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Example of an Inverse Isochron Plot
https://geoinfo.nmt.edu/labs/argon/data/home.html
The K/Ar and 40Ar/39Ar methods
Of the three naturally occurring isotopes of potassium, 40K is an unstable isotope having a total half-life of 1.25 x 109 years. Since K exists as a cation, it is chemically bonded to the host mineral structure. Silicaceous rocks are abundant in K, thus making this method attractive. Of the naturally occurring isotopes of argon, 40Ar is by far the most abundant isotope, and a portion of 40Ar is from the decay of 40K. With time, the rock or mineral content of 40K decreases due to decay, and the amount of its radiogenic daughter, 40Ar increases. By measuring total potassium and the argon isotope, and knowing the decay constant of 40K, an age of crystallization can be determined. Total K is measured by flame photometry (no longer used), wet chemistry or by inductively coupled plasma optical emission spectroscopy (ICP-OES). Argon is quantified by noble gas mass spectrometry. The age equation is thus:
t= 1/l ln[1+l/(le+lec)(40Ar*/40K)], where t=age of crystallization; l=total decay constant of 40K; le=decay constant for 40K-->40Ar by electron capture and l; lec=decay constant for 40K-->40Ar by electron capture alone; and 40Ar*= radiogenic argon, i.e. Ar from decay of 40K.
The K/Ar method has several limitations. It cannot detect mixed ages of crystallization; it cannot recognize atmospheric argon that is trapped within the crystal; and it cannot recognize Ar loss during re-melting or deformation. Thus, the 40Ar/39Ar method is useful.
In the 40Ar/39Ar method, a rock sample is irradiated with fast neutrons to eject a proton from 39K (the most abundant and stable K isotope) to form 39Ark. 39Ark serves as the proxy for stable K, since 39Ar is not naturally occurring. Using ICP-MS (ICP – mass spectrometry) or other technologies, the amounts of 39ArK (39K proxy), 36Ar (atmospheric component), 40ArCa (amount of 40Ar from decay of 42Ca and 43Ca), 37Ar (from decay of 40Ca) are measured.
By using the following equation, the ratio of radiogenic Ar and total K can be calculated:
40Ar*/39KK = {[(40Ar/39Ar)m – 298.55(36Ar/39Ar)m + 298.55(36Ar/39Ar)Ca(37Ar/39Ar)m]/[1-(39Ar/37Ar)Ca(37Ar/39Ar)m]/[1-(39Ar/37Ar)Ca(37Ar/39Ar)m]} - (40Ar/39Ar)K. The subscript “m” means “measured.” The factor 298.55 is a correction factor for the ratio of atmospheric 36Ar to 40Ar.
Once the ratio of 40Ar*/39KK is determined, that ratio is fitted into a refinement of the equation for the K/Ar method, as follows: t= 1/l ln[1+ J(40Ar*/40K)], where J is the neutron dose as compared to a 40Ar*/39Ar standard.
A way to graphically determine age is to set up a plot with 36Ar/40Ar ratios of readings on the y axis and plot the 39Ar/40Ar ratios on the x axis. Where the extrapolated line intersects the x axis, meaning that the 39Ar/40Ar is at its highest, and the 36Ar/40Ar is 0 (no atmospheric Ar), that intercept can be used to plug into the age equation to determine the age. This approach is called the Inverse Isochron Method. See example.
Stepwise, incremental heating of a sample, plotted with age calculated from the 40Ar*/39Ar ratio on the y axis and cumulative 39Ar fraction released on the x axis, can indicate partial reheating (ie. deformation), a mixed population of ages or excess (ie. inherited) Ar. With laser ablation, different areas of a crystal (often zircon) can be tested. See example.
The K/Ar and 40Ar/39K methods can provide constraints on the timing and rates of landscape evolution, such as fluvial incision rates (when knowing gorge depths) and can also provide information regarding the rates of surface uplift. The K/Ar method can be used to study the rates of weathering by dating clay minerals, and thus provide information of time of bedrock exposure to weathering. Knowledge of the ages of subsurface basalt flows derived by the 40Ar/39Ar can provide information for numerical models of groundwater flow and contaminant transport in aquifers. The timing of impact craters can also be determined, as well as the distribution of the associated shocked quartz.
Example of a spectrum plot, generated by step heating of a mineral.
https://geoinfo.nmt.edu/labs/argon/data/home.html
Fredin O, Vila G, Zwingmann H, et al. The inheritance of a Mesozoic landscape in western Scandinavia. Nature Communications. Apr. 28, 2017. P. 1-9. DOI: 10.1038/ncommms14870.
Using K/Ar methods, the authors studied size fractions of illite taken from saprolite over the granitic bedrock at three sites: 1. A kaolinitic site (IvÖ) on the southern coast of Sweden, 2. Core samples off the shore from the southwest coast of Norway (Utsira) and 3. At BØmlo, on the southwest shore of Norway, slightly north of the Utsira site. The IvÖ and Utsira sites are well constrained stratigraphically. The topography of these areas is described as a “strandflat” landscape, an uneven and partly submerged rock platform extending seawards from the coastal mountains. It consists of low rocky islands, shallow sea areas and low rock platforms that often abut on steep slopes.
By applying K/Ar methods to size fraction bins of illite (produced from weathering of k-feldspar and biotite), the authors determined that original basement exposure in these sites occurred in the Late Triassic (221.13 +/-7.0 – 206.2+/- 4.2 Ma), and that intense deep weathering was occurring during this time. Notable was the direct relationship between grain size and age, suggesting that the larger size illite fractions contain protolithic illite. The finest grain size fraction (<0.4mm) gave an age of 206.2 Ma. Thus, they found Mesozoic saprolites significantly predating Pleistocene glaciation. They emphasize that, although Scandinavia was entirely glaciated, glacial erosion is heterogeneous such that pre-glacial topography may be still preserved.
https://www.nature.com/articles/ncomms14879
Allen MB, Mark DF, Kheirkhah M, et al. 40Ar/39Ar dating Quaternary lavas in northwest Iran: constraints on the landscape evolution and incision rates of the Turkish-Iranian plateau. Geophysical Journal International 2011, 185:1175-1188.
This study focuses on the Turkish-Iranian plateau, which is part of the Arabia-Eurasia collision zone. This is an area that experienced basaltic lava flows through pre-existing river valleys for tens of kilometers. Following the eruptions, the valleys were still available for incision by the rivers. These rivers subsequently cut gorges that are up to 50 meters. To study fluvial incision rates, the authors used the 40Ar/39Ar ages on the volcanic rock to constrain landscape evolution. Given that this is an ongoing collision zone, some rate of uplift is anticipated, but it is small. GPS velocity field data indicate that internal deformation across the Iranian part of the plateau is less than 2 mm yr-1.
The study attempts to determine whether the relief and surface uplift occurred during crustal shortening, or whether it is related to magmatism after the shortening. Five basaltic samples were taken along two valleys. Each sample was covered by a thin layer of alluvium and/or soil, indicating little to no erosion from the surrounding landscape. Gorge depths were determined by plumb lines and SRTM data. Three of the samples, clustered on the eastern side of the study area, had low radiogenic argon signals, making age calculations less certain, but the range was 0.40 to 0.81Ma. The other two samples (one on the western section, the other not depicted on the map) had higher 40Ar* yields, giving an age of 0.49 and 1.869 Ma. Post-eruption rates at the sample sites ranged from 0.01 to 0.05 mm yr-1. This implies that Quaternary incision has been a relatively slow process. The gorges that are cut into the lavas represent only a small fraction of the total relief in each valley. The data therefore indicates that the volcanism did not significantly alter the overall pattern of incision and erosion, that the majority of relief pre-dates the lava flows. The authors also propose that surface uplift has also been slow, both before during the Quaternary volcanism. They favor the theory that earlier Late Cenozoic compressional tectonics caused the relief and elevation of the topography, and not Quaternary volcanism.
https://doi.org/10.1111/j.1365-246X.2011.05022.x
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