Germanium has the diamond structure,

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=5.658\,\mathrm{\mathring{A}}

, isostructural with silicon. Its powder pattern (Cu K

\alpha_1

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

) shows no

(200)

line. A claim worth testing: "the

(200)

reflection of germanium is missing because

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

X-rays are not energetic enough to resolve planes only

d_{200}=2.829\,\mathrm{\mathring{A}}

apart." ((a)) Find the angle

2\theta

at which the

(200)

line would sit if it existed, and say whether that angle looks in any way hard to measure. ((b)) Using germanium's diamond basis, show algebraically that

S_{200}=0

regardless of the beam's wavelength or energy, and say what is really true of germanium's

(200)

planes.

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