This is a free and open-source script written in Python to estimate the 'chemical' age or date¹ in monazites analyzed in electron microprobes.

For individual measures, it uses the following equation (Williams et al. 2007):

that relates the age (t, in years) and the concentrations of Th, U, and the total radiogenic Pb in parts per million. λ²³², λ²³⁸, and λ²³⁵ are the decay constants for Th²³² (4.95E-11/year), U²³⁸ (1.55E-10/year), and U²³⁵ (9.85E-10/year), respectively.

The script solves the ages iteratively by entering age guesses with the known concentrations of U and Th until the calculated Pb value matches the measured Pb with an error below 0.1. It uses a bisection search algorithm and returns the age in million years.

Since version 1.1, it also adds an experimental implementation of the CHIME method (Suzuki and Adachi 1991)².

¹Since individual ages may or may not have geological significance, Williams et al. (2006) refer to these as "dates" instead of "ages". They use term "age" for a result (a date or mean of dates) that is interpreted to have geological significance

²This method is only useful when monazites are cogenetic, Th-rich, and show a range of Th contents instead of similar values.

Download

https://github.com/marcoalopez/chemical_age_script/releases/
https://figshare.com/articles/Chemical_age_script/2815144

Getting started

The script requires Python 2.7.x/3.x. Also, from version 1.1 onwards it requires Numpy, Scipy, and Matplotlib scientific packages. See an example here for installing Python in different operating systems.

Once you open and run the script (Fig 1) and for estimating individual ages you need to write in the shell/console :

>>> find_chemage(64586, 2519, 1626)

where the three inputs separated by commas within the parentheses are the concentrations of Th, U and Pb, respectively. Press the Enter key and that's it. See an example below.

At left, running the script in the IDLE (the default Python's integrated development environment). At right, the Python shell window showing the results (in blue) after calling the find_chemage() Python function (in black)

To estimate ages in a data set (i.e. arrays) use:

>>> find_chemage_array(Th, U, Pb)

where Th, U and Pb are the arrays of data (Python list or Numpy arrays) that contains the values of Th, U and Pb in ppm.

Finally, to use the CHIME method use:

>>> CHIME(Th, U, Pb)

where Th, U and Pb are the values of Th, U and Pb in ppm in the form of Python lists or Numpy arrays. This method is currently in alpha version and returns the age, the slope of the isochron and a plot with the isochron and the data, but no the error in the estimation.

A detailed tutorial explaining how to use the script with tabular-like data will be released in the future

References

Suzuki, K. and Adachi, M., 1991. Precambrian provenance and Silurian metamorphism of the Tsubonosawa paragneiss in the South Kitakami terrane, Northeast Japan, revealed by the chemical Th-U-total Pb isochron ages of monazite, zircon and xenotime. Geochem. J. 25, 357-376. doi:http://doi.org/10.2343/geochemj.25.357

Williams, M.L., Jercinovic, M.J., Hetherington, C.J., 2007. Microprobe Monazite Geochronology: Understanding Geologic Processes by Integrating Composition and Chronology. Annu. Rev. Earth Planet. Sci. 35, 137–175. doi:10.1146/annurev.earth.35.031306.140228

Williams, M.L., Jercinovic, M.J., Goncalves, P., Mahan, K., 2006. Format and philosophy for collecting, compiling, and reporting microprobe monazite ages. Chem. Geol. 225, 1–15. doi:10.1016/j.chemgeo.2005.07.024

License

Chemical age script is a free script available under the Apache License, Version 2.0 (the "License")