A single crystal of rock-salt NaCl (face-centred cubic

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

Solid State Physics, Ch Diffraction as measurement: form factors, thermal motion and refinement

Problem

A single crystal of rock-salt NaCl (face-centred cubic, conventional lattice constant

a=5.640\,\mathrm{\AA}

) is examined with Mo K

\alpha

radiation,

\lambda=0.7107\,\mathrm{\AA}

. For an fcc Bravais lattice, a reflection

(hkl)

is allowed only if

h,k,l

are all even or all odd. ((a)) Find

k_{\rm in}=2\pi/\lambda

and the Ewald accessible-reflection limit

|\mathbf{G}|_{\max}=2k_{\rm in}

. ((b)) Along the

[100]^{*}

direction the reciprocal lattice vectors are

\mathbf{G}_{h00}

with

|\mathbf{G}_{h00}|=2\pi h/a

. Find the highest-order allowed reflection

(h00)

that this radiation can reach.

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