Problem 2 (50 points): A hypothetical material has three types of atoms (Formula ABX,) at the unit cell coordinates below. Atom 1 000 100 010 001 110 101 011 111 Atom 2 %%% Atom 3 % 0 % 0 % 0 %% 1% % %1% %%1 a. Make a 3D sketch of the unit cell. Make sure it is neat and that your coordinate system is well defined. Make sure it is large enough to draw planes without being overcrowded (I recommend making the sketch on its own separate page). (20 points) b. What crystal system does the material belong to? What is the name of the crystal structure? (5 points) c. With a different color for each, draw the planes (102),(-11-1), and (1-31) on your sketch from part a. (if you cannot draw the planes neatly on the sketch, drawing a separate figure(s) is acceptable.) (15 points) d. Make a "slice" diagram of (011) and (123) planes. (10 points) a