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Adiabat dT/dP too high?

Started by edmarshall4, April 10, 2020, 09:45:49 AM

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edmarshall4

Hi Paula,

I found that the mantle adiabats that I calculate using alphaMELTS have higher gradients, or dT/dP, than I would have expected. I'm essentially following the instructions in the tutorial, using alphaMELTS 1.9 with pMELTS in isentropic mode. I'm using a DMM bulk composition and suppressing the liquid phase. I set alphaMELTS to an entropy that corresponds to some mantle potential temperature and run the model. Although everything else makes sense, what I find is that the gradient of the adiabat ends up being too high (dT/dP = ~26 C/GPa), where the expected adiabat is closer to dT/dP = ~13 C/GPa. What might I be doing wrong?

Thanks again,
Ed

Paula

Hi Ed,

I'm looking at Figure 1 of Asimow et al. 2004 and the dT/dP for the 1380 oC adiabat is approximately 26 oC/GPa, rather than 13 oC/GPa. So I don't think you are doing anything wrong. Of course, this is only the adiabat for reversible decompression of the solid mantle; material in an actively upwelling plume could experience dT/dP closer to 13 oC/GPa.

Cheers,
Paula

P.S. Figure 1. was calculated using pHMELTS, rather than pMELTS, but that won't make any difference for the adiabat part as all the water would be in nominally anhydrous minerals along that (metastable) path.

edmarshall4

Hi Paula,

Thanks! I'd be curious to know why the difference exists. Maybe when the specific heats and thermal expansivities for mineral phases in the alphaMELTS database are summed together they result in a slightly different bulk rock specific heat and thermal expansivity than are typically cited for peridotites?

Ed

Paula

Hi Ed,

You didn't mention where you got the 13 oC/GPa value from, so it's a little hard for me to say.

Paula

edmarshall4

Hi Paula,

True! The ~13 C/GPa number is based on the Turcotte and Schubert (1982) calculation of the mantle adiabat (from dT/dP = aT/pcp ; where a is the thermal expansivity, T is temperature, p is density and cp is the specific heat capacity). I grabbed the values for those variables out of Phipps Morgan (2001): a = 3x10-5 C-1, T = 1600K, cp = 1200 J/Kg C, p = 3300. His values result in 12.1 C/GPa.

Ed

Phipps Morgan (2001) Thermodynamics of pressure release melting of a veined plum pudding mantle, G^3.

asimow

#5
Hi Ed,

What you are seeing here is a combination of two things. The conceptually most important is that the isentrope in pMELTS includes the effects of all pressure-dependent subsolidus mineral reactions, which mostly have positive Clapeyron slopes and so tend to steepen the actual equilibrium isentrope compared to a "frozen-phase" isentrope that is based only on the thermodynamic properties alpha and Cp. The less important thing is that the alpha of this peridotite calculated by pMELTS is 4.5 to 4.8 x 105 K-1.

You can see the effects of the mineralogical reactions that matter by plotting the following against pressure

  • dT/dP (by finite difference)
  • T (dV/dT) / Cp (put T in Kelvin, and divide everything by 1000 to get K/GPa)
  • the masses of all the solid phases

You will see:

  • On the 1350 °C isentrope, T (dV/dT) / Cp linearly increases form 18.3 at 1 bar to 19.6 at 3 GPa
  • dT/dP is large in the garnet field because of the continuous nature of the garnet-spinel transition in a Cr-bearing assemblage
  • As soon as garnet is exhausted the dT/dP drops to something close to the frozen-phase value for a while
  • dT/dP then increases again through the spinel field, this time associated with rapid decrease of opx and increase of cpx, which in turn is an artifact of forced metastable subsolidus calculation climbing up the 2-pyroxene solvus instead of melting out cpx
  • When plagioclase comes in it starts to take up Ca and stops the cpx ingrowth, which seems to bring the dT/dP back down to slightly less than the frozen-phase model

I've posted my output spreadsheet with these calculations here: https://www.dropbox.com/s/ymwhnkr95h8s1ef/pMELTS_subsolidus_isentrope.xlsx?dl=0

-- Paul