 Solution

ID: past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2015/paper-2/section-a/5/solution

Write

a = V_{c}^{1/3}

for the primitive cubic lattice spacing. With wavevector convention

e^{i k \cdot r}

2 π / a

- π / a \leq k_{j} \leq π / a

, hence

V_{BZ} = (\frac{2 π}{a})^{3} = \frac{( 2 π ) ^{3}}{V _{c}} .

It has the same volume as any primitive reciprocal unit cell. A reciprocal coordinate defined in cycles per metre would instead give

1/ V_{c}

; that is a different convention from this

k

-space convention.

 New to topics? Read the docs here!