Question

(a) Sketch, in a cubic unit cell, a [111] and a [112] lattice direction. (b) Use a trigonometric calculation to determine the angle between these two directions. (c) Use Equation 3.3 to determine the angle between these two directions.

Answer 1

Answer and Explanation:

a) The direction is shown in the cube diagram attached to this solution.

b) the angle between two planes (h₁, k₁, l₁) and (h₂, k₂, l₂) is given by the formula,

Cos Φ = (h₁h₂ + k₁k₂ + l₁)/√((h₁² + k₁² + l₁²)(h₂² + k₂² + l₂²))

For (111) and (112)

Cos Φ = (1.1 + 1.1 + 1.2)/√((1² + 1² + 1²)(1² + 1² + 2²))

Cos Φ = (1 + 1 + 2)/√((1+1+1)(1+1+4))

Cos Φ = 4/√(3×6)

Cos Φ = 4/√18

Φ = cos⁻¹ (4/√18) = 19.56°

c) equation 3.3 is missing from the question, I would be back to provide the answers to that as soon as the equation is provided!

Hope this Helps!!