Chromium is body-centred cubic

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

Chromium is body-centred cubic, with measured density

\rho=7.19\,\mathrm{g\,cm^{-3}}

and molar mass

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

. Its powder pattern (Cu K

\alpha_1

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

) has its first four lines at

2\theta=44.37

64.55

81.69

and

98.08

degrees. One way of indexing it assumes the first line is

(100)

and simply continues

h^2+k^2+l^2=1,2,3,4

for the four lines in turn. (a) Carry out that calculation,

a=d\sqrt{h^2+k^2+l^2}

for each line with this assignment, and check whether the four resulting values of

a

agree with each other. (b) Find what is wrong with this indexing, and redo it correctly to get a lattice constant consistent with the given density.

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