Solution

ID: past-exam-of-the-condensed-matter-physics-major-option-course-of-the-university-of-oxford/2015/2/b/a/solution

For the body-centered tetragonal direct lattice, conventional reciprocal labels are integer triples satisfying even. This follows because the extra translation must have phase one for a reciprocal lattice vector. In the section the condition is even. The reciprocal steps are
Within the strict index window , the reciprocal points are and . The neighboring and points lie on the excluded boundary but are useful for constructing the zone bisectors.
At the requested drawing scale, one conventional step in is cm and one step in is cm. Thus the four off-origin included points have drawing coordinates cm. Keeping these unequal physical scales avoids drawing a fictitious square reciprocal section.
Figure 1.
Physical h-zero-l reciprocal section and its first Brillouin-zone boundary
. Original Wigner-Seitz construction using the actual reciprocal lengths. Filled points satisfy h plus l even; open boundary points assist the construction outside the strict requested index window. The hexagon is the section of the three-dimensional first zone. Details.

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