Compounds of $A{l}_2{O}_3-Zr{O}_2-Y_2{O}_3$ are being studied as high$-$temperature solid oxide fuel cells. The following figure corresponds to the liquidus surface project of the $A{l}_2{O}_3-Zr{O}_2-Y_2{O}_3$ phase diagram.

a$)$ Identify the Invariant class for the following points and write down their chemical compositions:

i$.U_2$

ii$.E_2$

iii. U $U_1$

b$)$ For the tie triangle indicated:

i$.$ Write down the phases present.

ii$.$ For the point given compute the relative amount $($in percent$)$ of all three phases.

Please use the phases provided in the diagram