A crystal of a single element

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Condensed Matter Physics, Ch Diffraction: how a structure is actually measured

Problem

A crystal of a single element, known to be cubic, gives a powder pattern (Cu K

\alpha_1

\lambda=1.5406\,\mathrm{\mathring{A}}

) with lines at

2\theta=23.73

39.24

46.37

56.70

62.32

and

71.12

degrees, and no others below

72

degrees. Its measured density is

5.77\,\mathrm{g\,cm^{-3}}

and its molar mass is

118.71\,\mathrm{g\,mol^{-1}}

. (a) Show from the ratios of

\sin^2\theta

that the lattice is neither simple cubic nor body-centred cubic. (b) Decide between a face-centred cubic lattice with one atom at each lattice point and the diamond structure, using both the lines that are missing and the density; then index the six lines and find

a

to four figures.

Browse the problem library