 Solution

ID: past-exam-of-the-condensed-matter-physics-course-of-the-university-of-oxford/2017/1/c/ii/solution

The

(100)

(1, 0, 0)

. Its normalized dot product with

(1, 1, 1)

1/ 3

, so

ϕ = cos^{- 1} (\frac{1}{3}) = 54.735 6^{\circ} .

This is the acute angle between the lattice planes, rather than the complementary angle between a plane and the other plane's normal.

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