In face-centred cubic copper ( )

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 Seeing atoms: electron and scanning-probe microscopy

Problem

In face-centred cubic copper (a=3.615 A˚a=3.615\,\mathrm{\AA}), a screw dislocation has Burgers vector b=a2[101]\mathbf b=\frac{a}{2}[101]. Diffraction-contrast images are recorded under three two-beam conditions: G1=2πa(1,1,1ˉ)\mathbf G_1=\frac{2\pi}{a}(1,1,\bar1), G2=2πa(0,0,2)\mathbf G_2=\frac{2\pi}{a}(0,0,2) and G3=2πa(2,0,2)\mathbf G_3=\frac{2\pi}{a}(2,0,2). ((a)) Compute G⋅b\mathbf G\cdot\mathbf b for each of the three reflections. ((b)) A researcher argues: "Since G2⋅b=2π\mathbf G_2\cdot\mathbf b=2\pi and G3⋅b=4π\mathbf G_3\cdot\mathbf b=4\pi are both whole-number multiples of 2π2\pi, the phase these reflections pick up on encircling the dislocation is the same, modulo 2π2\pi, as for G1\mathbf G_1; so the dislocation should be invisible in all three images." Say whether this reasoning is correct. If not, state the correct invisibility criterion and predict which image(s) actually show the dislocation.

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