Calculating end member compositions for pyroxene quadrilateral diagram

[Bhuvan]

Hi all,

I am trying to calculate the molefractions of Ferrosilite (Fs) and Wollastonite (Wo) from the given mole fractions of Diopside (Di), Hedenbergite (Hd) and Clinoenstatite (Cli-En) so that I can plot the compositional variation of pyroxenes during fractional crystallization in the pyroxene quadrilateral diagram of Morimoto, 1988.

Like you have mentioned, I have used the relation: Fs = Cli-En  + Hd - 2Di and
similarly, I have used the relation: 2Di = 2Wo + Cli-En to calculate the mole fraction of Wollastonite, but ended up with a negative value for Wo. As pyroxene quadrilateral is a ternary diagram, negative values do not plot within the ternary.

Is there a mistake in my approach? Any leads would be highly appreciated.

[Paula]

Hi Bhuvan,

It's Fs = En + 2Hd - 2Di, but that's probably just a typo. The reason you are getting negative Wo is that you are not including the Ca in the hedenbergite or other components.

For a pyroxene that lies in the quadrilateral, using independent end members En, Di, Hd:

total Ca = moles(Di) + moles(Hd)
total Fe = moles(Hd)
total Mg = 2*moles(En) + moles(Di)

I don't have Morimoto 1988 to hand but it looks like the Wo apex is Ca2Si2O6, rather than CaSiO3 like the mineral, which means:

molfrac(Wo) = ( molfrac(Di) + molfrac(Hd) ) / 2

molfrac(Fs) = ( molfrac(Hd) ) / 2

More generally for cpx using the MELTS set of end members:

molfrac(Wo) = ( sum of molfracs(Di,  Hd, alumino-buffonite,  buffonite, essenite) ) / 2*( sum of molfracs(En, Di, Hd) )

molfrac(Fs) = ( molfrac(Hd) ) / 2*( sum of molfracs(En, Di, Hd) )

Check out GeoPlotters (https://www.geoplotters.com/find-a-plot) for more information. It's an excellent resource.

Paula