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Problem 3: Below is a hexagonal unit cell. Determine the indices for the direction listed as the green vector. To start with, define it term of the three vector system (a1, a2 and z). Next convert it a hexagonal system. The point should be transformed from (UVW] to (uvtw). Z C 02 a ai u = = }(2U V) ka = = }(20 V) v=} (2V U) t= (u + v) W=W Remember this is the general conversion process for translating between cubic and hexagonal systems. (UVW]> [uvtw] UV and W can be thought of the x, y and z-direction in the cubic system. In Hexagonal, u, v and t are the 3 basal plane vectors (a1, a2, a3, they are 60 apart, not 90 apart). Also, w is equivalent to win the cubic system (z-axis)