ALambdaR: Lambda shape coefficients to REE pattern

REE shape coefficients:

λ₀

λ₂

λ₄

λ₁

λ₃

Eu anomaly

Ce anomaly

x-axis type

y-axis type

y log scale

Y/Ho

Plot yttrium

Preset patterns

F matrix parameterisation

data for pie chart

Download data as csv

Choose csv file:

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Maximum file size is 64 KB.

Download results

This section allows upload of a file containing a list lambda coefficients. The app calculates REE contents for each λ combination and outputs the results. A button is provided to download the results in CSV format.

Instructions

The uploaded file must be a CSV with 9 comma separated values per line corresponding to λ₀ to λ₄ and τ₁ to τ₄. For example, an input file named patterns.csv with the following content:


                  5,-10,0,0,5000,0,0,0,0
                  

                  8,20,0,-500,0,1.1,2,4,1

will generate two sets of REE contents, with output given in ppm. Normalisation to the CI values given by O'Neill (2016) will give the smoothest patterns.
Currently, there is very little error handling and the app expects the input file to be in the correct format. Ensure that there are 5 numerical values separated by comma per line, and that the app shows you the correct λ values that you expect. Input entered in the wrong format will either not work, give error messages, or result in wrong numbers without an error message.

This section shows the REE oxide prices per kilogram used to calculate the dollar value of a REE pattern. The default values are estimates based on publicly available information, and may not necessarily represent actual values in the current market.

Note that some sources report CeO₂, Pr₆O₁₁, and Tb₄O₇ instead of the trivalent REE₂O₃ used here. This has a minor effect on oxide price as the metals in higher oxidation state are slightly diluted by additional oxygen.

The "Recovery" value is a weighting factor reported in percentage, with values lower than 100% used to exclude a portion of the REE from the total price budget.

Tetrad coefficients:

τ₁

τ₃

τ₂

τ₄

References

Main citation:

Anenburg M (2020) Rare earth mineral diversity controlled by REE pattern shapes.
Mineralogical Magazine, 84(4), doi: https://doi.org/10.1180/mgm.2020.70

Initial development of the λ shape coefficient concept:

O'Neill HSC (2016) The smoothness and shapes of chondrite-normalized rare earth element patterns in basalts.
Journal of Petrology, 57(8), 1463–1508, doi: https://doi.org/10.1093/petrology/egw047

In-depth mathematical treatment of the method including tetrad effect:

Anenburg M and Williams MJ (2021) Quantifying the tetrad effect, shape components, and Ce-Eu-Gd anomalies in rare earth element patterns.
Mathematical Geosciences, doi: https://doi.org/10.1007/s11004-021-09959-5

λ shape coefficient functionality in Python using pyrolite:

Williams MJ et al. (2020) pyrolite: Python for geochemistry.
Journal of Open Source Software, 5(50), 2314, doi: https://doi.org/10.21105/joss.02314

Williams MJ et al. (2020) morganjwilliams/pyrolite: 0.2.8.
Zenodo, doi: https://doi.org/10.5281/zenodo.3975537

Data sources for normalisation:

McDonough WF and Sun S-s (1995) The composition of the Earth.
Chemical Geology, 120(3–4), 223–253, doi: https://doi.org/10.1016/0009-2541(94)00140-4

Palme H and O'Neill HSC (2014) Cosmochemical estimates of mantle composition.
Treatise on Geochemistry (Second Edition), Volume 3: The Mantle and Core, 1–39, doi: https://doi.org/10.1016/b978-0-08-095975-7.00201-1

Pourmand A et al. (2012) A novel extraction chromatography and MC-ICP-MS technique for rapid analysis of REE, Sc and Y: Revising CI-chondrite and Post-Archean Australian Shale (PAAS) abundances.
Chemical Geology, 291, 38–54, doi: https://doi.org/10.1016/j.chemgeo.2011.08.011

Rudnick RL and Gao S (2014) Composition of the continental crust.
Treatise on Geochemistry (Second Edition), Volume 4: The Crust, 1–51, doi: https://doi.org/10.1016/b978-0-08-095975-7.00301-6

Sun S-S and McDonough WF (1989) Chemical and isotopic systematics of oceanic basalts: implications for mantle composition and processes.
Geological Society, London, Special Publications: Magmatism in the Ocean Basins, 42, 313–345, doi: https://doi.org/10.1144/GSL.SP.1989.042.01.20

Tetrad effects:

Irber (1999) The lanthanide tetrad effect and its correlation with K/Rb, Eu/Eu*, Sr/Eu, Y/Ho, and Zr/Hf of evolving peraluminous granite suites.
Geochimica et Cosmochimica Acta, 63(3/4), 489–508, doi: https://doi.org/10.1016/s0016-7037(99)00027-7

Monecke T et al (2002) Tetrad effect in rare earth element distribution patterns: a method of quantification with application to rock and mineral samples from granite-related rare metal deposits.
Geochimica et Cosmochimica Acta, 66(7), 1185–1196, doi: https://doi.org/10.1016/s0016-7037(01)00849-3

Minami M and Masuda A (1997) Approximate estimation of the degree of lanthanide tetrad effect from the data potentially involving all lanthanides.
Geochemical Journal, 31(3), 125–133, doi: https://doi.org/10.2343/geochemj.31.125

Miscellaneous:

Davidson et al (2013) Dy/Dy*: Variations arising from mantle sources and petrogenetic processes.
Journal of Petrology, 54(3), 525–537, doi: https://doi.org/10.1093/petrology/egs076

2021-07-19: Added Anenburg and Williams paper to references tab.
2021-03-25: Added range limits to inputs, unless specifically typed in.
2021-03-03: Added link to online workshop.
2021-01-25: Adjusted Ce and Eu anomaly notation.
2021-01-02: Tetrads now use corrected parabolas according to polynomial fit to ionic radii.
2020-12-18: Added Davidson's Dy/Dy*.
2020-12-15: Tweaked y-axis controls.
2020-12-14: Upload now supports tetrads.
2020-12-11: Now using tau symbols for tetrad coefficients.
2020-11-29: Added tetrad effect tab.
2020-11-18: Updated code URLs.
2020-11-09: Tweaks to REE value table.
2020-11-05: Added REE value tab and display options. Minor cosmetic fixes.
2020-10-21: Added license and source code download.
2020-10-20: Updated references.
2020-08-25: Added tooltips to most inputs. Help is no longer hidden in the documentation.
2020-08-10: Added preset representative mineral patterns.
2020-08-08: Updated F-matrix to use orthogonal terms derived by including Eu ("full"). The previous parameterisation excluding Eu used by O'Neill (2016) is now listed as "legacy".
2020-08-07: Added N-MORB, E-MORB, OIB from Sun & McDonough (1989)
2020-08-06: Initial release.

License

The MIT License

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the ‘Software’), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED ‘AS IS’, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Source code

Download in R format:

app.R