 Solution

ID: past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2016/paper-1/2/c/solution

The conventional cubic cell has volume

a^{3} = (0.52 \times 1 0^{- 9})^{3} = 1.40608 \times 1 0^{- 28} m^{3} .

Consequently the same effective carrier count is

N_{eff} = n_{eff} a^{3} = 0.9236 carriers per cell .

A noninteger mean is normal for a doped crystal: it describes an ensemble average, not a requirement that every cell contain the same number of defects. The fluorite structure has four cation sites and eight oxygen sites in this conventional cell.

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