Adventures in unfolding the Basalt Tetrahedron

It's Rodeo Time again in Houston, which means astronomical congestion around Reliant Stadium. Not only that, but the light rail on the weekends is full to the brim with rodeo-goers. Which means I'd rather stay holed up in my apartment than head to campus as usual. This weekend I revisited the Basalt Tetrahedron, oft the bane of intro petrology students. In my spare time I've actually been really getting into all the planes of the tetrahedron in a lot more detail than we ever covered in introductory petrology. Specifically, I decided to unfold the Di-Ne-Fo-Pl part (the critically undersaturated region) this time. Mostly this came about because of an increasing interest in ultrapotassic basalts, although that's really just a sideline thing at the moment as my main thesis project involves peridotites. So starting with our classic Yoder & Tilley tetrahedron:

Image from Dr. S. A. Nelson's petrology notes online at Tulane Earth & Environmental Sciences Mineralogy 211


From when I took this class at Tulane, I remember a big emphasis on this diagram (which can also be found in the lecture notes at the above link):



Of course, this is the 2 front faces (Ne-Di-Fo and Fo-Di-Qz) unfolded, projected from Plagioclase (Pl). I decided to investigate all the binaries that make up the ternaries of these two faces. Here's what I spent my Sunday afternoon making:



(A) Blue circles represent 1 atm experimental natural basalt liquids. The two front faces of the basalt tetrahedron (Di-Ne-Fo and Di-Fo-Qz) are plotted projected from Plagioclase (Pl). The Pl vertex has been projected onto the Di-Fo join (the low pressure “thermal divide”).

(B) and (C): Blowing up the back face of the tetrahedron (Ne-Di-Qz) elucidates some more mysteries involving the "thermal divide" (although technically the join Di-Ab is not the true thermal divide, but Fo-Ab is. Still don't really understand exactly why, but that's for another Sunday afternoon...). I highlighted the back face in green, and in (B) show the 2 binary eutectic systems (Ne-Ab and Qz-Ab) that comprise this face. Ne-Qz is just a binary system with an intermediate compound, Ab.

But the presence of Ab is the whole reason why the thermal divide exists in the first place. On the Ne-Qz, Ab melts at a local maximum, forming a shape that looks like a skateboarding "halfpipe" (or half a cylinder). If we parachute down onto the Ab surface (a thought exercise we were all variably subjected to in Intro Petrology), we can only go one way - either to E1 (and ultimately evolve to a phonolite) or to E2 (and ultimately evolve to a rhyolite). So that little halfpipe of Ab is responsible for the fact that no Si-undersaturated basalt can give rise to a critically Si-undersaturated basalt. It's actually more complicated than this when you consider the system Fo-Ne-Qz, which according to Morse (1981) is the ternary where you can find the "true" thermal divide.

Of course, we all know this already, but it's still a fun (and frustrating but ultimately rewarding) exercise to look at every face of the tetrahedron. Next time: the inner tetrahedron Di-Ab-An-Fo?