Ar-Ar Geo-/Thermochronology
(an introduction)
Jörg A. Pfänder
TU Freiberg
V20160616
Ar-Ar Geo-/Thermochronology
Introduction: K-Ar dating
Principle: K-Ar Method:
Electron capture decay
of 40K to 40Ar:
40
19
K →
40
18
Ar
(half life = 11.9 Ga)
Aldrich & Nier (1948): K-rich minerals have elevated 40Ar/36Ar ratios
when compared to atmospheric argon – this suggests that 40Ar is a
decay product of 40K
(Aldrich L.T. & Nier, A.O., 1948: Argon 40 in Potassium Minerals, Phys. Rev. 74, 876–877 –
Nachweis des Zerfalls von 40K zu 40Ca und 40Ar!)
Ar-Ar Geo-/Thermochronology
!
Introduction: K-Ar dating
Ar-Ar Geo-/Thermochronology
Introduction: K-Ar dating
Radioactive decay scheme of natural 40K
40K
10.32 % (ec1)
λ=
ln(2)
T1/ 2
Half life of the 40K –
40Ar decay:
11.93 Ga
λec = 0.581x10-10 1/a
~0.001 %
0.16 % (ec2)
89.52 %
40Ca
40Ar
p + + e− → n
n → p + + e−
Half life of the 40K –
40Ca decay:
1.397 Ga
λβ = 4.962x10-10 1/a
Half life (T1/2) of 40K:
1.25 Ga
λtot = 5.543x10-10 1/a
Ar-Ar Geo-/Thermochronology
40K
Introduction: K-Ar dating
branched decay to 40Ca (89.52%) and 40Ar (10.48%)
in the chart of nuclides:
Isotopes
p + + e− → n
n → p + + e−
Ar-Ar Geo-/Thermochronology
Introduction: K-Ar dating
Abundances of naturally occuring Ar isotopes:
36Ar
= 0.3364 ± 0.0006 %
38Ar
= 0.0632 ± 0.0001 %
Atmosphere: ~1% Argon
with 40Ar/36Ar ~ 298.56 ± 0.31
40Ar
= 99.600 %
(Lee et al., 2006)
Abundances of naturally occuring K isotopes:
39K
= 93.2581 %
40K
= 0.01167 %
41K
= 6.7302 %
Only ~0.011% of K consists of 40K,
and only ~10% of 40K decay to 40Ar
BUT
K is a major element in numerous
rock forming minerals!
Ar-Ar Geo-/Thermochronology
Introduction: K-Ar dating
What can be dated by K-Ar and Ar-Ar?
Basically all K-bearing rocks and minerals !
Commonly used minerals:
K-feldspar, biotite, muscovite, hornblende, plagioclase
Whole rocks:
Basalte, rhyolite, tuffs, meteorites, ….
Sanidine, anorthoclase
Plagioclase
Leucite
Biotite, Muscovite
Amphibole
Whole rock
1000 a (!)
Range of applicability [Ma]
Dateable age range:
~1000 a up to 4.6 Ga
Ar-Ar Geo-/Thermochronology
Introduction: K-Ar dating
Amount of radiogenic 40Ar in a sample/mineral is
proportional to:
K-concentration in sample/mineral
Age of sample/mineral
Amount of radiogenic 40Ar (40Ar*) in a sample or
mineral as a function of time and remaining K-concentration:
40
40
λec 40
λ t
Ar =
K (e − 1)
λtot
*
tot
Artot = 40Ari + 40Ar *
λtot = λec1 + λec 2 + λβ = 5.543 ×10 −10
λec 0.581×10 −10
=
= 0.1048
−10
λtot 5.543 ×10
Ar-Ar Geo-/Thermochronology
Introduction: K-Ar dating
Leading to the classical K-Ar isochron diagram:
one sample = one age !
λec λ t
slope =
(e − 1)
λtot
tot
slope ~ age
best fit
isochron
Ar  40 Ar 
=  36  +
36
Ar  Ar i
y = b
+
40
datapoints
(40Ar/36Ar)i
K-Ar whole-rock isochron of a tuff sample – each datapoint
represents a split of the same sample
K λec λtot t
(e − 1)
36
Ar λtot
40
x
m
Ar-Ar Geo-/Thermochronology
Introduction: K-Ar dating
Requirements to obtain a K-Ar age:
Decay constant‘s are constant over Earth‘s history
40Ar
in a sample is only radiogenic (40Ar*)
or
non-radiogenic Ar can be determined and corrected for
Samples/minerals remain a closed system after
crystallisation/cooling
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
What about ...
... samples/minerals need to remain a closed system after
crystallisation/cooling ?
Solid-state
Diffusion !
∂c
J = −D
and D = f ( T )
∂x
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
Brief excursion: Diffusion – diffusion pathways in minerals
∂c
J = −D
and D = f ( T )
∂x
one-dimensional & steady-state!
Fick‘s first law (Adolf E. Fick, 1855)
All from: Watson & Baxter, 2006,
Earth Planet. Sci. Lett.
J = Mass flow per area (e.g. mol/cm2s) in steady state
D = Diffusivity (diffusion coefficient)
dc/dx = Concentration gradient in x-direction
T = Temperature
In three dimensions: volume diffusion!
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
Brief excursion: Diffusion – diffusion pathways in rocks
a) intragranular
b) grain boundary diff.
c) pore space diffusion
non-volume
diffusion !!!
diffusion barriers
or pathways!
From: Watson & Baxter, 2006, Earth Planet. Sci. Lett.
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
Non-steady-state requires to consider time:
Relation between Fick‘s first law and time (Fick‘s second law):
∂c
∂J
=−
∂t
∂x
yields
yields
J = −D
∂c
∂x
∂c ∂  ∂c 
= D 
∂t ∂x  ∂x 
∂c
∂ 2c
=D 2
∂t
∂x
This equation describes the concentration of Argon in one
dimension (along the x-direction) as a function of space and time
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
Fick‘s second law in three-dimensions:
(and in cartesian coordinates):
∂ c ∂ c ∂ c
∂c
= D  2 + 2 + 2 
∂t
∂z 
 ∂x ∂y
2
2
2
∂c
2
= D∇ c
∂t
This differential equation describes the concentration of a
species (e.g. Argon in a mineral) at a defined location (x,y,z)
at a defined time (note that only volume diffusion is considered!)
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
Solution of Fick‘s second law for a plane sheet geometry
(one dimensional solution):
D = f(T)
(−1) n
(2n + 1)π R
2 2
2
c=
× exp(− D(2n + 1) π t / 4r ) × cos
∑
2r
π n =0 (2n + 1)
4c0
∞
c0 = Initial concentration at t = 0 over the whole plate
c = Concentration at time t at position R
D = Diffusivity (diffusion coefficient)
R = Position within the sheet
2r = thickness of the sheet
This equation describes the concentration of Argon in a plane
sheet as a function of space R and time t at a given temperature T
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
Solution of Fick‘s second law for spherical geometry in
spherical coordinates:
c0 2r ∞ (−1) n
nπ R
2 2
2
c=
sin
×
exp(
−
n
π
Dt
/
r
)
∑
r
π R n =1 n
c0 = Initial concentration at t = 0 over the whole sphere
c = Concentration at time t at position R
D = Diffusivity (diffusion coefficient)
R = Position within the sphere
r = radius of the sphere
This equation describes the concentration of Argon in a sphere
as a function of space R and time t at a given temperature T
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
For practical reasons, a simple approximation can be used to
calculate the diffusion length (i.e. the distance travelled by an atom or ion after time t):
x ≈ Dt
x = diffusion length (cm)
D = Diffusivity (diffusion coefficient; cm2/s)
t = time (s)
Example:
The diffusion coefficient of Ar in hornblende is ~10-12 cm2/s at 1250 K. How
long will it approximately take for a Hbl mineral with a diameter of 2 mm to loose
most of it‘s Argon? Note: The maximum diffusion lenght is ½ x 2 = 1 mm assuming a spherical geometry
Solution: t = 0.12/10-12 = 1x1010 s = 317 a @ 977°C (1 a = 31.56x106 s)
How long will it take at 1000 K (D = ~10-16 cm2/s)?
Solution: t = 1x1014 s = 3.1 Ma @ 727°C (1 a = 31.56x106 s)
This illustrates: D and therefore Ar loss is strongly
dependent on temperature !
Ar-Ar Geo-/Thermochronology
Loss of Argon as a function of Dt/r2
Diffusion & closure temperature
Argon loss increases with:
time (t)
increasing diffusivity (D)
temperature (T)
decreasing thickness/radius (r)
40Ar/40K
over time coupled to
diffusive loss of Ar or K
D = f(T)
From Allègre (2008) Isotope Geology, Cambridge U.P.
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
Dependency of D from temperature T:
Arrhenius relationship
D = D0 e
− E / ℜT
yields:
E 1
ln D = ln D0 −
ℜ T
ln D (1/sec)
y
=
b
- m x
Where D is determined from measured data
and for a given temperature T:
high T
low T
1/T (1/K)
(qf ) 2
D=
t
q = geometry factor
f = fraction of Ar released
t = heating time
Strong dependency of D from T allows to
define the blocking temperature!
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
From Braun et al., Quantitative Thermochronology
D0 and E values for Phlogopite, Biotite, Muscovite and Hornblende
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
Accumulation of radiogenic 40Ar in K-bearing minerals, closure
temperature concept (Dodson, 1973)
closed system
open system
cooling
crystallisation
Temp. /
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
Combining the Arrhenius relation to diffusion models leads to the
closure (blocking) temperature concept (Dodson, 1973):
from slope of Arrhenius plot
Tc =
E
Tc = closure temperature
E = activation energy
ℜ ln( Aτ D0 / r )
2
ℜ = gas constant
A = geometry factor
D0/r2 = diffusivity
ℜTc
τ=
E dT / dt
2
Intercept from Arrhenius plot
(frequency factor)
Geometry factors:
see also Harrison et al., 2005,
Rev. Min. Geochem.
A = 55 for a sphere
A = 27 for a cylinder
Examples (for Rb in biotite; Hofmann & Giletti, 1970):
E = 21 kcal/mol
A = 27 (assuming a cylindrical model)
D0/r2 = 10-12 1/s = 30 1/Ma
A = 8.7 for a plane sheet
assuming volume diffusion !!
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
Combining both terms:
2
2

E
A ℜ Tc D0 / r 

= ln 
ℜ Tc
 E dT / dt 
Tc = closure temperature
E = activation energy
ℜ = gas constant
A = geometry factor
Harrison et al. (2005)
This equation can be solved
iteratively for a specific type of
mineral (i.e. a given set of diffusion
parameters E and D0) by assuming
an appropriate cooling rate (dT/dt)
and a specific grain size (r)!
D0/r2 = diffusivity
Geometry factors:
A = 55 for a sphere
A = 27 for a cylinder
A = 8.7 for a plane sheet
assuming volume diffusion !!
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
Closure temperature calculation by using Mark Brandon‘s
CLOSURE Program
Example: Hornblende with r = 100 µm: TC ~ 486°C at a cooling rate of 3°C/Ma
TC ~ 507°C at a cooling rate of 10°C/Ma
Ar-Ar Geo-/Thermochronology
Diffusion & closure temperature
Closure temperatures of different minerals
Ar-Ar Geo-/Thermochronology
More closure temperatures...
Thermochronology
From Reiners et al., 2005, Rev. Mineral., 58, 1-18
Ar-Ar Geo-/Thermochronology
Thermochronology
Cooling histories from different coexisting minerals having
different closure temperatures: „Bulk-closure approach“:
From Braun et al., Quantitative Thermochronology
Ar-Ar Geo-/Thermochronology
Thermochronology
Example: Cooling rate of a syenite pluton determined by
dating of different minerals having different closure
temperatures for different chronometers
crystallisation age
Averaged cooling rate between
~1000°C and ~300°C:
12,5 °C / Ma
From this, a rough estimate of the
depth of intrusion can be calculated
for a given initial melt volume and
geothermal gradient!
Cooling to lower temperatures likely
controlled by exhumation!
Ar-Ar Geo-/Thermochronology
Practical aspects
Problems of the classical K-Ar method:
slope =
λec λ t
(e − 1)
λtot
tot
Concentrations of 40Ar and K have to be precisely determined in representative sample aliquots – difficult!
No (internal) control on potential argon-loss or -gain
during thermal overprints (metamorphism): one sample = one age
Solution to this problem:
39
19
Irradiation of samples in a nuclear reactor
to produce 39Ar by a (n,p) reaction:
39K
+n
39Ar
Natural abundance of
+ p+ + e-
39K
= 93.258 %
Amount of 39Ar produced from 39K:
39
ArK = 39K T ∫ φ ( E )σ ( E ) dE
K + 01n →
Ar +11H + Q
39
18
Ar-Ar Geo-/Thermochronology
Φ(E)
Practical aspects
58Ni(n,p)58Co
54Fe(n,p)54Mn
39K(n,p)39Ar
Reaction cross
sections for different
nuclear reactions
along with neutron
energy spectra from
235U fission,
calclated using
different models and
databases
From Rutte et al., 2015
Ar-Ar Geo-/Thermochronology
Practical aspects
Some nuclear reactions (amongst others!) that produce
Argon isotopes and typical production ratios:
39K(n,p)39Ar
40Ca(n,nα)36Ar
For the 10 MW reactor (LVR-15) in
Řež (Czech Republic):
(36Ar/37Ar)Ca ~
0.000227
40Ca(n,α)37Ar
(39Ar/37Ar)Ca ~
0.000602
42Ca(n,α)39Ar
(40Ar/39Ar)K ~
0.00183
40K(n,p)40Ar
(slightly variable for different reactor
types and irradiation positions within
the reactor)
Ar-Ar Geo-/Thermochronology
Practical aspects
Types of „Argon“ in a sample (terminology):
Atmospheric argon (Aratm):
40Ar/36Ar
= 298.6 (today!)
Radiogenic argon (40Ar*): From natural 40K-decay
Trapped (inherited) argon: has an atmospheric or excess
composition or is a mixture of both
Cosmogenic argon: Ar isotopes produced in extraterrestrial
rocks by cosmic ray from other elements (e.g. Ca, Ti, Fe)
Irradiation induced argon: Argon produce by neutronenirradiation in a nuclear reactor (from K, Ca, Cl)
Ar-Ar Geo-/Thermochronology
Practical aspects
Argon extraction, cleaning & measurement
1) Thermal release of argon (and other gases) from mineral/rock
2) Cleaning, i.e. sorption of all but the noble gases
3) Measurement of argon isotope abundances in a gas mass spec
Ar-Ar Geo-/Thermochronology
Practical aspects
Argon (gas) extraction: Thermal laser
Wavelength: 10.6 µm
Energie: 30 Watts
Spot size: 200 – 3000 µm
Step wise degassing by
step wise increase of the
laser power
Laser window &
sample chamber
CO2 - laser
CO2 laser specifications:
Ar-Ar Geo-/Thermochronology
Practical aspects
Argon (gas) extraction
Laser sample chamber
Sample
chamber
10.6 µm transparent
ZnSe window
Sample
holder
Ar-Ar Geo-/Thermochronology
Practical aspects
Sample crucible
Pfänder et al., 2014, Geochem. Geophys. Geosyst.
Argon (gas) extraction: Resistance furnace (HTC)
Ar-Ar Geo-/Thermochronology
Gas cleaning
Zirconium alloy
getter surface
„Getters“ made from a Zirconium metal alloy were
used for gas cleaning: Adsorption of active gases
One operates at 400°C, one at room temperature
Water cooled
getter housings
Practical aspects
Ar-Ar Geo-/Thermochronology
Practical aspects
Gas cleaning: Pumping speed vs. sorbed quantity for
St101 getter material (Zr-Al alloy)
getter alloy having a
large surface
From SAES webpages
Most (active) gases are sorbed, inert noble gases not!
Ar-Ar Geo-/Thermochronology
Argon isotope measurement
Practical aspects
ion
source
magnet
collector
unit
All five Ar-isotopes (mass 36 – 40)
were measured simultaneously
40Ar
39Ar
38Ar
37Ar
36Ar
peak coincidence
electron
bombardment
source
r=
1439 m
U
H
e
r = radius of ion flight path [mm]
H = magnetic field strength [Gs]
m = mass [amu]
e = charge units
U = acceleration voltage [V]
Ar-Ar Geo-/Thermochronology
Age calculation
How can we calculate an age from the measured
Ar isotope composition of an irradiated sample?
Age equation from decay law:
t = age of the sample
λ = decay constant
D = number of daughter isotopes (atoms) today
N = numer of parent isotopes (atoms) left (i.e. today)
D

t = ln  1 + 
λ  N
1
Quantity of 40K that decays to 40Ar (~10.5%):
λecI + λecII
f =
λ
with
λ = λecI + λecII + λβ
1
f
Yielding

t = ln  1 +
λ 
1
40
Ar*
40
K× f



which is:

t = ln  1 + 9.54
λ 
1
40
Ar*
40
K



Ar-Ar Geo-/Thermochronology
Age calculation
How can we get 40K from measured 39Ar?
Using the natural isotope abundances:
40
39
19
K = 0.000125 × K
39
K + 01n →
Ar +11H + Q
39
18
Quantity of 39Ar produced by neutron irradiation from 39K :
39
ArK = K T ∫ φ ( E ) σ ( E ) dE
J‘ „Conversion factor“
Combining yields:
39
40
T = duration of irradiation
Φ = neutron fluence (neutrons per cm2 x sec)
σ = effective cross section of 39K(n,p)39Ar reaction
E = Energy of the neutrons
39
ArK
K = 0.000125 ×
J'
40

Ar *
t = ln  1 + 9.54
λ 
0.000125 × ( 39ArK / J '
1


)
Ar-Ar Geo-/Thermochronology
Age calculation
Combining all constants yields to the 40Ar/39Ar age equation:

t = ln  1 + J
λ 
1
40
Ar *
39
ArK



where the constant J contains the abundances of the K isotopes, the decay
constants (i.e. the branching ratio) and the neutron fluence, reaction cross section
and the duration of irradiation and is commonly termed „irradiation parameter“
or „J-value“
J can not be calculated precisely – therefore, it needs to be
determined by using samples (minerals) with known ages („fluence
monitors“) that were co-irradiated with the samples
Ar-Ar Geo-/Thermochronology
Age calculation
How to determine 40Ar*/39ArK? Simplified version:
36Ar
atm
= 36Arm – 37Arm x (36Ar/37Ar)Ca
=
39Ar
= 39Arm – 37Arm x (39Ar/37Ar)Ca
K
40Ar
m
– 298.6 x
36Ar

t = ln  1 + J
λ 
1
40Ar*
atm
40
Ar*
39
ArK



The Index „m“ denotes the measured signal!
39Ar
Ca
40Ar
atm
37Ar
Ca
(39Ar/37Ar)Ca ~ 0.000602
39Ar
K
40Ar*
(36Ar/37Ar)Ca ~ 0.000227
not to scale!
(40Ar/39Ar)K ~ 0.00183
36Ar
Ca
36Ar
atm
40
39
38
37
36
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Data presentation in 40Ar/39Ar geochronology (step heating)
1) For each temperature step, an
age is calculated using:
40
1 
Ar * 

t = ln 1+ J 39
λ 
ArK 
2) For the plateau steps, a Weighted
Mean Age (WMA or WPA) is
calculated using:
n
Age spectrum diagram
WMA =
∑σ
i =1
n
2
i
ti
1
∑σ
i =1
3) The goodness of the plateau age is
quantified by calculating the Mean Square
of Weighted Deviates:
1
2
i
1 n ∆t 2
MSWD =
∑
n − 1 i =1 σ i2
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Data presentation in 40Ar/39Ar geochronology (step heating)
Age spectrum diagram yields:
Total gas age (TFA) = 25.4 Ma
Plateau age = 25.4 ± 0.1 Ma
The advantages of the Ar-Ar method
over the K-Ar method are thus:
> One sample = many ages!
Step-wise degassing of a sample provides
information about potential „artificial“
argon not related to radioactive ingrowth,
or about Ar-loss / K-gain ......!
Age spectrum of 12.2 mg K-feldspar from a
Latite from the Siebengebirge (Przybyla, 2013)
> „Easy“ to measure ... (everything is
relative!)
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Data presentation in Ar-Ar geochronology (step heating)
Complex release pattern of a hornblende (excess Argon and thermal overprint, i.e. Ar loss)
Age spectrum of 50.6 mg Hbl
from an andesite from the Alps
CS103 – Exp. No.1183
TFA = 140 Ma
(meaningless!!!!)
MSWD = 2377 !!!!!!!!
NO PLATEAU,
and thus in this case
„NO AGE“ !
K-Ar dating would
not resolve this
circumstance but
instead provide a
meaningless
age!!!
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Data presentation in Ar-Ar geochronology (step heating)
Amount of 40Ar* and K/Ca ratio of individual temperature steps
40
Ar*% Diagram
40Ar*
100
= 40Arm – 298.6 x 36Arcorr
40
Ar*%
80
60
Indicates the relative
proportion of radiogenic 40Ar
of each temperature step
40
20
0
0
10
20
30
40
50
60
70
80
90
K/Ca Diagram
K/Ca ~ 39ArK/37ArCa
0.8
K/Ca
0.6
100
Indicates the K/Ca ratio of
each temperature step
calculated from 39ArK / 37ArCa
0.4
0.2
0
0
10
20
30
40
50
%39ArK
60
70
80
90
100
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Degassing behaviour of an undisturbed sample
Concentration profile within a mineral
Resulting age spectrum
t = 25 Ma
constant 40Ar*/39ArK
results in a constant age
=
„perfect plateau“
ingrowth of 40Ar* over time
step heating
experiment
t=0
Evolution of radiogenic 40Ar over time
Undisturbed age spectrum
For (thermally) undisturbed minerals, the released gas fractions were expected to have
constant 40Ar*/39ArK ratios, as both isotopes were produced from decay reactions of Kisotopes
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Degassing behaviour of a thermally disturbed sample
Process
Minimum
cooling age
t = 30 Ma
Maximum age of
thermal event
≥ 50 Ma
Result
≤ 30 Ma
after 30 Ma
thermal event at 30.01 Ma
after 50 Ma
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Example 1: Undisturbed age spectrum (minimal loss indicated by first step)
Biotite GA1550, K-Ar age: 98.8 Ma
(Monzonite from M. Dromedary, NS Wales, SE Australia)
The perfect plateau indicates:
Sample developed as a closed system
since initial cooling (closure) or since
(complete!) thermal resetting!
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Example 2: Disturbed age spectrum (Argon loss indicated by first step)
Age spectrum (34
temperature steps) of 49.7
mg whole-rock
fragments from a tephriphonolite
Note the partial Ar-loss
revealed by the low
temperature steps
Przybyla, 2013
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Three (of much more!) age plateau definitions:
(or: what is disturbed, what is undisturbed?)
>50% 39ArK and no age difference at the 95% confidence level
(2σ) between any two steps (Fleck et al., 1977)
≥5 contiguous steps where all (or all except one) agree in age at
the 95% confidence level (a single discordant value is acceptable
if it represents a small gas fraction; Berger & York, 1981)
Maximal number of steps where the first and last step coincide
within the 2σ level, and all steps inbetween coincide with the
plateau age at the 1σ level (Foland et al., 1986)
Problem: Measurement precision increased over the years, as did the
number of measured steps! Statistical tests are model dependent!
Recommendation: A plateau can be defined if it represents more than 50%
of 39ArK released and if the steps are concordant with the inferred
plateau age within the 2σ level (exceptions will follow...)
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Isochron diagram
(each point represents a single temperature step)
40Ar/36Ar
40Ar/36Ar
39K
= (40Ar/36Ar)i + 39K/36Ar (eλt-1)
= 39Ar / J
http://www.encyclopedia-ofmeteorites.com/test/
5064_4126_268.jpg
(by J. Szkatula)
slope ~ age
m = (eλt-1)
Intercept: 40Ar/36Ar of trapped Ar
(298.6 in an ideal case!)
Bjurböle chondrite:
age ~4.3 Ga
39Ar/36Ar
Intercept provides the composition of the „trapped“ (initial) Argon component!
Problem: Virtually 36Ar-free steps and/or samples with high amounts of 40Ar* dominate the
regression and yield erroneous initial 40Ar/36Ar. Solution: inverse isochron diagram
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Inverse isochron diagram
If more than two isotopically different
(each point represents a single temperature step)
Ar components are present (e.g. a
radiogenic, an excess and an
atmospheric component), and if these
components are present in variable
Intercept:
(40Ar/36Ar)-1
of trapped Ar
proportions in each step:
36Ar/40Ar
NO LINEAR CORRELATION !!
Instead, the scatter then indicates a
inverse isochron
three- or multi-component isotope
mixture!
Intercept = 39ArK/40Ar*
39Ar/40Ar
40
1 
Ar * 


t = ln 1+ J 39
λ 
ArK 
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Three component isotope mixing:
1250
40
1 
Ar * 

t = ln 1+ J 39
λ 
ArK 
Intercept = 39ArK/40Ar*
10000
Whenever the RATIO between EXCESS and ATMOSPHERIC Ar changes
during degassing, there will be scatter in the linear correlation!
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Example: Anorthoclase from a volcanic tuff within a sedimentary
strata close to Lake Turkana (Kenia)
Intercept value
Intercept: 40Ar/36Arinitial = 296.4 ± 4.2
indicates: Only two
Argon components
are present:
atmospheric and
Inverses Isochronendiagramm:
Intercept: 40Ar/39Ar age =
3.01 ± 0.02 Ma
radiogenic Argon
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Example: Age spectrum diagram indicating excess Argon
Biotite Separate
Excess argon: high 40Ar/39Ar
at the beginning and end of a
heating experiment
Underestimation of initial
40Ar/36Ar
results in the
typical shape of the age
13 – 15 Ma
spectrum (undercorrection
of measured 40Ar by using
an atmospheric 40Ar/36Ar
ratio)
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
The same biotite sample plotted in an inverse isochron diagram:
Biotite Separate
0.00335
atmospheric argon
Intercept: 40Ar/36Ar = 375 ± 15
Correlation indicates a
fairly homogeneous
degassing of mainly two
components at various
proportions:
excess argon
and
radiogenic argon
Intercept: 40Ar/39Ar age =
12.8 ± 0.2 Ma
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Example: Biotite from a Qz-Diorite
Age spectrum
Inverse isochron diagram
Recalculated age spectrum
LT steps
U-Pb age: 154 Ma
HT steps
149.1 ± 1.1 Ma
Highly disturbed age
spectrum – no plateau!
Maximum age exceeds the
maximum possible
emplacement age derived
from U-Pb (154 Ma)!
Heating steps of the same
sample in an inverse
isochron diagram.
Two non-atmospheric Argon
components were detected
that degas from different
sites within the crystals at
different temperatures
Age spectrum
recalculated using the
trapped Argon composition
as derived from the inverse
isochron diagram
see next slide!
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Example: Biotite from a Qz-Diorite
Age spectrum recalculated using the trapped (initial) Argon compositions as
derived from the inverse isochron diagram:
~ 150 Ma
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
„Disturbed“ samples
Argon loss, gain or redistribution between minerals may result
from:
Thermally induced (volume) diffusion („reheating“)
Recrystallisation during metamorphism
Recrystallisation during alteration
What are the consequences of such processes with respect to the
measured isotope composition of a sample?
Note, that commonly only 40Ar and 36Ar are affected by such processes,
not 39Ar that is produced by neutron irradiation prior to measurement!
!
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Disturbed samples: Single site diffusion model
spheres with a uniform size
lognormal distributions
spheres with a
lognormal size
distribution
Bruderheim meteorite, whole-rock
model curve logn.
spheres 90% loss
Calculated Ar release patterns of uniform
spheres and spheres with a lognormal size
distribution assuming ideal volume diffusion
(age = 4.5 Ga, thermal event at 0.5 Ga)
Real meteorite sample: Age >3
Ga, Ar-loss at around 0.5 Ga
(from Turner et al., 1966)
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Disturbed samples: Example from host rocks adjacent to an intrusion
~340 Ma
No initial age
~300 Ma
preserved !!
367 Ma
calculated Argon
release spectra
measured
steps
~170 Ma
114 Ma
Age spectra of three 367 Ma old hornblende samples
taken at different distances from the contact to a younger,
114 Ma old granodiorite intrusion
But the lower estimate of
~340 Ma for the formation
age is close to the 367 Ma
intrusion U/Pb age, and the
upper estimate for the
thermal event is close to
114 Ma!
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Disturbed samples: Qz-Diorite from Alaska
Age spectrum of a hornblende separate from a Qz-Diorite from Alaska with a typical Ar-loss
profile. Minimum initial cooling age: 276 ± 1.8 Ma, maximum age of metamorphism: ~140 Ma
(from Falkowski et al., 2016)
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Mixed phases („whole rocks“)
Whole rock samples contain different minerals that may provide
different (virtual) ages due to:
Different closure temperatures (i.e. slow cooling!!)
(at 10°C/Ma cooling, a Hbl will be ~20 Ma older than a Bt from the same sample)
Different degrees of Ar loss during reheating (according to Tc)
Various amounts of excess Ar (inherited or gained)
Recrystallisation and/or formation of new minerals during
metamorphism, synkinematic recrystallisation or alteration
Therefore: Seperate individual minerals out of a rock!
Where not possible: Apply high-resolution dating!
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Mixed phases („whole rocks“)
Example: Shear zone samples with recrystallized muscovite
Degassing patterns of pure, prephengite
existing ~40 Ma old phengite, of
pure ~12 Ma old muscovite
(recrystallized during shear zone
mixture
metamorphism); and degassing
pattern of a mixture of both.
muscovite
The three samples were taken at different
distances from a shear zone (after Wijbrans
& McDougall, 1986)
Separate phases before dating!
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Mixed phases („whole rocks“)
Example: K-Ar ages of
different minerals isolated from
samples taken at
different distances from
a young intrusion, hosted by
precambrian basement
Age of host rock: 1.4 Ga
Basement: 1400 Ma
hornblende
biotite
Age of intrusion: 55 Ma
Different temperature
profiles due to different
closure temperatures
(i.e. different diffusion activation
energies within different minerals)
Intrusion: 55 Ma
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Mixed phases („whole rocks“)
Dating of (fine-grained) volcanic rocks applying
high resolution 40Ar/39Ar dating
Samoa Islands
Why?
Hawaii Emperor chain
From: Woods Hole Oceanographic
Institution (WHOI.edu)
To determine plate movement
velocities (and hence to quantify
mantle dynamics)
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Mixed phases („whole rocks“)
Comparison: Phenocryst vs. groundmass Ar-Ar ages
From Abratis et al., 2015
Whenever present, separate phenocrysts from volcanic rocks!!!
If no phenocrysts are present: High-resolution dating of groundmass
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Dating fine grained (volcanic) rocks: Problem
Effect of argon loss on a LT data point in an inverse isochron diagram
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Dating fine grained (volcanic) rocks: Problem
Effect of excess argon in a HT data point in an inverse ID:
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Dating fine grained (volcanic) rocks: Problem
Effect of argon loss in a LT step and excess argon in a HT step:
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Dating fine grained (volcanic) rocks: Problem
Effect of excess Ar in a LT step:
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Dating fine grained (volcanic) rocks: Problem
Effect of excess Ar in a LT and a HT step:
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Dating fine grained (volcanic) rocks: Example:
Ar-Ar Geo-/Thermochronology
Data presentation & interpretation
Dating fine grained (volcanic) rocks: Example:
Only 4 steps (comprising 38.8% of the 39Ar) contain the
required information, the age seems reliable!
That’s it !