Hi Greg, Sumit, Martin, and others,
Very interesting conversation.
To address the points raised by Sumit: agreed, there is no reason to believe that thermally mediated volume diffusion does not happen. However, a reasonable question is whether the rate-limiting diffusion mechanism(s) that operated in experiments are the same as the rate-limiting diffusion mechanisms that operated in natural samples (vacancy migration, interstitial diffusion, etc.). Differences in ambient conditions other than temperature (P, fO2, fH2O, activities of major elements, etc.) can have order-of-magnitude effects on elemental diffusivity, presumably by influencing the types and abundances of point defects, thereby changing the rate-limiting diffusion mechanisms.
Some examples of order-of-magnitude differences in elemental diffusivities from changes in intensive properties other than T: Elphick and Graham (1988, Nature), Sharp et al. (1991, EPSL), Jollands et al. (2014, CMP), Zhokova et al. (2014, CMP), Dohmen et al. (2018, Physics of Chemistry and Minerals; also addressed the role of trace-element concentration on diffusivity and diffusion mechanisms), Cherniak (1995, Chemical Geology).
Even if diffusivity is high enough to homogenize a mineral, grain-boundary effects might prohibit diffusive re-equilibration of that mineral with other minerals in the rock (lack of fluid to transport elements along grain boundaries, adjacent phase can't accommodate the element in question). This has been discussed in some detail for trace elements in rutile and might also be important for radiogenic isotope systems in some cases. Korhonen et al. (2014, EPSL), Kohn et al. (2016, CMP), Smye et al. (2018, Chemical Geology), Clark et al. (2019, JMG).
To address Martin's interest in dichotomies between the apparent behaviors of minerals in diffusional experiments and in natural rocks, I think the most illustrative examples are probably from diffusion in titanite. Diffusion experiments suggest Dodson Tc of ~575°C for Pb (Cherniak, 1993) and ~675°C for Zr (Cherniak, 2006) for a "typical" grain size and cooling rate (100–µm diameter, 10 K/Myr). Although some studies have documented bulk (TIMS) U–Pb titanite dates consistent with this closure temperature (Mattinson, 1978; Mezger et al., 1991, 1993; Spear and Parrish, 1996; Tucker et al., 1987, 1990, 2004; Verts et al., 1996), many more empirical studies—especially those documenting compositional zoning—have observed preservation of inherited titanite U–Pb dates and/or heterogeneity in U–Pb dates at the outcrop and grain scales in igneous, high-temperature-eclogite-facies, and granulite-facies metamorphic rocks that require little to no Pb diffusion in titanite at temperatures of 700–850°C (TIMS studies: Corfu, 1996; Kylander-Clark et al., 2008; Pidgeon et al., 1996; Schärer et al., 1994; Zhang and Schärer, 1996; SIMS studies: Castelli and Rubatto, 2002; Rubatto and Hermann, 2001; LA-ICP-MS studies: Gao et al., 2012; Garber et al., 2017; Kohn and Corrie, 2011; Marsh and Smye, 2017; Mottram et al., 2018; Spencer et al., 2013; Stearns et al., 2016, 2015; Walters and Kohn, 2017). Although most studies have focused on Pb, a similar lack of apparent Zr diffusion has also been observed in rocks with peak temperatures >750°C (e.g. Stearns et al., 2016; Holder and Hacker, 2019; Kohn and Corrie, 2011; Walters and Kohn, 2017). It remains unclear why the experimental diffusivities for Pb and Zr in titanite are apparently so much higher than in natural rocks. As discussed by Stearns et al. (2015, 2016) for U–Pb titanite and many of the references already given for Lu–Hf and Sm–Nd garnet, the ability to interpret of radiometric dates in the context of a volume-diffusion Tc depends on documentation of plausible diffusion profiles or some evidence of partial diffusive homogenization for the element(s) of interest (error-function decreases/increases toward grain rims or between different growth domains; smoothing of oscillatory zoning, annuli, or other originally sharp compositional gradients).
Best,
Robert
-----Original Message-----
From: Metamorphic Studies Group <[log in to unmask]> On Behalf Of Sumit Chakraborty
Sent: Tuesday, April 23, 2019 5:09 AM
To: [log in to unmask]
Subject: Re: Closure Temperature
Dear all,
This is a discussion that keep recurring - unfortunately, according to me. To question whether thermal energy moves atoms / ions is to question basically all of physics. The definition of temperature is the "average kinetic energy of particles", and motion of particles without kinetic energy is....very strange.
One needs to have a differentiated analysis. Fluids, are a form of material, and not energy - so, by themselves they do not do anything to affect kinetic energy. What is implied (but not explicitly analyzed) is that they affect the chemical energy (chemical potential of different components etc....leading to dissolution, transport etc.), which can then contribute to kinetic energy. One needs to deal with deformation in the same sense (strain energy, localized i.e. brittle vs. not so localized i.e. various forms of ductile, plastic etc. etc.).
And finally, how can the concept of closure temperature not make sense?
Things do freeze sometimes, don't they? So the question is to determine at what conditions that happens.
If one goes back to the original Dodson papers, one would find that the equations were set up for a very generic kinetic process that depends on temperature - did not have to be diffusion at all. It is only over time that diffusion has been associated one-to-one with the Dodson equation (resulting of course from the fact that Dodson himself took diffusion as the kinetic process to analyze as an example). Consider the case of fluids above. Fluids may facilitiate reactions - but those reactions do follow a kinetic rate law, and that is likely to follow an Arrhenius equation, and with that, is amenable to treatment by the Dodson equation and the concept of closure temperature. Again, to question that fluid reaction kinetics would not be temperature dependent is to question a large chunk of chemistry.
That, also addresses the point that Martin raises - closure calculated based on diffusion rates may not (and should not) reflect the closure of systems (natural or experimental) that were affected by other kinetic processes; however that does not mean that the concept of closure temperature is not valid, it just means we need to calculate it with the rate constants appropriate for the process in question. That is true of any equation in science.
I suggest that we be more careful about the larger implications of discussions we carry out, with some precision in our expressions.
Thanks,
Sumit
Am 23/04/2019 um 10:24 schrieb JAVIER RODRIGUEZ ALLER:
> Dear all,
>
> Once Greg has raised a question about it, I would like to take it to a
> general audience regardless the isotopic system or the metamorphic grade:
>
> What is the closure temperature? Does it make any sense?
> Is T by itself (kinetic energy) able to move cations in and out of a
> crystalline structure?
>
> Though I gave up studying metamorphic petrology more than 10 years
> ago, at that time there were quite a few pieces of evidence that
> isotopic systems may be reset at low grades (well below commonly
> assumed Tc), and that they may remain closed at T above empirically
> defined Tc, even for long-lasting metamorphic events.
> As it has already been suggested to Greg, and this seems to have not
> changed since I was a petrologist, you'd absolutely need to take melt
> (or fluids at lower T) and/or deformation into your equations to put
> the Tc concept to work. Moreover, you may take T out of the equations,
> and fluids +/- deformation will still give the right answer,
> irrespective of T.
>
> Respectfully,
>
> Javier Rodríguez Aller, PhD.
> Servicio de Geocronología y Geoquímica Isotópica
> SGIker- Facultad de Ciencia y Tecnología Universidad del País Vasco
> Barrio Sarriena s/n
> E48940 Leioa
> SPAIN
>
> [log in to unmask]
> http://www.ehu.eus/en/web/sgiker/geokronologia-eta-geokimika-isotopiko
> a-aurkezpena
>
> http://www.linkedin.com/in/javi-rodriguez-032a5360
>
>
> Gregory Dumond <[log in to unmask]> escribió:
>
>> These are a few questions about Lu-Hf garnet dating:
>>
>> 1) How well do we know the closure temperature of the Lu-Hf system in
>> garnet?
>>
>> 2) How reliable is this technique for dating granulites, especially
>> granulites that have experience protracted high-T metamorphism and/or
>> residence in the lower crust?
>>
>> If you have any references that pertain to the above questions, I
>> would sincerely appreciate them.
>>
>> With best regards,
>> Greg
>>
>> Department of Geosciences
>> University of Arkansas, USA
>>
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>
>
> Javier Rodríguez Aller
> SGIker - Geocronología y Geoquímica Isotópica Facultad de Ciencia y
> Tecnología Universidad del País Vasco
> E48080 Bilbao
> SPAIN
>
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--
**********************************************
Sumit Chakraborty
Professor, Institut für Geologie, Mineralogie und Geophysik and Director, RUBION
ACS Earth and Space Chemistry, Associate-Editor
Ruhr Universität Bochum,
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Germany
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