Question

2. Determine the indices of the following directions and planes. The direction AB refers to the vector drawn from A to B. Fractional positions are measured from the closest corner. (6) 1/2b 1/2 ta G (123) or (123] 1/2 c 1 Coordinate system All capital letters are at lattice corners. Planes Directions NU АЈН AGK abK NT Nd

Answer 1

Ans: Miller indices for given planes and directions can be find out as below

" NV^vector = nv^vector = -a^vector + b^vector - c^vector: a^vector, b^vector, c^vector are primitive vectors along x, y, z directions respectively and considered ""N"" be the origin. Now, Miller indices for NV^vector is [1^bar 1 1^bar] NT^vector implies NT^vector = -a^vector - c^vector rightarrow Miller for nt^vector is [T 0 T] Nd^vector implies Nd^vector = -b^vector- c/3 implies ND^vector = 1/3 (-3b^vector - c^vector) implies miller indices for ND^vector is [0 3^bar 1^bar] AJH plane, let ""G"" be the origin then, the intersects made by AJH plane interms of lattice parameters are a/ a, b/ b, c/c implies 1, 1, 1 here no need to take reciprocals of intercepts and convert. To smallest integers [because 1/ 1 = 1] implies Miller indices (1, 1, 1) Note: origin chosen should not be on the plane."