Lecture 3 - Geochronology I
K-Ar, Ar-Ar and Rb-Sr
0.712
m = eλt-1
87Sr/ 86Sr
0.710
0.708
0M
0
10
7
c = Initial Ratio
a
M
50
a
M
5 00
a
0.706
250 M a
0.704
0.702
0.00
0.10
0.20
0.30
87Rb/86Sr
0.40
0.50
0.60
Using isotope ratios to determine elemental concentration by Isotope Dilution
Mass Spectrometry (IDMS)
Normal
82.58%
9.86%
7.00%
0.56%
84 86 87 88
99.89%
Spike
Mixture
0.05%
0.13% 0.04%
84 86 87 88
84 86 87 88
If spike concentration and isotopic composition are known and sample
isotopic is known then sample concentration can be calculated from
measures isotopic composition of the mixture.
N = S.
{
AbAS – Rm. AbBS
Rm. AbBN - AbAN
}
where N and S are numbers of atoms of “normal” and spike, Rm is isotopic
ratio of the mixture and AbAN is abundance of isotope A in the normal etc.
Advantages
‰ Interference free if analyte is separated from matrix
‰ Very accurate if spike is well calibrated
‰ Quantitative recovery of analyte not required provided spike- sample equilm
‰ With a very enriched spike can determine isotope ratio and concentration in
a single measurement
Disadvantages
‰
‰
‰
‰
‰
‰
‰
‰
Spike calibration can be difficult
Element must have at least two isotopes but can use “artificial” isotopes
Instrumental mass fractionation must be corrected – serious algebra
Correction needs at least three isotopes e.g. Rb limited by lack of correction
Sample-spike mixture is critical
Spike concentration could change with time
Spike isotope ratio could change with time
N/S needs to be optimized to avoid error magnification
Propagated error (%)
Error Magnification in IDMS
Sample/spike ratio
Thus, it is advantageous to know the approximate concentration of the
analyte before attempting an accurate and precise IDMS determination,
although this is ameliorated by very pure spikes. e.g. 229Th, 236U.
The Potassium – Argon Method
39K
- 93.258%
40K - 0.0117%
41K - 6.7302%
40Ar*
β
40Ca
– 89%
40K
E.C.
= λ e/λ . 40K (eλt -1)
and
40Ar
•
•
•
•
t = 1/λ.ln[40Ar*/40K . (λ/λ e) + 1]
•
•
•
•
– 11%
Assumptions:
No
has escaped (Ar loss)
Mineral remained closed to 40 Ar
No initial or later incorporation of
(excess) Ar
Correction made for atmospheric
Ar
Mineral closed to K
Isotopic composition of K is
normal
Decay constants are known
40Ar and K concentrations
determined accurately
40Ar*
Ar loss
Instability of mineral lattice to retain Ar even at low T and P
Partial or complete melting and crystallization of new minerals
Metamorphism
Eldora Stock, Colorado, USA
Weathering and alteration
1600
Age (Ma)
Solution and redeposition of water
soluable minerals
Mechanical breakdown of minerals,
even excessive grinding in sample
preparation
1400
Country rock
1200
1000
Hornblende
Biotite
800
600
400
Feldspar
200
Intrusion
0
1
10
100
1000
Distance from intrusion (m)
10000
Excess Ar
The basic K-Ar age assumes that all initial Ar is atmospheric.
However, some of the Ar may be magmatic from the mantle or from
metamorphic fluids.
Under such circumstances, an isochron approach can be useful.
5000
40Ar/39Ar
Tuff IB Olduvai Gorge, Tanzania
4000
9 samples give mean age of
1.976 +/- 0.034 Ma
3000
Isochron from same samples
2000
2.04 +/- 0.02 Ma
1000
0
0
1
2
40K/36Ar
3
4 x 107
The 40Ar/39Ar Method
Irradiation of K-bearing samples in a nuclear reactor can generate the reaction
39 K (n,p) 39 Ar.
19
18
If we can calibrate the efficiency of this process then we can determine both
potassium content and 40Ar* by measuring Ar isotopes alone.
This is achieved by packing samples with standards of known age which serve
as flux monitors during the irradiation process.
Ar-Ar ages are still subject to the same limitations as conventional K-Ar dates
but do have some specific advantages.
1. No requirement to measure K concentration – reduces sample size.
2. Several “ages” can be derived from each sample by step-heating.
3. Laser sampling is feasible.
50
40
Age
(Ma)
30
Ar-Ar step heating profiles
20
10
0
Eldora Stock
Ar-Ar dating of Parana flood basalts
using laser step heating and spot analysis
Turner et al Earth Planet. Sci. Lett. 121, 333-348 1994
Armstrong et al. Earth Planet. Sci. Lett. 1, 1-19, (1966)
K-Ar and Rb-Sr ages on same biotites from Alps
400
K-Ar and Rb-Sr on biotites discordant
but muscovite Rb-Sr = biotite K-Ar
K-Ar Age (Ma)
350
300
250
200
150
100
1:1
50
0
0
50
100
Rb-Sr Age (Ma)
150
200
Closure temperature (Tc)
Similar in concept to the magnetic blocking temperature i.e. the
temperature at which the orientation and polarity of Earth’s magnetic
field is “frozen” into rocks.
Temperature
Temperature at the time corresponding to [its]
apparent age.
To
Dodson, Contrib. Mineral. Petrol. 40, 259-274 (1973).
For thermally activated diffusion:
Tc
D*/Po
Tc = R/[E . ln(A.τ.D0 /a2)
tc
R – Gas constant
E – Activation energy
A – Constant dependent on geometry and
radioactive decay constant
D – Diffusion coefficient
a – Characteristic diffusion size
τ – Time constant with which D diminishes
Closure temperature
For K-Ar, the temperature at which loss of 40Ar by diffusion out of a mineral
becomes negligible compared with its rate of accumulation.
Isotope System
Mineral
Tc (°C)
U-Pb
Zircon
Monazite
Titanite
800
750
600
Sm-Nd
Garnet
600
Rb-Sr
Muscovite
Biotite
500
300
K-Ar
Hornblende
Muscovite
Biotite
500
350
300
Cooling History of the Glen Dessary Syenite
After van Breemen et al. Scot. J. Geol. 15, 49-62 (1979)
470
U-Pb
Zircon
450
K-Ar
Hornblende
Age
(Ma) 430
U-Pb
Titanite
Rb-Sr
Muscovite
Rb-Sr
Biotite
410
K-Ar Muscovite
K-Ar Biotite
390
0
200
400
600
800
Temperature (°C)
1000
Valhalla Metamorphic Complex (British Columbia)
after Spear & Parrish J. Petrol. 37, 733-765 (1996)
80
Hornblende
Muscovite K-Ar
Rb-Sr
60
Biotite
K-Ar
Time
(Ma) 40
Allanite
U-Pb
Titanite
U-Pb
Muscovite
K-Ar
Apatite Fission track
20
0
0
200
400
600
Temperature (°C)
800
Parrish et al., Geology 34, 989-992, (2006)