Using geochemical data in igneous petrology

1. Using geochemical data in igneous petrology Trace elements behaviour during magmatic evolution

2. Trace elements behaviour and models • The melting equation • The fractionnation equation • The mixing equation • Worked examples

3. 5.1 Establishing the equation for batch melting • Batch melting = equilibrium • The solids and the liquids coexist and are equilibrated throughout the melting • A plausible assumption especially for reasonnably high melt fractions

4. A simple combination of • The mass balance equation: • The definition of bulk repartition coef.

5. NB: can also be rearranged as

7. Other melting model • Batch melting with partial equilibrium (aka « non-modal melting ») D0 : bulk repartition coef at the onset of the melting P: « pseudo repartition coef » of the phases involved in the melting

8. Fractionnal melting • Each melt increment is removed immediately after forming • You can look at the composition • Either of individual melt increments • Or at the amalgamated melt (average of all melt increments) • Largely the differential form of the batch melting equation – you can also write it for partially equilibrated melting

9. Fractional melting Composition of each melt increment Averaged (amalgamated) melt The demonstration is left to the reader as an exercise…

11. Comparison between models(was it worth all the trouble?) • Batch melting and amalgamated fractional melting are very similar • Fractional melting is different for markedly incompatible elements • So… more often than not, batch melting will do – except in some extreme cases

13. 5.2 Fractional crystallization • Equilibrium crystallization can be used (just like batch melting), and results in the same equation • But there is a fundamental difference for common magmas: crystallization is, indeed, fractionnal – not equilibrated

14. Rayleigh fractionnation (crystals immediately removed as they form):

16. Again, you can play with more complex equations involving partial equilibrium, etc. • … but in general, it’s probably not going to be worth the trouble, except in extreme cases

17. 5.3 Mixing • A plain average (= mass balance)

18. Basic equations for trace elements Mixing Partial melting Frac. Cryst.

20. Biggest difference for compatible elements

21. Comp. Vs. Incomp diagrams