Past exam of the condensed matter physics major option course of the University of Oxford / 2015 / 2 / b / a

For the body-centered tetragonal direct lattice, conventional reciprocal labels $(h,k,l)$ are integer triples satisfying $h+k+l$ even. This follows because the extra translation $(1/2,1/2,1/2)$ must have phase one for a reciprocal lattice vector. In the $k=0$ section the condition is $h+l$ even. The reciprocal steps areWithin the strict index window $-2<h,l<2$, the reciprocal points are $(h,l)=(0,0)$ and $(\pm 1,\pm 1)$. The neighboring $(\pm 2,0)$ and $(0,\pm 2)$ points lie on the excluded boundary but are useful for constructing the zone bisectors.

At the requested drawing scale, one conventional step in $h$ is $a^{\ast }/5=3.560$ cm and one step in $l$ is $c^{\ast }/5=1.197$ cm. Thus the four off-origin included points have drawing coordinates $(\pm 3.560,\pm 1.197)$ cm. Keeping these unequal physical scales avoids drawing a fictitious square reciprocal section.