This is nice to hear. Eutectic is a terminology used in chemistry. It denotes a mixture of two or more elements (in set proportions) which would melt and solidify at a single temperature that is lower than the melting points of the individual constituents.
Alloys made from Eutectic Oxides of CMC can be directionally solidified so that a single Crystal is formed and in turn they can improve the thermal performance properties of turbines. You can read a bit more in the link down below.
If we are working on these that is good news. I hope TEI is also planning to study adaptive cycle systems along side of the development of TF35K engine.
Its a complicated emerging field since about the 1970s (DS oxide composites).
You could technically use non-eutectic oxides and make DS. One would save cost and QC needs in the early production stage but severely increase them in the later stage (along with performance loss, I am unsure of the exact scale of the performance loss, but it would be lot worse than Single crystal superalloy for sure ). Basically the tradeoff is really bad for non-eutectics here (this does change somewhat for the semiconductor field, but thats another story).
It has to do with keeping the material as simple as possible regd grain boundaries and alignments (the overall integrals governing them in 3D-space). A eutectic always ensures presence of 2 rather than 3 factors.....or 3 instead of 4 ( n minus 1)....and so on (but composites rarely go past ternary and for good reason again due to benefit of simplicity and how that mitigates cascading in something later).
The great advantages (among others regarding the materials themselves) are thus baked in to harness in the directional solidification final stage and fabrication quality control....which are very much related to the crystallography of page 6 found in the paper you posted....a non-eutectic (though offering a wider temperature range benefit and cost savings there) would greatly increase the orientations in play (because of n instead of n - 1 in the "baking") and all failure modes associated would cascade and weaken both what you can do with fab and final performance and QC.
Its not my field (my integrals involve the fluids rather than solids in these engines), but I remember reading a paper couple years ago and there were still lot of challenges they are in the process of figuring out, so this field will take a while to come to manufacturing stage, not sure how long though.
There were iirc basically tradeoffs within choice of binary (2) or ternary (3). Intuitively with the "keep it simple as possible". one would think 2 is best here, but there are advantages with 3 that boil down to pros and cons of Zirconia (and I think other interesting elements too) in these setups that they are still figuring out w.r.t the whole end-end production final cost/benefit (to say proven single crystal). We have to see how this rationalisation evolves.
In end everything kind of boils down to mother nature though...metals are very special in their electronic configuration w.r.t their nucleus sizes. This is what undergirths all the combination potentials in this broader metallurgy, ceramics and composite RnD field.