# New Mexico Geochronology Research Laboratory

K/Ar and ^{40}Ar/^{39}Ar Methods

**Potassium-Argon System:**

Overview

K/Ar Dating

^{40}Ar/^{39}Ar Dating

## Overview

### Isotopes of Potassium and Argon

The isotopes the KAr system relies on are Potassium (K)
and Argon (Ar). Potassium, an alkali metal, the Earth's
eighth most abundant element is common in many rocks and
rock-forming minerals. The quantity of potassium in a
rock or mineral is variable proportional to the amount
of silica present. Therefore, mafic rocks and minerals
often contain less potassium than an equal amount of silicic
rock or mineral. Potassium can be mobilized into or out
of a rock or mineral through alteration processes. Due
to the relatively heavy atomic weight of potassium, insignificant
fractionation of the different potassium isotopes occurs.
However, the ^{40}K isotope is radioactive and
therefore will be reduced in quantity over time. But,
for the purposes of the KAr dating system, the relative
abundance of ^{40}K is so small and its half-life
is so long that its ratios with the other Potassium isotopes
are considered constant.

Argon, a noble gas, constitutes approximately 0.1-5%
of the Earth's present day atmosphere. Because it is present
within the atmosphere, every rock and mineral will have
some quantity of Argon. Argon can mobilized into or out
of a rock or mineral through alteration *and* thermal
processes. Like Potassium, Argon cannot be significantly
fractionated in nature. However, ^{40}Ar is the
decay product of ^{40}K and therefore will increase
in quantity over time. The quantity of ^{40}Ar
produced in a rock or mineral over time can be determined
by substracting the amount known to be contained in the
atmosphere. This is done using the constant ^{40}Ar/^{36}Ar
ratio of atmospheric Argon. This ratio is 295.5.

### Radioactive decay of parent isotope to daughter isotope

The nuclei of naturally occurring ^{40}K is unstable,
decaying at a constant rate (half-life = 1.25 billion
years). The decay scheme is electron capture and positron
decay. About 89% of the ^{40}K atoms will decay
to ^{40}Ca. For the K/Ar dating system, this decay
scheme to calcium isotopes is ignored. The remaining 11%
of the ^{40}K atoms decay to ^{40}Ar.
It is this scheme that makes the K/Ar method work.

The buildup of radiogenic ^{40}Ar (^{40}Ar*) in a closed system can be expressed by the equation:

## The K/Ar Dating technique

### General assumptions for the Potassium-Argon dating system

Certain assumptions must be satisfied before the age of a rock or mineral can be calculated with the Potassium-Argon dating technique. These are:

- The material in question is a closed system.
In other words, no radiogenic
^{40}Ar has escaped from the rock/mineral since it formed. In the case of a volcanic mineral, this means rapid cooling. Likewise, potassium has not been gained or lost. - A correction is made for atmospheric argon (
^{40}Ar from the^{40}Ar/^{36}Ar ratio = 295.5 subtracted). - No non-atmospheric
^{40}Ar was incorporated into the rock/mineral during or after its formation.

- The isotopes of potassium in the rock/mineral have
not fractionated, except by
^{40}K decay.

- The decay constants of
^{40}K are accurately known.

- The quantities of
^{40}Ar and potassium in the rock/mineral are accurately determined.

### The K/Ar age determination

Once the ^{40}Ar and potassium in a rock/mineral are accurately measured, the amount
of ^{40}K (based on the relative abundance of ^{40}K to total potassium) and ^{40}Ar*
(radiogenic ^{40}Ar) must be calculated. The
K/Ar method uses a spike (known quantity) of ^{38}Ar mixed with
the argon extracted from the rock/mineral to determine
the quantity of ^{40}Ar*. The resulting ^{40}Ar*
and 40K can be plugged into the age equation
as follows:

### Problems and Limitations of the K/Ar dating technique

Because the K/Ar dating technique relies on the determining
the absolute abundances of both ^{40}Ar and
potassium, there is not a reliable way to determine
if the assumptions are
valid. Argon loss and excess argon are two common
problems that may cause erroneous ages to be determined.
Argon loss occurs when radiogenic ^{40}Ar
(^{40}Ar*) produced within a rock/mineral
escapes sometime after its formation. Alteration and
high temperature can damage a rock/mineral lattice
sufficiently to allow ^{40}Ar* to be released.
This can cause the calculated K/Ar age to be younger
than the "true" age of the dated material.
Conversely, excess argon (^{40}Ar_{E})
can cause the calculated K/Ar age to be older than
the "true" age of the dated material. Excess
argon is simply ^{40}Ar that is attributed
to radiogenic ^{40}Ar and/or atmospheric ^{40}Ar.
Excess argon may be derived from the mantle, as bubbles
trapped in a melt, in the case of a magma. Or it could
be a xenocryst/xenolith trapped in a magma/lava during
emplacement.

## The ^{40}Ar/^{39}Ar Dating technique

### Principles of the ^{40}Ar/^{39}Ar method

The ^{40}Ar/^{39}Ar dating technique
is a more sophisticated variation of the K/Ar dating
technique. Both techniques rely on the measurement
of a daughter isotope (^{40}Ar) and a parent
isotope. While the K/Ar technique measures potassium
as the parent, the ^{40}Ar/^{39}Ar
technique uses ^{39}Ar.

Because the relative abundances of the potassium isotopes are known, the ^{39}Ar_{K} (produced from ^{39}K by a fast neutron reaction)
can be used as a proxy for potassium. Therefore, unlike
the conventional K/Ar technique, absolute abundances
need not be measured. Instead, the ratios of the different
argon isotopes are measured, yielding more precise
and accurate results. Additional advantages of the
single isotopic measurements of the ^{40}Ar/^{39}Ar
technique are decreased effects of sample inhomogeneity
and the use of smaller sample sizes.

### Sample Irradiation / Production of ^{39}Ar

Because ^{39}Ar_{K} can only be produced
by a fast neutron reaction on ^{39}K [ ^{39}K(n,p)^{39}Ar
], all samples dated by the ^{40}Ar/^{39}Ar
technique must be irradiated in the core of a nuclear
reactor. The amount of ^{39}Ar_{K} produced in any given irradiation will be dependant
on the amount of ^{39}K present initially,
the length of the irradiation, the neutron flux density
and the neutron capture cross section for ^{39}K.
However, because each of these parameters is difficult
to determine independantly, a mineral standard, or
monitor, of known age is irradiated with the samples
of unknown age. The monitor flux can then be extrapolated
to the samples, thereby determining their flux. This
flux is known as the 'J' and can be determined by
the following equation:

In addition to ^{39}Ar production from ^{39}K,
several other 'interference' reactions occur during irradiation
of the samples. Other isotopes of argon are produced from
potassium, calcium, argon and chlorine. These are:

As the table above illustrates, several "undesirable"
reactions occur on isotopes present within every geologic
sample. These reactor produced isotopes of argon must
be corrected for in order to determine an accurate age.
The monitoring of the interfering reactions is performed
through the use of laboratory salts and glasses. For example,
to determine the amount of reactor produced ^{40}Ar
from ^{40}K, potassium-rich glass is irradiated
with the samples. The ^{40}Ar/^{39}Ar
ratio of the glass is then measured in the mass spectrometer
to determine the correction factor that must be applied
to the rest of the samples in that irradiation. CaF is
also routinely irradiated and measured to determine the ^{36}Ar/^{37}Ar and ^{39}Ar/^{37}Ar
correction factors. The "desirable" production
of ^{37}Ar from ^{40}Ca allows us determine
how much ^{36}Ar and ^{39}Ar to correct
for, as well as the K/Ca ratio of the sample. The desirable
production of ^{38}Ar from 37Cl allows us to determine
how much chlorine is present in our samples. A salt of
KCl is irradiated to determine the ^{38}Ar/^{39}Ar
production ratio which can then be applied to other samples
to determine K/Cl ratios.

^{40}Ar/^{39}Ar age determination

Once the J (neutron flux parameter), ^{40}Ar*
and ^{39}Ar_{K} have been determined (ie.
subtracting atmospheric argon, system blank and interferring
reactor produced isotopes), they can be included in the ^{40}Ar/^{39}Ar age equation:

Because the ^{40}Ar/^{39}Ar technique
relies on ratios instead of absolute quantities, we are
able to extract and measure multiple aliquots of argon from a single sample.
Multiple argon extractions can be performed on a sample
in several ways. Step-heating is the most common way and
involves either a furnace or a laser to uniformily
heat the sample to evolve argon. The individual ages from
each heating step are then graphically plotted on an age
spectrum or an isochron. Mechanical crushing is also a technique capable of releasing argon from a
single sample in multiple steps.

Laser probes also allow multiple ages to be determined on a single sample aliquot, but do so using accurate and precise spatial control. For example, laser spot sizes of 100 microns or less allow a user to extract multiple argon samples from across a small mica or feldspar grain. The results from a laser probe can be plotted in several graphical ways, including a map of a grain showing lateral argon distribution.

^{40}Ar/^{39}Ar total fusion of a sample
is comparable to a K/Ar age determination in that it relies
on wholesale release of argon at one time. However, unlike
conventional K/Ar, ^{40}Ar/^{39}Ar total
fusion measures ratios, making it ideal for samples known
to be very argon retentive (eg. sanidine). Total fusion
is performed using a laser and results are commonly plotted on probability
distribution diagrams or ideograms.

### Some problems with the ^{40}Ar/^{39}Ar technique.

#### Standard Intercalibration

In order for an age
to be calculated by the ^{40}Ar/^{39}Ar
technique, the J parameter must be known. For the J to
be determined, a standard of known age must be irradiated
with the samples of unknown age. Because this (primary)
standard ultimately cannot be determined by ^{40}Ar/^{39}Ar,
it must be first determined by another isotopic dating
method. The method most commonly used to date the primary
standard is the conventional K/Ar technique. The primary
standard must be a mineral that is homogeneous, abundant
and easily dated by the K/Ar and ^{40}Ar/^{39}Ar
methods. Traditionally, this primary standard has been
a hornblende from the McClure Mountains, Colorado (a.k.a.
MMhb-1). Once an accurate and precise age is determined
for the primary standard, other minerals can be dated
relative to it by the ^{40}Ar/^{39}Ar
method. These secondary minerals are often more convenient
to date by the ^{40}Ar/^{39}Ar technique
(e.g. sanidine). However, while it is often easy to determine
the age of the primary standard by the K/Ar method, it
is difficult for different dating laboratories to agree
on the final age. Likewise, because of heterogeneity problems
with the MMhb-1 sample, the K/Ar ages are not always reproducible.
This imprecision (and inaccuracy) is transferred to the
secondary minerals used daily by the ^{40}Ar/^{39}Ar
technique. Fortunately, other techniques are available
to re-evaluate and test the absolute ages of the standards
used by the ^{40}Ar/^{39}Ar technique.
Some of these include other isotopic dating techniques
(e.g. U/Pb) and the astronomical polarity time scale (APTS).

#### Decay Constants

Another issue affecting the
ultimate precision and accuracy of the ^{40}Ar/^{39}Ar
technique is the uncertainty in the decay constants for ^{40}K. This uncertainty results from 1) the branched
decay scheme of ^{40}K and 2) the long half-life
of ^{40}K (1.25 billion years). As technology
advances, it is likely that the decay constants used in
the ^{40}Ar/^{39}Ar age equation will
become continually more refined allowing much more accurate
and precise ages to be determined.

**J Factor**

Because the J value is extrapolated from a standard to an unknown, the accuracy and precision on that J value is critical. J value uncertainty can be minimized by constraining the geometry of the standard relative to the unknown, both vertically and horizontally. The NMGRL does this by irradiating samples in machined aluminum disks where standards and unknowns alternate every other position. J error can also be reduced by analyzing more flux monitor aliquots per standard location.

^{39}Ar Recoil

The affects of irradiation
on potassium-bearing rocks/minerals can sometimes result
in anomalously old apparent ages. This is caused by the
net loss of ^{39}Ar_{K} from the sample
by recoil (the kinetic energy imparted on a ^{39}Ar_{K} atom by the emission of a proton during the (n,p) reaction).
Recoil is likely in every potassium-bearing sample, but
only becomes a significant problem with very fine grained
minerals (e.g. clays) and glass. For multi-phase samples
such as basaltic wholerocks, ^{39}Ar_{K} redistribution may be more of a problem than net ^{39}Ar_{K} loss. In this case, ^{39}Ar may recoil out of
a low-temperature, high-potassium mineral (e.g. K-feldspar)
into a high-temperature, low potassium mineral (e.g. pyroxene).
Such a phenomenon would great affect the shape of the
age spectrum.

## References

- McDougall, I., and Harrison, T.M., 1999, Geochronology and thermochronology by the
^{40}Ar/^{39}Ar method: New York, Oxford University Press, xii, 269 p.