Section 3.4 of this chapter indexed silicon's first two lines as at degrees and at degrees

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

Section 3.4 of this chapter indexed silicon's first two lines as

(111)

2\theta=28.44

degrees and

(220)

2\theta=47.30

degrees. Two further lines of the same pattern (Cu K

\alpha_1

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

) sit at

2\theta=56.12

and

69.13

degrees. ((a)) Using the diamond sequence of allowed

h^2+k^2+l^2

(

3,8,11,16,\ldots

), identify these two new lines and find silicon's lattice constant

a

from them. ((b)) Using Chapter 1's density-from-structure relation, predict silicon's density: the diamond structure has

Z_c=8

atoms in its conventional cell, and silicon's molar mass is

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

. ((c)) Using Chapter 2's cubic spacing formula, predict the spacing

d_{331}

of silicon's not-yet-measured

(331)

planes.

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