
paleoclimatic
components of coupled
earth system via
disparate records
•Calibrate events of
earth history to a
numerical (absolute)
time scale
•Provide independent
tests and anchor
points for
astrochronologic age
models
R. Troll
Cause and effect test
bolide impact
mass extinction
flood basalt
volcanism
R. Troll
Determine rates
of processes
Δt
paleobiological
magmatic
tectonic
metamorphic
R. Troll
Radiogenic Isotope Geochronology
• Radioactivity
• Birth of modern geochronology
• Isotopes and radioactive decay processes
• Radioisotopic dating: how it works
• mass spectrometry
• decay constants
• standards and reduction of bias
• Precision and accuracy
• systematic vs. random uncertainties
• what is an error bar?
• From dates to ages: geologic interpretation
• samples
• testing closed-system behavior
• statistical models for combining multiple dates
• High precision geochronology
• K-Ar clock and the 40Ar/39Ar variant
• U-Pb clocks
Radioactivity
Henri Becquerel b. 1852 / d. 1908
Becquerel (1896) Sur les radiations emises par
phosphorescence. Comptes Rendues Acad. Sci.
Paris, v. 122, 420-21.
• Discovered natural radioactivity (uranium 'rays' fog
photographic plate)
• Nobel Prize in Physics 1903 (with Pierre and
Marie Curie)
The Nobel Prize in Physics 1903 was divided, one
half awarded to Antoine Henri Becquerel "in
recognition of the extraordinary services he has
rendered by his discovery of spontaneous
radioactivity", the other half jointly to Pierre
Curie and Marie Curie, née Sklodowska "in
recognition of the extraordinary services they have
rendered by their joint researches on the radiation
phenomena discovered by Professor Henri
Becquerel".
Radioactivity and Chronology
Ernest Rutherford b. 1871 / d. 1937
Rutherford & Soddy (1903) Radioactive Change. Phil.
Mag. ser. 6, v. 576-91.
• Atomic "disintegration" theory of radioactivity
• Nobel Prize in Chemistry 1908
• Relationship between time and radioactive decay
Constant = 2.718
Number of
atoms at time “t”
N = Noe-lt
Number of atoms
when clock was set
Decay constant:
portion of atoms that
decays per unit time
• How do we measure l ?
• Half-life concept:
l = ln 2/thalf-life = 0.693/thalf-life
Radiogenic Isotope Geochronology
• Radioactivity
• Birth of modern geochronology
• Isotopes and radioactive decay processes
• Radioisotopic dating: how it works
• mass spectrometry
• decay constants
• standards and reduction of bias
• Precision and accuracy
• sytematic vs. random uncertainties
• what is an error bar?
• From dates to ages: geologic interpretation
• samples
• testing closed-system behavior
• statistical models for combining multiple dates
• High precision geochronology
• K-Ar clock and the 40Ar/39Ar variant
• U-Pb clocks
Modern Radiogenic Isotope Geochronology
Frederick Soddy b. 1877 / d. 1956
• (1913) Intra-atomic charge, Nature 92, 399-400
• Discovered isotopes or imbalances in the numbers
of protons and neutrons in the Ruthford atomic
"nucleus". These mass imbalances do not affect the
chemical properties of the element, but result in
different levels of radioactivity
• The term 'isotope', which means 'at the same place'
in Greek, was offered by Dr. Margaret Todd at a
dinner party in Glasgow to indicate their position at
a single place in the periodic table
• Nobel Prize in Chemistry 1921
Modern Radiogenic Isotope Geochronology
Arthur Holmes b. 1890 / d. 1965
• (1913) The Age of the Earth, Harper & Brothers
• First geologist to apply radioactivity to dating rocks
• First numerical timescale (counters Lord Kelvin's estimates of 20-100 Myr
for age of the Earth)
• Combined U-Pb date from Norway with Boltwood's results
• Phanerozoic >400 million years long
• Earth is >4 billion years old
Rutherford's mathematical model in practice
P + D = 100%
Increase of
Daughter isotope
Exponential decay
of Parent isotope
Radiogenic Isotope Geochronology
• Radioactivity
• Birth of modern geochronology
• Isotopes and radioactive decay processes
• Radioisotopic dating: how it works
• mass spectrometry
• decay constants
• standards and reduction of bias
• Precision and accuracy
• sytematic vs. random uncertainties
• what is an error bar?
• From dates to ages: geologic interpretation
• samples
• testing closed-system behavior
• statistical models for combining multiple dates
• High precision geochronology
• K-Ar clock and the 40Ar/39Ar variant
• U-Pb clocks
Radioactive decay
Dalrymple (1991)
Dickin (1997)
Only certain combinations of N (# of neutrons)
and Z (# of protons, atomic number) are stable
(black squares above – all others are radioactive.
Three decay mechanisms
• Beta decay ( - ), nucleus ejects electron
• N → Z, atomic mass unchanged
• Electron capture (e.c.), nucleus absorbs
electron
• Z → N, mass unchanged
• Alpha decay (), nucleus ejects He atom
• Z → (Z-2), N → (N-2)
Radioactive decay
• From Rutherford, the rate of decrease of radioactive parent isotope to a
stable daughter isotope is proportional to the number of atoms N of the
parent present at any time t:
dN

= lN
dt
• λ is the constant of proportionality – the decay constant – which defines
the probability that a given atom would decay in some time t (units of time1). Rearranging and integrating:
N

No
dN
=
N
t
  lt
0
• Where No is the number of atoms of the radioactive parent isotope present
at t=0. Integrating:
ln
• Which can be expressed as:
N
=  lt
No
N = N 0 e- lt
• Change N to P, for Parent isotope:
P = P0e
- lt
• The number of radiogenic daughter atoms formed is:
D = Po – P
• But from initial equation above, Po = Peλt, so that:
D = Peλt - P
D = P(eλt – 1)
• This gives the fundamental equation for radioisotopic dating:
D/P = eλt – 1
• If there are atoms of the daughter isotope present in the mineral when the clock starts
at t = 0, these can be accounted for by an initial amount, Do, so that the total number
of daughter atoms after time t is:
lt
0
D = D + P(e -1)
• This seems like an obstacle, but for the U-Th-Pb methods, and the 40Ar/39Ar variant of K-Ar
dating, there are ways to estimate these small amounts of initial Pb or Ar that may be
present in minerals when the clock starts
A complication: decay chains of the actinides
An example of decay chain systematics
Parent N1 decays to N2; intermediate daughter N2 decays to N3; final daughter N3 is
stable.
l
l
1 ® N ¾¾
2® N
N1 ¾¾
2
3
For example…
235U
231Pa
207Pb
Evolution of this system is described by the equations:
dN1
= -l1N1
dt
decay
dN2
= l1 N1 - l2 N2
dt production decay
dN3
= l2 N2
dt production
Substituting the already known solution for N1 :
N1( t ) = N1oe
- l1t
dN2
= l1 N1o e- l1t - l2 N2
dt
dN3
= l2 N2
dt
Decay chain systematics
The general solution for multiple N was discovered by Bateman (1910).
These solutions turn out to fall into two classes, depending upon l1/l2.
For l1/l2>1, all concentrations and ratios are transient:
Secular Equilibrium
For l1/l2<<1, (like the actinide series), the system evolves to a state called
secular equilibrium in which the ratio of parent to intermediate daughter is fixed:
l2 N2 = l1N1
It takes about 5 meanlives of N2 to reach
secular equilibrium. After
this the initial amount of
N2 is the system no
longer matters, and we
can treat the system
as a simple one-step
decay from N1 to N3 !
For the 238U decay chain, that equates to 5 times the half-life of 234U, the
longest-lived intermediate daughter… about 1.25 Ma
Radiogenic Isotope Geochronology
• Radioactivity
• Birth of modern geochronology
• Isotopes and radioactive decay processes
• Radioisotopic dating: how it works
• mass spectrometry
• decay constants
• standards and reduction of bias
• Precision and accuracy
• sytematic vs. random uncertainties
• what is an error bar?
• From dates to ages: geologic interpretation
• samples
• testing closed-system behavior
• statistical models for combining multiple dates
• High precision geochronology
• K-Ar clock and the 40Ar/39Ar variant
• U-Pb clocks
Mass spectrometry
• To calculate a date (t) from a mineral or rock using the age equation one must measure the
atomic ratio of D/P and know the decay constant λ
• The accuracy and precision of these values control the accuracy and precision of the
radioisotopic dates
• The D/P ratio is measured using a magnetic sector mass spectrometer
• Isotopes ionized under vacuum, accelerated through high potential, passed though poles of magnet, where
uniform magnetic field bends ions along curved paths of different radii
• Relative abundances of each mass determined by ion current captured in either a Faraday or electron
multiplier detector
• Accuracy of D/P ratios affected by:
• differential ionization
• fractionation of D/P during chemical
purification
• mass dependent fractionation during
mass spectrometry
• correction for non-radiogenic Do
• traceability of age standards (40Ar/39Ar)
• Isotope dilution eliminates fractionation
effects in the U-Th-Pb systems
• mix 'spike' enriched in artificial isotopes
with sample
Dickin, 1997
• Use of atmospheric argon as a standard
eliminates mass fractionation in the 40Ar/39Ar method
Mass spectrometry
5-collector Nu Instruments Noblesse Argon mass
spectrometer in the WiscAr lab.
Mattinson, 2013
Multicollector
thermal
ionization
mass
spectrometer
for U-Pb dating
Decay constants
• Decay contant λ of parent isotope in age equation is critical to accuracy of
date t
• Physical constants such as natural atomic ratios may also be important
(40Ar/36Aratm; 40K/39K; 238U/235U)
• How are decay constants determined?
• Direct activity counting of decay energy as function of time
• Ingrowth experiments
• Intercalibration: accuracy of one D/P system exported to another
• compromises independence of multiple systems
• Comparision to clock that is independent of radioisotopic systems, e.g.,
astrochronology
• Improving decay constants using the latter two approaches is an active
topic of current exploration
• Be careful to report the decay constants you use, and to compare dates
on the basis of a common decay constant !
• Demands careful reading of published and emerging literature !
Decay constants: 40K
Branched decay of 40K
Min et al., 2000
review of direct activity measurements
electron capture to 40Ar
β- decay to 40Ca
Schmitz, 2012 Geological Time Scale
Decay constants: Uranium
U-Pb geochronology still relies upon the high-precision alpha-counting
measurements of U decay constants by Jaffey et al. (1971).
This stability in the
usage of decay
constants and
present day
atomic ratios is
beneficial to
intercomparing all
published U-Pb
data, however…
Decay constants: Uranium
Recent efforts have been made
to refine the 238U/235U decay
constant ratio using natural
samples.
Decay constants: Uranium
The consensus 238U/235U
atomic ratio of 137.88 has
proven much less robust
with new measurements
of both standard metals
and natural samples.
When do we make a
change?
Ignore uncertainties in decay constants, age of mineral
standard, and/or isotope dilution spike, at your peril !
Preferred ages for 40Ar/39Ar standard minerals
• GTS2012 values
• Reference is astronomically calibrated age of FCs (Kuiper et al., 2008)
Schmitz (2012)
Radiogenic Isotope Geochronology
• Radioactivity
• Birth of modern geochronology
• Isotopes and radioactive decay processes
• Radioisotopic dating: how it works
• mass spectrometry
• decay constants
• standards and reduction of bias
• Precision and accuracy
• systematic vs. random uncertainties
• what is an error bar?
• From dates to ages: geologic interpretation
• samples
• testing closed-system behavior
• statistical models for combining multiple dates
• High precision geochronology
• K-Ar clock and the 40Ar/39Ar variant
• U-Pb clocks
Accuracy & Precision
Accuracy
•
Closenes of agreement between a measured quantity and its
true value
Precision
•
Closeness of agreement between measured quantity values
obtained by replicate measurements on the same or similar
objects under specified conditions
Schoene et al (2013)
Radiogenic Isotope Geochronology
• Radioactivity
• Birth of modern geochronology
• Isotopes and radioactive decay processes
• Radioisotopic dating: how it works
• mass spectrometry
• decay constants
• standards and reduction of bias
• Precision and accuracy
• sytematic vs. random uncertainties
• what is an error bar?
• From dates to ages: geologic interpretation
• samples
• testing closed-system behavior
• statistical models for combining multiple dates
• High precision geochronology
• K-Ar clock and the 40Ar/39Ar variant
• U-Pb clocks
20
From Dates to Ages: Geological
Interpretations
Interpretation of process
•
•
•
•
•
μm
Crystallization
Eruption
Metamorphism
Low-T precipitation
Cooling
Need to know how a date is
recorded by mineral
Strengths of in-situ vs. singlecrystal dating techniques
• temporal and spatial scales
important
Sample characterization
• field relationships
• petrography
• textural/geochemical
Test closed-system behavior
Statistical models for combining
multiple dates
• MSWD (see Ludwig Isoplot manual)
Schoene et al. (2013)
Radiogenic Isotope Geochronology
• Radioactivity
• Birth of modern geochronology
• Isotopes and radioactive decay processes
• Radioisotopic dating: how it works
• mass spectrometry
• decay constants
• standards and reduction of bias
• Precision and accuracy
• sytematic vs. random uncertainties
• what is an error bar?
• From dates to ages: geologic interpretation
• samples
• testing closed-system behavior
• statistical models for combining multiple dates
• High precision geochronology
• K-Ar clock and the 40Ar/39Ar variant
• U-Pb clocks
Roots of 40Ar/39Ar geochronology: The K-Ar method
Aldrich and Nier (1948) University of Minnesota
• 40Ar is decay product of the rarest naturally occurring isotope of potassium, 40K
• A potentially useful geochronometer
• 38Ar isotope dilution tracer allows measurement of 40Ar* (Wasserburg & Hayden, 1955)
Potassium is 7th most abundant element in crust (2.6 wt.%)
• Common in rock forming minerals
• Isotopic composition of K at any time in geologic history is uniform
• Presently: 41K: 40K: 39K = 6.7301: 0.01167: 93.2581
• 40K comprises 0.01% of all K. Its radioactive decay is branched:
• 10.48% via electron capture to 40Ar (λε = 0.580 x 10-11 yr-1)
• 89.32% via Beta decay to 40Ca
(λβ = 4.884 x 10-10 yr-1)
• Total decay constant
λtot = 5.463 ± 0.107 x 10-10 yr-1
[Min 2000/Kuiper, 2008]
Argon is highly variable in isotopic composition owing to radiogenic production from 40K
• Any closed system will accumulate 40Ar*
• Hydrosphere-atmosphere contains following proportions (Nier, 1950, Phys. Rev.)
• 40Ar: 38Ar: 36Ar = 99.60 : 0.0632 : 0.3364
[40Ar/36Arair = 295.5 ± 0.5]
• Recent revision of 40Ar/36Ar in air to 298.56 ± 0.31
(Lee et al., 2006)
• Argon is an inert gas—not bound to any mineral lattice
• Thus loss of 40Ar* via diffusion is common
The K-Ar age equation
é Dù
t = ln ê1+ ú
l ë Pû
1
P = number of radioactive atoms at time t,
D = number of daughter atoms at t.
  l 
t = ln 1    
l   l  
1
Ar * 

40
K 
40
Recall branched decay of 40K to 40Ar such that λ/λε = 9.54
Must determine concentrations of 40K and 40Ar* in mol/g independently
• Determine K by flame photometry (on separate split of solid mineral or rock)
• Determine 40Ar* by isotope dilution mass spectrometry
• Add calibrated volume of 38Ar tracer as an isotope dilution spike.
• Abundance of 40Ar determined by relative abundances of 40Ar to 38Ar in sample
• Also possible to determine 40Ar manometrically by adjusting volume/pressure in mass
spectrometer—the “unspiked” K-Ar technique.
• Correction for 40Ari
(this is the 40Ar present at the time the mineral or rock forms)
• 40Ar* - 40Art - 40Ari
• Assume all 40Ari derives from atmosphere in which: 40Ar = 298.56 x
• Thus, 40Ar* = 40Art – (298.56 x 36Ar)
36Ar
The 40Ar/39Ar age equation
in fast neutron flux:
39
ArK =39 KD ò f (E)s (E)dE
39Ar
:
39K :
Δ :
Φ(E) :
σ(E) :
K
no. of atoms of 39Ar produced from 39K
original number of 39K atoms present
duration of irradiation
neutron flux at energy E
neutron capture cross section at energy E
for 39K(n,p)39Ar nuclear reaction
Ar * 40 K lec 1
= 39
39
ArK
K l D
40
Radiation
[elt -1] OSU TRIGA REACTOR CORE--Cherenkov
McDougall and Harrison (1999)
ò f (E)s (E)dE
define dimensionless parameter, J:
K l
J = 40
D ò f (E)s (E)dE
K lec
39
J is a measure of the proportion of 39K converted to 39Ar and thus total K in sample
assuming the 39K/Ktotal ratio is constant in nature
The 40Ar/39Ar age equation
J is determined by measuring 40Ar*/39ArK in
standard of known t
The J value is determined by measuring the
40Ar*/39Ar ratio in several crystals of a
K
neutron fluence monitor that is co-irradiated
(adjacent to) with the unknown samples
OSU TRIGA REACTOR CORE--Cherenkov Radiation
The most widely used mineral standard is sanidine
from the Fish Canyon tuff (FCs) with an age of
28.201 ± 0.046 Ma, determined through
astrochronologic calibration by Kuiper et al (2008)
In practice:
é
t = ln ê1+ J
l ë
1
Ar * ù
ú
39
ArK û
40
1. measure 40Ar/39Ar ratio in sample;
insert J value from step 2; calculate t
J=
e lt -1
é 40 Ar *
ù
39
êë
ArK úû
2. measure 40Ar/39Ar ratio in
standard mineral
U-Pb geochronology: the Basics
U-rich accessory minerals are the key!
U-rich accessory minerals are the key!
The “negligible” amount of initial daughter
Pb in many U-rich accessory minerals
greatly simplifies the uncertainty in
calculating a “date” from a single isotope
ratio — actually three dates from three
ratios since most accessory minerals
incorporate both actinides…
In addition to the individual U-ThPb decay schemes, we can
combine the two U-Pb equations
to generate a fourth age equation,
which is solely a function of the Pb
isotope ratio and the “constant”
present day 235U/238U
Concordia diagrams to visualize the chronometers
conventional
Wetherill concordia
alternative
Tera-Wasserburg
concordia
U-Pb geochronology: many analytical opportunities