isotope compositions

[jakemoore]

Paula,
When it comes to putting in isotopes, does it matter how the ratio is constructed?  If I wanted to input a 87Sr/86Sr of 0.7025, can I do Sr87 = 0.7025 and Sr86 = 1, or does it need to be some ratio based on atomic abundance?  When it comes to using the source mixer or assimilations, both the numerator and denominator are needed to account for the non-linearity of mixing ratios, but does it matter how they're constructed as long as it's consistently so that the mixing trajectories don't get askew from starting the ratios at different points.
Thanks.  And I hope this makes sense,
Jacob

[Paula]

For a single source you could use ⁸⁷Sr = 0.7025 and ⁸⁶Sr = 1 but in general (i.e. for source mixer or assimilation calcuations) it would be better to use ⁸⁷Sr = 0.7025/(1+0.7025) and ⁸⁶Sr = 1/(1+0.7025), together with equivalent values for the second composition.  The trace element routine will multiply these input values the relevant total Sr to give working values, proportional to the actual concentrations in the source rocks, which will be used in the subsequent calculations.  ⁸⁷Sr and ⁸⁶Sr together make up about 17% of total Sr, normally, so these working values and the calculated concentrations reported in the results will be larger than the true concentrations but the ratios should be correct.

There is an implicit assumption here that the difference between the amount of radiogenic ⁸⁷Sr in the first source and the amount of radiogenic ⁸⁷Sr in the second source is small compared to the total Sr (including primordial ⁸⁷Sr, ⁸⁶Sr, as well as ⁸⁴Sr and ⁸⁸Sr).  This could break down for sources with extreme age-adjusted ⁸⁷Sr/⁸⁶Sr values.  Maybe there are other ways to construct the ratios but you could always repeat the calculations to see if you get similar results for different approaches.

Cheers,
Paula

[jakemoore]

Paula,
As usual, your help is beyond useful.  I seem to understand how to construct the ratios, but I don't think I'm getting the correct ⁸⁷Sr/⁸⁶Sr ratios out when I use the source mixer function.  To set it up, I'm trying to mix melts from DMM and MORB at 4 GPa and 1650 ^oC.  I ran each of the compositions at the pressure and temperature and wrote melts input files for the liquid generated.  I then ran these through the source mixer...

***Environment variables
ADIABAT_VERSION pMELTS
ADIABAT_MODE isentropic
ADIABAT_DELTAP -100
ADIABAT_MAXP 40000
ADIABAT_MINP 40000
ADIABAT_CRASH_FILE adiabat.out
ADIABAT_CELSIUS_OUTPUT true
ADIABAT_DO_TRACE true
ADIABAT_TRACE_INPUT_FILE dmm_static.trace
ADIABAT_TRACE_OUTPUT_FILE trace.out

***DMM derived liquid
Title: DMM of Workmann & Hart 2005 Liquid
Initial Composition: SiO2 40.435059
Initial Composition: TiO2 0.321095
Initial Composition: Al2O3 3.864795
Initial Composition: Fe2O3 0.375894
Initial Composition: Cr2O3 0.146770
Initial Composition: FeO 13.428545
Initial Composition: MgO 33.537220
Initial Composition: CaO 7.012580
Initial Composition: Na2O 0.819962
Initial Composition: P2O5 0.058080
Initial Trace: La 0.581848
Initial Trace: Yb 0.642805
Initial Trace: Sr 23.238064
Initial Trace: Sr87 9.602807
Initial Trace: Sr86 13.666946
Initial Mass: 32.713417
Initial Temperature: 1650.000000
Initial Pressure: 40000.00
log fo2 Path: None
Suppress: chlorite

***MORB derived liquids
Title: anhydrous adiabat morb Liquid
Initial Composition: SiO2 54.345318
Initial Composition: TiO2 1.809594
Initial Composition: Al2O3 13.404040
Initial Composition: Fe2O3 1.228620
Initial Composition: Cr2O3 0.047967
Initial Composition: FeO 6.483713
Initial Composition: MgO 4.996438
Initial Composition: CaO 12.856541
Initial Composition: Na2O 4.620939
Initial Composition: K2O 0.056408
Initial Composition: P2O5 0.150422
Initial Trace: La 7.413915
Initial Trace: Yb 1.346698
Initial Trace: Sr 209.983834
Initial Trace: Sr87 86.814059
Initial Trace: Sr86 123.227909
Initial Mass: 53.183535
Initial Temperature: 1650.000000
Initial Pressure: 40000.00
log fo2 Path: None
Suppress: chlorite

***run with the following commands
1 (load dmm melts file)
dmm4melt.melts
6 (source mixer)
1 (text file input)
morb4melt.melts
1 (trace and major mix)
0.5 (proportion)
4 (have to do this, otherwise won't output the trace.out file)
1
0


There are no problems with the Sr, ⁸⁷Sr or ⁸⁶Sr in the melts files for the DMM or MORB.  The problem is in the output after mixing.  Here is the output from the Bulk section of the trace.out file...
Pressure   La   Yb   Sr   Sr87   Sr86
40000   3.99788   0.994752   116.611   9226.35   13096.7

The mixed values for the trace elements seem correct, but the ⁸⁷Sr/⁸⁶Sr = 0.70448.  When I did the calculation manually [e.g., Langmuir et al., 1978, EPSL 37, 380-392], using the same proportions and concentrations, I get 0.70431.  This formulation is supposed to account for the non-linearity of the mixing because of the different concentrations.  From these calculations, it looks like the ratio is equivalent to mixing 90% MORB derived melt with 10% DMM derived melt, which happens to be about the same ratio of Sr concentrations in the MORB (209.98 ppm) and DMM (23.24 ppm) melts.

I'm pretty confident in what the isotope ratio should be, so I'm hoping it's something easy in the source mixer algorithm.

As always, I greatly appreciate the help.  If you need any clarification, please let me know.
Jacob

[Paula]

O.K. but when you do the mixing stage the trace element routine in the Adiabat_1ph program will again multiply the Sr87 and Sr86 values you input by the Sr value, whereas the output from the melting calculations is already multiplied by the total Sr.  Really that's a bug in the melts_file output routine so I'm glad you've been checking everything carefully enough to bring it to our attention - thanks!  I'll correct it in the next update.

In the meantime, just divide by the Sr concentration before using the liquid melts_files.  Or use the Sr87 and Sr86 lines from the original DMM and MORB melts_files, as melting at 4 GPa and 1650 ^oC won't have fractionated ⁸⁷Sr and ⁸⁶Sr anyway (this is a better alternative as it avoids rounding errors).  For example, the following lines in the DMM derived liquid file:

Initial Trace: Sr 23.238064
Initial Trace: Sr87 9.602807
Initial Trace: Sr86 13.666946

should actually be something like:

Initial Trace: Sr 23.238064
Initial Trace: Sr87 0.41324
Initial Trace: Sr86 0.58813

and similarly for the other liquid file.  Hopefully that will give a ⁸⁷Sr/⁸⁶Sr ratio a bit closer to the value you get manually.  Let me know if there's still a problem and I'll look into it.

Cheers,
Paula

[jakemoore]

Yes, that makes sense.  I was only looking at the ratios in the liquid melts_files, not thinking that they had been multiplied already.  I'll double check it, but I'm willing to bet it will work great.  Glad I can help out with the debugging!
Thanks Paula.

[Paula]

This old thread but...

I forgot to fix this bug in Adiabat_1ph 3.0. Instead it's fixed by update 3.0.1. For Adiabat_1ph 2 users it is fixed in update 2.0.2 too.

Cheers,
Paula