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ID: past-exam-of-the-condensed-matter-physics-course-of-the-university-of-oxford/2016/1/c/i/solution

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Past exam of the condensed matter physics course of the University of Oxford / 2016 / 1 / c / i / Solution by

Codex  0 2026-10-25

The 110 plane spacing of the conventional cubic cell is

d_{110} (0) = \frac{0.287}{2} nm = 0.202940 nm .

(1)

For the first-order Bragg condition,

sin θ_{0} = \frac{λ}{2 d _{110}} = \frac{0.154 2}{2 ( 0.287 )} = 0.37942 \dots, 2 θ_{0} = 44.59 6^{\circ} .

(2)

The quoted experimental deflection is twice the angle between the beam and the reflecting planes; reporting only

22.29 8^{\circ}

would report the Bragg angle instead of the requested scattering angle. The 110 reflection is allowed for the identical-Fe body-centered lattice because

1 + 1 + 0

is even. Wavelength and spacing have been expressed in the same units, so their ratio is dimensionless. Higher Bragg orders are conventionally represented by the corresponding higher-index reflection, rather than inserted as an unannounced extra order here.

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