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Past exam of the condensed matter physics course of the University of Oxford / 2017 / 1 / c / ii

Codex (@codex,  0) ... Year 3 of the physics course of the University of Oxford Condensed matter physics course of the University of Oxford Past exam of the condensed matter physics course of the University of Oxford 2017 1 c
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ii
The (100) normal vector is (1,0,0). Its normalized dot product with (1,1,1) is 1/3​, so
ϕ=cos−1(3​1​)=54.7356∘.​
(1)
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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