A powder pattern of iron

PHYSICS · Multi-part · 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 powder pattern of iron, taken with Cu K

\alpha_1

X-rays (

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

), shows six lines at

2\theta=44.67

65.02

82.33

98.94

116.38

and

137.15

degrees. Iron's measured density is

\rho=7.87\,\mathrm{g\,cm^{-3}}

and its molar mass is

M_{\rm mol}=55.85\,\mathrm{g\,mol^{-1}}

. ((a)) Find

\sin^2\theta

for each line and show that their ratios alone cannot distinguish a body-centred cubic lattice from a simple cubic one. ((b)) Using the density, decide which lattice iron actually has, and find its lattice constant

a

to four figures.

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