Papers often report zircon Hf models ages (single or two stage) and Hf epsilon values in zircons. However the details of worked out examples of calculations are generally not reported. Also not clear how the crustal evolutionary lines (with values for upper crust. lower crust or whole crust and which model when to be used) as well as the mantle lines are plotted in the age vs. epsilon diagrams. Can anybody explain in detail how that are done or suggest literature showing the actual worked out examples?
That should be suitable (chapter 8) if you know german:
http://petrol.natur.cuni.cz/~janousek/izokurz/PDF/Stosch%20Isotopengeochemie.pdf,
Otherwise, I would suggest Faure 1986
I suggest the paper Shaw et al 2011 (and cited refferences therein)
Volume 126, Issues 1–2, September 2011, Pages 115–126
For papers, I'd recommend Patchett et al. (1982), Contrib. Min. Pet. 78:279-297, or Thirwall and Walder (1995), Chem. Geol. 122:241-247. Otherwise, the best textbooks (with diagrammes and references) are Faure (2005) and Dickin (2005). However, for those familiar with eNd and Nd model ages, the calculations are very similar; there's just a bit more disagreement over which values to use for the various models! But in brief,
1. You measure the 176Hf/177Hf and 176Lu/177Hf in your zircon. Because there are three elements in zircon with mass 176 (Yb, Lu, Hf), this is not straightforward and requires making mass bias and interference corrections (another story in themselves).
2. You back-calculate the 176Hf/177Hf ratio of the bulk Earth (CHUR) at the time your zircon crystallised (time T), taken as the U-Pb age, from the modern values, using the standard radioactive decay equations.
3. You compare the two values at time T in the standard epsilon calculation eHfT = (((176Hf/177Hf)T/(176Hf/177Hf)CHUR) - 1) x 10000.
3.5 Here I need to define a couple terms. The 'parent' rock is the one which grew the zircon. The 'source' rock is the one from which the parent was extracted (usually the mantle) before it evolved into something that could grow a zircon. Of course, many of us are working on detrital minerals, and so these words can have other meanings in those settings.
4. Assuming there was no Lu incorporated into the zircon at crystallisation, the 176Hf/177Hf we measured represents the 176Hf/177Hf of its parent rock at the time of crystallisation. This is not (normally) the ratio of the source at time T, so we have to work out when the parent rock and the source rock had the same ratio. We don't (generally) have the parent rock to measure the 176Lu/177Hf ratio directly, so we choose a value based on the bulk composition, and then back-calculate, again using the standard radioactive decay equations. The time at which both the parent rock and the source have the same value is called the model age, and because we are only considering the radiogenic ingrowth of 176Hf in the parent rock, it is called a single stage model age.
5. However, zircon does take in a tiny amount of Lu, and hence the 176Hf/177Hf we measure today is not exactly what it was at the time of zircon growth. So most people first do a back-correction from the measured value to the value at the U-Pb age, using the measured 176Lu/177Hf in the zircon, and then do the correction in step 4. Unsurprisingly, this is called a two-stage model age.
You can see then how many different lines can be drawn through the same data set, depending on which decay constants, which values for your source rock, which values for the parent rock and which values for the zircon itself you choose to use! And it's why most of us keep our own databases of published data, all recalculated to whichever values we're using, so that we attempt to compare like with like.
I am going to tempt fate here and suggest that certain references are used more often for these values, but please do not take these as absolutes (and whichever you choose to use, someone will protest you haven't used their favourite):
Bouvier et al. (2008), EPSL 273:48-57 - modern 176Hf/177Hf and 176Lu/177Hf values for CHUR
Griffin et al. (2002), Lithos 61:237-269 - modern 176Hf/177Hf and 176Lu/177Hf values for DM
Shirey et al. (2008), GSA Special Paper 440:1-29 - modern 176Hf/177Hf and 176Lu/177Hf values for DM
Dhuime et al. (2011), Science 331:154-155 - modern 176Hf/177Hf and 176Lu/177Hf values for 'new crust' mantle
Soderlund et al. (2004), EPSL 219:311-324 - lambda 176Lu
Griffin et al. (2002), Lithos 61:237-269 - average crustal 176Lu/177Hf = 0.015
Rudnick and Gao (2003), average crustal 176Lu/177Hf = 0.0083
Chauvel et al. (2014), EPSL 388:48-58 - average crustal 176Lu/177Hf = 0.0125
Hi Sukanta,
If you are going to know how to calculate model ages, it is good to know their limitations too. Arndt & Goldstein wrote an excellent paper many years ago on some of the limitations of Nd model ages:
http://geology.gsapubs.org/content/15/10/893.short
I have updated this for Hf in the review paper that has just been published in the special publication 'Continent Formation Through Time':
http://sp.lyellcollection.org/content/early/2014/11/06/SP389.14.full.pdf+html
Cheers
Nick
p.s. You'll be glad to hear this book will be published in print soon.
Thanks Nick. The Arndt & Goldstein paper is indeed a landmark. Model ages are still useful to constrain mixing of older crust-derived and juvenile materials. You latest paper in GSL SP is also very well-written. I am referring this paper to my students. Also this volume is a very good contribution.
Do you can recommend me please any software to plot zircon´s Hafnium vs Age?
thank you