Dear Jean-Luc,
The issue is not that it does not use the Theorem of Duhem and is
therefore simple.....the question should be whether Henry's law is
applicable to and appropriate for the partitioning of Mn between garnet
and a complex pelitic matrix, where reactions occur in "pulses" (garnet
is produced, and sometimes resorbed in between, by various reactions at
different points along the P-T path of a rock depending on its bulk
composition), and Mn is not really a trace element. Having said that,
let me make it clear that I am not trying to underplay the contributions
of Evans (2004) - it goes quite a bit beyond the simple use of the
Rayleigh law and has many attractive aspects.
May I use this opportunity to frame the 1988 paper of Spear by its past
and future to place it in some historical context?
I am doing this from memory, so I make no claims for completeness here:
The early reports (1960's) of Mn zoning in garnet (Hollister, and Harte
and Henley) already looked at the use of Rayleigh Fractionation laws for
describing the bell shaped profile of Mn in garnets.
Loomis and Nimick (Can Min,, 1982), in a paper that used to be cited a
lot in those days, looked at trying to model the equilibrium growth
quantitatively, and discussed some consequences of resorption. There was
a partner paper on disequilibrium garnet growth, also in Can Min - I do
not remember the date. Some problems with Rayleigh fractionation were
also considered there, I seem to recall (but I do not have the papers on
hand here to check).
Loomis (1986 ?) wrote a more complete paper in J Met Geol modeling such
garnet growth within the framework of a thermodynamic database that he
was developing at the time, and discussed various consequences of
overstepping, resorbtion etc. (reasons why a simply Henry's Law may be
inadequate for a pelitic garnet).
Matt has mentioned Spear (1988) - I would like to add that the more
general concept that I think emerged from that work was the idea of
"internal metasomatism" at all - that an element "capsuled away" in a
phase may emerge later (by diffusion, or also by dissolution of that
phase at a later stage) to "muck up" the bulk composition of the rock
and its phase relations. This concept probably has wider applications
that could be explored more (e.g. what happens during allanite -
monazite reactions to the trace element contents of other existing
phases like garnet, zircon etc.? There have been lots of discussion of
this, but not always in the context of "internal metasomatism", the
concept of which comes from Spear, 1988).
And finally, Gaidies et al. (CMP, 2008) developed a software, Theria-G,
that addresses equilibrium fractionation in the context of minimization
of free energy (an expression of Duhem's Theorem) to look at the
evolution of zoning profiles of garnets, but also accounted for the
diffusion of the elements in and out of garnet quantitatively, using the
full multicomponent form. This also answers your question about whether
anybody has used it in the context of a pseudosection type calculation.
There are many more of course along the way between 1960 and
2013.....but that is my short summary focused on garnets in pelites.
Cheers,
Sumit
On 7/22/2013 10:26 AM, Jean-Luc Régnier wrote:
> Hello Matt,
>
> the method described by Evans (2004) is much more simple. It does not
> use the theorem of Duhem and therefore we don't need to express all
> phases in equilibrium with the garnet to solve the system (and the
> effective composition).
> This is "simply" based on the Henry' law for the manganese and
> Rayleigh's equation (first garnet mode given by thermocalc or other
> softwares) but I don't know if someone already tried to apply this
> method in doing their pseudosections (and P-T path)...
> Best regards,
> Jean-Luc
>
>
>
> ----- Original Message ----- From: "Matthew Kohn"
> <[log in to unmask]>
> To: <[log in to unmask]>
> Sent: Monday, July 22, 2013 4:22 AM
> Subject: Re: [geo-metamorphism] garnet fractionation
>
>
> Hi folks,
>
> This message reminds that next month is the 25th anniversary of Frank
> Spear's paper on - you guessed it! - the effect of garnet fractional
> crystallization on (reactive) bulk compositions and mineral assemblages.
>
> This approach first fully quantified chemical impacts in a
> fundamentally predictable fashion and became the cornerstone of all
> subsequent Gibbs method - type models.
>
> His paper also addresses the effects of diffusional relaxation of
> garnet growth zoning as rocks heat.
>
> Here's the reference: Spear, FS (1988) Metamorphic fractional
> crystallization and internal metasomatism by diffusional
> homogenization of zoned garnets. Contributions to Mineralogy and
> Petrology, v. 99, 507-517.
>
> It's founded on Duhem's theorem, which constrains P-T-X-M in rocks,
> and also published 25 years ago: Spear, FS (1988) The Gibbs method and
> Duhem's theorem - the quantitative relationships among P, T, chemical
> potential, phase composition and reaction progress in igneous and
> metamorphic systems. Contributions to Mineralogy and Petrology, v. 99,
> 249-256.
>
> Best,
>
> Matt
>
> On Jul 20, 2013, at 1:24 AM, Jean-Luc Régnier wrote:
>
>> Dear All,
>>
>> I got the opportunity to do a small application (.exe only for
>> windows unfortunately, but source code for Python27) calculating the
>> effective bulk composition after garnet fractionation. The program is
>> based on the work of Evans* (2004) with some modifications and might
>> be useful for people building pseudosections/P-T path from bulk rock
>> analyses and garnet analyses.
>> I would be happy to discuss with people working on this subject if any ?
>> Best regards,
>> Jean-Luc
>>
>> * Evans, T. P. (2004). A method for calculating effective bulk
>> composition modification due to crystal fractionation in garnet
>> bearing schist: implications for isopleth thermobarometry. Journal of
>> Metamorphic Geology 22, 547–557.
>
> ******************************************************************
> Dr. Matthew J. Kohn, University Distinguished Professor
> Department of Geosciences, Boise State University
> 1910 University Dr.; MS1535
> Boise, ID 83725-1535
> [log in to unmask]
> http://earth.boisestate.edu/mattkohn/
> phone: (208)-426-2757 fax: (208)-426-4061
> ******************************************************************
--
***************** Sumit Chakraborty ****************************************
http://www.gmg.ruhr-uni-bochum.de/petrologie
Institut fuer Geologie, Mineralogie und Geophysik;
Ruhr-Universitaet Bochum;
D-44780 Bochum; Germany
Email: [log in to unmask]
Tel: +49-(0)234-322 -4395 / -8521 / -8155
Fax: +49-(0)234-321 4433
****************************************************************************
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